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NORMAL DELAYED ESTABLISHMENT OF A SEMILUNAR BROODING AND LARVAL RELEASE CYCLE IN THE COURSE OF THE REPRODUCTIVE SEASON OF THE GHOST SHRIMP POPULATION ON A WARM TEMPERATE INTERTIDAL SANDFLAT.

1. INTRODUCTION

Decapod crustaceans in intertidal and semiterrestrial habitats of estuarine and coastal shores have two larval life history strategies. In the larval export group, newly hatched and released planktotrophic larvae are transported to the inner shelf, coastal ocean, whereas in the larval retention group, planktotrophic or lecithotrophic larvae are retained around natal habitats (Anger 2001, Queiroga & Blanton 2005). The present study focuses on the larval export type in warm temperate and tropical regions. Some fraction of the advanced-stage larvae is retained in the coastal ocean for a few weeks, and, finally, postlarvae are returned to adult habitats. Field and laboratory studies on this group, mostly on brachyuran crabs, have documented a semilunar or lunar rhythm (14.5- or 29-day cycle) and population-level synchrony in the hatching of embryos and the subsequent larval release by females. This synchronized rhythm is timed to varying combinations of the four environmental cues of (1) light-dark times, (2) high tide (H) and low tide (L) times, (3) lunar age, and (4) tidal range (TR) (Gifford 1962, Saigusa & Hidaka 1978, Christy 1982, Wolcott & Wolcott 1982, De Vries & Forward 1989, Paula 1989, Dittel & Epifanio 1990, Morgan 1996, Yamaguchi 2001d, Flores et al. 2002, Skov et al. 2005, Kerr et al. 2012). Hereafter, such population-level synchrony is called "larval release synchrony." Regarding this synchrony in decapods from geographic regions under the semidiurnal tidal regime, which is the most prevalent worldwide and includes a mixed, mainly semidiurnal, regime (Pugh 1987, Open University 1989), it has been advocated that the most conspicuous optimal timing in response to the aforementioned four cues is around the nocturnal H times on several days with the largest/larger/large TRs in the semilunar or lunar cycle of TR (Forward 1987, Morgan 1995, Christy 2011). Note: (1) although, in the decapod larval literature, the tidal "amplitude" (above and below the mean water level) has often been used to designate the TR [difference in water levels between one H (L) and the next L (H) (Pugh 1987)], the present article adopts "range" and restricts "amplitude" to its citation from original references; and (2) when "amplitudes" are referred to, the three adjectives, largest/larger/large, have been prefixed rather loosely or interchangeably. In semidiurnal tidal regimes, the largest TRs are expected to occur in spring tide periods, with each peak usually coming 1-2 days after the immediate syzygy date at full or new moon [cycle of the age of the tide (Pugh 1987, Open University 1989)]. Thus, the aforementioned view on the optimal larval release timing can be called the "age-of-the-tide-cycle-based (AOTTCB) view." Phenomena supporting this view are most often observed for semiterrestrial and high- to mid-intertidal species, but less or absent for the lowest intertidal and shallow subtidal species probably because of least or no constraints by tidal inundation (Salmon et al. 1986, Forward 1987, Kellmeyer & Salmon 2001, Hsueh 2002, Skov et al. 2005). The present study deals with species of the former type. Based on a generally accepted premise that tidal current velocity is correlated with TR, the adaptive significance for those larval releasing females is considered as rapid transport of their larvae to the coastal ocean by utilizing the highest/higher/high ebb tidal current velocities in the nighttime, enabling larvae to swiftly escape from planktivorous fish visually catching prey (Morgan 1990) or from adverse abiotic conditions around the adult habitats such as low salinity (Saigusa 1981, Brodie et al. 2007, Simith et al. 2014) and higher temperatures (Morgan 1987, Faleiro et al. 2012) of shallow estuarine waters. Mass larval release by females synchronizing with each other may induce a prey density-dependent satiation by predators, but the actual demonstration of this is absent for decapods. It is presumed here that larval release synchrony results from the sum of density-independent acts of each female (Christy 2003).

One complicated situation for decapod larval release synchrony with dark times is that larvae of a substantial number of species are released during daytime (and nighttime) (Forward 1987, Morgan 1995, Yamaguchi 2001d, Bueno & Flores 2010, Christy 2011). One possible morphological trait possessed by those larvae is surface cryptic color pigments [e.g., yellow-green against conspicuous red-orange in lit waters (Christy 1986, Hsueh 2002)]. Turbid or semiterrestrial vegetation-shaded waters in estuaries may provide larvae with a darker background in the daytime comparable to clearer waters in the nighttime (Forward et al. 1982, Morgan & Christy 1994, Kellmeyer & Salmon 2001, Moser & Macintosh 2001). The present study deals with species releasing larvae principally in the nighttime.

There are a number of phenomena that do not conform to the AOTTCB view. In several geographical regions where the nocturnal Hs occur only in some tide periods other than the spring tide period, larval release synchrony in decapods is centered around the neap tide period (around lunar quadrature) or some later before the spring tide period (Christy 1978, Paula 1989, Queiroga et al. 1994, Rodriguez et al. 1997, Pereira et al. 2000) or between spring and neap tide periods (Wooldridge & Loubser 1996); hereafter, the "mid-tide period" is used to designate the period either between spring and neap tide periods or between the converse. In brachyuran populations located in the Caribbean and Gulf of Mexico under mixed semidiurnal and diurnal tidal regimes, respectively, larval release synchrony varies in each species according to the different phase relationships among light-dark, H time, and tidal "amplitude" cycles (Morgan & Christy 1994, Morgan 1996). In these locations, nocturnal, large-"amplitude" ebb tides do not continue throughout the reproductive season, and, with time, synchronous larval release tracked nocturnal, intermediate-"amplitude" ebb tides occurring at dawn. Even within the same semidiurnal tidal regime, larval release timing varies intraspecifically according to the nocturnal H times or absolute TRs between different regions. In a meso-tidal region of Japan, with the 2.0- to 2.7-m largest year-round TRs, larval release synchrony in populations of the semiterrestrial brachyuran crab, Chiromantes (originally as Sesarma) hematocheir, was centered around spring tide periods on the shore of a small tidal river near the coastal waters of the Pacific Ocean (Saigusa & Hidaka 1978) and around neap tide periods or some later on a Seto Inland Sea shore (Saigusa 1982), whereas larval release occurred in any tide periods on a Japan Sea coast in the micro-tidal region with the less than 0.6-m year-round TR (Honma et al. 1981). In the aforementioned cases in which larvae are released in neap- or mid-tide periods, they are effectively transported to the coastal ocean by ebb tidal currents even with velocities lower than those associated with the largest/larger/large TRs in spring tide periods. For each adult population to be maintained on respective estuarine and coastal shores in those regions with different TRs, the following three parameters seem to be essential: velocity of ebb tidal currents around the adult habitat; time of peak larval release in the nighttime (e.g., availability of a unit travel duration from that peak to L times); and the magnitude of successful transport of larvae released from the adult habitat, which depends on its distance to the coastal ocean (Salmon et al. 1986, Paula 1989, Queiroga et al. 1994, Morgan 1996, Wooldridge & Loubser 1996, Pereira et al. 2000).

Besides the AOTTCB view, another view exists about the timing of decapod larval release synchrony with the spring tide period, which is hereafter called the "syzygy-cycle-based (SCB) view." The larval release times of a larval export-type female in the course of the reproductive season are determined by how she keeps pace with synchronized mating and how long it takes for newly deposited embryos to develop under temporally varying temperatures (Christy 1978, Wheeler 1978, DeCoursey 1983, Forward 1987). Here, the term "reproductive synchrony" is introduced to designate a set of population-level synchronies, as follows: "mating synchrony" at the time of courtship and mating by sexes, which is, immediately or some time later, followed by oviposition (and embryo deposition onto pleopods) by females ("oviposition or embryo deposition synchrony"). The courtship and mating are density-dependent behaviors. To interpret the pattern for the larval release timing by local populations of Chiromantes hematocheir, which was synchronized to the nocturnal H times every spring tide period (Saigusa & Hidaka 1978, Saigusa 1981), a laboratory experiment was conducted (Saigusa 1980). A 24.8-h artificial moonlight cycle entrained female crabs to the semilunar rhythm of oviposition (immediately followed by embryo deposition) synchrony, which was conducive to the larval release synchrony 1 mo later. The latter, in turn, was immediately ensued by oviposition synchrony with a few-day lag. Here, the term, oviposition synchrony (instead of reproductive synchrony) is used, because, from their second oviposition, these females were isolated from the males only to use the initial sperm stored in their seminal receptacles (i.e., under the density-independent females' own control). The aforementioned "1 mo" was the duration for both complete embryo development and full ovary restoration. The initial reproductive synchrony in the reproductive season was centered at syzygies (either full or new moon). The subsequent consecutive sets of oviposition and larval release synchronies took place three times in the laboratory, with two separate oviposition groups adjusted to either full- or new-moon cycles. The results of a further experiment suggested that oviposition synchrony and the subsequent larval release synchrony could be entrained by the initial exposure of females to moonlight for just a few days around the time of full moon (Saigusa 1988), in which the larval release synchrony was timed to different regional phase relationship between light-dark and H time cycles (Saigusa 1982). A similar mechanism as described above might be applicable to other semiterrestrial crab species exhibiting larval release synchrony on syzygy dates, which are supposed to rely on semilunar cycles of moonlight (Gifford 1962, Warner 1967). The existence of a syzygy-entrained reproductive synchrony coupled with the subsequent larval release synchrony was suggested also for lower intertidal Uca species (von Hagen 1970).

Both SCB and AOTTCB views are confronted with a requirement to explain how the start of distinct reproductive and larval release synchronies of decapods in warm temperate regions with nocturnal Hs every spring tide period is delayed normally in the course of the reproductive season. For example, in the female populations of several species of Uca and Sesarma, a semilunar or lunar cycle of the successive larval release and embryo deposition centered on each syzygy date is maintained in the mid-reproductive season (e.g., during midsummer to early autumn) under the higher air or water temperatures, with every 2- or 4-wk concomitant embryo development and ovary restoration, whereas, in the early season (e.g., during late spring to early summer) under the lower temperatures, the larval release dates tend to be extended over a syzygy date to around the subsequent quadrature date (Saigusa & Hidaka 1978, Wheeler 1978, Saigusa 1981, Christy 1982, Greenspan 1982, Saigusa 1982, Zimmerman & Felder 1991, Yamaguchi 2001a, Christy 2003). The reproductive season for those decapods starts when air or water temperature reaches some threshold [e.g., 20[degrees]C (Pillay & Ono 1978, Honma et al. 1981, Christy 1982, Rodriguez et al. 1997)], and the initial reproductive synchrony among individuals would be weak even if they might potentially be timed to, for example, a syzygy date (Greenspan 1982, Zimmerman & Felder 1991, Yamaguchi 2001a). Weak or aperiodic larval release rhythms in the early reproductive season were also reported for decapods releasing larvae in a neap tide cycle (Paula 1989, Queiroga et al. 1994). The variances both in dates of reproductive synchrony and in embryo developmental duration, together with the variance in ovary restoration duration, may lead to a delay in larval release dates to a mid- or neap tide period. Very few integrated approaches have been made toward the understanding of the process that generates a rather abrupt switch from weak to distinct synchronous reproductive and larval release cycle in the mid-reproductive season (Zimmerman & Felder 1991).

The TRs encountered by larval export-type decapods about to release larvae from warm temperate shores in a mid- or neap tide period during their early reproductive season may be suboptimal for the larval export efficiency. Even in their mid-reproductive season, larval release is not always confined to a narrow range of optimal dates in spring tide periods, i.e., around the syzygy or largest-TR date (Saigusa & Hidaka 1978, Wheeler 1978, Saigusa 1981, Christy 1982, Greenspan 1982, Saigusa 1982, Zimmerman & Felder 1991, Yamaguchi 2001a, Christy 2003). On a tropical intertidal sandflat with intermittent cold upwellings, the populations of two species of Uca appeared to adjust their larval release timing to the largest or large "amplitude" tides in spring tide periods during such months with lower temperatures by regulating either timing of mating or embryo-brooding duration (E-BD) by females moving through their vertical burrows with a temperature gradient (Kerr et al. 2012). Through the seasonal TR cycle in temperate regions with the nocturnal Hs occurring every spring tide period, the ebb TRs in neap tide periods are not necessarily much smaller than in spring tide periods, suggesting the achievement of substantial larval transport to the coastal ocean in these neap tide periods with "relatively large" TRs (Greenspan 1982, Johnson & Gonor 1982, Salmon et al. 1986, Hsueh 2002, Kim et al. 2004). The smallest TR in some spring tide period and the largest one at some neap tide period may be regarded as the two end points of a continuum.

The foregoing overview of research on larval export-type decapods under the semidiurnal tidal regime (including the mixed, mainly semidiurnal, one) in warm temperate and tropical regions has revealed that several fundamental subjects remain to be elucidated regarding the peak synchronous timing of larval release around the nocturnal H times on several days with the largest/larger/large-TR tides in the semilunar cycle of TR. These subjects can be compiled as the five core questions, as follows: Question (1): does the peak reproductive synchrony take place on a syzygy date? Question (2): does the peak larval release synchrony take place on either a syzygy date (the SCB view) or a date with the largest nocturnal ebb TR, which comes a few days after the immediate syzygy date (the AOTTCB view)? Question (3): in relation to question (2), how does the nocturnal ebb tidal current velocity around adult habitats vary with TR through the reproductive season? Question (4): are density-dependent reproductive synchrony and density-independent larval release synchrony tightly or loosely coupled? Question (5): in the case of the tightly coupled synchronies in question (4), when and how does the inseparable sequence of both kinds of synchronies arise and how is it maintained in the course of the mid- to late reproductive season? For answering these questions, the present study builds on a premise that the intensive monitoring of a single local decapod population and associated hydrodynamic variables over its reproductive season, not for fragmented time segments only, on a warm temperate shore under a semidiurnal (and mixed, mainly semidiurnal) tidal regime can provide a new integrated approach. Specifically for question (1), when trying to deal with a series of reproductive synchronies in the female population, to eliminate the uncertainty about whether each oviposition synchrony is derived from the immediate prior mating synchrony or from sperm stored since the past (synchronized) mating(s) (e.g., Yamaguchi 2001b, McLay & Lopez-Greco 2011), those species with no sperm storage [i.e., mating immediately before every oviposition (and embryo deposition)] are more tractable. For questions (2) and (3), the AOTTCB view builds on the assumptions that water velocity is correlated with TR and that a date with the largest ebb TR should have been selected as the local optimum for larval release (first paragraph). Practically, however, only an insignificant difference in the ebb tidal current velocities may exist between these two dates (e.g., 10s-cm TR difference per 100s-cm TR). Furthermore, because the water depth around adult habitats is shallow, both TR and water velocity are subjected to transient meteorological influences in addition to the cyclic tidal harmonic components. Only a few studies have recorded water velocities using water pressure and velocity gauges, and they were limited to discrete time segments (Christy & Stancyk 1982, Queiroga et al. 1994, Rodriguez et al. 1997, Pereira et al. 2000, Morgan et al. 2014). Most of these studies estimated larval flux ([equivalent to] product of larval density and water velocity) to assess a net larval abundance transported offshore in a unit time. This index may not represent a pure potential for the larval transport because it contains larval density to induce a tautological evaluation. The product of water velocity and duration from peak larval release time to L time for every nighttime, using their time-series measurements through the reproductive season, can serve as a better predictor.

Callianassid shrimp or ghost shrimp (Decapoda: Axiidea) dwell in generally deep burrows in estuarine or marine sediments and are known for their roles as community organizers and ecosystem engineers there (Atkinson & Taylor 2005, Pillay & Branch 2011). Ghost shrimp can be divided into two groups in terms of larval developmental mode: short lecithotrophic development with up to two zoeal and one decapodid (post-larval) stages and long planktotrophic development with three to seven zoeal and one decapodid stages (Kubo et al. 2006, Kornienko et al. 2015). Populations of ghost shrimp with the latter type of larval development inhabiting intertidal flats or shallow subtidal soft sediments on estuarine or coastal shores export larvae to the coastal ocean (Johnson & Gonor 1982, Strasser & Felder 1998, Tamaki & Miyabe 2000, Yannicelli et al. 2006, Golubinskaya et al. 2016). The reproductive and larval release synchronies in ghost shrimp populations have been investigated poorly except for one preliminary study (Tamaki et al. 1996).

