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Estimation of genetic neighborhood parameters from pollen and seed dispersal in the marine angiosperm Zostera marina L.

The extent of genetic subdivision in natural populations affects the rate of species evolution through its impact on the outcomes of ecological and genetic interactions. Genetic substructuring occurs in response to random genetic drift and natural selection, and the relative importance of each will depend on the spatial extent of gene flow (Wright 1946; Slatkin 1985). To quantify the effects of restricted gene flow on the extent of genetic differentiation in continuously distributed populations, Wright (1946) introduced the concept of the genetic neighborhood. The neighborhood describes the size of panmictic breeding units in a population and is defined as the area within which parents of a central individual can be considered to be drawn at random. Estimates of neighborhood area and the number of individuals within the neighborhood allow one to make predictions regarding the likelihood that drift creates genetic differentiation in natural populations (Wright 1946, 1951; Crawford 1984).

Neighborhood sizes estimated in natural populations of terrestrial plants suggest that both drift (Crawford 1984; Levin 1988; Fenster 1991; Campbell and Dooley 1992) and selection (Endler 1986; Schemske 1984; Kelly 1992) are important in causing observed patterns of genetic differentiation in a diversity of traits, including quantitative characters and allozymes. In contrast, we know almost nothing about the extent of gene flow in marine plants. The potential for long-distance gene flow provided by ocean currents and tides (Hedgecock 1986) suggests that neighborhood sizes in the marine environment are large. However, because a number of marine plants and invertebrates are sessile, clonal organisms, realized gene flow may be restricted, resulting in smaller neighborhoods and an increased role of genetic drift in evolutionary change. The conflicting effects of clonality and high dispersal potential on neighborhood sizes in the marine environment can only be evaluated with empirical studies.

Here I estimate neighborhood parameters in a genetically differentiated population of a clonal marine angiosperm, Zostera marina L. (eelgrass). Population-genetic substructuring has been documented for a number of marine invertebrate species (Burton 1986; Mladenov and Emson 1990) and in a few marine plant taxa (Miura et al. 1979; Bolton 1983; Innes 1984, 1988; Fain et al. 1992). Propagules carried by currents and tides can travel great distances, leading some to suggest that selection in the face of high rates of gene flow may be a major evolutionary factor contributing to genetic differentiation in populations of marine organisms (Ayre 1985; Hedgecock 1986). In addition, the high dispersal capabilities of many marine taxa may result in genetic differentiation resulting from temporal or spatial variation in colonization of available habitat (Johnson and Black 1984; Hoffman 1986; Grosberg 1987).

Aside from this study, there are no estimates of neighborhood sizes in marine organisms. Because of the logistical difficulties of estimating dispersal in the marine environment, the relative efficacies of random genetic drift and selection in causing population structure in marine organisms remain largely unexplored. I estimate the role that drift plays by calculating neighborhood parameters in eelgrass from dispersal distributions of pollen and seed. In addition, I include an estimate of outcrossing rates to describe more accurately the contribution of pollen-dispersal distances to neighborhood size. With this information, I can determine the relative importances of pollen and seed dispersal in determining neighborhood size in eelgrass.

MATERIALS AND METHODS

Study Organism

Zostera marina is a perennial angiosperm inhabiting soft-bottom marine habitats, ranging from the intertidal to depths of approximately 15 m in temperate latitudes (den Hartog 1970). It reproduces sexually by means of monoecious flowers and also undergoes extensive vegetative propagation (Phillips et al. 1983). The life span of eelgrass clones can be 20-50 yr, and sexual reproduction can begin as early as the second year (Setchell 1929; den Hartog 1970). Pollen is released in clusters of hundreds to thousands of grains, and, depending on the timing of anther dehiscence relative to tidal levels, the clusters can be transported either on or below the water surface (de Cock 1980; Cox et al. 1992). Estimates of maximum longevity of individual pollen grains range from 7-48 h (de Cock 1980; Cox et al. 1992); the actual length of time over which grains are viable is probably largely a function of water temperature (Pettit 1984). Eelgrass is self-compatible (de Cock 1980; Ruckelshaus 1994), but the mating system had not been assessed prior to this study. Seeds typically sink once shed from reproductive shoots; thus, most local dispersal occurs as a result of transport along the substratum by currents and tides (Orth et al. 1994). Longer-distance dispersal is possible by rafting of seed-bearing reproductive shoots and in the guts of migratory waterfowl that forage in eelgrass meadows (den Hartog 1970; Phillips and Menez 1988). Seed longevity is reported to be 1 yr (Phillips 1972; Orth and Moore 1983), but a low percentage of germination (approximately 10%) has been observed in 2-yr-old seeds stored in flow-through seawater tanks (Ruckelshaus, pets. obs.).

