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GENETIC INFLUENCES ON EXPERIMENTAL POPULATION DYNAMICS OF THE LEAST KILLIFISH.

JEFF LEIPS [1]

JOSEPH TRAVIS

F. HELEN RODD [2]

Abstract. When natural populations differ in density or in the dynamic fluctuations of population size, some of those differences may result from their different ecological conditions, and some may originate from genetically based differences in life history expression. Natural populations of the live-bearing pocciliid fish, Heterandria formosa, vary considerably in their population dynamics, with densities that differ between populations by as much as sevenfold. This system offers an excellent opportunity to explore the potential role of genetically based differences in life history expression in creating different dynamic patterns in a common environment. We created five different genetic stocks of H. formosa by carrying out a series of crosses using fish from two North Florida populations (the Wacissa River and Trout Pond) and used them to initiate replicate experimental populations in artificial ponds. The five stocks consisted of two "controls," which were pure Wacissa River and Trout Pond stocks, and three types of hybrid stocks. The hybrid stocks differed in a regular way in the proportion of genes from one population or the other. The crossing scheme was designed so that each hybrid stock would have the same proportion of heterozygous (or "heterodemic") loci but would differ in the proportion and/or identity of homozygous (or "homodemic") loci from the Wacissa River and Trout Pond populations. These populations were chosen because a previous study had found that population densities in the Wacissa River greatly exceeded those of Trout Pond and exhibited a higher range of population fluctuation during the breeding season. We addressed four questions in this experiment: (1) Are there genetically based differences in life history traits of fish from the two populations? (2) If so, do differences in life history expression produce differences in population dynamics in a common environment? (3) Which traits have the greatest influence on population dynamics? (4) How do changes in density affect the phenotypes of individual traits that govern the rates of birth and death in a population? We followed experimental populations of the five genetic stocks from their initiation at low density through 4-6 generations of population growth and decline. The mean offspring size differed among stocks by as much as 50%. At low densities, offspring size exhibited a trade-off with brood size: Trout Pond alleles were associated with more, smaller offspring. At higher densities, offspring sizes were similar among stocks, and the trade-off with offspring number was not evident. Stocks differed in realized population growth rate by as much as 70%; the rank order differences among stocks with respect to population growth rate appeared to match the genetic relatedness among stocks based on the expected percentage of Trout Pond alleles. Differences in population growth rate appeared to be due to differences in brood size among stocks at low density. Stocks did not differ in the equilibrium population size, which indicated the absence o f a trade-off between population growth rate and carrying capacity in this environment. Adult survival and recruitment of juveniles into the adult population both declined linearly with increasing density; and stocks did not generally differ in those rates after the effects of density had been taken into account.

The stocks differed in their response to the depressant effects of density on life history trait expression. The offspring size of the pure Wacissa River stock was much more sensitive to density than was the offspring size of the pure Trout Pond stock. However, the brood sizes of the Wacissa River stock were reduced much less than those of the Trout Pond stock when exposed to the same high density. These results suggest that life history distinctions among populations, both in the mean values and plasticity of traits, play a role in creating different dynamics. We discuss the ways in which phenotypic plasticity in reproductive traits potentially acts as a mechanism to stabilize population dynamics in this species.

Key words: demography; genetic differentiation; Heterandria formosa; life history; offspring number; offspring size; trade-off; plasticity; Poeciliidae; population dynamics.

INTRODUCTION

Natural populations exhibit a wide variety of dynamic patterns, from the relatively stable populations of Spanish Imperial Eagles (Ferrar and Donazar 1996) and pine beauty moths (Turchin and Taylor 1992), regular population cycles of the larch budmoth (Turchin and Taylor 1992), and unstable population fluctuations of the Soay sheep (Clutton-Brock et al. 1997) to the nearly chaotic dynamics of boreal voles (Turchin 1993, 1995). Previous studies of population dynamics have largely focused on how specific ecological factors perturb and perhaps regulate population size and other characteristics such as age structure (see reviews by Sinclair 1989, Crawley 1990, Berryman 1991, Murdoch 1994, Turchin 1995). Current theory suggests that two types of forces, endogenous and exogenous, contribute to the diversity of population patterns commonly observed. Endogenous forces are those that affect and are, in turn, affected by the demographic characteristics of populations (e.g., emigration rates, intraspecific life history responses to density, predator densities); exogenous forces are those that affect demographic aspects of the community but are not affected by them (e.g., abiotic conditions, immigration rates) (Ellner and Turchin 1995). Ellner and Turchin (1995) argue that the diversity of patterns in population dynamics results from variation in the relative strength of endogenous forces on the dynamics of a population and variation in the damping or amplification of externally mediated exogenous perturbations to the populations.

We know relatively little about why some populations are more strongly influenced by endogenous factors than others and about what causes the variation in the damping or amplifying of perturbations to population size. One possibility, that has rarely been addressed, is that genetically based variation in life history expression plays an important role in determining the relative influences of endogenous and exogenous factors and so leads to divergence in population dynamics. Variation in life history expression can take two forms, differences in the mean value of a trait across populations, and genetically based variation in the plastic response of that trait to changing environmental conditions (e.g., density). There are two general reasons why this variation should be important. First, field-oriented studies have provided broad interspecific contrasts between outbreak and non-outbreak species or invasive and noninvasive species (among other such dichotomies such as rare vs. common species) and imply that g enetically based differences in life history expression are responsible for some of the observable variation in population dynamic patterns (Cappuccino 1987, Hanski 1987, Nothnagle and Schultz 1987, Gaston and Lawton 1988, Hunter 1991, 1995, R[[acute]{e}]jmanek and Richardson 1996, Glutton-Brock et al. 1997). Second, there is considerable genetically based variation at the individual, population, and species level in how life history traits are altered plastically in response to population density or per capita resource level (Travis 1994). The way such traits respond to changes in population density can alter population stability (Hutchinson 1948, Gurney and Nisbet 1985, Prout 1986), especially if the numerical consequences of the life history response lag significantly behind the initial induction of that response (Ebenman 1988, Castillo-Chavez 1989, Gushing and Li 1992, Ginzburg and Taneyhill 1994). There is also good evidence that ecological factors that influence vital rates can also alter the expression of life history traits. For example, predators not only directly affect prey survival rates, but their mere presence can indirectly affect the expression of life history traits such as the size at metamorphosis or the initiation of reproduction (Crowl and Covich 1990, Skelly and Werner 1990). Such alterations in the timing of life history transitions or in traits such as body size, on which many vital rates depend, can affect subsequent population dynamics dramatically (Rossiter 1995, Wilbur 1996). Therefore, there is good reason to believe that genetic variation in life history traits among populations, as well as genetically based differences in the plasticity of life history trait expression, could contribute to variation in population dynamics. In fact, there has been little comparative work on natural populations at the intraspecific level, at which the genetic and environmental sources of variation in both life history expression and population dynamics could be dissected (Antonovics and Via 1987). Thi s is not for lack of intraspecific variation in dynamic patterns (Whittaker 1971. Elliott 1987, Belovsky and Joern 1995).

The attention of field-oriented evolutionary biologists has been focused in the other direction, i.e., clarifying the role of population density as an evolutionary force molding life history traits. The most prominent of these demonstrate that consistent, environmentally based differences in density regimes will select for genetic divergence in life histories (reviewed in Charlesworth 1994, Mueller 1997; examples include Law et al. 1977, Primack and Antonovics 1982, Bradshaw and Holzapfel 1989). However, such changes in life histories should themselves produce further divergence in population dynamic patterns, even in a common environment (Antonovics and Via 1987). Some attention has also been given to the theoretical problem of whether natural selection for a reduced sensitivity of vital rates to the effects of population density will cause the evolution of enhanced population stability (reviewed in Travis and Mueller 1989; see also Ferriere and Gatto 1993, Doebeli 1993, 1995).

The search for a link between life history expression and population dynamics has precedent in laboratory studies. Evidence from studies on a variety of taxa supports the notion that there can be a significant genetic component to divergent population dynamics (Drosophila spp.: Dobzhansky and Spassky 1944, Lewontin 1955, Birch et al. 1963, Ayala 1965a,b, 1966, Mueller and Ayala 1981, Marks 1982; E. coli: Luckinbill 1978; Lucilla cuprina: Nicholson 1960; Tribolium spp.: Sokal and Karten 1964, Lloyd 1968, McCauley and Wade 1980, Goodnight 1988, 1989, Wade 1991). In addition, density-dependent selection on Drosophila melanogaster populations can produce life history differentiation among populations resulting in genetically based differences in patterns of population dynamics in a common environment (Mueller and Huynh 1994).

While current theories of density-dependent selection predict population level responses (maximization of the density of the critical age group; Charlesworth 1994), they make no specific predictions about which traits should respond to density-dependent selection (Mueller 1997). A comparison of genetically based differences in life history traits between populations that are expected to differ in the probable degree of density regulation (and so potentially differ in the degree of density-dependent selection) would provide a valuable case study of how life histories may evolve as a consequence of this difference. Such studies have not been done outside of the laboratory because most natural populations are not suited for separating the environmental and genetic influences on both life history expression and population dynamics.