On an intertidal sandflat in Tomioka Bay located on the northwestern corner of Amakusa-Shimoshima Island, midwestern Kyushu, Japan (Tomioka sandflat; Fig. 1), under a mixed, mainly semidiurnal, tidal regime (Fujimoto 1990), the population of the ghost shrimp Nihonotrypaea harmandi (Bouvier 1901) has densely occupied the entire sandflat since 1983, reaching a highest mean density of 1,300 inds/[m.sup.2] on the lower shore (Tamaki et al. 1997, Tamaki & Takeuchi 2016). Note that the name Callianassa japonica was incorrectly applied to N. harmandi in previous articles (see Manning & Tamaki 1998, Yamada et al. 2017). Each adult shrimp dwells solitarily in a 30-to 60-cm deep, Y-shaped burrow on the sandflat (Tamaki & Ueno 1998). Both sexes become sexually mature at a total length (TL) of 18-20 mm (Tamaki et al. 1997; maximum TL, 47 mm), at which the female becomes ovigerous and one major cheliped begins to enlarge more in the male (sexual dimorphism; Shimoda et al. 2005). Males act combatively against other males, using major chelipeds (Shimoda et al. 2005). The sex ratio was slightly female biased (1.06:1; Tamaki et al. 1997). Individual adults tend to be distributed in a uniform spatial dispersion pattern at densities [greater than or equal to] ca. 50 inds/[m.sup.2] (Tamaki & Takeuchi 2016). Thus, each adult is expected to be surrounded by a few inter/intra-sexual neighbors (Fig. 2 in Tamaki et al. 2018). Most recently, mating behavior was revealed for one pair three times in the laboratory for the first time for Callianassidae (see Somiya & Tamaki 2017). Copulation occurred at night, at which time the female ovary was full-grown. A single spermatophore was attached externally to the last cephalothorax sternite of the hard-shelled female with no sperm-storage structure, ca. 20-40 min before embryo deposition onto pleopods 1-2 (mean number of embryos per female in the field population was 333: Tamaki et al. 1997). The embryos were brooded for 13-19 days before hatching. Subsequent larval release from the female in its burrow was observed twice, both of which occurred at night and were completed in ca. 30 sec per release bout. On one occasion, larval release was followed by copulation ca. 70 min later, which was ensued by oviposition from the restored ova and embryo deposition. In a previous field experiment, females released larvae and deposited a new batch of embryos the next day (Tamaki et al. 1996). In the field population, therefore, female oviposition synchrony, if any, can be derived not from the synchronized oviposition (and embryo deposition) using previously stored sperm but only from the immediate prior synchronized copulation. In addition, each of the larval release synchrony and the immediate subsequent reproductive synchrony (observable only as the embryo deposition synchrony) in the population could take place at a shortest interval of 2 wk. The larval development of N. harmandi consists of six zoeal and one decapodid stages (Tamaki et al. 2013, Somiya et al. 2014). Newly released zoeae-I are transported to a coastal ocean area (Amakusa-nada: 60-80-m deep inner shelf off midwestern Kyushu), 10-20 km north and west of the Tomioka sandflat (Fig. 1A; Tamaki & Miyabe 2000, Tamaki et al. 2010, 2013).

The life history and population dynamics of Nihonotrypaea harmandi on the Tomioka sandflat were most intensively studied for the period from May 1989 to April 1991, with sampling at an interval of 2 wk to 2 mo (Tamaki et al. 1997). The reproductive season was from early June through October. In this period, the mean monthly surface water temperature around the sandflat varied from 13[degrees]C (February) to 28[degrees]C (August), with those in the reproductive season greater than or equal to 20[degrees]C. As the sandflat in Tomioka Bay is located near the coastal ocean (Amakusa-nada), the mean monthly surface water salinity in the bay varied in a small range (32.5-34.5). The principal food source was estimated to be phytoplankton and benthic microalgae for adults (Yokoyama et al. 2005, Shimoda et al. 2007) and planktonic diatoms for zoeal larvae (Somiya et al. 2014, Umezawa et al. 2018). Thus, chlorophyll-a concentration in the water column off the Tomioka sandflat could be one measure of food abundance for the ghost shrimp population. The water-quality monitoring database from the measurement conducted regularly once a month (in spring tide periods) by the Kumamoto Prefecture Government at seven stations around the mouth of Ariake Sound (gray circle points in Fig. 1A) is available for the period from March 10, 1997, to March 26, 2009 [http://ay.fish-jfrca.jp/ariake/index.asp; accessed in Takeuchi et al. (2013)]. Based on this database, chlorophyll-a concentrations at a depth of 0.5 m at all stations in each month through the period are plotted in Figure 2A (blank circles), in which a spline curve for the plots [interpolated with the "loess" function in "R" 3.2.3 (R Core Team 2015); hereafter in the text, referring to "R" is omitted for such interpolations] and the mean ([+ or -]SD) values for the first and second halves of each month are shown (i.e., days 1-15 and day 16 to the final date; n = 17-44). The spline curve indicates the higher concentration season from June through November, with the peak on August 19. Specifically, the mean values were higher during mid-June to October (except for the first half of August) and the highest from mid-July to late September. This suggests that the higher primary production would be available to ghost shrimp in their reproductive season than in other seasons.

On the Tomioka sandflat, the E-BD in females of Nihonotrypaea harmandi varied from 13-15 days (mostly 14 days) in midsummer to 17-22 days in early summer and mid-autumn (Tamaki et al. 1996). Larval release from the adult population took place every spring tide period from mid-June to mid-October (Tamaki et al. 1997). In the laboratory rearing of larvae with rotifers and brine shrimp nauplii (Tamaki et al. 2013) or with diatoms only (Umezawa et al. 2018), it took 30 days for newly hatched and released zoeae-I to reach the maximum decapodid occurrence at water temperatures of 21[degrees]C-24[degrees]C. This suggests the occurrence of peak decapodid settlement on the Tomioka sandflat approximately at a 4-wk interval under the temperature of water depths mainly inhabited by larvae in Amakusa-nada during midsummer (30-40 m; Tamaki et al. 2010). Decapodids settled on the sandflat mainly every spring tide period from early July onward, and they were lumped into two major newly recruited groups (the first and second new recruitment cohorts; Tamaki et al. 1997). The first cohort comprised the decapodids that settled from early July to late August, with their peaks in late July to early August, whereas the second cohort comprised those individuals that settled from early September to early November, with their peaks in late September to early October. Each new recruitment cohort became reproductively mature in slightly less than 1 y in the fastest case (early June and early to late July in the first and second cohorts, respectively; hereafter, they are called the first and second 1-y-old cohorts). Some of these two 1-y-old cohorts survived their first reproductive season, in which the survival rate was higher in the second cohort. They merged into a fused cohort (the 2-y-old cohort) by early June of their second year, initiating the seasonal population reproduction and subsequently dying off by late August to mid-September.

During mid-June to mid-August in 1993, a quantitative sampling of the Nihonotrypaea harmandi population was conducted on the Tomioka sandflat at frequent intervals, mostly every 2 days (Tamaki et al. 1996). Females with eyed embryos about to release larvae occurred broadly in four groups over the period, with dates of both their peaks and boundaries between the adjacent ones not very distinct. This phenomenon is similar to weak synchrony of larval release in the aforementioned populations of several Uca and Sesarma species in their early reproductive season on warm temperate estuarine and coastal shores (fifth paragraph). The summer water temperature in 1993 was lower than in the other years of the early 1990s [Fig. 2B; a long-term monitoring of the surface water temperature in front of the Amakusa Marine Biological Laboratory, Kyushu University (AMBL, KU) located 1 km north of the present study site has been conducted at around 09:00 daily on a weekday basis, and the data for the present study period were provided courtesy of the laboratory staff]. By contrast, the summer water temperature in 1994 was much higher. Comparing the embryo deposition and larval release patterns in the population between 1993 and 1994 would give one clue to the understanding of how the inseparable sequence of reproductive synchrony and larval release synchrony arises and is maintained in a water temperature-dependent way in the course of the reproductive season.

The objective of the present study was to elucidate when and how the sequential flow of embryo deposition and larval release synchronies in the female population of Nihonotrypaea harmandi on the Tomioka sandflat became established in the course of its reproductive season, with the underlying dichotomous views taken into account--whether peak larval release is timed to a syzygy date (the SCB view) or the subsequent, largest-TR date (the AOTTCB view). Frequent population sampling was conducted in 1993 and 1994. Observations and experiments on embryo deposition and larval release, and measurement on water level and velocity were performed in other years. Harmonic analysis of tides was made on the water level and velocity and applied to those in 1994. Based on these water velocity estimates, larval export efficiency for each peak larval release was estimated. Finally, using an equilibrium-tide model, latitudinal and monthly variations in the availability of effective ebb TRs for larval export-type decapods on the shore was examined.

2. MATERIALS AND METHODS

2.1. Study Site

The Tomioka sandflat is located on the head of Tomioka Bay bounded by a northwest headland (Tomioka Headland) and an east small island (Tsuji-Shima Island) (130.037[degrees] E and 32.521[degrees] N; Fig. 1A, B). The maximum emersed area of the sandflat during low tide (L) in spring tide periods spans 3.5 km alongshore and 150-550 m across the shore. Tomioka Bay forms the largest westernmost coastal boundary layer (8.5 km alongshore X 2 km across the shore, with water depths [less than or equal to]30 m) in the largest estuary-to-coastal ocean system of midwestern Kyushu (from Ariake Sound to Tachibana Bay and Amakusanada). The present water area is under a mixed, mainly semidiurnal, tidal regime [Form Factor, F (Pugh 1987) = 0.34 (Fujimoto 1990)], with the average tidal range (TR) of 3 m in Amakusa-nada in spring tide periods, which is amplified to 6 m at the innermost Ariake Sound. The highest elevation of the Tomioka sandflat is at around the mean low water level in neap tide periods, ca. 60 cm above the mean low water level in spring tide periods (MLWS), and the entire sandflat area is submerged twice a day year-round (Tamaki & Kikuchi 1983). In the former time including the early 1990s, the expected peak tide times and water levels above the chart datum were available for Nagasaki Harbor 30 km northwest of Tomioka Bay [Japan Meteorological Agency (http://www.data.jma.go.jp/kaiyou/db/tide/suisan/suisan.php?stn=NS); accessed November 16, 2017], and from 2012, data nearer to Tomioka Bay became available as the local town name, Reihoku. As there is only a few-min lag in the respective peak tide times between the two locations, hereafter, no mention is made about the locations with tide gauges. The [M.sub.2] tidal currents are dominant in the water-velocity field of the present study area, with much prevalence of their east-west over north-south components close off Tomioka Bay (Fujiie et al. 2006). The highest surface-water velocities are 150 cm/sec around Hayasaki Straits located between Amakusa-nada and Ariake Sound (Fujiie et al. 2006) and ca. 60 cm/sec in spring tide periods and ca. 20 cm/sec in neap tide periods, respectively, at a 19-m deep station in central Tomioka Bay (Stn E in Fig. 1B; see Section 3.10.1).

2.2. Water Temperatures in the Ghost Shrimp Reproductive Season in the Early 1990s

The variations in the surface water temperature recorded in front of the Amakusa Marine Biological Laboratory, Kyushu University (AMBL, KU) in Tomioka Bay from May to November in 1992, 1993, and 1994 are shown in Figure 2B. The values about 20[degrees]C-21[degrees]C in early June and the end of October were recorded in the three years. As compared with the previous data set for June to October of 1989-1990 (ca. 20[degrees]C-28[degrees]C in each mean monthly average: Fig. 2 in Tamaki et al. 1997), the period from late July through September in 1993 was characterized by the lower temperatures, with a highest value around 25[degrees]C maintained during mid-July to early September. By contrast, in 1994, the water temperature rapidly increased from 21[degrees]C to 27[degrees]C during mid-June to early July, followed by 27[degrees]C-29[degrees]C until early September, from which it gradually decreased to 21[degrees]C at the end of October. In 1992, the pattern during June to mid-August was similar to that in 1993 except for the higher values in the latter half of July, and the temperature increased rapidly from mid-August to early September, with the pattern thereafter similar to that in 1994.

2.3. Sampling Ghost Shrimp Population on the Sandflat during the Reproductive Season

2.3.1. Sampling through Reproductive Season in Hot Summer Year (1994)

To detect embryo deposition and larval release cycles in the population of Nihonotrypaea harmandi on the Tomioka sandflat. sampling was conducted at frequent intervals through the reproductive season of 1994. The sampling site was placed on the lower shore around the northwestern corner of the sandflat, 260-280 m seaward of the upper shoreline and 30-50 m landward of the MLWS (Stn A in Fig. 1B). The elevation of the site was approximately 25 cm above the MLWS. There was a total of 44 sampling occasions (= dates) from May 26 to November 6. The second and third sampling dates were June 11 and 25, from which the intervals of 2-6 days between two successive dates were kept, 3 days most frequent. During L on each date, sand-column samples reaching the shell-hash layer above the bedrock were collected using an acrylic cylindrical corer with a 100-c[m.sup.2] cross-sectional area X 1 -m length within a haphazardly chosen ca. 3-m X 3-m area. The overlapped use of the identical areas among different sampling dates was avoided. The sand column, ca. 50 cm in mean thickness, was loosely packed because of bioturbation by shrimps at high densities (Wardiatno et al. 2003, Tamaki et al. 2018), so that they were easily pierced through by the corer. The corer was lifted, with a rubber lid on top and a hand on the bottom. On the dates with the lowest tidal heights greater than ca. 70 cm above the chart datum, the sampling site was submerged. There, a float with the sampling equipment on it was moored, and the coring was performed under shallow water coverage. Each core sample was passed through a 0.5-mm mesh sieve in situ, and the retained material was fixed with 10% neutralized seawater formalin. Ovigerous (precisely, embryobrooding) females were individually fixed in small polyethylene bags to prevent loss of embryos. Sixteen core samples were taken on each of the initial three dates, after which 20 samples per date were taken except for two dates under adverse weather conditions [three samples (12 August) and 15 ones (25 September)].

2.3.2. Sampling during First-Half Reproductive Season in Cold Summer Year (1993)

During May 31 to August 19 in 1993, sampling of the Nihonotrypaea harmandi population was conducted 30 times on the site near to that in 1994 at an interval of 1-6 days, most frequently 2 days, using the same collection procedure as in 1994 (Tamaki et al. 1996). Twenty or 25 core samples were taken on each sampling date as a rule (on 26 dates), with 19-22 samples on the other four dates.

2.4. Laboratory Treatment of Collected Specimens

The first step in the laboratory treatment of the specimens of Nihonotrypaea harmandi collected from the Tomioka sandflat in 1993 and 1994 consisted of the following five substeps.

(1) Sex identification. Most adult females were identified by the presence of ovaries or embryos. The other key traits included the presence (female) or absence (male) of the second pleopods and the gonopore position [at the base of third (female) and fifth (male) pereiopods]. No identification was made for juveniles < 10 mm in total length (TL) (see Tamaki et al. 2013 for detailed juvenile definition). In a few cases for small shrimp [greater than or equal to] 10 mm, their sexes were unidentified from damage, in which each shrimp was allocated equally to each sex (i.e., 0.5 shrimps). In the present study, only females were targeted for the population analysis based on a nearly equal sex ratio (Section 1).

(2) Determination of embryo developmental stage (EDS). The EDS was subdivided into three groups based on Rodrigues (1976) and Yamaguchi (2001c): EDS-I: stage from just after fertilization to just before germinal disc formation; EDS-II: egg nauplius (or embryonized nauplius) stage; and EDS-III: eyed-embryo stage before hatching. At its earliest time, the germinal disc in EDS-II is recognized as a small transparent yolk-free portion. For some partially damaged females with embryos retained, their EDS was determined.

(3) Total length measurement. The TL is defined as the mid-dorsal curvilinear length from rostrum to telson tips. Under a stereomicroscope with the drawing tube, that curve on lateral aspect was traced at magnifications of ca. 5X (for adults) and 12X (for juveniles) and its curve length measured to 0.1 mm. For any specimen with pleon damaged, sex identified (e.g., from a partially retained anterior pleon), and carapace left intact, TL was estimated from carapace length (CL: mid-dorsal length from rostrum tip to carapace rear depression), using the linear regression equation, TL = 4.68CL - 1.09 (Tamaki et al. 1997). These estimated TLs comprised 4.8% of the whole TL data set.

(4) Total length-frequency distribution construction and cohort separation. The TL-frequency distribution of the adult female population on each sampling date was made, with a class interval of 2.0 mm and the smallest class of 4.05-6.05-mm TL (cf., Tamaki et al. 1997). The newly recruited individuals in the same year were removed from the data (e.g., the first individual emerged on July 13 and June 29 in 1993 and 1994, respectively). The remaining TL-frequency distribution was separated into three normal-distribution groups each corresponding to one of the three adult cohorts (i.e., the 2-y-old cohort; the first and second 1-y-old cohorts). The smallest-TL class number in the second 1-y-old cohort was four (10.05-12.05-mm TL) in both years (recorded on May 31 and June 6 in 1993 and on May 26 and June 11 in 1994). Generally, the first cohort of newly recruited shrimp in any one year (i.e., the first 0-y-old cohort) is largely well separated from the older cohorts in their TLs, but a small portion of the former cohort catches up with the smallest-TL class of the second 1-y-old cohort in the mid- to late reproductive season of that year (Tamaki et al. 1997, 2013). The latter phenomenon did not occur until the final sampling date in 1993 (August 19). In 1994, the overlap between the first 0-y-old and second 1-y-old cohorts first occurred during August 18 to September 22 at the class number six (14.05-16.05-mm TL; see Section 3.7). From September 25 onward, the overlapped class number became eight (18.05-20.05-mm TL). For all these cases with the overlaps between the two cohorts, to determine the number of individuals belonging to the smallest-TL class in the second 1-y-old cohort, one-seventh the individual number at the second smallest-TL class in this cohort was adopted uniformly for every date, based on the averaged ratio values over the sampling dates in a past TL-frequency distribution data set (Fig. 5 in Tamaki et al. 1997). To smooth out the fluctuation in individual numbers across the size classes on each sampling date, the data from every three successive sampling dates were pooled for normal-distribution separation, in which the aforementioned "one-seventh rule" was also applied to the pooled TL-frequency distribution; the initial and final pools were for the respective two successive dates. Following Aizawa and Takiguchi (1999), with a modification to Hasselblad (1966), the composite normal-distribution group on each pooled date was separated into the three component groups. The probability of occurrence of individuals belonging to each adult cohort in each TL class for every pooled date was applied to the middle of the three successive component dates; the pooled date from the initial two dates for the first date and that from the final two dates for the last date. The allocation of individuals to the three cohorts in each TL class using this probability set was conducted in an identical manner for each of the three EDS groups (i.e., EDS-I to EDS-III).