The eelgrass population that I studied is located in False Bay, San Juan Island, part of the San Juan archipelago in northern Washington state. The population occupies a 2 [km.sup.2] intertidal mudflat (i.e., plants are exposed to air during low tides), and plants are distributed in patches ranging in size from 0.25 to 4400 [m.sup.2] (mean patch size, 122.5 [m.sup.2], mode, 22.8 [m.sup.2]) (Ruckelshaus 1994). Electrophoretic analyses (n = 290 individuals, five polymorphic loci) indicate that the False Bay eelgrass population is genetically substructured; 15.4% of the genetic diversity in this population is distributed among patches (Ruckelshaus 1994).

Pollen Dispersal

The distribution of pollen dispersal distances was estimated experimentally by means of two arrays of traps designed to catch pollen released from a fixed source in the field [ILLUSTRATION FOR FIGURE 1 OMITTED]. Each array consisted of five traps affixed to a polypropylene line: one trap was positioned at each of five fixed distances from the source of pollen (3, 6, 9, 12, and 15 m). Traps were attached to alternate sides of the line to minimize their disruption of water-mediated pollen flow. Flow patterns of fluorescein dye introduced upstream of the traps confirmed that the water deflected around a trap was redirected into a linear trajectory 0.3-0.5 m beyond each trap. Traps were constructed of two 0.6 x 10 [cm.sup.2] Plexiglas squares fitted at right angles to one another by attachment to 2.5 x 30 [cm.sup.2] plywood squares (the plywood also provided flotation for the Plexiglas). The Plexiglas squares were oriented vertically in the water column (one parallel to water flow, one perpendicular), with approximately 3 cm extending above the surface of the water, and the remaining 7 cm below the surface. Each square was coated with a thin layer of petroleum jelly to capture pollen grains. An anchored buoy secured the line to the pollen source, a plastic mesh (Vexar[R]) bag containing 20-30 mature reproductive shoots of eelgrass that were releasing pollen. The far end of the line (18 m away) was tied to a slightly weighted buoy such that the polypropylene line remained taut while allowing the array to rotate freely around the pollen source with tidal and current fluctuations. This design ensured that the traps remained at fixed distances and constantly downstream of the point of pollen release.

A single experiment consisted of two arrays, each of which was deployed for 48 h (i.e., encompassed four full tidal cycles). To avoid potential contamination of the traps with pollen from naturally occurring plants, the arrays were deployed in deep water (i.e., [greater than or equal to] 3 m at lowest tide) over subtidal eelgrass beds completely lacking flowering individuals. The arrays were separated by 500 m and a floating dock; thus transport of pollen between arrays was not a concern. The bays surrounding the location of the experiments were thoroughly checked for the presence of eelgrass in flower, and no reproductive shoots were found. Because this design did not include intervening plants to interrupt pollen transport through the water, the pollen-dispersal distributions generated in these experimental arrays will most closely represent pollen transport from the edges of eelgrass patches. At the end of each experiment, the traps were collected and brought into the laboratory, where I counted the number of pollen grains on each Plexiglas square. Eelgrass pollen grains are 0.2-0.7 mm long and are readily detected under a dissecting microscope. Seven experiments were executed in June-July 1992, during the period of peak flowering in intertidal eelgrass populations in northern Puget Sound, Washington (Ruckelshaus, unpubl. data).

The distribution of pollen-dispersal distances was generated from the proportion of total grains trapped at each distance, calculated separately for each array during each experiment. The mean variance in dispersal of all experimentally determined distributions was used in calculations of neighborhood parameters (see Calculation of Neighborhood Parameters).

