Editor’s Note. The research results reported below were originally published in my 1982 dissertation , extracted for Biological Conservation back in 1988 , and more completely published in the FMCS Newsletter Ellipsaria just last year , if you are looking for something citable.
Last month we left our hard-working graduate student in his carrel at the University of Pennsylvania library, xeroxing manila-folders-full of references on intrapopulation dispersal in freshwater gastropods . And planning, as he did, his own study to see if gene flow of such slow tempo but inexorable advance might be sufficient to maintain panmixia in populations of his own favorite study organism, Pleurocera (Goniobasis) proxima, in streams of the southern Appalachians.
I already had a great study site in mind. In the fall of 1978, I had conducted a preliminary survey of allozyme variation in pleurocerid populations across a 100 km swath of the Virginia / North Carolina border using old-style starch gel electrophoresis . Almost all 12 of the populations I surveyed were almost all homozygous at almost all allozyme loci. But I did find one population of P. proxima inhabiting a small tributary of the Yadkin River in NW North Carolina demonstrating four alleles at the octopine dehydrogenase locus (Odh) and two alleles at the mannose-phosphate isomerase locus (Mpi).
|Naked Creek culvert, 1980|
Focusing first on the 10 meters of stream between sites 2 and 3. Although the graph below does not evince especially striking variation in the frequencies of the most common allele, Odh106, the jump in Odh 113F at the expense of Odh109F between sites 2 and 3 was significant at the 0.05 level. This is clear evidence of a barrier to dispersal, much like rocky rapids served as a barrier to the dispersal in Bovbjerg’s population of Campeloma . It is hard to escape the conclusion that the evolution of the Naked Creek population of Pleurocera proxima has indeed been directly affected by a corrugated metal pipe.
Further downstream, we see evidence of isolation by distance. Although Odh106 remained the most common allele down the 5 km length of stream inhabited by P. proxima, the frequency of Odh109F continued to increase at the expense of Odh113F, such that Odh109F became the second-most common allele at site 7. As far as I can tell, there are no waterfalls or other barriers to dispersal in that section of the stream. Nevertheless, the Odh allele frequency differences among all downstream sites 3 – 7 were also significant.
I would suggest that my 1979 observations are consistent with a “Wahlund Effect in time,” rather than in space. Within-site heterozygote deficiencies may be attributable to the migration of the snails themselves. Populations of P. proxima in this part of the world demonstrate a two-year generation time – eggs laid in the early spring hatch into tiny juveniles which crawl upstream for (perhaps) 18 months, mating their second fall, continuing to crawl upstream, laying their first eggs in their second spring. And adults can live quite a few years beyond maturity, continuing to crawl upstream, continuing to lay eggs. Thus, snails are born (at least) two years upstream from where their parents were born, and possibly further. When I dropped my Surbur sampler in Naked Creek and collected a mixture of one-year-olds and two-year-olds and three-year-olds, and so forth, I was sampling a much longer section of stream bed than I imagined.
Deviations from Hardy-Weinberg expectation are conventionally quantified with the inbreeding coefficient, F. In 1978 Sewall Wright  proposed a method by which the total deviation from Hardy-Weinberg expectation in a sample taken from several subpopulations (which he called FIT) can be partitioned into two components: the deviation within subpopulations (FIS – presumably due to factors such as inbreeding, assortative mating, and so forth) and the deviation between subpopulations (FST – due to isolation by distance, barriers to dispersal, and so forth). This latter component of the inbreeding coefficient F may be used as an indirect measure of average gene flow between subpopulations.
So setting aside sites 1 and 2, which we strongly suspect are isolated by a barrier to dispersal, the values of Wright’s statistics across sites 3, 4, 5, 6, and 7 are FIT = 0.388, FIS = 0.365, and FST = 0.013 . It would appear that almost all of the deviation from Hardy-Weinberg equilibrium I recorded in the P. proxima population of Naked Creek is due to within-site factors, Wahlund Effects in time, not space.
But that little between-site value, FST = 0.013, is nevertheless highly significant . Sites 3 - 7 are all spaced approximately 1 km apart and arranged linearly in what has been called "stepping stone" fashion , migrants being exchanged by adjacent populations only. In such situations, Slatkin & Barton  have suggested a method by which values of FST can be converted to a statistic called “Nm,” the average number of migrants moving among subpopulations per generation. An FST value of 0.013 implies that the average number of P. proxima moving 1 km per generation in Naked Creek is approximately Nm = 6.5.
Now let’s take another step back and turn our attention to the P. proxima populations inhabiting Sites 8 and 9, apparently isolated from the Naked Creek population by uninhabited waters. Both populations show highly significant differences at the Odh locus , missing Odh113F entirely, as well as the (rare) Odh111.
|P. proxima in Naked Creek|
But my Naked Creek studies did not end in May of 1979. For in August, I once again found myself in Wilkes County, NC, driving down Rom Eller Road. And I was surprised to discover that the owner of the property directly above the culvert had bulldozed and cleared several acres for a house trailer. Ensuing rains had eroded the newly-exposed soils into the creek, which by August had settled in the pool at Site 3, and apparently allowed thousands of snails to pass upstream.
So in May of 1980 I returned for a second year of sampling, focused only on the area around the Rom Eller Road culvert, and just on allele frequencies at the Odh locus. By that date the sediment had cleared from Naked Creek, and the waterfall reestablished. The photo that opened this essay way up above was actually taken in May of 1980, not May of 1979, and shows the recently-cleared land directly upstream, with new grass growing.