(5) Tracking the density of each cohort through the reproductive season. The individual density of each of the three adult female cohorts on each sampling date in the reproductive season of both years was standardized to the number of shrimps per 2,000 c[m.sup.2] (= 100 c[m.sup.2] x 20 samples). The temporal change in the density of each female cohort was tracked across its three EDSs (and nonovigerous stage) through the season. The nonovigerous female group is composed of (i) immature females, with <18.05-mm TL (Tamaki et al. 1997); (ii) mature ones, with [greater than or equal to] 18.05-mm TL, before their first brooding; (iii) mature ones that have released larvae and with well-restored ovaries, and are now ready for re-brooding; and (iv) mature ones that have ceased reproductive activity, especially around the end of the reproductive season.

2.5. Estimation of Time Lag between Successive Female Broodings by Field Experiment

In a laboratory observation for one pair of female and male of Nihonotrypaea harmandi for 3 mo, the female brooded three times (Somiya & Tamaki 2017). At one brooding event, the female with well-developed ovary released larvae, copulated, and re-brooded within a single night. The successive brooding was recorded also in a field experiment conducted in 1992 on the Tomioka sandflat (Tamaki et al. 1996)--females brooding the late EDS-III embryos were collected during a daytime L, and substantial females released larvae by the next daytime in the laboratory or in sediment-filled polyvinyl chloride (PVC) pipes buried in the sandflat substrate. Then, several females were confined to a pipe with several males and buried in the substrate within that daytime L. One day later, the presence of females with new broods was checked. Each re-brooding female was maintained in a new pipe for determining her brooding duration. The nonovigerous ones were left in the former pipe with the males. Such daily (as a rule) procedures were repeated for a maximum of five consecutive dates per spring tide period, beyond which observations were stopped owing to continuous submergence.

There was a minimum resolution of 1-day lag between larval release and re-brooding by a female in the aforementioned experimental setting, but such a female could have re-brooded within a single night (i.e., 0-day lag). In addition, in determining the brooding durations, a maximum of 3-day uncertainty, because of pipe retrieval schedules, was adopted (Table 2 in Tamaki et al. 1996; 42 females). Including three unadopted females beyond this uncertainty limit in that article, the data on the time lag between larval release and re-brooding were compiled.

2.6. Dates of Larval Release and Re-brooding in Field Population with Regard to Syzygy

Although the date of peak larval release by the Nihonotrypaea harmandi population on the Tomioka sandflat can be determined by monitoring the daily change in newly released larval density in the water column around the sandflat over these dates, instead, the present study examined the daily changes in the frequency distribution of eye size of the EDS-III embryos in the female population and in the density of females with re-brooded embryos. The embryo eye was noted because its size was expected to grow to reach some threshold immediately before embryo hatching (Tamaki et al. 1996).

Daily population sampling was conducted 20 m off the upper shoreline of the northwestern part of the sandflat during each daytime L from August 26 (mid-tide period) to September 1 (mid-tide period) in 2011, including the syzygy date of August 29 (at new moon). Using a yabby pump, ca. 70 females were randomly collected daily. They were individually kept at -25[degrees]C in a portable freezer, thawed, and divided into ovigerous and nonovigerous categories. The ovigerous females were subdivided into those with eyed or uneyed embryos. For the females with eyed embryos, the images of 10 randomly chosen embryos per female were obtained using a CCD camera system (Leica DFC280 connected to a personal computer). The cross-sectional areas of each embryo (inside the chorion) and its eye in plane aspect were measured on the computer display, as follows. Using Renda! ver. 1.2.1 (http://nodakoubou.net/program2/vb/renda.html; accessed November 16, 2017), the (x, y) coordinates of multiple points along the outline of each embryo or eye were acquired. The area inside the traced polygon was calculated to 0.001 mm', using the "areapl" function in the "splancs" package (Rowlingson & Diggle 2015) of "R" 2.15.2 (R Core Team 2015). The mean ratio of the cross-sectional areas of eye to that of embryo body was defined as the degree of eye development in each female and the degree-frequency distribution made for each date. It was expected that the frequencies with those degree values greater than some threshold decreased markedly from before to after the peak embryo hatching (= larval release) date. The degree of eye development was related to the daily change in the proportions of the females with eyed or uneyed embryos and nonovigerous females to all specimens.

2.7. Estimation of EDS Durations by Field Experiment

To estimate the duration of each of the three EDSs in Nihonotrypaea harmandi females, field experiments were conducted twice on the Tomioka sandflat, in September to October 1994 and July to August 1995, following the method briefly mentioned in Section 2.5 based on Tamaki et al. (1996). The detailed procedure was as follows. Nonovigerous females with well-developed ovaries or females with the latest EDS-III embryos about to hatch were collected during a daytime L and brought to the laboratory; most of the latter females released larvae during the immediate nighttime. During the following daytime L, the experiment was performed at an area 100 m landward from the regular sampling site in 1994 (Section 2.3). Those 5-6 females and the equal number of males with comparable (and greater) body sizes were housed in a sediment-filled PVC pipe (12-cm [phi] X 33-cm length; nylon nets of 0.5-mm and 2-mm mesh openings attached to the bottom and top, respectively). These pipes were buried vertically in the sandflat substrate, with their tops 3-4 cm above the surface, until the daytime L the next day, when the content of each pipe was gently emptied onto a coarse-mesh sieve. The females with newly deposited embryos were enclosed individually in sediment-filled PVC pipes (7.4-cm [phi] X 33-cm length). Subsequently, one or two females were retrieved per date and fixed with 10% neutralized seawater formalin until the expected embryo-brooding duration (E-BD) for later determining their EDSs and estimating the synthesized duration of each EDS. At the same time, a minimum-maximum thermometer (Tokyo Galasu-Kikai) was buried in the sandflat, with its sensor at a 30-cm depth, and those extreme values during each preceding period recorded at irregular intervals (when the experimental plot was emersed). Interstitial waters at that depth were sampled for measuring salinity with a refractometer (S-100, ATAGO).

2.S. Tracking Each Brooding-Female Batch Based on Temperature-Dependent Brooding Duration

The E-BD of Nihonotrypaea harmandi females on the Tomioka sandflat has been shown to vary with water temperature, ranging from 13 to 22 days (Tamaki et al. 1996). This can affect the sequence from a batch of females with newly brooded embryos (the earliest EDS-I embryos) to that batch with embryos about to hatch (the latest EDS-III embryos) in the population through its reproductive season [Section 2.4, sub-step (5)]. The several-day duration of each EDS may add a further uncertainty to tracking the sequence of these female batches. One way to examine such a combined uncertainty with the progress of the EDSs of each female batch is estimating the position of a batch with EDS-I embryos on the time axis back from the corresponding batch with EDS-III embryos under the field water temperatures. The estimated individual-density-frequency distribution in each female batch with EDS-I embryos over time may help detect the true peak date of new embryo deposition by that female batch. Such estimation is most effective when the synchronized larval release by the population peaks sharply on a particular date in each spring tide period (e.g., syzygy date; Section 2.6) and when this is reflected on the individual-density-frequency distribution of that female batch with EDS-III embryos. This back-calculation was made by using the following two steps:

(1) The E-BD of females was regressed to water temperature, based on the data set obtained in the reproductive season of 1992 (Tamaki et al. 1996). This set comprises (i) individual female's brooding duration (day), starting from each specific date of new embryo deposition on the Tomioka sandflat [objective variable (v): Table 2 in Tamaki et al. 1996] and (ii) water column temperature near the sandflat averaged over that duration [explanatory variable (x): original data provided by the AMBL, KU; the water column temperatures were close to the highest sediment temperatures (at a 30-cm depth) in the summertime (Fig. 2B; Table 3 in Tamaki et al. 1996)]. In the case for brooding duration given as a range, the mean value was used (e.g., 19.5 days for 19-20 days; 21 days for 20-22 days). The daily temperature values for 9-13 dates spread over each established brooding duration was required for an unbiased average temperature; 36 (x, y)-data sets were extracted. The least square regression was conducted using Microsoft Office Excel 2010 solver.

(2) The regression equation in item (1) was applied to the time-series data on the population (Section 2.4) and water column temperatures (Fig. 2B) for the reproductive seasons of 1993 and 1994. The individual density in each cohort with EDS-III embryos on each sampling date was shifted back to the density with that cohort's new brooding state by the corresponding regressed duration. For determining that duration, the water temperature value averaged over a 17-day period precedent to the aforementioned sampling date was used as the variable, x. The 17 days were adopted as half the entire range of E-BD (13-22 days). Intermittently lacking daily temperature values were estimated by linear interpolation between the respective, two successive actual data.

2.9. Larval Hatching Times during Nighttime in the Laboratory

In previous experiments, Nihonotrypaea harmandi females with the latest EDS-III embryos were collected from the field in a daytime L, and most of them released larvae over the immediate night in the laboratory (Tamaki et al. 1996, Konishi et al. 1999). To determine the larval release-time distribution during darkness in the laboratory in relation to the expected local high tide (H) and L times, monitoring of larval release bouts was conducted twice in 2014. Females with embryos were collected at a site 20 m from the upper shoreline on the Tomioka sandflat during the daytime L on August 24 (33 females for experiment 1) and September 10 (36 females for experiment 2). These females were kept in the field-collected seawater and transported to the laboratory by the expected nighttime H time on each date [19:54 and 21:02, with sunset (SS) at 18:56 and 18:34 and sunrise (SR) at 05:50 and 06:01 the next day, respectively]. The room temperatures were held at 25[degrees]C. The females were maintained individually in small transparent polyethylene bags or glass containers in the dark (within polystyrene boxes with lids), each filled with filtered (with 10-[micro]m mesh) seawater at 32.6 salinity and containing no sediment. As the larval release bout in N. harmandi female is made within a short duration (10s sec), the time of the first finding, by quick inspection with each box lid removed, a dense "cloud" of newly released larvae was regarded as the embryo hatching time for each female. In experiment 1, the setting was ready at 19:30, when no females had released larvae. The inspection started at 19:45, from which the recordings were continued at an interval of 15 or 30 min until 05:30 the next day. In experiment 2, the setting was ready at 20:00, with no larvae present. The inspection started at 20:30, followed by the recording at 30-min intervals until 06:00 the next day.

2.10. Larval Release Times in Relation to 24-h Light-Dark and Tidal Changes in the Field

To examine the distribution of times of larval release by the Nihonotrypaea harmandi population on the Tomioka sandflat during a 24-h segment around a spring or neap tide period with different combinations of light--dark and tidal cycles, vertical hauling of a plankton net was conducted from anchored boats in Tomioka Bay, as follows.

(1) Around spring tide period. Sampling was made at a 1-4 m deep (L-H depths) station ca. 60 m off the sandflat (Stn C in Fig. 1B) 12 times from 12:56 on August 11 to 11:45 the next day in 1992; the syzygy (full moon) was on August 13. The interval between two successive sampling times varied from 103 to 150 min. The SS and SR were at 19:10 and 05:42. The expected peak tide times were 13:06 (L), 19:48 (H), 01:36 (L), and 07:08 (H). The weather was fine to cloudy and calm. At each time, after the water depth to the seabed was recorded with a sounding line, a conical nylon plankton net with a 2-kg weight (mouth, 45-cm [phi]; lateral length, 100 cm; mesh opening, 0.33 mm) was dropped to the seabed, left for 30 sec, lifted to the surface at a speed of 0.5 m/sec, and washed from the outside. The cod-end content was fixed with 5% neutralized filtered-seawater formalin. Four casts were made, and it took 7-9 min to accomplish the procedures. (2) Around neap tide period. Sampling was made at a 7-10 m deep station 1.2-1.5 km off the sandflat lower shoreline (Stn D in Fig. 1B) 143 times from 09:40 on August 31 to 09:33 on September 1 in 1994; the quadrature was on August 29. The interval between two consecutive sampling times was 10 min (except for 20 min on one occasion). The SS and SR were at 18:47 and 05:55, respectively. The expected peak tide times were 09:27 (L), 16:52 (H), 22:32 (L), 03:57 (H), and 10:48 (L). The weather was fine and calm. Each sampling was made within 3 min, following the same procedure as in item (1) except for a single plankton net cast and no water-depth measurement.

2.11. Measuring Water Level and Velocity for Evaluating Potential Larval Transport Rate (PL TR)

2.11.1. Instrument Installation and Retrieval on the Sandflat

In general, larvae released from burrow-dwelling decapods are first subjected to water flows above the adult-inhabited substrate, which affects their subsequent transport. To obtain a data set on the temporal variation in water velocity in relation to the water level close above the substrate surface through the reproductive season of Nihonotrypaea harmandi on the Tomioka sandflat, measurement was made using a 2-dimensional electromagnetic current meter (Compact-EM, JEF Advantech) and an underwater pressure-type wave meter (HJ-401, IO Technic), respectively, from May 27, 2010 to May 10, 2011, at a lower shore station, 50 m landward from the MLWS on the northwestern part of the sandflat (Stn B in Fig. 1B). The main body of each cylindrical shaped instrument was buried vertically and fixed with sandbags in the substrate. The sensor was 10 cm above the sandflat surface. The east-west and north-south water velocity components were recorded every 20 min for 30 sec at 1-sec intervals. The water level was recorded continuously at 0.1-sec intervals. The retrieval of the instruments (for data downloading, sensor cleaning, and battery exchanges) and their reinstallation were carried out approximately every 2 mo, causing the lack of data five times (from 12:10 on July 12 to 17:18 on July 13, 2010; 11:02 on September 6 to 14:37 on September 7, 2010; 17:59 on November 5 to 03:14 on November 6, 2010; 14:39 on January 6 to 05:34 on January 7, 2011; 13:49 on March 4 to 04:03 on March 5, 2011). At the time of each retrieval, the height of the sensor above the sandflat was checked, which was always at the right position. The data set on water levels and velocities was used to (1) estimate the temporal change in PLTRs during the reproductive season of N. harmandi in 2010 (see Section 2.11.2) and (2) reconstruct the water levels for the reproductive season in 1994 (see Section 2.11.3).

2.11.2. Estimation of PLTR for Ghost Shrimp Reproductive Season of 2010

The time-series data for the water level above the sandflat over the reproductive season of Nihonotrypaea harmandi in 2010 (May 27 to November 5), which were composed of the three subperiods (subperiods 1-3) and intervening gaps in the measurements, were smoothed out. Starting from 11:00 on May 27 (subperiod 1), 14:00 on July 13 (subperiod 2), and 11:00 on September 7 (subperiod 3), respectively, the mean water level every 60 min was plotted at each hourly midpoint (e.g., 11:30 on May 27) through each subperiod, for which the time segments with water levels less than 30 cm were defined as the emersed durations and the corresponding (less than 30 cm) data treated as "not applicable (n/a)." This treatment was to eliminate possible large fluctuations in the shallowest water depths that are particularly subjected to meteorological vagaries. The mean-value plots were interpolated with the interpSpline function in "R" 3.2.3 (R Core Team 2015). The times corresponding to alternately occurring local maximum and minimum values on the spline curve were regarded as the H and L times, respectively. The period from H to L times was defined as the flood (tidal) phase, and the converse as the ebb (tidal) phase.

The mean water velocity for the 30-sec interval every 20 min was calculated over each of the aforementioned three sub-periods, in which any 60-min period with its mean water level less than 30 cm was treated as "n/a." Then, the shore-normal (i.e., northeast; Fig. 1B) component of each velocity was extracted, with its seaward value defined as positive and landward one as negative. Hereafter, this component is simply termed "water velocity."

The time-series data on SS and SR times, and lunar age (at 00:00 each day) at the instrument installation site were downloaded from a database of the National Astronomical Observatory of Japan (http://eco.mtk.nao.ac.jp/cgi-bin/koyomi/koyomix.cgi; accessed November 16, 2017). Daytime was defined as the period from SR to SS and the nighttime as the remainder. The lunar age at the halfway time between the times of a successive set of H (L) and L (H) was estimated by the linear interpolation of the two immediate lunar ages.

From the aforementioned data set, the following three parameters were obtained: (1) the highest water velocity with its time of occurrence at each flood or ebb phase, (2) the mean ([+ or -]SD) water velocity for each flood or ebb phase, and (3) the duration of each nighttime ebb phase and mean ([+ or -]SD) water velocity there. In general, in larval ecology of intertidal decapods, an assumption that the highest tidal current velocity is positively correlated with the TR is taken for rationalizing the adoption of TR as a proxy for water velocity, but it has not been well established by actual data (Section 1, seventh paragraph). In addition, the water velocity is composed of tidal, density-driven, and wind-induced currents. Based on the data for the aforementioned parameters (1) and (2), the relationship between TR and water velocity was examined. The data for parameter (3) were also required, as the larval release in the Nihonotrypaea harmandi population took place during the nocturnal ebb phase (Tamaki et al. 2010, Somiya & Tamaki 2017; see Sections 3.5 and 3.6). There are eight possible cases for the order of the times of SS, SR, H, and L in light of the position of the first H-to-L time segment with either no or a single SS or SR involved (see Fig. 13A-C for their example panels). The duration of the nighttime ebb phase for each order was defined as follows: (1) for SS-H-L-SR: from H to L, (2) for H-SS-L-SR: from SS to L, (3) for H-SS-SR-L: nil (i.e., nonexistence of this combination), (4) for SS-H-SR-L: from H to L, (5) for SR-H-L-SS: zero (by definition), (6) for H-SR-L-SS: from H to L, (7) for H-SR-SS-L: nil [same as in (3)], and (8) for SR-H-SS-L: from SS to L. In the aforementioned orders, the following three points should be noted: (i) for cases in which the two partial ebb phases are contained in a single nighttime [e.g., H-SS-L-H-SR-L, with the SS-L and the H-SR being these two (as in Fig. 13A)], the two phases were treated separately; (ii) in order (2), it is assumed that larval release by adults does not occur during H to SS; and (iii) in orders (4) and (6), the inclusion of the duration from SR to L in the "nighttime" was based on the assumptions that larval release in the field occurs soon after the H time during the dark hours (see Section 3.6) and that those larvae would be continuously transported offshore to the time of L in their first export process regardless of daylight hours. The mean ([+ or -]SD) duration for each of the orders (l)-(8) was calculated, and the proportions of the respective orders were compiled for each of the three subgroups of the whole TRs (mm): 0 < TR [less than or equal to] 1,100 (around neap tide periods), 1,100 < TR [less than or equal to] 2,200 (around mid-tide periods), and 2,200 < TR [less than or equal to] 3,300 (around spring tide periods). Potential larval transport rate per nighttime ebb phase was defined as the product of the previously defined, each duration [(1)-(8)], and the mean water velocity in that duration, giving a length dimension. Each PLTR was plotted versus time, including the case in the aforementioned point (i). The plots of PLTR through each of the subperiods 1-3 were interpolated with the loess function, and finally, these three spline curves were joined by the same interpolation as before to generate a single spline curve. The relationship between TR and PLTR was examined, with special reference to the dates of the syzygy and the largest nocturnal TR every spring tide period.