Seed Dispersal

The distribution of seed-dispersal distances was estimated in two ways: (1) by census of naturally occurring seeds at increasing distances from a patch (source) and (2) by census of seedlings arising from marked seeds released from a known point. Both seed-dispersal distributions were estimated in the intertidal eelgrass population in False Bay. I estimated the distribution of naturally occurring seeds by sieving 114 liters of sand and counting all seeds at each of four distances (5, 10, 20, and 50 m) along a transect extending landward in one direction from a large (85 [m.sup.2]) patch of eelgrass. The patch was assumed to be the sole source of seeds along the transect. Because no other plants occurred between the patch and the 50 m sampling point, import of seeds to the transect area from different patches is very unlikely. Sand was collected and censused in March 1992, after all seeds had been shed from parent plants (September-January).

The distribution of seed-dispersal distances was generated from the proportion of total seeds or seedlings censused at each distance.

A mark-release-recapture experiment was conducted during the same seed dispersal period described above. In October 1991, 2000 eelgrass seeds were painted with Krylon[R] "California Pink" spray paint and released at low tide from a single point in the large eelgrass patch used as the starting point for the sieving transect described above. During low tides in March 1992, all seedlings within a 50 m radius of the release point were censused. Because the seeds were released onto the sand at low tide, the only means of dispersal for these marked seeds were tidal and wave-induced transport. Because the seed coat of eelgrass remains attached to the roots of seedlings (Ruckelshaus, pers. obs.), seedlings containing pink seed coats were known to have originated from the release point and could be scored for distance dispersed.

Mating System

For estimation of the mating system, 40 reproductive shoots bearing developing seeds were collected from within the False Bay intertidal population in August 1991. The reproductive shoots were individually secured in mesh bags and stored in flow-through seawater tanks at Friday Harbor Laboratories for an additional month to allow seeds to mature fully. At least five (n = 5-10) seeds from each of 40 maternal parents were chosen for electrophoretic estimation of the mating system. In preparation of samples for electrophoresis, [TABULAR DATA FOR TABLE 1 OMITTED] embryos were first dissected out of the seed coat to improve resolution of banding patterns on the gels. Each embryo was crushed with a mortar and pestle in the "needle crushing" extraction buffer (Mitton et al. 1979), and the exudate was absorbed onto Whatman filter-paper wicks and loaded onto 11% (w/v) hydrolyzed-potato-starch gels. Two polymorphic phosphoglucomutase loci, PGM-1 and PGM-2, were stained according to procedures described by Soltis et al. (1983) and Werth (1985). Tris-EDTA-borate (pH 8.6) and morpholine-citrate (pH 6.1) gel buffer systems were used in scoring PGM-1 and PGM-2, respectively (Soltis et al. 1983; Wendel and Weeden 1989). The outcrossing rate, t, was estimated according to a maximum-likelihood procedure, and its standard error was calculated by bootstrapping (Brown and Allard 1970; Ritland and Jain 1981; Ritland 1989).

Calculation of Neighborhood Parameters

Neighborhood Area

The following formulation of neighborhood area ([N.sub.a]) was used (Crawford 1984):

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are variance in pollen- and seed-dispersal distances, respectively. The variance appropriate to this equation is the one-way, or axial, variance (Wright 1943), which is the mean of the squared dispersal distances measured in one direction along a single axis from a source individual. Pollen- and naturally occurring seed-dispersal distances were measured axially; thus, no correction in the variances of the distributions was necessary (Crawford 1984). As an additional estimate of variances in pollen- and seed-dispersal distributions, the best-fit probability density for the dispersal data was found, and the variance was calculated from the parameters of the best-fit probability function.

The calculation of [N.sub.a] from equation (1) assumes that parent-offspring dispersal distances are normally distributed. Distributions that showed significant departures from zero kurtosis were detected by a two-tailed t-test (Sokal and Rohlf 1981). For those distributions that were significantly kurtotic, I corrected in the following manner (Wright 1969, 1977):

[N.sub.a] = [2.sup.2a][Gamma] (2a + 1)[Gamma](a)[[Gamma].sup.-1](3a)[Pi][[Sigma].sup.2] (2)

in which [Gamma] denotes a gamma function, and a is approximated by the following relationship (Crawford 1984):

[log.sub.[10.sup.a]] = 0.341 [log.sub.10[[Gamma].sub.2]] - 0.156, (3)

where [[Gamma].sub.2] is equal to the kurtosis of the distribution. The estimation of neighborhood area from equation (1) also assumes that the parent-offspring dispersal distribution has a mean of zero, the population is constant in size, and the distribution of progeny among parents approximates a Poisson distribution (Crawford 1984).