The least killifish, Heterandria formosa, offers an opportunity to examine this question in both natural and experimental contexts. This small poeciliid fish occupies a variety of freshwater habitats in the coastal plain of the southeastern United States where it encounters widely varying abiotic characteristics and a diverse set of food sources, potential competitors, predators, and pathogens. Previous work on the dynamics of four natural populations in North Florida uncovered a series of divergent attributes that implicated a strong causal link between life history expression and population dynamics (Leips and Travis 1999). Between the most divergent populations, the Wacissa River and Trout Pond, densities were up to seven fold higher and fluctuated to a much greater extent in the Wacissa River than in Trout Pond, female body size was 35% smaller, and, after adjustment for female body size differences, brood size was 33% smaller and offspring size 45% larger. The Trout Pond population appeared to have the greatest capacity for rapid increase, given the relative difference in female body size (which is positively correlated with brood size) and greater size-specific brood size. Despite this capacity, it consistently displayed the lowest population densities.

In this paper, we present the results of an experimental study designed to investigate the extent to which the differences in the dynamics of populations of H. formosa, such as those seen between the Wacissa River and Trout Pond, may result from genetically based differences in life history traits. We also explore how the general and population-specific sensitivity of traits to density contribute to the stage structure and numerical behavior of populations. We address four broad questions using the Wacissa River and Trout Pond populations: (1) Are there genetically based differences in the life history traits of fish from the two populations? (2) If so, do the genetically based differences in life history expression produce differences in population dynamics and stage structure in a common environment? (3) Which traits have the greatest influence on population dynamics? (4) How do changes in density affect the phenotypes of individual traits that, in turn, govern the birth and death rates of the population? We use the answers to these questions to elucidate the role of life history expression on the dynamics of H. formosa populations, the stabilizing effect of life history plasticity on population dynamics, and the presence of any trade-off between the capacity for rapid increase at low densities and the capacity for sustained persistence at high densities.

MATERIALS AND METHODS

Natural history

The least killifish, Heterandria formosa, is a small, live-bearing topminnow in the Poeciliid family. They are native to the southeastern coastal plain of the United States and occur in freshwater bodies throughout Florida and along the coastal regions from Louisiana to North Carolina. Small body size and visual indicators of sexual maturity make this an ideal species for field and laboratory studies. In optimal lab conditions, females reach sexual maturity at 8-10 mm (standard length) in [sim]30-40 d; maturity is indicated by the appearance of a small black dot on the anal fin (Fraser and Renton 1940). Males mature at larger body size (10-14 mm), take longer to mature (40-50 d), and maturity is indicated by development of the gonopodium, a modified anal fin used for sperm transfer (Constanz 1989).

Individual females are prolific breeders, producing offspring continuously from March to October in many natural populations in North Florida (Colson 1969, Leips 1997). Females exhibit superfetation, in which several different broods of offspring are carried simultaneously, each at different stages of development. This allows for short intervals between successive broods (from 7-21 d; Travis et al. 1987, Leips 1997) and results in several overlapping generations per breeding season. Females are matrotrophic; embryos are nourished by direct provisioning of nutrients from the female (Fraser and Reaton 1940, Scrimshaw 1944), enabling changes in resource availability to be translated directly to developing offspring.

Overview of experiment

We followed the numerical dynamics and life history trait expression of H. formosa from replicated experimental populations composed of one of five different genetic stocks. We created these stocks from laboratory crosses of individuals from Trout Pond and Wacissa River. Each replicate population was put in an experimental mesocosm and followed for an estimated 4-6 overlapping generations (defined as the minimum predicted time between the birth of an individual and the birth of its offspring; Begon et al. 1986). Three replicates of each population were run in each of two phases (the first set, phase I, was started in the summer and the second set, phase II, was started in the fall). We did a complete census of all populations every five weeks during the breeding season and monitored numbers, sex and stage (juveniles and adults) of individuals. At each census we also drew a sample of females for analysis of reproductive traits.

Creation of genetic stocks

We created stock fish in the laboratory for two reasons. First, by rearing stocks in a common environment, we minimized the influence of nongenetic maternal effects that could result from differences in the environment between the Wacissa River and Trout Pond. Second, by producing genetic stocks that varied linearly in the proportion of alleles drawn from each population of origin, we could compare the similarity of population trajectories against the genetic similarity of various stocks. We could also test for the additivity of genetic effects and the significance of nonadditive effects to evaluate whether the nature of genetic inheritance of particular traits had an observable signature on population trajectories (Falconer and Mackay 1996).

The five stocks used in the experiment were initiated with 112 gravid females and 60 males obtained from each population (Trout Pond and the Wacissa River) between 16-19 September 1993. Trout Pond is a 5-ha pond in the Apalachicola National Forest, [sim]10 km west of Tallahassee, Florida, USA. The Wacissa River is a spring-fed river in Jefferson County, [sim]35 km east of Tallahassee (see Leips and Travis [1999] for a detailed description of the differences in these sites).

Breeding individuals were maintained in five gallon aquaria; six females and two or three males per tank. Tanks were arranged on shelves in a temperature- and light-controlled laboratory (maintained at 30[degrees]C, 14 : 10 light: dark cycle). The laboratory temperature and day length reflected the typical condition experienced by natural populations during the breeding season (Leips 1997). Newborn offspring were removed and placed in new tanks every two weeks to minimize the chance of inbreeding with parents. As females in the offspring tanks matured, they were moved to separate tanks to prevent sib mating. As an additional precaution to minimize inbreeding, tank pedigrees were maintained for all offspring born in a given tank. First generation individuals ([F.sub.1]) and subsequent generations were only crossed with individuals that had never shared a tank.

In the first step, [F.sub.1] individuals were those born of gravid, field-caught females or produced by crossing Wacissa River (WW) males with WW females and Trout Pond (TT) males with TT females in the laboratory. In December 1993, [F.sub.1] TT and WW individuals were either crossed with other [F.sub.1] individuals from the same stock, or crossed between stocks (Table 1). Sixty [F.sub.1] females and 30 [F.sub.1] males were used in the WW and hybrid (TW) crosses. Trout Pond females produced fewer offspring in the laboratory, so only 42 [F.sub.1] females and 21 [F.sub.1] males were used to produce the next generation of pure TT stock. The [F.sub.1] hybrid crosses were produced by an equal number of matings between Wacissa males and Trout Pond females, and Wacissa females and Trout Pond males. This crossing procedure produced four different genetic stocks of [F.sub.2] offspring: TT, WW, and two types of hybrids, TW (from the TT female X WW male cross) and WT (from the WW female X TT male cross). In April 1994, pure F3 offspring (TT and WW) were produced by crossing [F.sub.2] individuals from the same stock (e.g., TT X TT). Three types of [F.sub.3] hybrid stocks were also produced. The first type was produced by crossing [F.sub.2] hybrid individuals to other hybrids (e.g., TW X TW), using all possible combinations of male and female parent type. Crossing [F.sub.2] offspring of the TT and WW stocks to the [F.sub.2] hybrid stocks (TT X WT and TT X TW, WW X WT and WW X TW) produced the two other types of hybrid.

This breeding design created two pure stocks, and three different "hybrid" stocks that differed in a regular way in the proportion of genes from one population or the other (TTTT, TTTW, TTWW, TWWW, WWWW). The crossing scheme was designed to produce hybrid stocks with the same proportion of "heterozygous" (or "heterodemic") loci (50% TW), that differed in the proportion and/or identity of "homozygous" (or "homodemic") alleles from the Wacissa River and Trout Pond populations. Thus, phenotypic differences among the three hybrid stocks should not have resulted from different mean levels of heterozygosity across loci, but instead from specific effects of the alleles of origin, their interaction with the rest of the genome, and stock-specific differences in gene expression in a given environment.

Initiation of experimental populations

Experimental populations were started in Nevr-rust polyethylene cattle watering tanks (850 L maximum volume) with 25 juveniles, haphazardly chosen from the pooled [F.sub.3] offspring from a given stock. Thirty cattle tanks were used, six tanks per genetic stock. Tanks were located in a former agricultural field at the Florida State University Mission Road Greenhouse Facility, Tallahassee, Florida, United States.

We executed the experiment in two temporal phases to avoid confounding seasonal differences in the expression of individual traits with responses to density. In phase I, we started three replicate populations of each stock in July 1994. We started the second set of replicates (phase II) forty days later (September 1994). This staggered design allowed us to measure phenotypic traits of each stock at the same time under a range of densities. One replicate of WWWW stock was extirpated after September and was subsequently restarted with 25 WWWW offspring. This tank was subsequently counted as a phase II tank, leaving only two replicates of the WWWW stock in phase I but four replicates in phase II. All populations were followed until August 1995.