2.11.3. Reconstruction of Water Levels for the Ghost Shrimp Reproductive Season of 1994

To reconstruct the water levels on the Tomioka sandflat for the reproductive season of Nihonotrypaea harmandi in 1994, those measured values over the whole monitoring period (May 2010 to May 2011; Sections 2.11.1) were interpolated with the loess function, to which harmonic analysis of tides by least square method was applied using 14 tidal components (Sa, Ssa, Mm, MSf, Mf, [Q.sub.1], [O.sub.1], [P.sub.1], [K.sub.1], [[mu].sub.2], [N.sub.2], [M.sub.2], [S.sub.2], and [K.sub.2]) and mean sea level. The water levels in 1994 were reconstructed using the mean sea level and diurnal and semidiurnal tidal components ([Q.sub.1], [O.sub.1], [P.sub.1], [K.sub.1], [[mu].sub.2], [N.sub.2], [M.sub.2], [S.sub.2], and [K.sub.2]). Based on this, it was examined how the density of N. harmandi females with EDS-III embryos in each of the three cohorts [Section 2.4, substep (5)] and in the whole population (combined cohorts) varied with the cycle of the nocturnal TR during the reproductive season of 1994. The results were used to evaluate whether the dates of the maximum larval release were timed to the dates with the largest nocturnal ebb TRs in the spring-to-neap tide cycle.

2.12. Back-Estimating Larval Release Times on the Sandflat in 1994 and 1992

As the sampling point for monitoring the larval release times of Nihonotrypaea harmandi from August 31 to September 1, 1994, was 1.2-1.5 km off the Tomioka sandflat [Section 2.10, item (2); Stn D (Fig. 1B)], the actual times of release by adults on the sandflat were estimated. At Stn E, located 390 m northeast of Stn D, a time series of water velocity was obtained, using a 600-kHz acoustic Doppler current profiler (Express-ADCP; Teledyne RD Instruments) moored at a mean of 18.7-m deep station from 12:30 on October 14 to 12:15 on November 13 in 2009. The main body of the cylindrical shaped instrument was buried vertically and fixed with sandbags in the substrate, with the sensor 9 cm above the seabed. The installation and retrieval of the instrument was conducted by scuba-equipped divers. The east-west and north-south water velocity components were recorded every 5 min for 120 sec at 1-sec intervals for 15 depth layers, which were every 1 m upward from 1.7 m above the sensor. The data at the uppermost layer was discarded to eliminate echo effects from the sea surface, and harmonic analysis by least square method was applied to the data at the lower 14 depth layers between 4 and 17 m below the mean sea surface level, using six tidal components ([Q.sub.1], [O.sub.1], [K.sub.1], [N.sub.2], [M.sub.2], and [S.sub.2]) and the mean current velocity. Based on this, the tidal currents during the target time segment in 1994 at Stn E were reconstructed, and the times of the larval release bout on the sandflat back-estimated. The water depths on the sandflat during that time segment were reconstructed by using harmonic analysis for the water levels (plus 10 cm: gauge sensor height) (Section 2.11.3).

As the sampling point for monitoring the larval release times during August 11-12, 1992, was only 60 m off the Tomioka sandflat [Section 2.10, item (1); Stn C in Fig. 1B], the actual times of release by adults on the sandflat were estimated, using water velocities recorded at Stn B in 2010.

3. RESULTS

3.1. Water Temperature-Dependent Embryo-Brooding Duration (E-BD)

The E-BD (day) of Nihonotrypaea harmandi females decreased linearly from ca. 3 to 2 wk with the increasing water temperature averaged over each duration [T ([degrees]C); based on the records near the Tomioka sandflat in 1992 (Tamaki et al. 1996); the Amakusa Marine Biological Laboratory, Kyushu University (AMBL, KU)] to 25[degrees]C, from which it became a constant (Fig. 3). The linear regression equations were as follows:

E-BD = -1.5877 + 54.093 (for 20[degrees]C [less than or equal to] T < 25[degrees]C. n = 14,P< 0.001), E-BD = 14.418 (for T [greater than or equal to] 25[degrees]C, n = 22).

3.2. Duration of Embryo Developmental Stages (EDSs) Based on Field Experiment

In 1994, two batches oi Nihonotrypaea harmandi ovigerous females were tracked on the Tomioka sandflat (Section 2.7): (1) from September 8 (day 0) to days 1-3 and 7-10; and (2) from September 23 (day 0) to days 4-6 and 11-14. A single individual was retrieved on each day number except for two on day 13. The ranges in pore water temperature and salinity in the period for the first batch were 23.5[degrees]C-28.1[degrees]C [n (number of measurement dates) = 4] and 35.2-35.5 (n = 2). Those values for the second batch were 22.3[degrees]C-26.2[degrees]C (n = 4) and 35.2 (for all n = 3), respectively. For the two batches combined, the periods for EDSs-I, -II, and -III were days 0-4, days 5-8, and day 9 and thereafter, respectively. On day 13 in the second batch, one of the two females had released larvae. On day 14, the female had embryos with maximum eyes, which appeared to hatch in the immediate night.

In 1995, five batches of ovigerous females were tracked: (1) from July 27 (day 0) to days 1 and 2; (2) from July 29 (day 0) to days 5 and 6; (3) from August 10 (day 0) to days 7-9; (4) from August 12 (day 0) to days 3, 4, and 10-13; and (5) from August 14 (day 0) to days 4, 6, 14, and 15. A single individual was retrieved on days 1-3 and 7-15, and two on the other day numbers. The ranges in pore water temperature and salinity during the period for all batches were 24.9[degrees]C-28.4[degrees]C (n = 12) and 34.0-34.5 (n = 11). For all batches combined, the periods for EDSs-I, -II, and -III were days 0-4, days 5-8, and from day 9 and thereafter, respectively. On days 14 and 15, each female had released larvae.

3.3. Specifying Dates of Larval Release and Re-brooding in Field Population with Regard to Syzygy

The daily change in the proportion of each of the females with eyed embryos, those with uneyed embryos, and non-ovigerous females to all female specimens of Nihonotrypaea harmandi (total numbers = 71-75) on the Tomioka sandflat from August 26 to September 1 in 2011 is shown in Figure 4A. The decrease in the proportion of females with eyed embryos over these dates was accompanied by the increase in that with uneyed embryos. Here, the day-to-day increment in the proportion of females with uneyed embryos was defined as the proportion of newly emerging ovigerous females per date, which exhibited a clear peak on August 29 (syzygy date; Fig. 4B). The daily change in the degree-of-eye-development-frequency distribution in the females with eyed embryos is shown in Figure 4C, in which the frequency in each class with 0.25% interval is expressed as the proportion of the individuals to all specimens on each date. The degree values ranged from 0.400% to 6.064%. From August 26 to August 28, the eye size grew evidently, its mode finally reaching the class of 3.75%-4.00%. The total number of females with eyed embryos decreased markedly from August 28 to August 29. The day-to-day change in the proportion of females in each class is shown in Figure 4D. From August 28 to August 29, the proportion in the degree of eye development decreased markedly, exhibiting a maximal decrement at the class of 3.75%-4.00%. From this class to the greater degree classes, the sum of decrements (minus values) exceeded the sum of increments, with the grand total of-0.13 gain. Such daily gain values from August 26 to August 27 and from August 27 to August 28 were +0.07 and +0.06. Those values from August 29 to September 1 were -0.06, -0.11, and +0.03. Overall, the daily changing pattern in the degree-of-eye-development classes greater than or equal to 3.75%-4.00% indicates that substantial eye growth occurred from August 26 to August 28, but not from August 28 onward. Thus, the aforementioned negative gain values from August 28-29 to August 30-31 were highly likely to be caused by embryo hatching, with its peak occurring in the nighttime from August 28 to August 29. The females with eyed embryos of which degree-of-eye-development classes were at 3.75%-4.00% and greater can well be regarded as the females about to release larvae in the immediate nighttime. The daily change in the proportion of these females to all female specimens again exhibited the peak on August 28 (Fig. 4E). This appears tightly coupled with the daily occurrence pattern for the new ovigerous females, which peaked on August 29 (Fig. 4B).

3.4. Time Lag between Larval Release and Subsequent Re-brooding in Field Experiment

In total, 45 Nihonotrypaea harmandi females were tracked regarding the day lag between larval release and subsequent re-brooding in the experiment on the Tomioka sandflat (from original and unpublished data for Tamaki et al. 1996): 1 day for 26 females, 1-2 days for seven, 2 days for two, 2-3 days for two, 2-4 days for one, 3 days for one, 3-4 days for one, 4 days for three, and 5 days for two. The four cases given in day ranges arose because of the nondaily retrieval of containers. Equally allocating these females to each component day duration (e.g., 3.5 to 1 day and 2 days) and assuming a shorter time lag by 1 day under the natural conditions (Section 2.5), the aforementioned values could become: 0 day (i.e., re-brooding within each same night) for 66% of all females, 1 day for 15%, 2 days for 6%, 3 days for 8.5%, and 4 days for 4.5%.

3.5. Larval Hatching Times during Nighttime in the Laboratory

In experiment 1 in the laboratory (Section 2.9), 24 of the 33 females of Nihonotrypaea harmandi released larvae during the nighttime following the daytime collection from the Tomioka sandflat [on August 24-25, 2014; expected high tide (H) at 19:54 and low tide (L) at 01:56] (Fig. 5A). The embryo hatching occurred from 21:53 to 04:53, with 71% of those females having released larvae before the L time and the peak being at 00:38. In experiment 2, 30 of the 36 females released larvae during the nighttime following the daytime collection (on September 10-11; expected H at 21:02 and L at 03:21) (Fig. 5B). Embryo hatching occurred from 22:15 to 02:45, with all females having released larvae before the L time and the peak being during 00:15-01:15 (three identical values). When the duration from H to L times is standardized to unity [0 (H) to 1 (L)], the aforementioned peak hatching times were positioned at 0.80 and 0.51-0.67 (median = 0.59).

3.6. Larval Release Times in Relation to 24-h Light-Dark and Tidal Changes in the Field

In the nighttime from August 11 to August 12 in 1992 (spring tide period) in Tomioka Bay, each H and L occurred once, with the H coming shortly after the sunset (SS) (Fig. 6A). Only zoeal stage-I larvae for Nihonotrypaea harmandi were collected, and almost all were at night. The larvae emerged immediately after the H time, and density reached a peak mean value 130 min after it and then declined rapidly. When the duration from H to L times is standardized to unity, the peak larval occurrence time was positioned at 0.37. Around the nighttime from August 31 to September 1 in 1994 (neap tide period), the Hs occurred twice, 115 min before SS and 118 min before sunrise (SR), intervened by the L near midnight (Fig. 6B). Only zoeal stage-I larvae were collected. As their numbers per haul (maximum: 28 inds) were much smaller than in 1992, the three-term simple moving average value for each time is shown in the panel to make a possible pattern clearer. The higher two peaks occurred at 22:10 and 06:50. These peak occurrence times were positioned at 0.96 and 0.45 in the standardized duration from H to L times, respectively.

The aforementioned peak larval occurrence times need corrections for the actual larval release times on the sandflat located landward from the larval sampling sites, using the reconstructed water velocity data (see Sections 2.12 and 3.10.1).

3.7. Population Density Change and Reproductive Cycle on the Sandflat in 1994

3.7.1. Temporal Change in Densities of Whole Population and Three Cohorts

Based on the temporal change in the total length (TL)-frequency distribution of the adult female population of Nihonotrypaea harmandi on the Tomioka sandflat on every sampling date from May 26 to November 6 in 1994, the separation of the frequency distribution into the three cohorts (2-y-old, first 1-y-old, and second 1-y-old) on each middle of the three (or edge of the two) successive pooled sampling dates was made (Fig. 7). Based on this cohort separation, the temporal change in the densities of the whole population and three cohorts on every sampling date is shown in Figure 8A-D. The temporal change in the proportion of each of the three cohorts to the whole population and to the mature-individual group are shown in Figure 8E and F, respectively. All these panels are presented in stacked columns, with subdivision into the three cohorts (Fig. 8A, E, F) and the immature, mature and non-ovigerous, and ovigerous individuals (Fig. 8B-D). To smooth out the fluctuation in density over the sampling dates, a spline curve interpolated with the loess function was superimposed on each data set (Fig. 8A-D). The temporal change in the ovigerous rate in each cohort, as defined as the proportion of ovigerous individuals to the total females in that cohort, is shown in Figure 8G.

Through the reproductive season, the whole population density decreased from ca. 140 to 50 inds/2,000 c[m.sup.2] (hereafter, "/2,000 c[m.sup.2]" is omitted for density), with the first large inflection point on the spline curve, as detected with the second derivatives and a steeper gradient thereafter, on July 24 (estimated date; syzygy on July 23; Fig. 8A). All members of the 2-y-old cohort were mature, and their density decreased monotonically from the initial value of ca. 30 inds until the final occurrence date of August 18 (Fig. 8B). Except for a very few individuals on the initial two dates, all members of the first 1-y-old cohort were mature, and their density decreased from ca. 45 to 10 inds over the reproductive season, with the first large inflection point on the spline curve on July 24 (Fig. 8B). The densities of the second 1-y-old cohort were at around a constant value of ca. 70 inds until August 8 (syzygy: August 7), from which they gradually decreased to 40 inds (Fig. 8D). The initial high proportion of the immature individuals in the cohort (ca. 70%) decreased rapidly to 30% through June, 10% through July, 5% through August, and zero through September (Fig. 8D: broken spline curve).

The mean ([+ or -]SD) proportion of the 2-y-old and first 1-y-old cohorts inclusive to the whole population was 45.4 ([+ or -]7.7)% during May 26 to August 12 (n = 18), from which it dropped precipitously to 27.2 ([+ or -]8.6)% through August (n = 6), and thereafter, stayed at a constant value [21.6 ([+ or -]5.8)%; n = 19] (Fig. 8E). The 2-y-old cohort occupied maximally 21%-24% of the whole population until July 11 (syzygy: July 9), from which its proportion decreased until August 18.

The proportion of the 2-y-old and first 1-y-old cohorts inclusive to the mature-individual group largely linearly decreased from 78% on May 26 to 48% on August 12, which was caused mostly by a large decrease in the 2-y-old cohort from the initial value of 39% (Fig. 8F). From August 12 onward, the proportion of the first 1-y-old cohort largely linearly decreased to 29% on September 11, and thereafter, stayed at a constant mean ([+ or -]SD) value [21.9 ([+ or -]6.1)%; n = 17].

In the 2-y-old cohort, the low ovigerous rate on May 26 (3.7%) rapidly increased to 68.3% on June 11, from which a high mean ([+ or -]SD) value of 63.0 ([+ or -]18.2)% was maintained until August 18 (n = 20; Fig. 8G). In the first 1-y-old cohort, the virtually zero ovigerous rate on May 26 rapidly increased, via 43.6% on June 11, to 79.4% on June 25, from which a high mean ([+ or -]SD) value of 73.4 ([+ or -]15.3)% was maintained until October 19 (n = 37). Finally, the ovigerous rate decreased from 22.7% on October 25 to virtually zero on October 31. In the second 1-y-old cohort, the virtually zero ovigerous rate on May 26 rapidly increased, via 20.3% on June 11, to 41.3% on June 25, from which a medium mean ([+ or -]SD) value of 34.0 ([+ or -]9.4)% continued until August 9 (n = 15). From August 12 to October 19, a high mean ([+ or -]SD) value of 69.5 ([+ or -]16.5)% was maintained (n = 22). Finally, the ovigerous rate decreased from 16.3% on October 25 to zero on November 3.

3.7.2. Sequential Flow of Each Female Cohort across Three EDSs The water temperatures in Tomioka Bay through the reproductive season of Nihonotrypaea harmandi in 1994 are indicated by solid circle plots in Figure 9A (same data as in Fig. 2B). The 17-day average water temperature back from every date is indicated by the broken line. The E-BD back from each date is indicated by the gray column on that date, which was estimated using the above average temperature value and either of the two equations given in Section 3.1.