Neighborhood Number

To calculate the effective number of individuals in the neighborhood, [N.sub.b], I used the following equation (Crawford 1984):

[Mathematical Expression Omitted],

where [d.sub.e] is equal to the effective density, estimated as the harmonic mean of the densities of reproductive individuals within the study area (Crow and Kimura 1970). Here I use [N.sub.b] to refer to the effective size of a neighborhood distributed within a continuous population (Slatkin and Barton 1989), to distinguish it from most reported values of [N.sub.e], in which populations are considered to be isolated islands experiencing no gene flow from other populations (Wright 1946; Slatkin and Barton 1989). To account for the mating system, the following equation was used in the calculation of neighborhood size (Crawford 1984):

[Mathematical Expression Omitted],

where t is equal to the outcrossing rate.

RESULTS

Pollen Dispersal

A total of 3524 pollen grains were trapped and counted during the pollen-dispersal experiments ([Mathematical Expression Omitted], 271 grains per run; Table 1). Pollen dispersal in eelgrass declines steadily with distance [ILLUSTRATION FOR FIGURE 2 OMITTED]; the mean proportion of pollen grains trapped dropped from 0.44 (range, 0.17-0.63) at 3 m to 0.05 (range, 0.01-0.17) at 15 m from the source. The overall mean standard deviation of pollen-dispersal distributions from all experimental runs was s = 1.1 m and ranged from 0.9-1.4 m (Table 1). The variance and kurtosis were calculated separately for pollen-dispersal distributions from each experimental run, then were combined to yield mean values. Five of the 13 pollen-dispersal distributions were significantly kurtotic, but the mean value was not ([[Gamma].sub.2] = -0.05; Table 1).

The mean one-way (axial) variance in pollen dispersal, [Mathematical Expression Omitted], is 47.3 m (range, 33.8-77.3 m) calculated by the mean-squared displacement method. For the curve-fitting method, both the pollen- and seed-dispersal distributions were best described by an exponential probability density ([R.sup.2] = 0.96 and 0.97, respectively). The [Mathematical Expression Omitted] calculated by the curve-fitting method is to 26.3 m (range, 1.0-53.3 m).

Seed Dispersal

In 456 liters of sifted sand, n = 226 seeds were found. Their dispersal from the source patch declines with distance: 83% of the total seeds collected occurred within the first 5 m, and no seeds were detected at 50 m [ILLUSTRATION FOR FIGURE 3 OMITTED]. The mean dispersal distance of these naturally occurring seeds was 1.27 m (SD = 0.71 m), and the distribution is significantly platykurtic ([[Gamma].sub.2] = -0.71; P [less than] 0.025). The mean and kurtosis of the seed dispersal distribution estimated from marked seeds ([Mathematical Expression Omitted], SD = 0.27 m, [[Gamma].sub.2] = -0.69) was similar to that generated from naturally occurring seeds and was also significantly platykurtic (P [less than] 0.025). However, only 25 marked seedlings were recovered from n = 2000 seeds; thus, seed-dispersal variances were calculated from only the naturally occurring seed-dispersal distribution. The one-way (axial) variance in seed dispersal, [Mathematical Expression Omitted], calculated by the mean-squared displacement method is 52.4 m. The [Mathematical Expression Omitted] estimated by curve-fitting is 28.3 m.

Mating System

Phosphoglucomutase locus 1 (PGM-1) and 2 (PGM-2) each had two alleles at relatively high frequencies in the False Bay population (PGM-1-1 = 0.48, PGM-1-2 = 0.52; PGM-2-1 = 0.61, PGM-2-2 = 0.39). The mating system of eelgrass in False Bay was primarily outcrossing; from allozyme analyses, the outcrossing rate, t, was estimated as 0.905 ([+ or -] 0.181).

Neighborhood Parameters

The variances in dispersal distributions estimated with both the mean-squared displacement and curve-fitting methods are high and differ by approximately a factor of two. Variances estimated by the curve-fitting method will be used throughout the results because they are smaller than those using the mean-squared displacement method. If neighborhood parameters are found to be high even when the smaller variances generated by the curve-fitting method are used, the role of drift in small neighborhoods can be confidently dismissed.