Cattle tank setup

Aquatic communities were established and maintained in each tank to mimic many aspects of the natural habitat of Trout Pond. Cattle tanks were filled with well water two months before the initiation of each phase of the experiment. Movable standpipes were placed in each tank to allow drainage of excess water (the opening of each standpipe was screened to prevent the loss of fish) and adjusted to ensure that each tank contained the same water volume throughout the experiment. The water level in each tank was subsequently maintained by copious rainfall. The pH was adjusted to 4.7 (and maintained throughout the experiment between 4.7 and 5.3 reflecting the natural pH of Trout Pond; Leips 1997) with a 10% solution of sulfuric acid. Approximately 20 L of leaf litter and pine needles, 100 g of Purina Rabbit Chow, and 500 mL of suspended plankton from Trout Pond were added to each tank. In addition, floating and submerged aquatic vegetation from Trout pond and potted wetland plants (Sagittaria lancifolia) were adde d to each tank to provide additional cover. Tanks were covered with Lumite screens to prevent colonization by insects and amphibians. The resulting aquatic communities were allowed to sit undisturbed until initiation of the experiment.

During the course of the experiment, [sim]1 L of concentrated plankton (collected using a 64 micron plankton net) from Trout Pond was added to each tank monthly. Along with plankton, invertebrate predators (e.g., fishing spiders, Dolomedes triton, and various species of Libellulid dragonfly larvae) and potential competitors (freshwater snails, Physella sp. and Helisoma sp.) were inadvertently introduced into the tanks. At each census, all predators and competitors that were caught were removed.

Sampling

Populations were completely censused every five weeks by repeated seining (using a 2 mm mesh seine that completely spanned the depth and diameter of each cattle tank) until fewer than five individuals were captured in three consecutive samples. Adult males, adult females, and immature individuals were sorted by visual inspection. Each different class was placed separately in water-filled plastic bins containing a metric ruler where each group was photographed. Photos were used to obtain total census counts for each category of each stock. Body size distributions of males and females were obtained by measuring individuals from photographs using an image analysis system. Individuals were measured from the dorsal view, from the tip of the mouth to the area where the body tapered to a point (a close approximation to standard length) (J. Leips, unpublished data).

The minimum body size of adult males and adult females from each tank were used as estimates of the sizes at sexual maturity. Male poeciliids grow at reduced rates after attaining sexual maturity (Snelson 1989, Trexler et al. 1990), and so the minimum size should be a fairly precise estimate of the actual size at maturity (there is no substantial male size polymorphism in Heterandria formosa like that seen in Xiphophorus spp. and Poecilia spp.). Females continue to grow after sexual maturity, albeit slowly; the difference between the mean size of adult females and the minimum size of adult females offers a crude estimate of a combination of female longevity and postmaturation growth (under the assumption that there is no substantial seasonal variation in the size at maturity).

At each census, [sim]10% of the total number of females in each tank were sampled to measure the proportion gravid, the number of broods carried simultaneously (a measure of superfetation), the number and mass of embryos in each developmental stage, and the overall proportion of biomass devoted to reproduction. Females were euthenized by an overdose of MS 222 (3-aminobenzoic acid ethyl ester) and preserved for dissection in 10% formalin. A total of 559 females were examined in this way throughout the course of the experiment.

Reproductive traits were determined by dissecting all developing embryos and ovarian tissue from preserved females. Embryos were counted and scored for their developmental stage following Reznick (1981). Female body tissue, ovarian tissue, unfertilized eggs, and similar-staged embryos were freeze dried separately in microcentrifuge tubes for 24 h. Dry mass was measured to the nearest 0.01 mg on a Cahn C-31 microbalance.

We used the number and mass of stage-4 embryos (the penultimate pre-parturition stage) as a surrogate for the number and size of offspring per brood. Although embryos in the most advanced developmental stage would have been a better surrogate for these traits, stage-5 embryos were uncommon, likely indicative of the short duration of time that embryos remain in this stage before birth (Travis et al. 1987).

Estimation of adult mortality and juvenile recruitment rates into the adult population

The effects of density on adult survival rates and recruitment rates of juveniles into the adult population (the proportion of juveniles that matured between censuses) were estimated over three periods (November to December, May-June, and June-August) by a mark-recapture technique using the fluorescent dye, calcein. Calcein binds to calcium in tissues and can be seen in fin rays and scales using an epifluorescence microscope. This dye had no effect on survival or maturation rates of H. formosa in a preliminary study and was still visible for up to five weeks in the laboratory (J. Leips, C. T. Baril, F. H. Rodd, J. Travis, and D. N. Reznick, unpublished manuscript).

In each tagging event, all adults from four of the six replicate tanks of each stock were tagged. At the following census, all adults from each tank were returned to the lab. Tagged and untagged individuals were separated (see Leips [1997] for details of this procedure), photographed, and returned to the tanks on the following day.

The number of unmarked adults in each sample period was used as an estimate of the recruitment rate of juveniles into the adult population (indicating the number of juveniles that had matured during the period between censuses). The adult mortality rates were calculated as the difference in numbers of marked adults between censuses. Because checking all adults from each population for marked individuals took several days, the time interval between censuses was not the same across all tanks. We converted the observed rates to a 35-d period for statistical comparison among stocks using the standardization procedure outlined in Krebs (1989:413).

Statistical analyses

All population and demographic parameters were calculated separately for each phase of the experiment. Population growth rates were calculated during the initial period of population growth (the period immediately following the initiation of each population) as the difference between initial and final numbers of individuals, divided by the time elapsed between censuses. The period of initial population growth was determined by visual inspection of the population trajectories (calculated from the July to September 1994 census totals for phase I, and from the September to November 1994 census totals for phase II, Fig. 1). We analyzed differences among stocks in population growth rate with ANOVA (Snedecor and Cochran 1980). Subsequent population trajectories were analyzed using a repeated-measures profile analysis of variance (Simms and Burdick 1988). The stage structure (proportion of the entire population that was immature), and sex ratio (proportion of adults that were female) were also analyzed using a repe ated-measures profile analysis. Except where noted, all population variables were transformed to natural logs prior to statistical analysis to meet the assumptions of ANOVA (we examined the residuals from the analyses to check the validity of the transformations).

Analysis of population trajectories after the initial growth phase was complicated by extirpations in many tanks in the period from April to June. The prolific growth of a floating aquatic fern, Salvinia rotundifolia, occurred in all tanks during this period. Complete coverage of the water's surface caused the extirpation of 14 fish populations, perhaps a result of oxygen depletion. Five of the 14 populations lost were from phase I and the remaining nine from phase II. Extirpations were not evenly distributed across stocks. Three TTTT, one TTTW, five TTWW, three TWWW, and two WWWW tanks were lost due to the Salvinia bloom. As a consequence, data taken from the TTWW stocks after May must be interpreted cautiously because only a single replicate remained after this time. An additional consequence is that all profile analyses had to be restricted to censuses from September to April for the phase I tanks, and from October to April for phase II tanks.

Survival rate data were arcsine transformed and recruitment rate data square root transformed and analyzed using ANCOVA, with stock as the categorical variable and the density at the previous census period as the covariate. Total density at the previous census period (indicating a lag time of [sim]35 d) was used as the covariate because it consistently explained a greater proportion of variance than the effects of concurrent density or that of previous censuses (determined by separate regressions of the traits of interest against the density at the concurrent and two prior censuses). Data from both phases of the experiment (populations initiated in July and September) were pooled for these analyses. This pooling of data ignores potential block effects due to time (so results should be interpreted with caution), but it allowed us to examine survival and recruitment rates over a range of population densities that spanned two orders of magnitude; this certainly enhanced our power to detect the effects of stock, density, and any stock by density interaction.

Analyses of the mean and minimum body sizes of adult males and females among stocks were carried out on pooled data from both phases at each census with ANCOVA. Stock was the categorical variable and previous density the covariate (except for the census immediately following the initiation of the population, where the concurrent density was used).

Reproductive traits of females were analyzed with ANCOVA with stock as the categorical variable and the dry mass of females as the covariate. Total mass of reproductive tissue, embryo size, and female body size were transformed to natural logs to meet the assumptions of the statistical analyses. Counts of the number of broods carried simultaneously and offspring number were transformed to the ([sqrt{count + 1}] + [sqrt{count}]) as per Snedecor and Cochran (1980). In the first set of analyses (September) during the initial period of population growth, reproductive traits were only measured on a single female from each tank (three replicates per stock). This was necessary because, in most cases, no more than 10 reproductive females occurred in any given tank (these were the older females from the initial cohort); all other females were newly matured. Sample sizes from subsequent periods varied, depending on the number of mature females in the population.

