Volatility in the effective size of a freshwater gastropod population

Abstract Despite the utility of gastropod models for the study of evolutionary processes of great generality and importance, their effective population size has rarely been estimated in the field. Here, we report allele frequency variance at three allozyme‐encoding loci monitored over 7 years in a population of the invasive freshwater pulmonate snail Physa acuta (Draparnaud 1805), estimating effective population size with both single‐sample and two‐sample approaches. Estimated N e declined from effectively infinite in 2009 to approximately 40–50 in 2012 and then rose back to infinity in 2015, corresponding to a striking fluctuation in the apparent census size of the population. Such volatility in N e may reflect cryptic population subdivision.


| INTRODUCTION
Since the introduction of the concept by Wright (1931), effective population size (N e ) has been adopted as a parameter in scores of evolutionary models, adaptive and neutral alike (Crow, 2010). The concept has found important applications in animal breeding (Caballero, Santiago, & Toro, 1996) and in conservation biology (Nunney & Elam, 1994). Two categories of methods to estimate N e from field data were developed in the early 1980s, a single-sample approach based on disequilibrium between alleles at unlinked loci and a two-sample approach based on variance in allelic frequencies between generations (Caballero, 1994).
Several single-sample methods not relying on linkage disequilibrium have more recently been proposed.
Despite the importance of the concept, however, effective population size has rarely been estimated for any gastropod population in the field. Crow and Morton (1955) used variance in progeny number to estimate the N e /n ratio in a laboratory culture of the freshwater pulmonate Lymnaea (Pseudosuccinea) columella. The earliest field estimates were those of Murray (1964) and Greenwood (1974), who applied simple single-sample approaches to shell color polymorphism in an English population of the important land snail model Cepaea nemoralis. But another thirty years would elapse before estimates of effective population size were offered for other land snail populations, those of Arnaud and Laval (2004) using microsatellite markers and a two-sample method, and Ursenbacher, Alvarez, Armbruster, and Baur (2010) using a one-sample approach.
We are aware of two estimates of the effective size of marine gastropod populations, both inhabiting the European intertidal. Fernandez et al. (2005) followed variation at allozyme-encoding loci over 14 years in incipient species of Littorina saxatilis, estimating effective population size using a two-sample approach. Riquet, Le Cam, Fonteneau, and Viard (2016) analyzed microsatellite variation in an invasive population of Crepidula fornicata over 9 years, comparing both one-sample and two-sample estimates.
In the freshwater gastropods, Meunier, Hurtrez-Bousses, Durand, Rondelaud, and Renaud (2004) used both one-sample and two-sample analyses of microsatellite polymorphism to estimate the effective sizes of six French populations of the (predominantly self-fertilizing) pulmonate Lymnaea (Galba) truncatula. Microsatellites and two-sample techniques were also used by Trouve, Degen, and Goudet (2005) on six populations of L. truncatula sampled from Switzerland. The literature contains two single-sample microsatellite studies on Chinese populations of viviparid snails-Bellamya quadrata  and B. purificata .
Native to North America, invasive populations of P. acuta have been introduced around the world and are now established on six continents, typically in rich, disturbed, and lentic environments (Albrecht, Kroll, Terrazas, & Wilke, 2009;Dillon, Wethington, Rhett, & Smith, 2002). The snail is simultaneously hermaphroditic and capable of self-fertilization (Dillon, McCullough, & Earnhardt, 2005), although outcrossing is preferred (Escobar et al., 2011;Wethington & Dillon, 1997). Generation time in the laboratory can be as short as 6 weeks (Wethington & Dillon, 1993), although wild populations typically complete only one or two generations per year, both effectively semelparous (Life cycles A or C of Dillon, 2000: 158).
We originally sampled the population of P. acuta inhabiting the Quarterman Park "Duck Pond" in North Charleston, SC, as part of a 1991 population genetic survey of the Carolina Sea Islands (population "NPK" of Dillon & Wethington, 1995). The population demonstrated allozyme variation interpretable as the product of codominant alleles segregating in Mendelian fashion at three loci: isocitrate dehydrogenase (Isdh), 6-phosphogluconate dehydrogenase (6pgd), and esterase-3 (Est3). Mendelian inheritance at the (strong, slow) Est3 locus has been confirmed by Dillon and Wethington (1994).
The Duck Pond drains directly into the brackish Cooper River, effectively isolating the population of freshwater snails it contains by both land and sea. The nearest neighboring population of P. acuta is probably that inhabiting the upper, freshwater marshes of Filbin Creek, approximately 2 km north overland. Ducks and other waterfowl doubtless visit both habitats, providing some opportunity for genetic exchange, albeit infrequent. The effects of migration on N e have been studied by Gilbert and Whitlock (2015).