Neighborhood Area ([N.sub.a])

Neighborhood area calculated from equation (1) is 521 [m.sup.2] (SD = 112.2), when the mean [Mathematical Expression Omitted] of all pollen-dispersal experiments [Mathematical Expression Omitted] and the [Mathematical Expression Omitted] of the naturally occurring seed-dispersal distribution [Mathematical Expression Omitted] are used. [N.sub.a] is 362 or 691 [m.sub.2] when low or high values, respectively, of [Mathematical Expression Omitted] estimated from the pollen dispersal arrays are used. Seed dispersal contributes more than twice as much as pollen dispersal to the total variance in parent-offspring dispersal and therefore has a greater influence on neighborhood area. [N.sub.a] based on [Mathematical Expression Omitted] alone is 165 [m.sub.2], as compared to neighborhood area based on seed-dispersal variance alone, [N.sub.a] = 356 [m.sup.2].

The above calculations of neighborhood area assume that parent-offspring dispersal distributions are normal, an assumption that is violated for the seed- and some of the pollen-dispersal distributions measured here. Kurtosis values for the pollen-dispersal distribution are generally small and statistically indistinguishable from normal (Table 1) and therefore do not have a discernible effect on estimates of [N.sub.a]. Even after the kurtosis value from the most highly leptokurtic pollen distribution is substituted into equation (2), [N.sub.a] 167 [m.sup.2], nearly identical to the value of 165 [m.sup.2] obtained when kurtosis was not accounted for in equation (1). Likewise, neighborhood area estimated from the variance in the seed-dispersal distribution was only slightly affected by the kurtosis of the distribution in spite of its significant departure from normality; [N.sub.a] 359 [m.sup.2] using equations (2) and (3). The total neighborhood area after correction for kurtosis is [N.sub.a] = 524 [m.sup.2].

Neighborhood Number ([N.sub.b])

The effective number of individuals in a neighborhood of 524 [m.sup.2] is [N.sub.b] = 6812, calculated with an effective density of 13 reproductive shoots [m.sup.-2]. Reproductive-shoot densities in False Bay in 1990 ranged from 8.6 to 16 [m.sup.-2] (Ruckelshaus 1994), which would result in neighborhood numbers ranging from 4506 to 8384 throughout a flowering season. The most realistic estimate of [N.sub.b], calculated from equation (5), was slightly lower than the neighborhood number calculated under the assumption of random mating; [N.sub.b] = 6255 (t = 0.905).

DISCUSSION

Neighborhood Size in Eelgrass

The neighborhood parameters estimated for eelgrass here are among the highest reported for plants or animals. Water-mediated pollen and seed dispersal in the marine environment appear to result in high gene-flow distances for eelgrass. The smallest neighborhood number estimated is [N.sub.b] = 4524, which would only be relevant during periods of lowest flowering-shoot densities. The most realistic neighborhood number is [N.sub.b] = 6255, which incorporates the effects of a mating system only slightly different from random outcrossing. In development of his theory of isolation by distance, Wright (1946) suggested that, in populations consisting of neighborhoods smaller than [N.sub.b] = 200, genetic differences among neighborhoods were likely to arise as a result of the effects of drift. Because my estimates of [N.sub.b] are 10 times larger, it is clear that drift in small neighborhoods is highly unlikely to play a role in eelgrass population genetic differentiation.

Seed dispersal in Z. marina contributes most to the large neighborhood size. Neighborhood area estimated on the basis of seed-dispersal variance alone ([N.sub.a] = 356 [m.sup.2]) is more than two times greater than that based solely on pollen dispersal variance ([N.sub.a] = 165 [m.sup.2]). Contributing to this effect is the possibility that the pollen-dispersal-based neighborhood area is an overestimate because the viability of some trapped pollen grains could be less than the 48-h sampling interval (see Materials and Methods). Furthermore, because the False Bay eelgrass population is predominantly outcrossing, incorporation of the mating system does little to reduce the estimate of neighborhood number. Neighborhood size recalculated using only the variance in seed-dispersal distance is [N.sub.b] = 4628, still a number at which the effects of drift on population structure would be very weak.

There are no other studies of neighborhood sizes in water-pollinated plants to permit generalizations about the effects of pollination system on gene flow. The few estimates available for herbaceous plants with another abiotic pollination vector, wind, have smaller neighborhood areas and numbers than do plant species that are insect pollinated (Crawford 1984; Tonsor 1985; Bos et al. 1986; Levin 1988; Eguiarte et al. 1993), especially when the effects of pollen carryover and realized paternity are included in estimates (Schmitt 1980; Fenster 1991; Campbell and Dooley 1992). Wind-pollinated trees (Wright 1953; Bannister 1965) and some insect-pollinated herbs (e.g., Lithospermum caroliniense, Kerster and Levin 1968) represent exceptions to this trend; the extent to which neighborhood size can be predicted from pollination system remains unclear.