Tank extirpations resulted in insufficient replication to analyze statistical differences among stocks in the above traits at separate censuses from March through August. Instead, we pooled the data from these four censuses and used the tank mean values as replicates. To incorporate the influence of different conditions in these tanks across the months that were sampled, we first calculated the adjusted mean value of each trait for a given tank, adjusting for the effects of female body size using ANCOVA. These adjusted values were then used to examine the effects of stock and density on the trait of interest in ANCOVA, using density as a covariate.

When stocks differed significantly for any of the traits examined, patterns of inheritance among stocks were analyzed with orthogonal contrasts (Judd and McClelland 1989). Because the crossing design produced stocks that differed in a regular, ordered way in the proportion of genes from one or the other pure stocks, linear contrast codes were assigned to stock categories in the following way to extract the additive component of trait inheritance: (contrast code follows stock) TTTT, -2; TTTW, -1; TTWW, 0; TWWW, 1; WWWW, 2.

All ANOVA and ANCOVA analyses were done using SYSTAT (Wilkinson 1990). Type III sums of squares were used to account for unequal sample sizes. When significant differences among stocks were detected, post hoc comparisons were made using the Tukey-Kramer adjustment of Tukey's hsd test for unequal sample sizes (Day and Quinn 1989).

RESULTS

Population and demographic parameters

The initial population growth rate of pure Trout Pond stock exceeded that of the pure Wacissa River stock by 70% in the phase I tanks (Fig. 1A; [F.sub.4,9] = 4.05, P = 0.04, [r.sup.2] = 0.64). Hybrid stocks had intermediate rates of population growth; the rank order closely matched the genetic resemblance predicted by the breeding design (Fig. 1A). The subsequent trajectory of the total population size appeared to reach equilibrium after the initial phase of population growth. Adult female and immature numbers of all stocks were relatively stable throughout this period, while male numbers exhibited more variability (Leips 1997).

Initial population growth rates of phase II tanks were lower than those of phase I, and not significantly different among stocks (Fig. 1B; [F.sub.4,5] = 0.61, P = 0.67). The pattern of results was consistent with those of phase I (the pure stocks bracketed the range of growth rates with TTTT having the highest rate and WWWW the lowest), but low growth rates and high variance in phase II replicates probably obscured genetic differences among stocks. One of the populations initiated in September was extirpated before the October census, while three others decreased in size, producing negative growth rates. Because these populations were started late in the breeding season, (for normal breeding phenology see Travis et al. [1987] and Leips [1997]), most individuals probably never initiated reproduction or ceased shortly after they started.

The final population size of stocks did not differ in either phase (phase I Wilks' lambda = 0.05, P 0.33, phase II Wilks' lambda = 0.06, P = 0.11). Population trajectories of phase II tanks were much more variable than those of phase I and never appeared to stabilize (Fig. 1B). This instability appeared to result from extreme variation within each population class (females, immatures, and males) during this period (Leips 1997). While the high variance in phase II stocks may cause the lack of significance, there is no indication in the phase I data that the carrying capacities of the stocks were substantially different.

The proportion of the population comprised of immature individuals in the WWWW stock was 20% lower than for all other stocks during the initial growth of phase I populations (Fig. 2A; [F.sub.4,9] = 4.45, P = 0.03). This stock also had a 30% lower proportion immature than the TTTT stock in phase II (Fig. 2B), but this difference was not significant. Stocks did not differ in the proportion immature after the initial period of population growth (phase I, Wilks' lambda = 0.03, P = 0.17, phase II Wilks' lambda = 0.02, P = 0.62).

The numbers of adults were biased toward females throughout the experiment (Figs. 3A, B); the mean proportion of adults that were female ranged from 0.55 in September 1994 to as high as 0.69 in March 1995. In general, the female bias was higher in the nonbreeding season. The number of extirpations in the last third of the experimental period makes it difficult to interpret the patterns further with any confidence. During the initial period of population growth, the TTTT and TTTW stocks appeared more female biased than the others. However the variance among replicates was high and there were no significant differences in sex ratio among stocks (phase I, Wilks' lambda = 0.06, P = 0.10, phase II, Wilks' lambda 0.30, P = 0.51).

Adult survival

Mean adult survival rates among stocks from the November to December census ranged from 0.79 to 0.96 for males and from 0.80 to 0.90 for females (Table 2). Male and female survival rates declined equally with density for all stocks; although the slope of the relationship between density and adult survival was comparable for males and females (Figs. 4A, B), density accounted for more of the variation in female survival (41%) than that of males (27%; Table 3).

Adult survival rates were highly variable among populations from May to June. Male survival ranged from 0.21 to 1.0 and female survival from 0.32 to 1.0. Low survival rates probably resulted from the combined effects of high population density and the prolific Salvinia growth that occurred in most tanks. Neither stock nor density significantly affected male survival in this period, but female survival was negatively associated with density (Table 3). Although the range of densities in this period was comparable to that of the previous period (November range: 6-577; April range: 13-562), the weakening of the density effect here suggests that other factors (e.g., natural deaths from an aging population, or a history of high density in the tanks) minimized the more proximate effects of density on survival.

Adult survival rates were also highly variable during the period from June to August. Mean survival rates ranged from 0.25 to 0.66 for males and from 0.40-0.84 for females (Table 2). Neither stock nor density significantly affected male survival during this period (Table 3). Density did not affect female survival, but for the first time, the stock effect was significant. Density among populations during this period ranged from 153--1045 individuals. A post hoc comparison of treatment means indicated that the adjusted survival rate of the WWWW stock (0.37 [pm] 0.11, n = 2) was significantly lower than that of the TWWW stock (0.96 [pm] 0.09, n = 3); in this case, stock differences explained 69% of the total variance. Despite these results, it is uncertain whether this difference is truly due to genetic differences between stocks. Sample sizes were small, and in no other census had the stock effect been significant.

Juvenile recruitment

The mean proportion of juveniles recruited into the adult population between November and December ranged from 3-15% for males and from 9-30% for females (Table 4). Recruitment rates for both sexes declined with increased density but there were two notable distinctions between the sexes in this relationship. First, the effect of density accounted for much less of the variance in male ([r.sup.2] = 0.28) than female ([r.sup.2] = 0.72) recruitment rates (Table 5); this result is an echo of the stronger density dependence in female survival rates. Second, the slope of the relationship of recruitment rate to density is substantially steeper for females than for males (Figs. 5A, B); this distinction is a significant one ([F.sub.1,33] = 6.89, P = 0.01). The net effect was that female recruitment rates were much higher than those for males at lower densities but comparable to those for males at the higher densities. Stocks did not differ in recruitment rates after the effects of density had been taken into account.

Recruitment rates were higher in the May-June period than they were from November-December period (Table 4). In this period, unlike the previous one, the rates for the genders were comparable (25% to 32% for males, 23% to 38% for females). Neither stock nor density significantly affected male or female recruitment rates (Table 5). The higher recruitment levels in this period, despite the higher mean densities, most likely reflect the enhanced productivity during this season and the resulting enhancement of juvenile survival and growth.

Recruitment rates from June to August ranged from 6% to 26% for males and from 12% to 38% for females (Table 4). Just as in the November-December period, and unlike the May-June period, increasing density significantly reduced the recruitment rates. However in this period the strength of the effect was comparable in the sexes (male [r.sup.2] = 0.87, female [r.sup.2] = 0.85) and no significant difference between the slopes for each gender was detected.

It is possible that the fluorescent tag faded between censuses; this would underestimate the number of marked adults in the second census and result in an overestimate of recruitment rate and an underestimate of survival rate. If this had occurred, the estimated recruitment and survival rates would not be independent of each other and would exhibit an inverse correlation across replicates. This was generally not the case. A single negative correlation was observed for male survival and recruitment from May to June (r = - 0.39, P = 0.03). On all other dates the correlation was positive and not significant (Pearson product-moment correlation coefficients ranged from 0.08 to 0.74).

Body size

The mean body size of mature females decreased with increasing density in five of the seven censuses ([r.sup.2] ranged from 0.23 to 0.81), but did not differ among stocks (Table 6) after the effects of density were taken into account.

The minimum body size of mature females also declined with increased density in six of the seven censuses, and density explained from 45-81% of the variance (Table 7, Figs. 6A, B). However, density increases reduced the minimum size to a much lesser extent than they reduced the mean female size (not shown). This suggests that the size at maturity is less affected by density than are postmaturation growth and/or survival rates. There was no significant difference in minimum size among stocks except in the May census period, where the adjusted minimum size of WWWW females was 12-14% larger than the females of TTWW, TTTW, and TTTT stocks. In fact, the minimum size of WWWW females tended to be larger than that of TTTT females throughout the experiment, although that distinction was significant at only one census.

The mean size of mature males was extremely variable among stocks, ranging from 10.4 mm to 15.7 mm, and decreased significantly with increasing density (Table 8). The strength of the density effect, as indicated by the coefficients of determination, was comparable between the sexes. However, the slope of the decrease in size with increasing density was shallower in males than in females, which indicates that male size is less sensitive to density effects than female size (not shown). Stock differences in mean male size were not significant except in June, when a significant stock-by-density interaction suggested that some stocks were responding differently to changes in density. Because the stocks were not different in any other census, it is unlikely that the June results reflect genetic differences in body size.