Based on the cohort separation for each sampling date (Section 3.7.1), the temporal change in the density of females with each EDS for the three cohorts through the reproductive season is shown in Figure 9B-D. At each EDS, there were multiple clumps in the plots of female density. A unit clump can be regarded as a synchronized embryo deposition group and its descendant, which is hereafter called a batch. There were four batches in the 2-y-old cohort and eight in each of the first and second 1-y-old cohorts [termed batch i (EDS-j); i = 1 (first) to 8 (last); j = I-III]. The boundary between any two adjacent batches is indicated by a vertical dotted line (for only EDSs-I and -III for simplicity of the following description: Fig. 9B, D), which is on either the shared edge date for both batches or on their halfway (unsampled) date. Although two sub-batches appear to exist in batch 2 (EDS-I) of the 2-y-old cohort, they were not demarcated; each batch 2 of the younger two cohorts with higher densities seemed to be a single entity, probably with less sampling errors.

In the 2-y-old cohort, females of batch 1 (EDS-I) first occurred on May 25. The boundary between batches 1 and 2 (EDS-I) was clear (on June 25), whereas that boundary situated on June 25 and 29 in the first and second 1-y-old cohorts, respectively, occurred as a shallow dip. For all cohorts, the switch from batch 2 to batch 3 (EDS-I) was distinct on July 20. Each of batches 3 and 4 (EDS-I) in the 2-y-old cohort and of batches 3-8 (EDS-I) in the first and second 1-y-old cohorts stood sharp, separated from the adjacent two batches largely by 2 wk. Females of batch 1 (EDS-I) occurred until August 15 in the 2-y-old cohort and until October 16 in the younger two cohorts. In the first and second 1-y-old cohorts, the variance about the peak in each batch was larger in batches 1, 2, and 8 (EDS-I) than in batches 3-7 (EDS-I). The variance in each batch was generally larger in the first than in the second 1-y-old cohorts. The variances were smallest in batches 3-6 (EDS-I) in the second 1-y-old cohort.

Across the three EDSs, there were eight sets of three batches labeled an identical number. The correspondence between batches within each set was clear for batches 3-8 and less so for batches 1 and 2 (Fig. 9B-D). In the earliest reproductive season, the outline over the density plots for batches 1 and 2 was smoother at EDS-III than at EDS-I, because the sampling dates with the first occurrence of females with EDS-III embryos came behind the initial three dates with the longest intervals between them. The (back-)estimated E-BD shortened rapidly from 20.9 days around June 23 to 14.4 days around July 12 (Fig. 9A). This could have reduced the variance about the peak in batch 2 (EDS-III) of all cohorts. The sharp stands with the smaller variance about each peak in batches 3-6 (EDS-III) of the first and second 1-y-old cohorts and in batches 3 and 4 (EDS-III) of the 2-y-old cohort would have been maintained by a constant E-BD of 14.4 days in the mid-reproductive season. Toward the end of the season with decreasing water temperatures, the variance about each peak became larger in batches 7 and 8 (EDS-III) of the first and second 1 -y-old cohorts, with the E-BD gradually lengthening from 14.4 days around September 27 to 17.2 days around October 14. The effect of the protracted brooding duration on these variances was most clearly observed in the shift from EDS-I to EDS-III in batch 7's.

In batches 3-8 (EDS-III) of the first and second 1-y-old cohorts and batches 3 and 4 (EDS-III) of the 2-y-old cohort, the date of each peak density was exactly or nearly coincident with the immediate syzygy date (Fig. 9D). In the 14 pairs of these peak-density and syzygy dates, there were five 0-day lags, five 1-day lags, three 3-day lags, and one 4-day lag. Such a high degree of coincidence in each pair accorded well with the previous result that the peak embryo hatching (and larval release) took place on a syzygy date (Section 3.3). Thus, it can reasonably be assumed that during the mid- to late reproductive season of 1994, the distribution of batches at EDS-III with time well represented the larval release timing for at least batches 3-8 of the first and second 1-y-old cohorts and for batches 3 and 4 of the 2-y-old cohort. In these 14 pairs of batches 3-8 at EDS-III and their back-corresponding batches at EDS-I, each peak-to-peak duration ranged from 6 to 14 days, with mean ([+ or -]SD) of 9.7 [+ or -] 2.5 days, which was shorter than the shortest E-BD of 14.4 days (Fig. 9A, B, D). This suggests that the distribution of those batches at EDS-I with time does not reflect the actual new embryo deposition dates, with each EDS-1 duration spanning up to 4 days (Section 3.2). By back-calculation for every plot in all batches at EDS-III (including batches 1 and 2) using the estimated E-BD on a daily basis (Fig. 9A), more accurate timing of new embryo deposition in the batches at EDS-I could be estimated (i.e., estimated EDS-I: Fig. 9E). In batches 3-8 (estimated EDS-I), the closest correspondences between peak embryo deposition and syzygy dates were found for the second 1-y-old cohort, with two 0-day lags, one 1-day lag, one 2-day lag, and two 4-day lags (in batches 3 and 8). The correspondences between these dates in the first 1-y-old cohort comprised one 0-day lag, one 1-day lag, two 2-day lags, and two 4-day lags. Those in the 2-y-old cohort comprised one 1 -day lag and one 4-day lag. These time-lag distributions suggest that the peak new embryo deposition took place closely around each syzygy date. The highest frequencies of 0- to 2-day lags to syzygy date observed for both embryo hatching and new embryo-deposition timings accorded well with the previous two independent findings that the successive embryo hatching to embryo re-deposition events occurred most frequently with time lags of 0-2 days (Sections 3.3 and 3.4).

In batches 1 and 2 (EDS-III) of all cohorts, the peak female-density plots were not necessarily positioned right on or close to the syzygy dates (Fig. 9D): (1)2 days before the quadrature date in batch 1's of the 2-y-old and first 1-y-old cohorts; (2) 3 days after that date (or 5 days before the syzygy date) in batch 1 of the second 1 -y-old cohort; (3)3 days before the syzygy date in batch 2's of the 2-y-old and second 1-y-old cohorts; and (4) 6 days before that syzygy date (or 1 day after the quadrature date) in batch 1 of the first 1-y-old cohort. The peak densities were not so high compared with the subpeak densities, and the variance in dates about each peak was fairly large. These led to a low degree of isolation between batches 1 and 2. Based on both estimated new embryo deposition dates back from EDS-III (i.e., dates at estimated EDS-I: Fig. 9E) and dates at the actual EDS-I (Fig. 9B) in these two batches, it was found that (1) the first seasonal embryo deposition peaked around the syzygy date in batch l's of the 2-y-old and first 1-y-old cohorts (0- to 2-day lags) and at least 7 days later from that syzygy date in batch 1 of the second 1-y-old cohort, (2) in the actual batch 2's of the first and second 1-y-old cohorts, their common peak was 1 day before the syzygy date, whereas, in the expected batches, it was 1 day (the first 1-y-old cohort) or 3 days (the second 1-y-old cohort) after the quadrature date, and (3) at the estimated EDS-I of batch 2 of the 2-y-old cohort, the peak was 3 days after the quadrature date. Such a wide range in the time lags suggests a weak synchronization in embryo deposition in batches 1 and 2 (EDS-I).

One measure for the rate of embryo re-deposition event subsequent to a preceding embryo hatching event in each female cohort is defined as the [average population density over time in batch i (EDS-I)]/[that density in batch (i - 1) (EDS-III)] for i = 2-8. In cases in which the female density plot was shared by two adjacent batches on their boundary date, this density value was allocated equally to these batches. For each batch, the female density on the sampling date immediately before the earliest date or after the latest date with nonzero densities was set at zero. The time (= sampling date)-averaged density was calculated for those nonzero ones in each batch. In the 2-y-old cohort, the embryo re-deposition rates were: 117% [from batch 1 (EDS-III) to batch 2 (EDS-I)], 77% (batches 2 to 3), and 93% (batches 3 to 4). In the first 1-y-old cohort, those rates were: 93% [from batch 1 (EDS-III) to batch 2 (EDS-I)], 107% (batches 2 to 3), 119% (batches 3 to 4), 80% (batches 4 to 5), 62% (batches 5 to 6), 56% (batches 6 to 7), and 52% (batches 7 to 8). In the second 1-y-old cohort, those rates were: 116% [from batch 1 (EDS-III) to batch 2 (EDS-I)], 137% (batches 2 to 3), 107% (batches 3 to 4), 122% (batches 4 to 5), 81 % (batches 5 to 6), 85% (batches 6 to 7), and 36% (batches 7 to 8).

3.8. Population Density Change and Reproductive Cycle on the Sandflat in 1993

3.8.1. Temporal Change in Densities of Whole Population and Three Cohorts

Based on the temporal change in the TL-frequency distribution of the adult female population of Nihonotrypaea harmandi on the Tomioka sandflat on every sampling date from May 31 to August 19 in 1993, the separation of the frequency distribution into the three cohorts on each middle of the three (or edge of the two) successive pooled sampling dates was made (Fig. 10). The temporal change in the densities of the whole population and three cohorts is shown in Figure 11A-D. The temporal changes in the proportion of each of the three cohorts to the whole population and to the mature-individual group are shown in Figure 11E and F, respectively. The temporal change in the ovigerous rate in each cohort is shown in Figure 11G.

Through the sampling period, the whole densities varied in a small range, their mean ([+ or -]SD) being 114.9 [+ or -] 12.3 inds/2,000 c[m.sup.2] (n = 30; Fig. 11 A). All members of the 2-y-old cohort were mature, and their densities were mostly high at around ca. 50 inds until July 7, from which they decreased in a linear way to ca. 20 inds on August 1 and below 5 inds thereafter (Fig. 11B). Virtually all members of the first 1-y-old cohort were mature, and their density ranged from 28 to 59 inds (Fig. 11C). The seemingly increasing trend until July 21 was probably due to sampling errors. This also appears true for the densities of the second 1-y-old cohort in the range of 20-73 inds, increasing toward the end of the period (Fig. 11D). Compared with the second 1-y-old cohort in 1994 (Fig. 8D), the immature individuals in the cohort persisted for a longer time in 1993 [mean ([+ or -]SD) proportions of 31.5% [+ or -] 13.0% (n = 12; from July 3 to July 30, 1993) versus 15.2% [+ or -] 7.3% (n = 10; from July 4 to July 31, 1994)], and the first occurrence of ovigerous females was delayed in 1993 by 3 wk (July 3 versus June 11).

The mean ([+ or -]SD) proportion of the 2-y-old cohort to the whole population was 43.1 ([+ or -]6.4)% from May 31 to July 11 (n = 14), from which it decreased in a linear way to 18% on August 1 and less than 4.5% thereafter (Fig. 11E). The proportion of the first 1-y-old cohort stayed at a constant mean ([+ or -]SD) value of 28.6 ([+ or -]3.1)% from May 31 to June 20 (n = 9) and at another constant value of 41.0 ([+ or -]3.6)% from June 24 to August 19 (n = 21). The proportion of the second 1-y-old cohort stayed at a constant mean ([+ or -]SD) value of 24.2 ([+ or -]3.6)% from May 31 to July 11 (n = 9), from which it increased in a linear way to 53% on August 3 and 60% on August 13 and 19 (combined average).

The mean ([+ or -]SD) proportion of the 2-y-old cohort in the mature-individual group was 56.2 ([+ or -]3.5)% from May 31 to June 20 (n = 9), from which it decreased in a linear way to 20% on August 1 and less than 5% thereafter (Fig. 11F). The proportion of the first 1-y-old cohort stayed at a constant mean ([+ or -]SD) value of 34.0 ([+ or -]3.8)% from May 31 to June 20 (n = 9) and at another constant value of 44.7 ([+ or -]4.5)% from June 24 to August 19(71 = 21). The proportion of the second 1-y-old cohort stayed at a constant mean ([+ or -]SD) value of 9.9 ([+ or -]2.8)% from May 31 to July 3 (n = 12), from which it increased in a linear way to 52% on August 3 and 57% on August 13 and 19 (combined average).

Embryo deposition started from June 3 virtually by the 2-y-old cohort only (Fig. 11G). The ovigerous rates maintained a low value until June 12 [mean ([+ or -]SD) = 5.9 ([+ or -]4.7)%; n = 6], reached a medium value (30%-39%) from June 16 to June 20, and thereafter, stayed at a high value [68.7 ([+ or -]17.8)%; n = 21], In the first 1-y-old cohort, embryo deposition started virtually from June 10. The ovigerous rates maintained a low value (7%-12%) until June 20, reached a medium value (29%-42%) from June 16 to July 7, and rapidly increased to 66% on July 11, from which they stayed at a high mean ([+ or -]SD) value [64.3 ([+ or -]14.7)%; n = 17]. In the second 1 -y-old cohort, embryo deposition started virtually from June 20. The ovigerous rates maintained a low value (1%-I0%) until July 7, reached a medium value (18%-34%) from July 11 to August 1 (except for 50% on July 25), and rapidly increased to 47% on August 3, after which they stayed at a high mean ([+ or -]SD) value [51.3 ([+ or -]4.8)%; n = 5].

3.8.2. Sequential Flow of Each Female Cohort across Three EDSs

The water temperatures in Tomioka Bay through the sampling period for Nihonotrypaea harmandi in 1993 are indicated by solid circle plots in Figure 12A. The 17-day average temperature back from every date is indicated by the broken line. The E-BD back from each date is indicated by the gray column on that date. These durations were longer in 1993 than in 1994 for most of their corresponding periods. In 1993, they were 19.7 days on June 20, 17.0 days on July 20, and 14.4 days (shortest duration) for the first time on August 15. In 1994, they were 20.8 days on June 20, 19.2 days on June 30, 17.3 days on July 5, 16.8 days on July 6, and 14.4 days for the first time on July 12 (Fig. 9A).

Based on the cohort separation for each sampling occasion in 1993 (Section 3.8.1), the temporal change in the density of females with each EDS for the three cohorts through the sampling period is shown in Figure 12B-D. The boundary between each pair of two adjacent batches is indicated by a vertical dotted line. The estimated new embryo-deposition dates back from EDS-III to EDS-I, as in Section 3.7.2, are indicated as EDS-I (estimated) (Fig. 12E), in which the plots for the first and second 1-y-old cohorts on July 31, August 2, and August 6 (indicated in gray) were based on another assumption, as follows. Examining the flow of the batches at EDS-I to EDS-III in August and each presumed paired date between EDS-I and EDS-III, the densities on August 1, 3, and 11 at EDS-I appear to have corresponded to those on August 11, 13, and 19 at EDS-III, respectively. Because no sampling was performed between August 13 and 19, the data corresponding to August 5, 7, and 13 at actual EDS-I are lacking for the estimated EDS-I (on July 31, August 2, and August 6, respectively). Each of these three lacks in each cohort at the estimated EDS-I was filled as the product of (1) the ratio of the sum of densities at EDS-III from August 11, 13, and 19 to the sum of densities at EDS-I from August 1, 3, and 11 and (2) each actual density at EDS-I on August 5, 7, and 13.

In the 2-y-old cohort, there were four batches at EDS-I, occurring from June 3 to June 6, June 10 to June 29, June 29 to July 25, and July 25 to August 19 (Fig. 12B). The boundary between any two adjacent batches was clear. The first batch (batch 1) was small in total number, with the date of peak density on June 4 (syzygy). Each of the second and third batches (batches 2 and 3) spanned a wide time range, with the peak density on the dates 3-4 days after the immediate syzygy date being not distinct from several subpeak densities. The fourth batch (batch 4) showed a very low profile, terminating in its longevity. Through EDS-II and EDS-III, batch 1 appeared merged into batch 2 [indicated as batch (1 +2): Fig. 12C, D]. At EDS-III, the boundary between batch (1 + 2) and batch 3 became less clear, with the date of each peak density positioned on the respective syzygy dates (i.e., July 4 and 19). At the estimated EDS-I, the peak densities came 1 day after the quadrature date [batch (1+2)] and 3 days before the syzygy date (batch 3).

In the first 1-y-old cohort, there were three batches at EDS-I, occurring from June 10 to June 29, June 29 to July 30, and August 1 to August 13 (batches 2-4: Fig. 12B). The boundary between any two adjacent batches was clear. Each of batches 2 and 3 spanned a wide time range, with the peak density 4 days after the syzygy date (June 20) and 1 day after the quadrature date (July 12), respectively. Batch 4 stood distinctly, with its peak density 5 days after the immediate syzygy date (August 2). A sign of the final increasing trend from August 13 to August 19 was observed (syzygy: August 18). The shapes of the three batches appeared basically retained through EDSs-II and -III (Fig. 12C, D), although batch 4 (EDS-III) was not fully represented around the right edge of the panel because of the sampling-time limit. In batch (1 + 2) (EDS-III) (note: actually, there was no batch 1 in this cohort), the dates with the densities near the peak density value spanned 10 days from July 3 to July 13 (syzygy: July 4), whereas in batch 3 (EDS-III), the peak density was observed on the syzygy date (July 19). The peak density for batch 4 (EDS-III) could have occurred closer to the immediate syzygy date (August 18). At the estimated EDS-I, the dates with the peak densities were not very clear for batches (1 + 2) and 3, whereas that estimated for batch 4 was on the syzygy date (August 2).

In the second 1-y-old cohort, there were two substantial batches at EDS-I, occurring from July 3 to July 30 and August 1 to August 13 (batches 3 and 4: Fig. 12B). Batch 3 spanned a wide time range, with a low profile in the density and its peak on July 25 (quadrature: July 26). Batch 4 stood sharp, with its peak density 3 days after the immediate syzygy date (August 2). Although batch 4 (EDS-III) was not fully represented in the panel because of the sampling-time limit, the shapes of the two batches appeared basically retained through EDSs-II and -III (Fig. 12C, D), with the peak density in batch 4 (EDS-III) on August 5 (syzygy: August 2). At the estimated EDS-I, the dates of the peak densities in the two batches (July 20 and July 31 to August 2, respectively) were close to each immediate syzygy date.