Estimates of genetic structure in the False Bay eelgrass population based on five polymorphic allozyme loci corroborate the results reported here (Ruckelshaus 1994). The eelgrass population in False Bay is significantly genetically differentiated ([F.sub.ST] = 0.154). Because Wright (1946) defined the neighborhood area as the size of the breeding unit within which mating occurs as if at random, the inbreeding coefficient within neighborhoods should approach 0. Inbreeding coefficients ([F.sub.IS]) were calculated at a number of spatial scales throughout the False Bay population, and the [F.sub.IS] were closest to 0 in patches whose area (25 m x 25 m) is close to the neighborhood size estimated here.

This report of high gene-flow distances in Z. marina offers new insight into two interesting aspects of seagrass biology. First, the large neighborhood size estimated for Z. marina here may offer a partial explanation for the astounding difference in diversity between marine and terrestrial angiosperms. Although angiosperms have inhabited the oceans since the Late Cretaceous (den Hartog 1970), there are only 48 species of marine seagrasses (Phillips and Menez 1988), compared to at least 230,000 species of terrestrial angiosperms (Raven et al. 1981). If marine angiosperms as a rule have large neighborhoods, the resulting lack of genetic isolation may contribute to lower rates of diversification than in their terrestrial counterparts. Second, high gene-flow levels may have exacerbated the susceptibility of Z. marina to a devastating disease in the 1930s. The so-called wasting disease struck on both sides of the North Atlantic and resulted in destruction of all but 1% of eelgrass populations throughout the region (Muehlstein 1989). Large neighborhood sizes would have resulted in little opportunity for eelgrass to take advantage of ecological or genetic refugia from the causative agent (possibly a marine slime mold).

Effects of Additional Biological Details

Pollen-dispersal distances here were measured in the absence of intervening vegetation and therefore may be realistic only for pollen transport from the edges of patches. Because of the distribution of eelgrass patch sizes in False Bay (mean patch size, 122.5 [m.sup.2], mode, 22.8 [m.sup.2]), estimates of pollen-dispersal distances are representative for all but those plants releasing pollen from within larger patches. Any pollen dispersing through a large eelgrass patch is likely to be trapped by neighboring vegetative or reproductive shoots, especially if pollen release occurs during low tides when transport occurs at the surface (Cox et al. 1992). Pollen-dispersal variance is therefore likely to be smaller under these conditions, resulting in smaller neighborhood areas within large patches of eelgrass (see eq. 1), but it is unlikely that pollen-dispersal distributions generated from experimental arrays are gross underestimates for even large patches in the False Bay population. Reproductive-shoot densities are lower in the largest eelgrass patches (Ruckelshaus, unpubl. data), which would increase the effective dispersal distance of pollen to stigmas, at least partially offsetting decreased dispersal resulting from intervening vegetation.

Additional details of eelgrass biology not included in calculation of the effective neighborhood number are the effects of age structure and variance in family size. Because of eel-grass' iteroparous life history, individuals of different ages and longevities will contribute to the total reproductive output of the population. Because of the potentially long life span of eelgrass clones (Ruckelshaus 1994) and the resulting higher variance among individuals in progeny number, the actual [N.sub.b] for this population may be lower than [N.sub.b] = 6255 calculated without allowance for age structure (Hill 1972, 1979; Falconer 1981; Felsenstein 1985; Heywood 1986). To assess adequately the magnitude of the change in [N.sub.b] because of age structure would require estimates of the lifetime variance among individuals in the number of offspring surviving to reproduce (Hill 1979; Waples 1991) and the mean age of reproduction for eelgrass clones. Because such life-history attributes are notoriously difficult to estimate, few studies including estimates of [N.sub.b], for long-lived perennials have considered the effects of overlapping generations (Zimmerman 1982; Gliddon and Saleem 1985; Eguiarte et al. 1993).