I resampled 100 snails from sites 1, 2 and 3 in 1980, and added a fourth site approximately 500 m downstream from site 3 . And I was not surprised to discover that the Odh allele frequencies across the Rom Eller Road culvert had equilibrated. And I returned yet again in May of 1985 for a third set of samples around the Rom Eller Road culvert. And five years after perturbation, the same significant bump in Odh113F (at the expense of Odh109F) that I had observed in 1979 had become reestablished . I published a paper reporting just my results around the Rom Eller Road culvert in 1988  and left the remainder of the results from my 1979 survey to languish in my dissertation for 40 years, until just last year .
So the answer to the question with which I closed my essay last month is, no. Gradual migration upstream plus episodic migration downstream are not, apparently, sufficient to maintain panmixia in Pleurocera proxima populations. And this month I will leave you with another question, which I will not promise to answer any time soon . Given the great difficulty P. proxima obviously manifest in negotiating even 12-inch waterfalls, the achingly-slow rates at which they disperse upstream even if unobstructed, and no evidence of downstream dispersal between isolated populations whatsoever, how in the Haich-Ye-Double-Hockey-Sticks has this snail spread 500 km from southern Virginia to North Georgia on both sides of the rugged Appalachian divide?
 Dillon, R.T. Jr (1982) The correlates of divergence in isolated populations of the freshwater snail, Goniobasis proxima. Ph.D. Dissertation, University of Pennsylvania. 182 pp. Dissertation Abstracts 43: 615B
 Dillon, R.T., Jr. (1988) The influence of minor human disturbance on biochemical variation in a population of freshwater snails. Biological Conservation 43: 137-144. [PDF]
 Dillon, R. T. (2020) Fine scale genetic variation in a population of freshwater snails. Ellipsaria 22(1): 24 - 25. [PDF]
 To contextualize the research results reported here, it might help the reader to be familiar with last month’s essay:
- Intrapopulation gene flow: King Arthur’s lesson [7Sept21]
 Dillon, R.T. and G.M. Davis (1980) The Goniobasis of southern Virginia and northwestern North Carolina: Genetic and shell morphometric relationships. Malacologia 20: 83-98. [PDF]
 That’s an estimate the District Engineer offered me back in 1985.
 Neither the site numbers nor the allele numbers I am using for this essay are those that I originally used in Chapter 2 of my 1982 dissertation. I followed up my 1979 study with a second survey in 1980, and a third in 1985, and added some sites and removed others, and continued to discover new allozyme alleles as my dissertation progressed across the southern Appalachians, the numbering systems evolved. I actually made a fresh start on the site numbering systems for the note I published in Ellipsaria in 2020 , which I am following here.
 The inverse correlation between stream size and population density in P. proxima was already well-documented when I started my research program. The phenomenon is striking all over the Southern Appalachians, from Virginia to North Georgia. Pleurocera populations often reach into the hundreds per square meter in the smallest creeks, thrive in trout-sized streams, and dwindle to negligible in bass-sized rivers. It looks as though they are crawling over one another in a relentless race to the mountaintops. See:
- Crutchfield, P.J. (1966) Positive rheotaxis in Goniobasis proxima. Nautilus, 79:80-86.
- Foin, T.C. & A.E. Stiven (1970) The relationship of environment size and population parameters in Oxytrema proxima (Say) (Gastropoda: Pleuroceridae). Oecologia (Berl.) 5:74-84.
 I ultimately confirmed Mendelian inheritance at the Odh locus in a series of breeding experiments I conducted several years later. See:
- Dillon, R.T. (1986) Inheritance of isozyme phenotype at three loci in the freshwater snail, Goniobasis proxima: Mother-offspring analysis and an artificial introduction. Biochemical Genetics 24: 281-290. [PDF]
 Wright, S. (1978) Evolution and the Genetics of Populations. Volume 4, Variability within and among natural populations. University of Chicago Press.
 To calculate my values of F I used the subroutine “FSTAT” in Swofford & Selander’s BIOSYS-1. See:
- Swofford, D.L., and R.B. Selander (1981) BIOSYS-1: A FORTRAN program for the comprehensive analysis of electrophoretic data in population genetics and systematics. Journal of Heredity 72: 281 – 283.
 The significance of a value of FST based on a single locus can be estimated using a chi-square test. See:
- Workman, P.L. and J.D. Niswander (1970) Population studies on southwestern Indian tribes. II. Local genetic differentiation in the Papago. Am J Hum Genet 22: 24 – 49.
With N=500 snails, s = 5 populations and k=4 alleles, a value FST = 0.013 is highly significant (X2 = 111.0, 12 df).
 Kimura, M. and G.H. Weiss (1964) The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49: 561 – 576.
 Slatkin, M. and N.H. Barton (1989) A comparison of three indirect methods for estimating average levels of gene flow. Evolution 43: 1349 – 1368.
 Assuming the mean frequency of 24% demonstrated by allele 113F in Naked Creek, the binomial probability of drawing no individuals bearing Odh 113F in 29 attempts, as in Site 8, is 5 x 10^-6.
 It seems quaint today, but there was a time in the history of evolutionary biology when observations such as those I made at the Naked Creek culvert 1979 – 1985 might have been interpreted as evidence for natural selection. My mentor, Arthur Cain, certainly thought so. Although conscious of the evolutionary effects of barriers to dispersal in his chosen model, the land snail Cepaea nemoralis, he interpreted even very small-scale variance in the frequencies of shell color genes as adaptation to very local selective pressures. My 1985 observation that gene frequencies returned to their 1979 values after perturbation in 1980 is consistent with some sort of selective differential across the Naked Creek culvert. Arthur Cain would have hastened to point that out. Worth a footnote today, I suppose.
 But I do have an hypothesis, which I called the “jet-lagged wildebison” model of gene flow in pleurocerid populations. See:
- Mitochondrial superheterogeneity: What it means [6Apr16]