The minimum size of mature males ranged from a mean of 9.0 to 13.8 mm among stocks, and declined throughout the course of the experiment (Figs. 7A, B). Increasing density significantly reduced minimum size, and explained from 34% to 93% of the total variance (Table 9). However, as with mean male size, the effect of density on the minimum male size was much smaller than the effects in females. There were no significant differences among stocks.

Female life history traits

The proportion of biomass devoted to reproduction was highly variable, ranging from a low of 1% in the November and December samples to a high of between 13% and 20% in September (Leips 1997). Reproductive mass increased significantly with female size ([F.sub.1,9] 5.27, P = 0.05, [r.sup.2] = 0.37) but stocks were not different in this relationship ([F.sub.4,9] = 1.18, P = 0.38). In the May through August period, the mean reproductive tissue mass declined with increased density ([F.sub.1,49] = 10.40, P [less than] 0.01) and density explained 14% of the variance.

The mean number of broods carried simultaneously varied with season and density, ranging from 0 to 4.3 broods (Leips 1997). Neither female size ([F.sub.1,9] = 1.74, P = 0.22), nor stock ([F.sub.4,9] = 2.19, P = 0.15) affected the number of broods carried during the period of initial population growth. This is not surprising because female sizes did not differ among stocks and most females carried the maximum number of broods in this period. In each census from April to August, large females carried significantly more broods than small females (April: [F.sub.1,90] = 10.75, P [less than] 0.01; June: [F.sub.1,44] = 22.31, P [less than] 0.05; August: [F.sub.1,41] = 9.94, P [less than] 0.01), and body size explained 6% to 20% of the variation. Increased density had a significant negative effect on brood numbers, independent of its effect on female size [F.sub.1,44] = 7.42, P [less than] 0.01, [r.sup.2] = 0.13), but there was no difference among the stocks ([F.sub.4,44] = 1.5, P = 0.22). These results are similar to the patterns observed in field data (Leips and Travis 1999).

The mean mass of stage-4 embryos (the penultimate stage before birth) differed dramatically among stocks during the initial period of population growth (September census, Fig. 8A; [F.sup.4,9] = 7.29, P [less than] 0.01, [r.sup.2] = 0.70) although the total mass devoted to stage-4 embroyos did not differ ([F.sup.4,9] = 0.82, P = 0.54]. The mean embryo mass of the WWWW and TTWW stocks were as much as 50% larger than the that of the TTTT stock. Analysis using linear contrast codes indicated that both additive and nonadditive genetic effects were significant (additive effects: [F.sub.1,9] = 5.92, P = 0.04; nonadditive effects: [F.sub.3,9] = 7.67, P = [less than 0.01], accounting for 14% and 56% of the variance respectively. The mean offspring mass for the WWWW stocks was comparable to values seen in the natural population in the Wacissa River, whereas the mean offspring mass of the TTTT stocks was about 10%-15% below values seen in the natural population in Trout Pond (Leips and Travis 1999).

During the period when densities were very high (May-August), the mean embryo mass did not differ among stocks ([F.sub.4,38] = 1.82, P = 0.14) although a power calculation (Zar 1984) indicated that we had little power to detect stock-related differences in embryo size. Mean embryo mass was not affected by density during this period ([F.sub.1,38] = 1.82, P = 0.11). The pattern of inheritance among stocks was remarkably consistent with the pattern observed in September (compare Figs. 8A and B) but the mean embryo mass was smaller during the May to August period and the range in offspring mass among stocks was smaller (the range was from 0.33 to 0.53 mg, a 37% reduction). The values observed at this time were also [sim]15%-20% below values in the respective natural populations. The smaller range in the experimental stocks in this period was caused by a decrease in the mean offspring size of the stocks that had the largest offspring in September (the WWWW and TTWW stoks); offspring sizes of WWWW and TTWW stocks declined by 22% and 26% (between September and May-August) respectively. In contrast, the mean size of offspring in the TTTT stock dropped by only 8%. These results indicate that the embryo masses of the TTWW and WWWW stocks are three times as plastic as those of TTTT in response to density.

Density significantly reduced the total biomass devoted to stage-4 embryos during the period of high density ([F.sub.1,35] = 18.41, P [less than] 0.01) but there was no difference among stocks in total allocation of biomass to these late stage embryos ([F.sub.4,35] = 1.20, P = 0.33).

Brood sizes (the number of stage-4 embryos) were not significantly different among stocks in the low density phase of population growth in September ([F.sub.4,9] = 2.33, P = 0.13), although a power calculation indicated that we lacked sufficient power to detect stock differences in this period. Brood sizes were unrelated to female body size ([F.sub.1,9] = 1.35, P = 0.28). As with the pattern in brood number at low density, the lack of a relationship with female body size probably indicates that all females were reproducing at nearly maximal rates. The brood sizes in the TTTT and WWWW stocks during this period were almost twice the values observed in the respective natural populations. Although brood sizes did not differ significantly among stocks, those with the largest offspring (WWWW, TTWW) had the fewest embryos per brood, while those with the smallest offspring (e.g., TTTT) had the largest brood sizes, suggesting a trade-off in offspring size and number (compare Figs. 8A and 9A). We investigated this tra de-off by estimating the partial correlation between offspring mass and brood size across replicates, holding female size constant. We used partial correlations on female size because, although female size did not account for a statistically significant proportion of the variance in either brood size or mean offspring size at low density, previous studies have shown that female size does affect brood size (Leips and Travis 1999). In addition, there was an effect of female size on the total mass of all stage-4 embryos that would probably have been significant with a larger number of replicates ([F.sub.1,9] = 4.46, P=0.06). The partial correlation was negative (r = -0.63, P [less than] 0.01), which indicates that there was a general compromise between offspring size and number.

In the period of high density (May-August), the mean brood sizes among stocks exhibited a very different pattern than the one observed in the low density period (Fig. 9B). At the high densities, the mean number of embryos per brood ranged from 1 to 4.4; thus, the maximum brood size in this period was 95% smaller than the maximum number of offspring per brood in September. There was a significant negative effect of density on brood size ([F.sub.1,38] = 4.47, P 0.04) but it accounted for only 8% of the overall variance. After adjustment for female body size and density, stocks differed significantly in mean brood sizes ([F.sub.4,38] = 3,49, P = 0.02, [r.sup.2] = 0.25). The WWWW stock had significantly more offspring per brood than the TTTT and TTTW stocks (Tukey's had P [less than] 0,05). Analysis using linear contrast codes indicated that only additive genetic effects were significant ([F.sub.1,38] = 8.10, P = [less than] 0.01) and accounted for 18% of the variance. Although brood sizes of all stocks were low er at high density (May-August) compared to low density conditions (September), the brood size of the TTTT stock was most affected by density. The adjusted brood size of TTTT females in the high density period decreased by 67% from the low density period (September); in contrast, the brood size of WWWW females decreased by only 43% over the same period. The relative plasticity of brood size in these stocks is the reverse of the pattern of plasticity for mean offspring size. This relative difference in plasticity altered the relationship between offspring size and number for individual females observed earlier in the experiment; partial correlation of these variables indicated that unlike the results from the September analysis, there was no trade-off between offspring size and number during the May-August period (r = 0.05, P = 0.58).

DISCUSSION

To summarize the results of this study, genetically based differences in life history traits were apparent for late stage embryo mass and brood size but only observable in a subset of environmental conditions. A trade-off between offspring size and number appeared to contribute to differences in initial population growth rates among stocks (stocks with the largest but fewest offspring had slower initial population growth rates than those with many, small offspring). Stock-specific differences in population growth rates were only evident in one phase of the experiment (the replicate populations initiated in July). This emphasizes the importance of accounting for seasonal effects on life history expression when inferring a relationship between life history differentiation and population characteristics. Body sizes and the mean values of reproductive traits were negatively associated with density, although the plastic response of offspring size and number to density differed among the stocks. Convergence on a c ommon reproductive phenotype at higher densities appeared to minimize the genetic distinctions that were apparent at low density, and stocks did not differ in the eventual density that could be sustained in a given tank.

The demography of Heterandria formosa and the effects of density

The population size of the experimental stocks grew rapidly, increasing by more than an order of magnitude and attaining the carrying capacity of the tanks in just two generations. Increasing population densities reduced adult survival and recruitment rates, the minimum and mean body sizes of mature males and females, and all measures of female reproduction.

Changes in density induced similar effects on adult male and female survival rates but affected male and female recruitment rates differently. At low densities, adult survival rates dropped slowly in a linear fashion with increasing density; at high densities, survival rates continued to decline but the effects of density became weaker. There was no substantial difference between the adult survival rates of males and females as a function of density. In contrast, the recruitment rates of females declined strongly and consistently with increasing density while the rates of male recruitment declined weakly. These different relationships with density imply that recruitment rates will be much higher for females than males at lower densities and roughly equivalent, although much lower, at higher densities.