Incorporating the effects of another aspect of eelgrass biology, its prolific vegetative propagation, could increase or decrease estimates of neighborhood parameters. On one hand, the effective density ([d.sub.e]) of genets will decrease in areas where vegetative proliferation of ramets is high, thus reducing the effective number of individuals in the neighborhood ([N.sub.b]). To explore this effect in the False Bay eelgrass population, I set equation (4) equal to [N.sub.b] = 200, the rule of thumb offered by Wright as the neighborhood size below which the effects of drift are apparent in the distribution of genetic variation. In the face of gene flow via pollen and seed, the effective density of eelgrass would have to be less than 0.38 genets per square meter for drift to have a significant effect on population structure in False Bay. Such a low effective density is highly unlikely in a habitat such as False Bay, where the turnover of eelgrass patches results in high clonal diversity on a small spatial scale (Ruckelshaus 1994). Many eelgrass habitats are much less dynamic than False Bay, and high rates of clonal propagation may result in effective densities low enough for drift to play a significant role in causing population structure.

In addition, if effective dispersal by vegetative propagation is included in the total variance in parent-offspring dispersal, [N.sub.a] could increase (Gliddon and Saleem 1985; Gliddon et al. 1987). The intertidal eelgrass population in False Bay is characterized by high patch turnover rates (Ruckelshaus 1994), and because younger patches will be composed of individuals with lower net dispersal by vegetative growth, their neighborhood areas will be smaller than those in older patches where individuals have undergone vegetative "dispersal" for a longer period of time.

Estimation of Dispersal Variance

I used two methods to estimate the variance in dispersal distributions: (1) the traditional method of calculating the mean-squared displacement of pollen grains or seeds from a source, and (2) that of fitting the dispersal data to a best-fit probability density and calculating the variance from the probability function. The latter approach avoids potential bias in the estimates of variance because of arbitrary positioning of traps for estimates of dispersal distances. To evaluate this bias, I recalculated [Mathematical Expression Omitted] and [Mathematical Expression Omitted] using several hypothetical experimental designs in which trap distances varied. Using the exponential probability densities fitted to the original data, I estimated the number of pollen grains or seeds expected at each "new" experimental distance and then calculated the "new" variances as mean-squared displacements. With the same number of traps, the recalculated variances differed from the variances estimated with the original trap locations by as much as a factor of three. Increasing the number of traps at distances less than 5 m reduced the variance in the recalculated pollen-dispersal distribution, and traps spread more evenly across a 50-m distance resulted in a greater variance. These calculations show that the mean-squared displacement method of estimating variances is highly sensitive to the experimental design.

Here the two methods of estimating variances in dispersal distributions do not result in qualitatively different conclusions regarding the role of genetic drift in creating spatial structure. The curve-fitting method, however, allows one to evaluate errors in variance estimates resulting from trap locations, and it is a useful tool for assessing reliability in dispersal-variance estimates from field experiments.

Drift or Selection?

Estimates of neighborhood sizes from this study suggest that random genetic drift in small neighborhoods is not a primary cause of population-genetic differentiation, but the overall contribution of drift to population structure will also depend on the effects of longer-distance dispersal events and spatially varying selection. Whether selective differences among patch locations contribute to the pattern of observed differentiation in this population is the subject of ongoing study.

As previously mentioned, eelgrass seeds can be dispersed by rafting of reproductive shoots and through transport in the guts of waterfowl. The patch dynamics in False Bay are characterized by frequent patch extinctions, resulting in empty but suitable habitat for colonizing seed or vegetative shoots (Ruckelshaus 1994). Although the establishment probabilities of seeds or adults dispersed over long distances are likely to be very low (Ruckelshaus 1994), to the extent that colonization of available habitat occurs beyond the scale measured here, drift-induced genetic differences arising among patches as a result of founding events could be important (Wade and McCauley 1988).

ACKNOWLEDGMENTS

I greatly appreciate the advice and encouragement that D. Schemske has given me throughout this study. I thank A. O. D. Willows for permission to use Friday Harbor Laboratory facilities and L. Hadac for access to False Bay. B. Husband, P. Kareiva, J. Heywood, S. Williams, M. Parker, G. Vermeij, R. Paine, and two anonymous reviewers have provided helpful comments and discussion, and I am indebted to S. Shabb and D. Grunbaum for spending time with me on the mudflats during winter nights. This research was supported in part by funds from the Washington Sea Grant Program, project R/F-94, and the National Science Foundation (NSF) doctoral dissertation grant NSF BSR-9101166.

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Date:Apr 1, 1996
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