3.9. Water Level and Velocity, and Potential Larval Transport Rate (PLTR) on the Sandflat in 2010

As an example of the spline curves for water level and the columnar plots for water velocity (northeast component) on the Tomioka sandflat in the daytime-nighttime cycle during the reproductive season of Nihonotrypaea harmandi in 2010 (May 27 to November 5), three 2-day segments are shown in Figure 13 A-C; note that Figure 13 A and B are similar to Figure 6B and A, respectively. The offshore (seaward) and onshore (landward) water velocities were not always associated with the ebb and flood(-tidal) phases, respectively.

The plots for every pair of tidal range (TR) and mean or highest water velocity in that range through all ebb and flood phases are shown in Figure 14A and B, respectively. The whole TR (mm) was subdivided into three groups (0 < TR [less than or equal to] 1,100; 1,100 < TR [less than or equal to] 2,200; 2,200 < TR [less than or equal to] 3,300). The mean ([+ or -]SD) water velocity in each group is indicated also in these panels. In Figure 14A, the plots are indicated in solid or blank circles according to the starting time of ebb and flood phases positioned either during the nighttime or daytime; no demarcation for the starting time is made in Figure 14B. For all ebb phases of nighttime and daytime origins inclusive, every line joining the plots for water velocity versus time standardized to the duration from H to L times [0 (H) to 1 (L)] over each TR is indicated in black in Figure 14C, in which the spline curve interpolated with the loess function for all plots is indicated by the red solid line. The highest water velocity on the spline curve was 1.93 cm/sec at the time of 0.63. In the smallest-TR group, the proportion of mean water velocities at the ebb phase of nighttime origin was much smaller (8.9%) than that of daytime origin (Fig. 14A). In both mean and highest water velocities at the ebb phase, their mean ([+ or -]SD) values (cm/sec) increased with the larger-TR groups [-0.15 [+ or -] 0.92, 0.74 [+ or -] 0.91, and 1.58 [+ or -] 1.04 (mean [+ or -] SD of means); 2.03 [+ or -] 1.53,3.77+ 1.68, and 5.51 [+ or -] 2.20 (mean [+ or -] SD of maxima)] (Fig. 14A, B). Irrespective of a large variance in water velocities at each TR value, there was a high positive correlation between mean water velocity and TR (r = 0.77, n = 603, P < 0.001) and a much higher one between highest water velocity and TR (r = 0.91, n = 603, P < 0.001). The linear regression line in the latter crossed a point close to the (0, 0) coordinate. The larger variance of water velocity in the mean than in the highest values suggests transient meteorological influences on the tidal current.

The proportions of the eight possible orders for the times of SS, SR, H, and L in light of the position of the first H-to-L time segment in each of the three TR groups through the monitoring period are shown in Figure 15. The mean (+SD) durations of the ebb phase were 6.26 [+ or -] 0.53 h (n = 99) for the largest-TR group (in the spring tide periods), 6.23 [+ or -] 0.68 h (n = 162) for the medium-TR group (mid-tide periods), and 5.71 [+ or -]0.69 h (n = 45) for the smallest-TR group (neap tide periods). No H-SS-SR-L and H-SR-SS-L occurred in all TR groups. The values of the proportions for the eight orders in each TR group are given in the caption for Figure 15.

The time series on the TRs starting from daytime and nighttime through the monitoring period are shown in Figure 16A and B, respectively, on which the spline curves interpolated with the loess function are superimposed. The blue vertical lines in Figure 16A designate the TRs from each H to the next L in two of the aforementioned orders (Fig. 15; n = 306): H-SS-L-SR (n = 30) and SR-H-SS-L (n = 19). These blue lines are transferred to the corresponding gaps in Figure 16B to generate Figure 16C, with a new spline curve. This alteration was necessary to evaluate any relationship between TR of (broadly defined)-nighttime origin and PLTR through the monitoring period, as the duration from SS to L and the mean water velocity during that time segment in each of the H-SS-L-SR and SR-H-SS-L orders were multiplied to obtain the estimates for those corresponding PLTRs (Section 2.11.1). The mean ([+ or -]SD) ratio of the duration of H-SS to that of H-L was 0.23 [+ or -] 0.14 in H-SS-L-SR [all 30 cases belonged to the medium- and smallest-TR groups (Fig. 15)] and that ratio was 0.79 [+ or -] 0.17 in SR-H-SS-L (all 19 cases belonged to the medium- and smallest-TR groups, mostly to the latter). The 10 local maxima in each of the three TR groups are indicated by the red vertical lines with the serial encircled numbers (0-9) (Fig. 16A-C). Following the 27.55 (solar)-day lunar apogee-perigee cycle (Pugh 1987), the smaller and larger of the local largest TRs alternately occurred every spring tide period, each of which lagged behind the immediate syzygy date by the range of 0.08-2.39 days [mean ([+ or -]SD) = 1.47 [+ or -] 0.68 days; n = 10] in the TR of (strictly defined)-daytime origin (Fig. 16A), by the range of 0.99-3.72 days [mean ([+ or -]SD) = 2.73 [+ or -] 0.74 days; n = 10] in that of (strictly defined)-nighttime origin (Fig. 16B), and by the range of 1.15-4.09 days [mean ([+ or -]SD) = 2.70 [+ or -] 0.81 days; n = 10] in that of (broadly defined)-nighttime origin (Fig. 16C). The difference in TRs between each successive pair of spring and neap tide periods was smaller in the TR of (strictly defmed)-nighttime origin than in the (strictly defined)-daytime origin, especially so during June to mid-July (Fig. 16A, B). The rise and fall became more distinct in the broadly defined than strictly defined nighttimes (Fig. 16B, C).

The time series on the plots of PLTR and spline curve interpolated with the loess function are shown in Figure 16D, in which the three sets of continuous gray spline curves corresponding to those separate time segments are joined by a single (dotted) spline curve through the monitoring period. The 10 local maxima on the spline curve from June to October are indicated by the red vertical lines with the serial encircled numbers from 0 to 9. The spline curve for PLTR was largely in parallel with the curve for the TR of (broadly defined)-nighttime origin (Fig. 16C), with each peak coming after the immediate syzygy date by the range of-1.89 to 4.42 days [mean ([+ or -]SD) = 2.38 [+ or -] 1.99 days; n = 10; "minus" means "before"] and after the immediate largest-TR date by the range of -4.13 to 1.87 days [mean ([+ or -]SD) =-0.31 [+ or -] 2.12 days; n = 10].

Based on Figure 16C, the plots for every pair of the lunar age at the halfway point of each (broadly defined)-nighttime H to L times and the TR during that time segment through the monitoring period are shown in Figure 16E, in which the (nonexistent) data for the lunar ages of 29.5-36.875 were assumed to be the same as the actual data for the lunar ages of 0-7.375. The spline curve interpolated with the loess function detected that the two local maxima (dotted vertical lines) lagged behind the syzygy lunar ages of 14.75 and 29.5 (solid vertical lines) by 1.75 and 1.69, respectively, and that the two local minima lagged behind the quadrature lunar ages of 7.375 and 22.125 by 2.19 and 1.39, respectively. Similarly, based on Figure 16D, the spline curve for the plots from every pair of the lunar age at the halfway point of each successive (broadly defined)-nighttime H to L times and the corresponding PLTR through the monitoring period is shown in Figure 16F. The lunar ages for the two local largest PLTRs (dotted vertical lines) lagged behind the syzygy lunar ages of 14.75 and 29.5 (solid vertical lines) by 1.75 and 1.69, respectively, and those for the two local minima lagged behind the quadrature lunar ages of 7.375 and 22.125 by 2.41 and 2.27, respectively. Thus, the dates of the maximum PLTRs lagged behind the dates with the largest (broadly defined)-nighttime TR in the spring tide period by 0.55-1.00 lunar ages, and those of the minimum PLTRs lagged behind the dates with the smallest (broadly defined)-nighttime TR in the neap tide period by 0.22-0.88 lunar ages. All data combined through the monitoring period, there were (1) a moderately positive correlation between PLTR (m) and TR (mm) (r = 0.45, n = 193, P < 0.001) (dots in Fig. 16G) and (2) a significant linear regression equation of PLTR = -80.988 + 0.147TR (solid line in Fig. 16G, P < 0.001; PLTR = 0 for TR = 551). These positive relationships were mainly derived from the higher mean (ebb) water velocities and the longer (strictly defined)-nighttime ebb phase durations in the larger TRs (Figs. 14 and 15). Thus, the (broadly defined)-nighttime ebb TR can be regarded as a proxy for the PLTR, enabling the use of the former parameter for the subsequent TR-related, deterministic analysis. Here, the variation in the peak values of (broadly defined)-nighttime ebb TRs during the monitoring period is worth being summarized (Fig. 16C): (1) the largest TRs during late June to late July were 1,778 mm (serial no. 1) and 2,321 mm (serial no. 2), and the mean ([+ or -]SD) value during late July to October was 2,591 [+ or -] 309 mm (n = 7; serial nos. 3-9); (2) of the serial nos. 3-9, the mean value for the larger of the successive largest TRs (serial nos. 4, 6, and 8) was 2,861 mm, whereas that value for the smaller of the successive largest TRs (serial nos. 3, 5, 7, and 9) was 2,389 mm; and (3) through the serial nos. 3-9, the mean ([+ or -]SD) difference in the TRs between a syzygy date and its immediate largest-TR date was 304 [+ or -] 146 mm [12% of the mean TR in the corresponding period given in item (1)].

There was a large variance in the PLTR for each TR (Fig. 16G). The two thin dotted curves and two thick broken curves in the panel indicate the 95% confidence interval for the linear regression line and 95% prediction interval for the plots, respectively, based on the "predict" function in "R" 3.2.3 (R Core Team 2015). The range of the latter interval over the TRs was 692.2-708.5 m, which corresponds to 5,260-5,371 mm in TR. Thus, half the median of these TR values (2,660 mm) was equivalent to the mean value for the maximum TRs for the period from late July to October (2,590 mm; preceding paragraph). Both the large variance in PLTR values and the extended time lag between each maximum-PLTR date and immediate syzygy date as compared with the time lag between each largest-TR date and immediate syzygy date (Fig. 16E, F) might be caused by meteorological influences. During June to mid-July, including the rainy period (see the next paragraph), the shape of the PLTR spline curve exhibited a somewhat distorted, lower profile than that expected from the corresponding profile of the (broadly defined)-nighttime TR spline curve (around serial no. 1; Fig. 16C, D). Regarding the interval between the peaks of each corresponding TR and PLTR, that in each of the first and second peaks in June (serial nos. 0 and 1) was greater than those in the other peaks during July to October. This suggests a seasonal rainfall influence on the water level and/or flow. Another disaccord between the shapes of TR and PLTR was observed during mid-October to early November, suggesting a seasonal, northerly wind-induced wave influence.

To examine a possible stochastic influence of meteorological variables on PLTR, all pairs of PLTR and TR at the (broadly defined)-nighttime ebb phase are plotted in Figure 17. In these panels, all plots through the target period (May 27 to November 5 in 2010) and the plots for each month (data for May were included in those for June) or for some particular subperiods are indicated in blank and colors (black and red), respectively, with the linear regression line for PLTR versus TR for all plots superimposed (based on Fig. 16G, solid line). There is a distinct wet monsoon season in Kyushu, characterized by the rainy period of June to July and the prevalence of the southwesterly winds in June to September. The frequency of the northerly winds gradually increases from mid-September to November (in the dry monsoon season). The plots corresponding to the "greater rainfalls" and to the "greater waves" generated by the northerly winds are indicated in red in Figure 17A-F and J-L, respectively. How these red plots were specified is given in Appendix. Specifically in June and October, most red plots were below the regression line. The positive relationship between "greater rainfall" and lower PLTR was most evident for the June to July months, in which the rainy period was demarcated from the other two periods (solid plots in Fig. 17G-I). This suggests that the landward water flows were generated even at the ebb phase. Increased freshwater discharge into Ariake Sound might cause density-driven surface currents in Tachibana Bay and Amakusa-nada (Matsuno et al. 1999; Fig. 1A), affecting the water-velocity field in Tomioka Bay. The influence from local small rivers emptying into Tomioka Bay (Fig. 1B) might also be responsible for the change in fine-scale water flows. Although the northerly wind-induced water currents might generate landward water flows against ebb tidal currents, the large downward deviations from the regression line in PLTR were observed only for three plots through October and November (red plots in Fig. 17J-L).

3.10. Estimation of Larval Release Timing and PLTR

3.10.1. Back-Estimating Larval Release Bouts on the Sandflat from Offshore Data

Using the reconstructed tidal current velocities in Tomioka Bay for 1994 (Fig. 1B; Section 2.12), it was examined whether the two peaks in Nihonotrypaea harmandi zoeae-I densities recorded at Stn D during August 31 to September 1 in 1994 (Fig. 6B) could be derived from the immediate larval release bouts by the sandflat population. This case was one of the time order of H-SS-L-H-SR-L (e.g., Fig. 13A). Larvae released from the sandflat were expected to be transported offshore during the nighttime ebb tidal phase from 18:50 (SS) to 22:30 (L). Larvae released from females in laboratory aquaria tend to swim up to the water surface [A. Tamaki, personal observation; cf., older zoeae-I (up to 1 wk) in the coastal ocean were positioned below 20-m depth in the water column (Tamaki et al. 2010)], which may be an adaptive behavior to utilize the higher ebb tidal current velocities than in the lower water column under the field situation. The temporal change in tidal current velocities at a 4-m depth from the mean surface water level at Stn E during the target time segment is shown in Figure 18. The tidal current began to be directed northeast at 21:20, from which time the larval transport distance in this direction for 2 h was estimated at 630 m by using the mean velocity. It is now assumed that the tidal currents at Stn D were the same as those at Stn E, the two stations aligning with the northwest direction, and that the first larval pulse passing Stn D was the clump of densities recorded for 2 h from 21:20 to 23:20 (Fig. 6B). As the shortest distance from Stn D to the sandflat is 1,200 m (on the north-south line; Fig. 1B), larvae first released from the sandflat at the SS time (18:50; 0.34 in the standardized duration from H to L times) must be transported that distance in 2.5 h until 21:20. This requires a mean speed of 13.3 cm/sec. As the tidal currents during 18:50 to 21:20 at Stn E were directed northwest to north, with the comparable absolute speeds (Fig. 18), those larvae released from some place on the eastern part of the sandflat at the SS time could have satisfied that requirement.

The second pulse of Nihonotrypaea harmandi larvae recorded at Stn D (Fig. 6B) could not be ascribed to their release bout on the sandflat at the immediate H time (around 04:00) because the water velocities at Stn E were landward during 04:00 to 07:00 (Fig. 18). These larvae would be a part of the preceding (first) larval clump that was transported back from an offshore area. The time order of H-SS-L-H-SR-L, as in the present case, accounted for 12.8% of all time orders (Fig. 15), with 66.7% in those of the smallest-TR group, 5.6% in the medium-TR group, and zero in the largest-TR group. Nevertheless, in calculating PLTRs in Section 3.9, all cases for the H time positioned in the second half of the nighttime (as in the present case and Fig. 13A, C) were included because the potential seaward transport immediately after the release from the sandflat was the matter for the zoeae-I.

By using the mean water velocity at the ebb phase in the largest-TR group on the Tomioka sandflat recorded for 2010 (i.e., 1.58 cm/sec; Section 3.9), it was estimated that the peak Nihonotrypaea harmandi zoeae-I density recorded at Stn C (60 m off the sandflat) during August 10-11 in 1992 (Figs. 1B and 6A) was derived from the larval release bout by the sandflat population ca. 67 min after the H time and that the first release took place around 19:03 (SS time: 19:10). The estimated peak larval release time was positioned at 0.19 in the standardized duration from H to L times.

3.10.2. Potential Larval Transport Rate Evaluated by Nocturnal Ebb TR

Following the existence of a significant positive correlation between PLTR and (broadly defined)-nighttime ebb TR for the monitoring period in 2010 (Section 3.9; Fig. 16G), the PLTRs for the eight batches of the three cohorts and of the whole population of Nihonotrypaea harmandi females with EDS-III embryos on the Tomioka sandflat in 1994 were evaluated based on the (broadly defined)-nocturnal ebb TRs during the end of May to early November in 1994. The TRs starting from each (broadly defined)-nighttime H time on the sandflat were reconstructed by the harmonic analysis of tides using the water level data in 2010 (Sections 2.11.3 and 3.9) and the SS and SR times in 1994 (http://eco.mtk.nao.ac.jp/cgi-bin/koyomi/koyomix.cgi; accessed November 16, 2017). These TRs in 1994 and the spline curve for them interpolated with the loess function are shown in Figure 19A-C, E, in which the former three panels and last panel are for the 2-y-old cohort, first 1-y-old cohort, second 1-y-old cohort, and the whole population of N. harmandi, respectively. The 10 serial encircled numbers (0-9) along the uppermost horizontal line in Figure 19A indicate the dates with each local largest TR from June to October. By summing the individual densities of the three cohorts (Fig. 9D), the density of the whole population was obtained, with the boundary between each adjacent pair of batches 1-8 indicated by a vertical dotted line (Fig. 19D). The rule to determine that boundary date, the shrimp densities on that date, and the immediate adjacent dates with zero densities for the respective batches was the same as for those of the three component cohorts (last paragraph in Section 3.7.2). To determine which part of the spline curve for the TRs corresponded to a time segment ranging from the earliest "sub"-highest, via the highest, to the latest "sub"-highest densities of females for each batch of the three cohorts and the whole population, that time segment and the values of the "sub"-highest densities were defined as follows. The profile of each batch of females with EDS-III embryos in 1994 formed a polygon. This can be regarded as a triangle or trapezoid composed of the left and right halves about the apex (= local highest density; Fig. 9D). The date at this apex is indicated by each red vertical line (Fig. 19A-E). The dates corresponding to the left and right edges for the "sub"-highest densities were defined as those corresponding to the 70% of the respective whole half-polygon area, which is indicated by a gray band [hereafter, the time range for the area combined from the two halves is called "main larval release span (MLRS)" for each batch]. The value of 70% was to be analogous to the value of 68% in the total area of the range with [+ or -]1 SD about the mean in a normal-distribution curve.