The sex biased recruitment pattern at low densities could have three sources. First and most obviously, females at low densities mature 10-14 d faster than males (J. Parrino, J. Leips, and J. Travis, unpublished manuscript). The equal recruitment at higher densities could occur through an inhibitory effect of density on growth and maturation rate that affects females more than males; greater plasticity in female poeciliids is known for some species (see Trexler et al. 1990) and our data on the response of female body size to density is consistent with this notion. Second, females may be more likely to survive to maturity than males. This difference might be caused by an innate viability difference, but it might also be an indirect effect of the shorter development time for females: if juveniles experience a constant probability of daily mortality, then females, by virtue of faster maturation, experience a substantially smaller cumulative probability of mortality before maturation. Third, sex ratios may be fe male biased at parturition at low density but approach a 1: 1 ratio at higher densities. Female-biased ratios at birth are known in some poeciliid species (Kallman 1984; J. Travis, unpublished data) but there is no information on its possible density dependence.

In general, male survival and recruitment appeared to be less strongly influenced by density than female survival and recruitment, and in fact, male numbers appeared to fluctuate far more over the course of the experiment than did female numbers. Although the forces driving this dynamic behavior are unknown, this pattern of fluctuation in male numbers is also observed in natural populations (Leips and Travis 1999). Together these data suggest that male dynamics are primarily density independent, while female dynamics may be more likely to offer evidence of true regulation. There is good reason to suspect that females may be more sensitive to the effects of high density (e.g., reduced food availability) than males for the simple fact that females must devote energy to egg production. Female poeciliids in particular may suffer from food limitation more than males for two reasons. First, females have higher rates of post maturation growth than males (Snelson 1989). Second, unlike lecithotrophic species, the liv e-bearing, matrotrophic reproductive strategy requires that female H. formosa constantly supply food to growing and developing embryos until birth (Fraser and Renton 1940, Scrimshaw 1944), which greatly increases the cost of reproduction to females over that of males. In contrast, the reproductive investment of males ends at conception as there is no parental care of young after birth in this species.

Indeed, female reproductive traits did show a strong response to density. Females were smaller at higher densities, and the dependence of reproductive parameters on body size was more marked at higher densities, probably because females were no longer operating at maximum reproductive capacity. The total biomass devoted to reproduction decreased with increases in density. This decrease was observed in every component of reproduction: number of broods carried simultaneously, number of offspring per brood, and mean offspring size. The pattern of response of these traits to increased density closely match the patterns exhibited when females encounter a reduction in food availability (Reznick et al. 1996). These changes combined to make the per capita reproductive output at higher densities a small fraction of the output at lower densities. The effect of density was transmitted with a significant lag presumably for two reasons. First, density influenced female body size, which then secondarily affected female fe rtility rates. Second, density affected brood sizes independently of female size. In this case, the lagged effect of density results from the fact that once fertilized, embryos within a single brood must grow and develop within the female prior to birth. Thus there is a lag between fertilization of available eggs and eventual birth of offspring.

It is unclear whether the lagged response of female body size and reproductive traits to density acts to destabilize the dynamics of natural populations of this species. The destabilizing effects normally associated with lagged responses to density may be partly alleviated in H. formosa by the combined effects of the plasticity of female size at maturity, matrotrophy, and superfetation in response to density. These characteristics allow changes in resource levels to be translated almost immediately to changes in offspring size as well as the interval between successive broods (Travis et al. 1987, Reznick et al. 1996), allowing reproductive output to be modulated quickly in response to changing environmental conditions. Those systems in which a similarly lagged density effect has been shown to destabilize population trajectories are characterized by some combination of fixed adult female body size, batch reproduction, and significant further lag between energy accrual and reproductive response (e.g., Prout an d McChesney 1985, Wilbur 1996). It is interesting to speculate whether one of the evolutionary advantages of matrotrophy and superfetation is the considerable control over reproductive allocation it provides to females, resulting in the enhancement of numerical stability that such control can generate (Travis and Mueller 1989).

Genetic effects: life history traits

Genetically based differences in life histories between the Trout Pond and Wacissa River populations were most apparent in two traits, the embryo mass and the number of embryos per brood. However, population differences in these traits were only evident under a subset of the environmental conditions; changes in density acted to either magnify or obscure differences among stocks. For example, in low density, the mean embryo mass of WWWW females exceeded that of the TTTT females by [sim]40% but, at high density, embryo masses were not significantly different. There was no significant difference in brood size between the TTTT and WWWW females at low density (although the mean TTTT brood size was 20% larger than the brood size of WWWW females). This pattern was reversed at high density; WWWW females carried 25% more offspring per brood than TTTT females and this difference was significant.

The stock-specific responses of each trait suggests that the natural populations have evolved different responses to density. We examined this possibility by plotting the mean values for each of these traits (adjusted for female size variation) against the cumulative population density (the summed density of each experimental population until the sample date; Fig. 10). The cumulative density is important to consider in this case as this measure incorporates the history of population density in a given tank; a variable that is likely to affect available resources. Fitting a linear least squares regression line to these data indicates that the general response to density is similar in both populations, although clearly the Wacissa River stock has a greater range of offspring size, while the Trout Pond stock exhibits a greater range in offspring numbers. Of course there is no a priori reason to believe that these relationships are linear; adding a higher order term to the regression model improves the fit of th e model to the data (as expected) and also begins to reveal divergent responses of these populations to changes in density (not shown). Nonetheless, given the post hoc nature of these analyses, all we are prepared to say at this point is that these populations may have evolved different norms of reaction in response to density, but the degree to which they differ and the nature of the response requires additional experiments under more controlled conditions.

The patterns of inheritance of embryo mass and brood size among stocks provide evidence that the effects of the Trout Pond and Wacissa River "alleles" are trait- and environment-specific, and also depend on the genetic composition of the stock. Considering embryo mass first, strong additive and nonadditive allelic effects contributed to stock differences in low density. The relatively large nonadditive effects appeared to result from a combination of both dominance and epistasis. This can be seen by first comparing the mean values of the pure Trout Pond and Wacissa River stocks with that of the intermediate hybrid (TTWW). The embryo size of two stocks containing W alleles in this comparison were not different, but were significantly larger than embryos of the TTTT stock. Considered alone, this pattern would indicate complete dominance of the W alleles (regardless of the number of loci that actually affect the mean value of this trait). However, extending this comparison over all stocks reveals a more complex picture of the nature of inheritance of this trait. Specifically, the mean size of TWWW embryos is smaller than those of the WWWW and TTWW stocks (even though the TWWW stock is assumed to have a higher proportion of W alleles than the TTWW stock). Thus, the degree of dominance of the W alleles appears to depend in part on the genetic background of the individual, and illustrates the potential importance of epistasis in determining the mean trait values.

While stocks were not significantly different in brood size at low density, the rank order of stock means for brood size was reversed compared to that of embryo mass. This reflects the trade-off in offspring size and number and also suggests that additive and nonadditive genetic effects influence inheritance of this trait. At high density, significant genetic differences among stocks resulted solely from additive genetic effects indicating that the allelic effects on this trait are environment dependent.

Of course our interpretation of the genetic bases of trait variation across stocks is based on simple analyses of patterns derived from population means. A more accurate picture of the genetic details underlying the patterns of inheritance of these traits requires a more detailed quantitative genetic study, and at the minimum would necessitate a controlled mating design (see Lynch and Walsh 1998).

Genetic effects: population level traits

Genetic differences among the stocks were clearly reflected in the differences in the initial rates of population growth; however, those differences were no longer apparent once the populations reached the carrying capacities of the tanks. The population growth rate of the TTTT stock grew as much as 70% more rapidly (22% on the natural log scale shown in Fig. 1A) than the WWWW stock, and the genetic intermediates were generally aligned in accordance with their relative proportions of T and W alleles. Two factors, brood size and age at maturity, probably contribute to this pattern. First, brood sizes of TTTT fish were slightly larger than those of WWWW fish at low densities, although the difference was not significant. The higher proportion of immatures in the TTTT replicates by the September census is consistent with this observation. Second, TTTT fish may mature at smaller sizes than WWWW fish (the trend was always in this direction and was statistically significant in one period). In this species (Henrich 1986, Forster-Blouin 1989), and in all poeciliids studied to date, smaller size at maturation is associated with a shorter time to maturation, for a given density and resource level (Kallman 1989, Travis 1989). Thus, genetically based distinctions among stocks that were not statistically distinguishable or were not directly measured, (e.g., time to maturity, inter-brood intervals) probably combined to contribute to the differences observed among stocks in initial population growth rates.