| MATERIALS AND METHODS
The Quarterman Park Duck Pond (32.87822, −79.98077) was constructed from a marshy embayment of the Cooper River in the early 20th century. For most of its history, it was tidally influenced and slightly brackish, but recent drainage improvements have rendered it entirely fresh, fed by local runoff. Its area at present is approximately 1.0 hectare, and depth is no more than 2 m. The pond is maintained by city personnel at irregular intervals and has been kept free of macrophytic vegetation in recent years. Water temperatures can rise above 35°C during summer months, depressing dissolved oxygen to low levels, despite city efforts at artificial aeration.
Its population of P. acuta reaches maximum density on allochthonous leaves and debris floating at the eastern (windward) end of the pond, at the drain.
We visited the pond each spring from 2009 to 2015, beginning in March, examining debris at the eastern end to qualitatively assess snail densities. If the apparent census size was sufficient to yield several hundred snails with reasonable effort, an annual sample was taken. Otherwise, we postponed the sample and returned a few weeks later. Approximately 150-200 P. acuta were ultimately sampled every spring, with one exception. The exception was 2012, when the snail population never reached an abundance at which it could be sampled, from March to August.
Snails collected at each sampling year were returned to the laboratory and frozen individually in 80-160 μl of tris tissue buffer for analysis of allozyme polymorphism. We used horizontal starch gel electrophoresis in a TEB8 buffer system to resolve variation at the Est3, Isdh, and 6pgd loci and an aminopropylmorpholine pH 6 buffer system for a second examination of Isdh and 6pgd. Details regarding our electrophoretic methods, including a description of our equipment and recipes for all stains and buffers employed, have been published by Dillon (1992) and Dillon and Wethington (1995). F I G U R E 1 Physa acuta (9 mm shell length), courtesy D. Liebman Allele frequencies and tests of fit to Hardy-Weinberg expectation were calculated using GenePop version 4.5.1 (Raymond & Rousset, 1995;Rousset, 2008). Values of F IS were computed using the method of Weir and Cockerham (1984), and exact p-values were by the Markov chain method.
NeEstimator v2.01 is freely available software designed to estimate effective population size using three single-sample methods and three-two-sample (moment-based temporal) methods (Do et al., 2014). Among the single-sample methods, Gilbert and Whitlock (2015) reported that the linkage disequilibrium (LDNe) method of Waples and Do (2008) consistently returned the lowest root square mean error across the range of effective population numbers simulated, absent migration.
The three-two-sample methods implemented by NeEstimator 2.01 employ the standard temporal method (ST) of Waples (1989), with different approaches to computing standardized allele frequency variance: the Fc of Nei and Tajima (1981), the Fk of Pollak (1983), and the Fs of Jorde and Ryman (2007). The simulations of Gilbert and Whitlock (2015) suggested that all three of these two-sample methods perform with equivalent efficiency. Thus, we elected to estimate the effective population size of the Quarterman Park P. acuta population using four approaches: LDNe, STFc, STFk, and STFs. Jackknife methods were used to calculate 95% confidence intervals (CI) for all N e estimates.

| RESULTS
We resolved allozyme variation apparently encoded by two codominant alleles at the Est3 and 6pgd loci and three codominant alleles at Isdh. These alleles were named by the mobility of their allozyme bands relative to the standards set by Dillon and Wethington (1995) and plotted by their frequencies in Figure 2.
Sample sizes, values of F IS , and values of p from goodness-of-fit tests to Hardy-Weinberg expectation are reported in Table 1. Over the entire data set of 3 loci × 6 years, 15 of the values of F IS were positive, some strikingly so, and three were slightly negative. Four values of F IS suggested significant heterozygote deficiencies (three at the Est3 locus and one at 6pgd), although not significant after Bonferroni correction.
The six single-sample estimates of effective population size based on linkage disequilibrium between the three loci are reported at the bottom of Table 1, with 95% CI. Table 2 shows the five-two-sample estimates of effective population size based on allele frequency variance across pairs of consecutive samples. Each two-sample calculation was performed using Fc, Fk, and Fs methods, yielding 3 × 5 = 15 N e estimates, with confidence intervals. Both the effective size and the apparent census size of the P. acuta population in the Quarterman Duck Pond apparently returned to many thousands (at minimum) in just 2 years, perhaps four generations. So F I G U R E 2 Allele frequencies at three allozyme-encoding loci in the Quarterman Park Physa acuta population, sampled over 7 years. Bars are 95% CI the most obvious hypothesis to account for the depression in effective size observed between 2011 and 2013 would be a population bottleneck. But N e is not expected to recover from such a striking bottleneck event until many generations have passed, absent migration (Caballero, 1994).

| DISCUSSION
A less obvious hypothesis might be fluctuation in the selfing rate, such that the population of P. acuta in Quarterman Park shifted from outbreeding to inbreeding and then back again over the study interval.
The only estimates of N e remotely comparable to ours in the published literature are the works of Meunier et al. (2004) and Trouve et al. (2005) on European populations of the preferentially selfing Lymnaea (Galba) truncatula. The French populations studied by the former authors generally demonstrated N e < 30, and the Swiss populations studied by the latter N e < 10. But the selfing rates inferred for all L. truncatula populations in both studies, estimated from F IS , consistently exceeded 80%.
The heterozygosities we observed in our study population of P. acuta did not vary from expectation through our 7-year observation period.
We suggest that cryptic population subdivision may be the most likely hypothesis to account for the apparent volatility of N e in our 7-year record. We sampled the Quarterman Park population of P. acuta at the east end of the pond for convenience. Snails were also observed elsewhere around the entire margin of the one-hectare pond, but not in densities sufficient to sample in the quantities required. Perhaps the striking dip in apparent population census size we observed in 2012 was localized on the east end, and its subsequent recovery was due to immigration from elsewhere within a subdivided population. Some of the most influential studies of population subdivision published to date have been conducted using land snail models. Cain and Currey (1963) described small-scale variation in the frequencies of shell color morphs in the English land snail Cepaea as "area effects," attributing the phenomenon to genetic drift. Among the earliest examples of parapatric speciation to be proposed was that of Murray and Clarke (1968), working with the localized clines in shell color polymorphisms demonstrated by the tropical land snail, Partula. Selander and Kaufman (1975)