In the tidal range spline curve (TRSC), the date of each peak TR lagged behind the immediate syzygy date by the range of 1.40-3.59 days [mean ([+ or -]SD) = 2.44 [+ or -] 0.74 days; re = 10] (top horizontal line in Fig. 19A). From batch 1 to batch 8 in the whole population, the durations of MLRS were: 18.3 days, 11.3 days, 6.0 days, 6.7 days, 4.2 days (= shortest at batch 5 in early September), 6.9 days, 10.1 days, and 9.2 days (Fig. 19E). In batch 1, the MLRS occupied nearly a one-wavelength segment from one bottom to the next in the TRSC, with the peak female density at the midway of a falling part of the TRSC. The date with the peak female density lagged behind the immediate syzygy date by 6 days and the immediate largest-TR date by 4.0 days. In batch 2, the MLRS occupied nearly a one-wavelength segment from one top to the next in the TRSC, with the peak female density near the bottom of that TRSC segment. The date with the peak female density preceded the immediate syzygy date by 3 days and the immediate largest-TR date by 5.4 days. In batches 3-6, the MLRS occupied a varying portion of each rising part of one bottom to the subsequent top of the TRSC. The date with the peak female density shifted from the midway point of that part in batch 3 to near each top in batches 4-6. In batches 7 and 8, the date with each peak female density was close to the date with the immediate top of the respective TRSC which passed over that top. In batches 3-8, the date with each peak female density preceded the immediate syzygy date by the range of-1 to 1 days and the mean ([+ or -]SD) of 0.3 [+ or -] 0.8 days (n = 6) and the immediate largest-TR date by the range of 1.0-4.2 days and the mean ([+ or -]SD) of 2.5 [+ or -] 1.2 days (n = 6). The aforementioned characteristics regarding peak female density and MLRS for each batch of the whole population accorded well with those for the dominant cohort(s) of each batch: the first 1-y-old and subordinate, 2-y-old cohorts in batches 1-3, and the second 1-y-old and subordinate, first 1-y-old cohorts in batches 4-8 (Figs. 19A-C and 8E, F, respectively).

4. DISCUSSION

The magnitude of transport of initial stage larvae to the coastal ocean plays a significant role in local population persistency for larval export-type decapods. It appears natural to think that the larger the nocturnal ebb tidal range (TR) is, the faster newly released larvae reach the coastal ocean (Forward 1987, Morgan 1995, Christy 2011). One derivative hypothesis is that the optimal timing of peak larval release by the adult population has been selected so as to be adjusted to the date with the largest nocturnal TR in each spring tide period [age-of-the-tide-cycle-based (AOTTCB) view]. Alternatively, according to the syzygy-cycle-based (SCB) view (e.g., Saigusa 1980, 1988), peak larval release in a local population is expected to be timed to a syzygy date. As this date generally comes 1-2 days before the date with the largest TR in a spring tide period (Pugh 1987), a question arises as to whether such a suboptimal larval release timing, with somewhat smaller TRs, could really be disadvantageous to the maintenance of local populations. In some geographic regions, conspecific or different species populations can never realize the larval release cycle that is timed to the largest/larger/large nocturnal ebb TRs occurring in spring tide periods (Section 1, third paragraph). Even for a same local population in the warm temperate shore, the nocturnal ebb TRs can vary in the course of the reproductive season, following the latitude-specific year-round diurnal tidal inequality cycle (Pugh 1987). With the widespread occurrence of all these suboptimal settings born in mind, the present study has tried to determine which of the AOTTCB or SCB views can provide a more reasonable explanation for the switch from a weak larval release rhythm in the early reproductive season to a distinct rhythm mid-season onward in a local ghost shrimp population. As decapod larval release synchrony is preceded by reproductive synchrony with its subsequent embryo brooding with temperature-dependent durations (Forward 1987, Paula 1989, Zimmerman & Felder 1991), these three tightly coupled events were examined in a synthetic way by comparing the reproductive patterns of the Nihonotrypaea harmandi population between 1993 and 1994, with their contrasting cold and hot summers.

Individual larval release bouts of Nihonotrypaea harmandi last 10s sec (Somiya & Tamaki 2017), and the present study assumed that a pulsed larval mass from the adult population was derived from its synchronized act in a short duration. In the laboratory observation for the larval release events on two separate occasions, they occurred only during each nighttime and at 0.59 or 0.80 in the expected standardized duration from high tide (H) to low tide (L) times (Fig. 5). These values were near the time with the highest water velocity at ebb tidal phase on the Tomioka sandflat (i.e., 0.63; Fig. 14C, red curve). This accordance may be adaptive for field larvae to be transported seaward most rapidly. The actual peak larval release on the Tomioka sandflat, however, was estimated to occur ca. 1 h after the H time following the sunset (SS) or at around the SS subsequent to the late afternoon H (Fig. 6A, B; Section 3.10.1). The embryo-brooding females used for the aforementioned laboratory observations were collected from the upper intertidal, which begins to be emersed 3 h before the L time. Thus, those field females would have had to forward their larval release to the time with enough water depths, scarifying the theoretically best time for the seaward larval transport while avoiding being stranded (cf., Salmon et al. 1986, Morgan 1995). In continuous hourly records of sesarmid (Saigusa & Hidaka 1978) and carcinid (Queiroga et al. 1994) brachyuran species' larval release events during a substantial period of time every day over a month or two, the daily peak release time shifted from the SS to nocturnal H times in accordance with the daily shift in the H times across the SS. All these observations suggest that embryo hatching may occur around the H time not only in the nighttime, but also in the late daytime and that those females under the latter situation may suppress releasing larvae until the SS, securing them from visual predators. Release of larvae around the nocturnal H time was suggested for the ghost shrimp, Neotrypaea californiensis, promoting their export from estuarine adult habitats to the coastal ocean in the nighttime (Breckenridge & Bollens 2011, Morgan et al. 2014). A mass of N. harmandi zoeae-I recorded at the ebb tidal phase in the second half of the nighttime 1.2-1.5 km off the Tomioka sandflat was regarded as a fraction of that released in the first half (Fig. 6B; Section 3.10.1). At a South African estuarine mouth, larval release of the mud shrimp, Upogebia africana, took place twice in a single night with two ebb phases (Wooldridge & Loubser 1996). Thus, the ebb phase in the later nighttime on the Tomioka sandflat was also included in the calculation of potential larval transport rates (PLTRs; Fig. 16D) as a possibility, despite the landward water velocity off the sandflat reproduced for that time (Fig. 18). Overall, the larval release patterns of TV. harmandi (Figs. 5 and 6) gave a rationale for having defined the transport duration in the PLTR (Section 2.11.2).

In batches 3-8 of the first and second 1-y-old cohorts and batches 3 and 4 of the 2-y-old cohort in the female population of Nihonotrypaea harmandi on the Tomioka sandflat during the mid- to late reproductive season in 1994, (1) embryo deposition synchrony was coupled with the subsequent larval release synchrony (Section 3.7), (2) that larval release synchrony was succeeded by the embryo re-deposition synchrony mostly within 0-2 days after the former's peak (Sections 3.3, 3.4, and 3.7), and (3) it is highly likely that embryo (re-)deposition synchrony and larval release synchrony were centered on one syzygy date to the next, respectively (Sections 3.3 and 3.7). These results appear to support the reality of a syzygy cycle in the batches listed above. The two underlying processes in generating the coupled embryo (re-)deposition and larval release synchronies in that specific period of the reproductive season were the dominance of the youngest (i.e., the second 1-y-old) cohort over the older two (i.e., the 2-y-old and first 1 -y-old) cohorts and a constant, shortest embryo-brooding duration (E-BD) of 14.4 days under the (nearly) highest water temperatures in the year (Sections 3.1, 3.2, and 3.7). At densities [greater than or equal to] 50 inds/[m.sup.2] in the population on the sandflat, each individual is expected to be surrounded by only a few neighbors (Tamaki & Takeuchi 2016, Tamaki et al. 2018). There, mating made just before every time of embryo deposition (Somiya & Tamaki 2017) would be governed by the dominant cohort(s) comprising the highest density of mature individuals. In 1994, the dominance by the mature individuals of the second 1-y-old cohort was first established in batch 3's shortly after mid-July. In addition to the longevity of the 2-y-old cohort by mid-August, the lower survival rates of the larger-sized individuals in the older two cohorts under the higher water temperatures (Tamaki et al. 1997; A. Tamaki, personal observation) could have accelerated that dominance by the youngest cohort owing to both the earlier rise in water temperature (to 25[degrees]C in early July) and the hotter summer ([less than or equal to] 25[degrees]C until early September) in 1994 than in the other early 1990s (Fig. 2B). The summertime of 1994 might partially cut out the year-round high-temperature conditions such as occurring in the tropics. In 1993, the mature individuals of the first and second 1-y-old cohorts first attained the shared dominance in batch 4's in early August, when the water temperature first reached 25[degrees]C.

The observation on the first initiative by the second 1 -y-old cohort in batch 3's of the Nihonotrypaea harmandi population on the Tomioka sandflat during the mid- to late July in 1994 has led to the inference that the first substantial reproductive synchrony (both absolute density-dependent and proportional cohort density-dependent mating synchrony conducive to embryo deposition synchrony) by that cohort was centered on the immediate syzygy date (Fig. 9). The subsequent, sequential cycle of density-independent larval release synchrony shortly followed by density-dependent embryo re-deposition synchrony centered on the respective syzygy dates would be automatically progressed continuously until mid-September under the stable (nearly) highest water temperatures. During late September to mid-October, the rhythm was more or less perturbed most probably because of the decreasing water temperatures, causing a longer embryo developmental duration and because of the gradually ceasing reproductive activity (batches 7 and 8). The mechanism about how mature individuals of the second 1-y-old cohort could become entrained to any syzygy-associated environmental cues initially in midsummer remains to be investigated.

In contrast to batches 3-8 of the Nihonotrypaea harmandi population on the Tomioka sandflat in 1994, the embryo deposition and larval release synchronies were weak in batches 1 and 2 in 1994 (Section 3.7) and in batches 1-3 in 1993 (Section 3.8). In these five batches, the 2-y-old and first 1-y-old cohorts dominated the mature-individual group of the population, especially in 1993. This was owing to the higher survival rates of these cohort members under the lower water temperatures (Figs. 9 and 12). The initiation of the seasonal reproduction by the larger-sized individuals of the older age cohorts was recorded for the present population in 1989-1991 (Tamaki et al. 1997) and for several brachyuran crab populations on warm temperate shores; the differential degrees of maturity between older and younger age cohorts and of gonadal development between members within the older age cohorts may be common for these crabs' early reproductive season (Greenspan 1982, Zimmerman & Felder 1991, Yamaguchi 2001a, Flores et al. 2007). The lower food abundance than in the mid-season such as occurring in the present study region (Fig. 2A) might partly be responsible for the varying gonadal development. In the early reproductive season, the prolonged durations of (1) embryo development (e.g., greater than 2 wk or greater than 4 wk) under lower temperatures (Saigusa 1982, Zimmerman & Felder 1991, Yamaguchi 2001c) and (2) ovary restoration under poorer food conditions would further bring about a wider range in the larval release dates. In the present study, each peak individual density in the aforementioned five batches was not much higher than the surrounding subpeak densities. The peak densities in batch 1's of the 2-y-old and first 1-y-old cohorts in 1994 and in batch 1 of the 2-y-old cohort in 1993 appeared to occur on the respective syzygy dates, although the latter batch was very small in size. The peak densities in batch 2's of all cohorts in 1994 and in batches 2 and 3 of all cohorts in 1993 were not positioned on the syzygy dates. Under the lower water temperatures during early June to mid-July (20[degrees]C-23[degrees]C in 1994 and 20[degrees]C-22[degrees]C in 1993), the initial 3-wk embryo developmental duration inevitably resulted in the position of peak larval release of the first batch at around a quadrature date even when the first embryo deposition peak was timed to a preceding syzygy date. At an estuary mouth in the northwestern United States, with cold upwelling waters, the density of newly released zoeae-I of Neotrypaea californiensis was higher in the neap than spring tide periods (Johnson & Gonor 1982). On the Tomioka sandflat, the large variance in N. harmandi larval release dates in the early reproductive season could be caused by both large variance in embryo deposition dates and progressive shortening of embryo developmental durations to 17-15 days (Figs. 9 and 12). Accordingly, in 1994, the embryo re-deposition dates in batch 2's could have been protracted. The gradually increasing first participants in the mating might also be involved in batch 2's (Fig. 8G). Joining by those participants would have been the main process for the formation of batch 2 in 1993, which was the first substantial embryo deposition batch (Figs. 11G and 12). The consequent extended larval release dates were succeeded by batch 3 in 1993, but not batch 3 in 1994.

To interpret the early reproductive seasonal pattern for the Nihonotrypaea harmandi population on the Tomioka sandflat under the different water temperatures between years, one scenario can be raised, as follows: (1) initially in the earliest season, even if individual mature shrimps were entrained to any syzygy-associated environmental cues, strong reproductive synchrony (conducive to embryo deposition synchrony) was not realized by the constraints of the lower water temperatures and poorer food conditions; (2) such initial weak reproductive synchrony was automatically maintained for 1.5-2 mo until the dominance of the older cohorts terminated, thereby giving way to the youngest cohort; (3) the progressively increasing water temperatures shortened embryo developmental durations from 22 to 15 days in an accelerating way, leading to the larval releasing dates in batch 2 (in 1994) and batch 3 (in 1993) positioned at around a lunar quadrature date immediately before the subsequent syzygy date; (4) the progressively higher food abundances (Fig. 2A) made ovary restoration smoother for embryo re-deposition; and (5) all these processes set the stage for the distinct syzygy-timed, coupled embryo deposition and larval release synchronies performed mainly by the youngest cohort (i.e., the second 1-y-old) starting from late July (in 1994, with forwarded higher water temperatures than in usual years) or early August (in 1993, with delayed higher water temperatures). The early to midsummer (June to July) of 1993 might partially cut out the year-round low temperature conditions such as occurring in the temperate upwelling coasts in which weak larval release synchronies were recorded for decapods (e.g., Morgan et al. 2011). The aforementioned scenario considers that under the law of logical parsimony, the SCB view provides a more reasonable explanation for the sequential occurrence of both reproductive and larval release synchronies than the AOTTCB view. First, in the deterministic aspect of TR, the latter view cannot provide a consistent optimal criterion regarding the difference in the TRs between (1) early reproductive season and mid- to later season, (2) adjacent spring tide periods with alternately occurring lunar apogee and perigee, and (3) any syzygy date and a few-day-later date with the local largest TR (Fig. 16C-F). Second, in the stochastic aspect of TR owing to transient meteorology, the TR value often exceeds that expected from the deterministic cycle (Figs. 16G and 17). Finally and most importantly, before its reaching any specific date with the seemingly best fit between peak larval release and largest-TR timings in the mid- to late reproductive season (e.g., batch 7 in Fig. 19E), the AOTTCB view would encounter all interpretative inconsistencies with the varying E-BDs and the timings of a series of reproductive and larval release synchronies not in so good agreement with the date with each local largest TR, being forced to interchangeably use the three adjectives, largest/larger/large (Forward 1987, Christy 2011), whereas the SCB view can give a simpler interpretation from the start of the reproductive season onward (e.g., Gifford 1962, Warner 1967, Greenspan 1982, Zimmerman & Felder 1991, Yamaguchi 2001a). It would now be fruitful to accept that normally, some local populations manage to sustain themselves under temporally varying suboptimal conditions for larval export efficiency. Thus, instead of persisting in the largest TR, emphasis should rather be directed toward to what magnitude the initial seaward larval transport is realized under sub-largest TRs. A simple imaginary setting would help understand the difference between "largest" and "sub-largest" circumstances--a small straight tidal river with a constant width emptying into the coastal ocean at a normal angle, with a larval export-type brachyuran crab population dwelling in the intertidal flat along a length of the river banks from its mouth upstream. Under a sub-largest TR, the upriver distribution range of adults will be shorter than that under the largest TR by the length converted from the difference between the two TRs for larval transport efficiency caused by the difference in the ebb tidal current velocities. Note that a later extension of the adults' upstream distribution may occur by their secondary movement or postlarvae' returning from the coastal ocean (Lipcius et al. 1990, Rodriguez et al. 1997, Tamaki et al. 2013). In this case, that uppermost adult assemblage may become a sink for the downstream one.