Interestingly, the large difference in initial population growth rates did not lead to differences in subsequent population trajectories. This is an unexpected result. If we assume that a simple logistic model of population growth with a time lag can describe the dynamics of our populations, differences in population growth rates such as those seen between the stocks should have produced dramatically different population trajectories (May 1974). There are at least two (not mutually exclusive) explanations for the observed patterns. First, the timing of the winter shutdown of reproduction coincided with the populations reaching the carrying capacity of the tanks (in phase I); this coincidence may have prevented any drastic overshoot of the carrying capacity of the tanks by the faster growing stocks and so stabilized the population size. An alternative explanation is that the females of the TTTT and TTTW stocks were finely tuned to density changes, adjusted their reproductive output and so minimized time lag e ffects.

There was no evidence of a trade-off across stocks between the capacity for rapid population increase and carrying capacity, a result found in many other experimental studies on a variety of organisms, including Drosophila spp. (Ayala 1965a, 1968), Escherichia coli (Luckinbill 1978), Paramecium spp. (Luckinbill 1979), and Tribolium castaneum (Schlager 1963). However, there are cases in which a trade-off between population growth rate and carrying capacity has been found (Mueller 1997), making it difficult to generalize about the conditions under which such a trade-off may occur.

We hypothesize that there is a trade-off in H. formosa, but that it occurs through the plastic response of offspring size and number to changes in density. Although there was no inter-stock difference in the total amount of biomass allocated to late stage embryos, the way that this energy was packaged across density gradients differed among stocks. At higher densities total reproductive allocation declined across all stocks but TTTT stocks reduced the brood size much more than the WWWW stocks. In contrast, WWWW stocks reduced offspring size more than did the TTTT stocks in response to increased density. The proportion of the populations composed of immatures did not differ between stocks at the higher densities, suggesting one of two possibilities. Either the TTTT juveniles were experiencing slightly higher survivorship than the WWWW juveniles or the TTTT stocks had shorter intervals between successive broods than WWWW stocks. Both of these would have given the stocks an equivalent net reproductive rate at t he higher densities. However, inter-brood intervals did not differ between these two stocks when examined in the lab following the end of this experiment (Leips 1997). This suggests that juvenile survivorship differed between stocks at high density. If this was the case, the reduced survivorship of the WWWW offspring may have been a function of their substantially reduced offspring sizes at the higher densities: larger offspring are more viable than smaller ones in laboratory conditions (Henrich 1988). The minimal effect of density on the offspring size of the TTTT stocks may have translated into a minimal decrease in juvenile survivorship. We propose that the trade-off in reproductive performance among stocks has two elements. The first trade-off is that the ability to have high fecundity at low density comes at the cost of greatly reduced fecundity at high density (exemplified by the response of offspring numbers of TTTT stocks to density). A different kind of trade-off occurs with the WWWW stocks. In this case, the reduction in offspring size at higher density forces a decrease in offspring viability. The net effect is that because the responses to density differ among stocks, the trade-off with density is not reflected in different carrying capacities.

This explanation does not address why these reproductive traits in the two natural populations respond differently to density. One hypothesis is that the populations may differ due to drift, and/or relative differences in the degree of inbreeding. In one experiment on laboratory populations of Drosophila melanogaster, inbred lines had reduced population growth rates but similar carrying capacities compared to wild type lines (Mueller and Ayala 1981). Although this pattern is similar to the one we observed in our study, differences in the degree of inbreeding between H. formosa populations is not a likely explanation because there was no clear evidence of inbreeding depression in the pure stocks from either population. An alternative hypothesis is that fish in Trout Pond and the Wacissa River experience characteristically different density regimes that have selected for different combinations of offspring size and number in each habitat. The Wacissa River population not only has a much higher average density, but also exhibits a higher range of densities during the breeding season than Trout Pond (Leips and Travis 1999). The Wacissa River environment may place a premium on enhanced early survival, and larger mean sizes of offspring may well represent the evolutionary response (Brockelman 1975). The greater plasticity in offspring size in the Wacissa River population may also be advantageous given the large range of population densities that occur in this habitat across seasons. In the laboratory, females in high density increase the size of their offspring when resources are not limited; at low density offspring sizes are reduced, but the rate of offspring production increases (F. H. Rodd and J. Travis, unpublished data). In the current experiment, the net response of offspring size to increased density probably resulted from the joint effects of reduced food availability (Reznick et al. 1996) and the density of conspecifics. In Trout Pond, where densities are consistently low, the favored strategy appears to be the production of higher offspring numbers and a relative inflexibility of offspring size. Even at low density, offspring sizes of the pure Trout Pond stocks never approached that of the pure Wacissa River stocks. Thus, the different responses to density may exist because densities never drop to the Trout Pond range in the Wacissa River and never rise to the Wacissa range in Trout Pond during the breeding season (Leips and Travis 1999). Therefore, selection pressures are presumably quite different in the two localities and so may select for different norms of reaction.

In a common garden experiment similar to ours, Scribner (1993) found no trade-off in population growth rate and carrying capacity in a comparison of two species of poeciliid fish, Gambusia affinis and G. holbrooki, and their interspecific hybrid. Also, despite finding genetically based differences in gestation time, age and size at maturity, and individual growth rates, no differences in population growth rates among the species or the hybrid were found although there were differences in the equilibrium population sizes. Importantly though, females of the Gambusia species and the hybrid had similar fecundities (Scribner 1993). If fecundity differences as a function of density drive differences in population growth rate (between species or populations), this may explain our disparate results with regard to population growth rates. Additionally, the differences Scribner observed in carrying capacities were correlated with differences in body size distributions of the populations and offspring recruitment. Our stocks exhibited no differences in either of these traits.

The role of intrinsic characteristics in population regulation

The reproductive characteristics of this species may be an important intrinsic feature affecting population regulation. Females produce offspring continuously throughout the breeding season, allowing constant adjustment of allocation to reproduction in response to environmental change. Direct nutritional provisioning to developing offspring also provides females with a direct mechanism to alter offspring phenotypes in response to changes in environmental conditions. One such change that occurs during the breeding season is population density (Leips and Travis 1999). The current study showed a strong effect of density on most reproductive traits, both directly and also indirectly through the effects of density on female body size that could lead to population regulation. While there have been a number of studies on how maternal effects influence offspring fitness (reviewed by Mousseau and Dingle 1991, Bridges and Heppell 1996) there are few studies that have examined their influence on population regulation ( but see Ohgushi 1995, Rossiter 1995). Investigation of these phenotypic responses as mechanisms for population regulation, or as mechanisms that account for the variation among groups in their ability to respond to perturbations, would appear to be a fertile area for additional research. In any case, the results of this study indicate clearly that population dynamics are driven by intrinsic characteristics as well as the more obvious external agents that influence mortality, growth, and reproduction.

ACKNOWLEDGMENTS

We thank M. Allen, C. Baer, C. Bowling, M. Childress, A. Davis, T. D'Souza, C. Hays, C. Johnson, C. Kindell, M. Kuhlmann, N. Martin, T. McGovern, C. McManus, M. McManus, T. Miller, C. Morrison, M. Ptacek, K. Silvestre, T. Spears, A. Weglinski, and A. Winn for help at the cattle tanks. Kim Riddl[acute{e}] provided technical help with the epiflourescent microscope. Karen Graffius at the F.S.U. Mission Road Greenhouse helped in a variety of ways with the set up and maintenance of the cattle tanks. C. Baer, L. Horth, K. Hughes, M. McPeek, J. Richardson, P. Wainwright, A. Winn, D. Reznick, and two anonymous reviewers provided helpful comments on the manuscript. Support for this research was provided by a grant from Sigma Xi (to J. L.), a Florida State University Fellowship (to J. L.), the NSERC (to F. H. R.), and two NSF grants (DEB 92-20849 and BSR 88-18001 to J.T.)

(1.) Present address: Department of Genetics, Box 7614, North Carolina State University, Raleigh, North Carolina 27695-7614 USA. E-mail: jwleips@unity.ncsu.edu.

(2.) Present address: Department of Zoology, University of Toronto, Toronto, Ontario, Canada M5S 3G5.

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                             Breeding design.
          [F.sub.1] off-                   [F.sub.2] off-
Parentals spring         [F.sub.1] crosses spring         [F.sub.2] crosses
TT X TT   TT             TT X TT           TT             TT X TT
                                                          TT X TW,
                                                           TT X WT
                         TT X WW           TW             TW X TW
                                                          TW X WW,
                                                           WT X WW
WW X WW   WW             WW X WW           WW             WW X WW
                           Expected [F.sub.3]
Parentals [F.sub.3] stocks genotypes [+]
TT X TT   TTTT             100% TT
          TTTW             50% TT,
                            50% TW
          TTWW             25% TT,
                            50% TW,
                            25% WW
          TWWW             50% WW,
                            50% TW
WW X WW   WWWW             100% WW
Note: TT = Trout Pond, WW = Wacissa
River, TW = hybrid (For the [F.sub.2]
crosses, WT = hybrid produced from a
Wacissa dam and Trout sire, TW =
hybrid produced from a Trout dam and
Wacissa sire).
(+.)Expected genotypic composition of
[F.sub.3] stock individuals.
                 Mean survival rates of males and females
                   of each stock [pm] 1 SE using pooled
                          data from both phases.
           Nov-Dec             Apr-Jun          Jun-Aug
   Stock   Survival rate  N Survival rate  N Survival rate  N
A) Males
   TTTT    0.82 [pm] 0.10 4 0.26 [pm] 0.12 3 0.44 [pm] 0.22 2
   TTTW    0.83 [pm] 0.05 4 0.42 [pm] 0.14 4 0.25 [pm] 0.12 4
   TTWW    0.84 [pm] 0.08 4      1.0       1      0.39      1
   TWWW    0.79 [pm] 0.03 4 0.21 [pm] 0.09 3 0.66 [pm] 0.13 3
   WWWW    0.96 [pm] 0.04 3 0.59 [pm] 0.12 3 0.52 [pm] 0.40 2
B) Females
   TTTT    0.90 [pm] 0.04 4 0.63 [pm] 0.37 2 0.53 [pm] 0.13 2
   TTTW    0.89 [pm] 0.05 4 0.45 [pm] 0.11 3 0.50 [pm] 0.10 4
   TTWW    0.86 [pm] 0.09 4      1.0       1      0.42      1
   TWWW    0.89 [pm] 0.06 4 0.32 [pm] 0.03 3 0.84 [pm] 0.04 3
   WWWW    0.80 [pm] 0.15 3 0.65 [pm] 0.18 3 0.40 [pm] 0.04 2
Note: N = sample size (number of
replicate populations).
                 Analysis of covariance summary statistics
                  for survival rates of males and females
                   by season using pooled data from both
                                  phases.
Dates   Sex    Source   df     F          P        [r.sup.2]
Nov-Dec Male   Density 1, 13  6.82            0.02   0.27
               Stock   4, 13  0.08              NS
        Female Density 1, 13 12.85 [less than]0.01   0.41
               Stock   4, 13  1.05              NS
May-Jun Male   Density 1, 6   0.01              NS
               Stock   3, 6   0.07              NS
        Female Density 1, 6  15.92 [less than]0.01   0.51
               Stock   3, 6   2.72            0.12
Jun-Aug Male   Density 1, 7   4.44            0.08
               Stock   3, 7   0.05              NS
        Female Density 1, 7   3.56            0.11
               Stock   3, 7   7.0             0.02   0.69
Note: The statistic [r.sup.2] is the
coefficient of determination.
                    Mean recruitment rates of males and
                   females of each stock [pm] 1 SE using
                       pooled data from both phases.
               Nov-Dec            Apr-Jun            Jun-Aug
   Stock   Recruitment rate N Recruitment rate N Recruitment rate N
A) Males
   TTTT     0.03 [pm] 0.02  4  0.32 [pm] 0.12  2  0.26 [pm] 0.16  2
   TTTW     0.07 [pm] 0.03  4  0.29 [pm] 0.08  3  0.06 [pm] 0.05  4
   TTWW     0.03 [pm] 0.01  3  0.25 [pm] 0.18  3       0.10       1
   TWWW     0.05 [pm] 0.01  5  0.28 [pm] 0.08  4  0.19 [pm] 0.08  3
   WWWW     0.15 [pm] 0.06  3  0.23 [pm] 0.16  2  0.21 [pm] 0.12  3
B) Females
   TTTT     0.27 [pm] 0.12  4  0.38 [pm] 0.24  2  0.33 [pm] 0.15  2
   TTTW     0.29 [pm] 0.15  4  0.36 [pm] 0.18  3  0.12 [pm] 0.04  4
   TTWW     0.09 [pm] 0.07  3  0.33 [pm] 0.33  3       0.33       1
   TWWW     0.13 [pm] 0.06  5  0.23 [pm] 0.10  4  0.23 [pm] 0.06  3
   WWWW     0.30 [pm] 0.10  3  0.34 [pm] 0.05  2  0.38 [pm] 0.12  3
Note: N = number of replicate
populations from which the estimate
was made.
                      Analysis of covariance summary
                    statistics for recruitment rates of
                    juvenile males and females into the
                  adult population by season using pooled
                          data from both phases.
Dates   Sex    Source   df    MS     F           P       [r.sup.2]
Nov-Dec Male   Density 1, 13 0.053  8.66            0.01   0.28
               Stock   4, 13 0.014  2.22              NS
        Female Density 1, 13 0.670 64.74 [less than]0.01   0.72
               Stock   4, 13 0.028  2.89            0.06
May-Jun Male   Density 1, 6  0.020  0.65              NS
               Stock   3, 6  0.007  0.24              NS
        Female Density 1, 6  0.044  0.81              NS
               Stock   3, 6  0.025  0.46              NS
Jun-Aug Male   Density 1, 7  0.209  9.83            0.02   0.87
               Stock   3, 7  0.008  0.37              NS
        Female Density 1, 7  0.122 13.55 [less than]0.01   0.85
               Stock   3, 7  0.130  1.42              NS
                   Analysis of covariance of mean female
                   body size using pooled data from both
                                  phases.
Month Source   df     F           P        [r.sup.2]
Sep   Density 1, 6   5.17             0.06
      Stock   4, 6   1.70               NS
Nov   Density 1, 21 47.99  [less than]0.01   0.66
      Stock   4, 21  1.02               NS
Dec   Density 1, 24 52.64  [less than]0.01   0.66
      Stock   4, 24  0.53               NS
Mar   Density 1, 23 10.67  [less than]0.01   0.81
      Stock   4, 23  0.64               NS
May   Density 1, 21 32.39  [less than]0.01   0.52
      Stock   4, 21  2.097              NS
Jun   Density 1, 12  5.40             0.04   0.23
      Stock   3, 12  2.05               NS
Aug   Density 1, 10  1.86             0.20
      Stock   3, 10  0.57               NS
                 Analysis of covariance of minimum female
                  body sizes using pooled data from both
                                  phases.
Month Source   df     F           P        [r.sup.2]
Sep   Density 1, 6    5.61            0.06
      Stock   4, 6    1.16              NS
Nov   Density 1, 15  29.55 [less than]0.01   0.61
      Stock   4, 15   0.98              NS
Dec   Density 1, 19  33.46 [less than]0.01   0.61
      Stock   4, 19   0.71              NS
Mar   Density 1, 23 118.88 [less than]0.01   0.81
      Stock   4, 23   0.80              NS
May   Density 1, 21  47.20 [less than]0.01   0.56
      Stock   4, 21   4.04            0.02   0.19
Jun   Density 1, 11   5.50            0.04   0.50
      Stock   3, 11   1.20              NS
Aug   Density 1, 10   8.30            0.02   0.45
      Stock   3, 10   0.01              NS
                 Analysis of covariance of mean male body
                 size using pooled data from both phases.
Month Source   df     F           P        [r.sup.2]
Sep   Density 1, 8   0.126              NS
      Stock   4, 8   1.362              NS
Nov   Density 1, 18 30.48  [less than]0.01   0.59
      Stock   4, 18  0.67               NS
Dec   Density 1, 22 50.44  [less than]0.01   0.67
      Stock   4, 22  0.77               NS
Mar   Density 1, 23 39.72  [less than]0.01   0.63
      Stock   4, 23  0.12               NS
May   Density 1, 18 30.95  [less than]0.01   0.60
      Stock   4, 18  0.734              NS
Jun   Density 1, 8  16.8   [less than]0.01   0.32
      Stock   3, 8   4.60             0.04   0.26
      D X S   3, 8   4.54             0.04   0.26
Aug   Density 1, 9   4.10             0.07
      Stock   3, 9   1.24               NS
                  Analysis of covariance of minimum male
                   body size using pooled data from both
                                  phases.
Month Source   df     F          P        [r.sup.2]
Sep   Density 1, 8   0.00              NS
      Stock   4, 8   0.35              NS
Nov   Density 1, 18 12.88 [less than]0.01   0.83
      Stock   4, 18  2.18              NS
Dec   Density 1, 22 91.63 [less than]0.01   0.79
      Stock   4, 22  0.46              NS
Mar   Density 1, 23 55.99 [less than]0.01   0.93
      Stock   4, 23  0.38              NS
May   Density 1, 18 30.93 [less than]0.01   0.60
      Stock   4, 18  0.73              NS
Jun   Density 1, 11  8.65           0.013   0.34
      Stock   3, 11  1.13              NS
Aug   Density 1, 9   3.66            0.09
      Stock   3, 9   2.97            0.09
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Author:LIEPS, JEFF; TRAVIS, JOSEPH; RODD, F. HELEN
Publication:Ecological Monographs
Article Type:Statistical Data Included
Geographic Code:1U5FL
Date:May 1, 2000
Words:16191
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