The PLTRs for the eight batches of the whole Nihonotrypaea harmandi population on the Tomioka sandflat during its reproductive season of 1994 are shown in Figure 20, in which the peak and range of each PLTR corresponding to those of the main larval release span (MLRS) in each cohort (Fig. 19E; Section 3.10.2) were converted from the TR values, using the linear regression equation of PLTR on TR (Section 3.9), and plotted as the black solid circle with a vertical line. The gray band with a solid horizontal line in its center indicates the mean ([+ or -]SD) of the first three PLTRs corresponding to the respective largest TRs each of which was within or closest to the MLRS for each of batches 1-3. The two broken horizontal lines indicate the range for these three PLTRs. Similarly, the blue bands and associated horizontal lines are for batches 4-8. The red solid circles with each vertical line indicate the PLTRs corresponding to the TRs of the daytime origin (Fig. 16A) for each same MLRS as given previously. This was to show a hypothetical set of the PLTRs with the ebb tidal phases of the nighttime origin reversed from those of the Tomioka sandflat. Such a geographic location could exist within the same latitude, which is on a co (= same phase)-tidal line different from that for Tomioka. The three blank circle plots around batches 6-8 indicate the PLTRs for the population of the trochid gastropod, Umbonium moniliferum, on the Tomioka sandflat (Mandal et al. 2010); mature adults spawn gametes in the three neap tide periods exclusively during the end of September to early November in the year, with 3-9-day lecithotrophic larval development--a typical retention-type development. The three PLTR plots for batches 1-3 of this species correspond to the respective lowest TRs during the end of September to early November in 1994 (Fig. 16D). Tamaki and Takeuchi (2016) estimated that the physical retention rate of those gastropod larvae (with no mortality assumed) in Tomioka Bay for 2-9 days after fertilization was 43%, with the remainder being lost to the coastal ocean, and they inferred that the Tomioka sandflat population should be a sink in the regional metapopulation. The bay's location close to the coastal ocean (Fig. 1A) would preclude full larval retention even in the neap tide period. The mean value for the theoretically maximum PLTRs for batches 1-3 of TV. harmandi (solid horizontal line in the gray band) was 84% of that for batches 4-8 (solid horizontal line in the blue band). The mean actual PLTR value for batches 1-3 was 68% of their mean theoretical maximum value. That value for batches 4-8 was 89%. The lowest values of the PLTR ranges through all batches were at around 100 m, which was nearly the same as the values for the three batches of U. moniliferum. This suggests that at least half the larvae of TV. harmandi released from the Tomioka sandflat could be exported out of Tomioka Bay even in the worst case. Indeed, settlement of decapodids onto the sandflat occurred throughout the reproductive season (Tamaki & Ingole 1993, Tamaki et al. 1996, 1997, 2013). By contrast, the lowest range values of PLTR for batches 1 and 3 in the hypothetical, reversed daytime-nighttime phase were almost zero, suggesting no successful larval export to the coastal ocean. In the early reproductive season of such local populations, the mismatch between larval release timing and TR above that threshold, which is primarily caused by the extended embryo brooding, could bring about a complete failure of larval export to the coastal ocean and the consequent no recruitment. These local populations may go extinct or be maintained only as sinks in the metapopulation (Tamaki & Takeuchi 2016).

For the Nihonotrypaea harmandi population on the Tomioka sandflat, (1) quasi-match of the dates with larval release synchrony (and its preceding reproductive synchrony) and those with the local largest TRs in the mid- to late reproductive season and (2) mismatch (or sub-match at best) between them in the early reproductive season were observed (Section 3.10.2). This may represent one general pattern for the present study's target decapod crustacean group dwelling on intertidal flats in the warm temperate region of the midlatitude (Saigusa & Hidaka 1978, Wheeler 1978, Saigusa 1981, Christy 1982, Greenspan 1982, Saigusa 1982, Zimmerman & Felder 1991, Yamaguchi 2001a, Christy 2003). As a standard of comparison, patterns expected for the group of the tropical region would be worth noting (Salmon & Hyatt 1983), with year-round (1) higher air/water temperatures, (2) fairy equal durations of nighttime and daytime, and (3) least diurnal tidal inequalities in the semidiurnal tidal regime (Pugh 1987). Nishimura (1981) presented a hypothesis that some group of estuarine brachyuran crabs in the midlatitudinal eastern Asia including Japan, such as the sesarmids, Chiromantes haematocheir and Chiromantes dehaani, and the varunid, Helice tridens, were originated from each ancestral species in the tropical Indo to western Pacific biogeographical region. Some ancestral species of TV. harmandi in this region is assumed to have existed for the following argument. In general, decapods in the tropical shores tend to perform continuous reproduction year-round, with a successive cycle of both embryo brooding and ovary restoration in females (e.g., Warner 1967, Bauer 1989, Gunamalai & Subramoniam 2002, de Oliveira et al. 2016). Associated with its adaptive radiation, any ancestral species in the tropics may have undergone a range extension toward both poles through larval dispersal. Those descendants have encountered with the seasonality in air/water temperatures, nighttime/daytime durations, and diurnal tidal inequalities, which may have caused irregular, negative or positive effects on the persistence of metapopulations, each comprising a set of local populations connected by larval transport. Including the case for the present TV. harmandi, the reproductive season of decapods in warm temperate shores tend to start only when air/water temperature reaches 20[degrees]C (Pillay & Ono 1978, Christy 1982, Rodriguez et al. 1997). The smoothest successive reproductive and larval release synchronies of the present TV. harmandi population took place under the water temperatures greater than or equal to 25[degrees]C (Section 3.7). The year-round continuity in the reproduction by tropical shore species may be guaranteed primarily by water temperatures exceeding 25[degrees]C (Fig. 21 A) and by presumed temporally stable food supply (primary production) to adults and larvae in the coastal waters. For these species, the daily maximum nighttime duration for newly-released larval transport is ca. 12 h year-round, which becomes shorter toward both poles in their summertime (Fig. 21B).

The magnitude of diurnal tidal inequality can affect the efficiency of newly-released larval transport seaward, as follows. Here, equilibrium-tide models are of a heuristic value despite their limited reproducibility for the actual tidal patterns. According to Foreman (1977) and Japan Coast Guard (1992), a time series of the equilibrium tides in 1994 were constructed every 1[degrees] in both latitudes from the equator, where eight major harmonic components ([Q.sub.1], [O.sub.1], [P.sub.1], [K.sub.1], [N.sub.2], [M.sub.2], [S.sub.2], and [K.sub.2]) were used to include the variations of spring-neap tides, diurnal tidal inequality, and lunar perigee-apogee cycle [Fig. 22A (mid-June to mid-July example for 32.5[degrees] N: Tomioka) and Fig. 22B (for 0[degrees]: equator)]. The gray bands in the panels indicate each 48-h segment with its center on either syzygy or quadrature date. Then, first, the mean diurnal TR inequality in each time segment was defined as the mean value for every ratio of one TR to the adjacent TR [r = [DELTA][n.sub.s] (: smaller TR)/[DELTA][[eta].sub.L] (: larger TR); 0 < r [less than or equal to] 1] contained in that segment, in which the r values were regarded as valid only in the cases with 9 h [less than or equal to] [duration between the adjacent H (L) times] < 18 h and with the total number of the extreme tidal levels [greater than or equal to] 8. The smaller mean r values indicate the larger diurnal TR inequalities. The latitudinal variations in the mean r values on each date in the spring tide periods (as [r.sub.1]) and neap tide periods (as [r.sub.2]) during mid-June to early November are shown in Figures 23A and B, respectively. Note that the truncated lines in Figure 23B correspond to the limited data sets with the total number of the extreme tidal levels [greater than or equal to] 8 for each. Second, to examine the latitudinal variation in the TR difference between spring and neap tide periods, another TR ratio index, r', comprising [r'.sub.1] and [r'.sub.2], was introduced, following the five steps: (1) [DELTA][[eta].sub.S]-spring (: smallest TR in spring tide) and [DELTA][[eta].sub.L-Spring] (: largest TR in spring tide) were defined as the smallest and largest TRs in the 48-h segment of a spring tide period, respectively (Fig. 22A); (2) [DELTA][[eta].sub.S-Neap] (: smallest TR in neap tide) and [DELTA][[eta].sub.L-Neap] (: largest TR in neap tide) were defined as the smallest and largest TRs in the 48-h segment of a neap tide period, respectively (Fig. 22A); (3) relative to the aforementioned [DELTA][[eta].sub.L-Neap], the smaller of the [DELTA][[eta].sub.S-Spring] values on either side of the neap tide period was selected; (4) similarly, relative to the aforementioned [DELTA][[eta].sub.S-Neap] (*) the larger of the [DELTA][[eta].sub.L-Spring] values on either side of the neap tide period was selected; and (5) [r'.sub.1] was defined as the ratio of the [DELTA][[eta].sub.L-Neap] to the smaller [DELTA][[eta].sub.S-Spring], and their variations in latitude on the neap tide dates of each month during mid-June to late October were calculated (Fig. 23C); and [r'.sub.2] was defined as the ratio of the [DELTA][[eta].sub.S-Neap] to the larger [DELTA][[eta].sub.L-Spring], and their variations in latitude on the aforementioned neap tide dates were calculated (Fig. 23D) [note that the pattern in the southern latitude is symmetrical to that in the northern latitude with respect to the equator (not shown in the panels)]. The larger [r'.sub.1] values indicate the smaller differences in large neap to small spring TRs, whereas the larger [r'.sub.2] values indicate the smaller differences in small neap to large spring TRs. After the r and r' were that defined, the following latitudinal pattern became evident, as exemplified for the equator and 32.5[degrees] N. On the equator, daily TR inequalities in both spring and neap tide periods were virtually absent year-round (Figs. 22B and 23A, B). Under this setting, with the constant E-BD of 14.4 days at the stable water temperatures greater than or equal to 25[degrees]C [for the population of a presumed ancestral species of Nihonotrypaea harmandi: preceding paragraph; Figs. 3 and 21 A], once a peak reproductive synchrony is set to be timed to any syzygy date, the subsequent chain of the peaks of larval release synchrony and the immediate embryo re-deposition synchrony (Section 3.4) every syzygy date could automatically be continued throughout the year. Here, an important point is that a stable availability of nocturnal ebb phase for seaward larval transport is expected because of the near absence of diurnal TR inequality irrespective of the location of adult habitats on the shoreline under the different tidal phases. This means that the number of potential adult habitats with larval export efficiency exceeding some threshold is at a high level, securing a substantial number of local populations maintaining a metapopulation. By contrast, seasonally on the 32.5[degrees] N, the diurnal TR inequality in spring tide periods shifted from the maximum (in June to July), through an intermediate (in August), to the minimum (in September), followed by the return to the intermediate during October to November (Fig. 23A), and the inequality in neap tide periods shifted largely from an intermediate (in mid-June to mid-July) to the maximum (in the remainder months) (Fig. 23B). This pattern appears to qualitatively reproduce the actual seasonal change (Fig. 16). Thus, in theory also, in the midlatitude region with varying tidal phases, a mismatch could occur between the daily larger TR and either of the nocturnal or diurnal ebb phases during both spring and neap tide periods of the early reproductive season (as seen in the red vertical lines in Fig. 20). Such a mismatch would lead to a reduction in the number of potential self-sustaining local populations supporting a metapopulation in light of nocturnal ebb tidal larval transport efficiency. To overcome this mismatch, some species may have adopted a daytime larval release strategy, given sufficiently turbid waters (cf., Moser & Macintosh 2001) or equipment of some kinds of pigments in larval bodies to escape from visual predators. From August to September, the medium to smallest diurnal TR inequalities in the spring tide periods and the largest ones in the neap tide periods could provide the present N. harmandi population with the better to best syzygy-timed cycle of both reproductive (embryo depositional) and larval release synchronies under the highest water temperatures in the year, which approximates to the circumstance for the presumed ancestral species population on the equator (Figs. 9 and 19). One complicated, positive situation in the midlatitude region is that during the early reproductive season, the relatively large TRs are available to newly released larvae even in the neap tide periods, which is comparable with the TRs in the spring tide periods. Indeed, on the 32.5[degrees] latitude, both [r'.sub.1] and [r'.sub.2] values in the early season were at their respective maxima, shifting toward each clump with the lower values in the mid- to late season (Fig. 23C, D). Such a tidal pattern in the early reproductive season may enable those newly released larvae encountering neap tide periods (because of their parents' weak reproductive synchrony and of the subsequent prolonged E-BD to 3 wk under the lower water temperatures: Figs. 2 and 3) to be transported to the coastal ocean in some high suboptimal efficiency, not to say in the optima (Fig. 20).

5. CONCLUSIONS

Despite its concealment in deep burrows in the sediment, the population of Nihonotrypaea harmandi on the Tomioka sand-flat has three reproductive traits suitable for detecting a coupled semilunar cycle of the density-dependent, embryo-deposition synchrony and the density-independent, larval release synchrony through the reproductive season in a warm temperate region: (1) habit of each female with full-grown ovary to copulate with one of a few males in her close vicinity immediately before each embryo deposition, which makes the embryo deposition synchrony governed by the numerically dominant of the three cohorts--the older two in the early season and the youngest from the mid-season onward owing to the decline in the older two, including the longevity of the oldest; (2) basically successive larval release synchrony immediately followed by embryo re-deposition synchrony; and (3) a constant, 14.4-day embryo-brooding duration (E-BD) under water temperatures greater than or equal to 25[degrees]C. The first peak embryo deposition synchrony by the youngest cohort in the mid-season was most likely to be timed to a syzygy date, which provided the basis for proposing the syzygy-cycle-based (SCB) view. As a corollary, it is anticipated that the first peak embryo deposition by the older two cohorts in the earliest season was also attempted to be timed to a syzygy date, with the most members of the oldest cohort being the overwintering survivors of the youngest cohort the previous year. Throughout the reproductive season, therefore, the occurrence of only two mating synchronies, one in the earliest season and the other in the mid-season, would automatically trigger all subsequent larval release synchronies in both water temperature-dependent and dominant cohort-dependent ways. This makes the peak larval release dates not necessarily accordant with the dates with the largest nocturnal ebb tidal ranges (TRs), especially in the early reproductive season. On the other hand, the age-of-the-tide-cycle-based (AOTTCB) view contends that the peak larval release synchrony ought to be timed to a date with the largest nocturnal ebb TR to achieve the most efficient larval transport to the coastal ocean, e.g., the central date in each spring tide period (i.e., the largest-TR date) that comes a few days after the syzygy date in a region under the semidiurnal tidal regime. Compared with the SCB view with a forward interpretation from the start of the reproductive season, the AOTTCB view requires a backward time schedule from the date of a peak larval release synchrony to one previous date with the peak embryo (re-)deposition synchrony to be timed to the local largest ebb-TR date when the E-BD is, for example, ca. 2 wk in the period of the reproductive season with the highest water temperatures and to another date in a neap tide period when that duration is 3 wk in the periods with the lower water temperatures. This scenario will be confronted with difficulty in keeping a logical consistency. Another possible inconsistency in the AOTTCB view arises when treating with (1) the difference in deterministic TR between syzygy and central spring tide dates, between multiple central spring tide dates in a lunar apogee-perigee cycle, and between dates in spring tide periods and those in neap tide periods and (2) the stochastic TR differences caused by meteorological variations. Both SCB and AOTTCB views assume the equipment of a hydrostatic pressure sensor detecting the local high tide (H) and a daylight sensor detecting the sunset (SS) and sunrise (SR) in each individual shrimp or crab, which seems generally accepted by researchers. In addition, the SCB view assumes the equipment of a sensor detecting a syzygy-associated cue such as moonlight to which individuals are entrained for synchronized mating (leading to the subsequent embryo deposition), whereas the AOTTCB view implicitly assumes the equipment of a sensor to memorize the hydrostatic pressure difference across dates with different TRs. Both sensors are unknown for any callianassid species. For the SCB view, elucidating how individual adults in their earliest reproductive season attempt to become timed to a syzygy date for their mating synchrony and yet how it can only be weakly realized is a future major subject. The AOTTCB view seems to pay less attention to the earliest seasonal pattern in the first place. Overall, under the law of logical parsimony, the SCB view has provided a simpler and more consistent interpretation for the switch from the weak larval release synchrony in the early reproductive season to the distinct one in the mid-season onward in the present N. harmandi population. Furthermore, the SCB view could have a broader perspective for the mechanism about the maintenance of local populations under the suboptimal larval export efficiency in the contexts of both metapopulation persistence and possible latitudinal range extension from a presumed ancestral species in the tropical region into the warm temperate region with the seasonally greater variations in water temperature, nighttime duration, and diurnal TR inequality.

ACKNOWLEDGMENTS

We thank the director and staff of the Amakusa Marine Biological Laboratory, Kyushu University for providing the facilities, and T. Kikuchi, I. Goto, and S. Arakaki for allowing the use of water temperature data. The water depth data in the study region were provided by Hydrographic and Oceanographic Department, Japan Coast Guard. We also appreciate the help from Y. Fukuda, H. Tanoue, I. Goto, T. Sameshima, T. Kawamoto, H. Shimoda, S. Sen-ju, and T. Nakano in the field sampling and data acquisition, the help from Y. Fukuda, N. Naragino, Y. Hatamura, and M. Furuya in the laboratory treatment of larval samples, and the information about tides from H. Takeoka and T. Yanagi. The manuscript was improved by constructive comments from the two reviewers. This study was partly supported by the Environment Research and Technology Development Fund (4D-1104) of the Ministry of the Environment, Japan, and the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research JP26440244 to A.T.

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APPENDIX. DEFINITIONS FOR THE CATEGORIES OF "GREATER RAINFALLS" AND "GREATER WAVES" ON THE TOMIOKA SANDFLAT, AS MENTIONED IN THE CAPTION FOR FIGURE 17 IN THE TEXT

AKIO TAMAKI, (*) JUN-ICHI ITOH, YUICHIRO HONGO, SEIJI TAKEUCHI AND TETSUTARO TAKIKAWA

Graduate School of Fisheries and Environmental Sciences, Nagasaki University, Bunkyo-machi 1-14, Nagasaki 852-8521, Japan

(*) Corresponding author. E-mail: tamaki@nagasaki-u.ac.jp

DOI: 10.2983/035.037.0309
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