Editor’s Note – This essay was subsequently published as: Dillon, R.T., Jr. (2023c) The best estimate of the effective size of a gasttropod population, of any sort, ever. Pp 185 – 193 in The Freshwater Gastropods of North America Volume 7, Collected in Turn One, and Other Essays. FWGNA Project, Charleston, SC.
First, a quick refresher on week #4 of your population
genetics class. One of the assumptions
of Hardy-Weinberg equilibrium is that population size is effectively
infinite. If that assumption is met
(together with all the other ones) gene frequencies will not change. But if the population is small, gene
frequencies will change by sampling error, for the same reason that if I flip a
fair coin three times, there is a 25% chance of all heads or all tails. That
phenomenon is called “genetic drift.”
So, suppose we were standing on the edge of a huge field of
peas, say 100,000 plants, polymorphic at the seed color locus – green and
yellow – meeting all the Hardy-Weinberg assumptions (no selection, no
migration, random mating and all that, Note 1).
And suppose we sampled 100 plants, and shucked a bunch of pods, and
estimated the frequencies [2] of the green and yellow genes in the remaining
99,900. And then we waited a year, let
all 99,900 plants reproduce, cover the field with a new generation, and sampled
another 100. And we didn’t obtain exactly
the same gene frequencies in year 2 that we did in year 1.
Much of the reason that the year-2 gene frequencies didn’t
match the year-1 frequencies would certainly be our own sampling error – that
we sampled a finite number from year 1 and a finite number from year 2. But part of that allele frequency variance
(new term) might also be due to the sampling error of the peas themselves – only
a finite number of peas reproduced to yield the year-2 population. Might we have been wrong about that 99,900
estimate? Maybe, effectively, there weren’t
100,000 peas in the field at all?
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| The Duck Pond at Quarterman Park |
So effective population size (Ne) is the size of an
idealized population that demonstrates the same allelic frequency variance as
the population under study. There are
many possible reasons why Ne is always less than or equal to N, the headcount
(or stem count) population size. Often
much less.
Well, I hate to be pedantic, but there’s another (equivalent,
but somewhat more difficult) definition of Ne.
Suppose we were to sample 100 peas from our population at a
single date but analyzed gene frequencies at two polymorphic loci, not just
one. So, say seed color (green/yellow)
and seed shape (wrinkled/smooth). There
is no reason to expect any relationship between seed color and seed shape – knowing
green shouldn’t allow you to predict wrinkled.
That is true regardless of whether the seed color locus and the seed
shape locus are on the same chromosome or not, because (in a large, randomly-breeding
population) crossing-over would ultimately erase any initial relationship
between the alleles.
But what if you did find a relationship between seed color
and seed shape in the pea field? This is
often called “gametic phase disequilibrium” to distinguish it from the (hard)
linkage disequilibrium you might discover between loci on the same chromosome
using a controlled cross. That would
mean that the population wasn’t infinitely large and randomly-breeding.
So finally. Effective
population size is the size of an idealized population that demonstrates the
same allelic frequency variance or the same gametic phase disequilibrium as the
population under study. Geeze, that
turned out to take longer to explain than I imagined when I started this essay
eight paragraphs ago. I appreciate your
forbearance.
Effective population size is a parameter in every model of
theoretical population genetics ever published, neutral or otherwise. That number is really, REALLY important. And also, really difficult to obtain.
I only know of ten estimates of Ne in gastropod populations
ever published, in total, for all environments: two marine, four terrestrial, and four freshwater
[3]. And frankly, many of those ten are
pretty darn spurious.
OK, I’m going to change subjects entirely here. But don’t forget all the boring population
genetics stuff you had to slog through above, because you’re going to need it
again, shortly.
I taught Genetics Laboratory 305L at The College of
Charleston for 33 years. And
Investigation #9 in my Genetics 305L lab manual was “The analysis of genetic
polymorphism in a natural population using allozyme electrophoresis.” I needed a sample of 31 individual somethings
from some polymorphic population for each section, which toward the latter half
of my career [4], became three sections per semester, two semesters per year,
that’s N = 186 somethings. And after
years of messing around with pleurocerid snails and Mercenaria hard clams, those
somethings became Physa acuta.
Now my second-favorite population of Physa in the world [5] inhabits
the Duck Pond at Quarterman Park in North Charleston. Amy Wethington and I first sampled that
population (“NPK”) in 1990 in conjunction with our study of sea island
biogeography [6], and I knew it was polymorphic at three allozyme-encoding
loci: Isocitrate dehydrogenase (Isdh, 3 alleles), 6-phosophogluconate
dehydrogenase (6pgd, two alleles) and Esterase-3 (Est-3, two alleles, Note 7).
So, in May of 2009 I collected my first big sample of Duck
Pond Physa for the students working on Genetics Lab Investigation #9. In many respects the one-hectare pond at
Quarterman Park is perfect Physa habitat – shallow, quiet, and very rich, fed
by runoff from the neighborhood. Every
day the kids bring bags of stale bread to feed the ducks, which they empty and
throw into the pond with all the other picnic garbage. Occasional whiffs of sewage. Physa paradise.
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| Physa paradise |
Only three factors keep that pond from becoming a block of
Physa solid enough to walk across. One
is the flocks of ducks and geese, which probably prefer the Physa over the bread.
A second is the general lack of habitat. Some 15 – 20 years ago the City of North
Charleston undertook a complete renovation of the Duck Pond, draining it and
shoring up the walls with bulkheads. So,
the modern pond has no vegetation of any sort, nor indeed any littoral
zone. Physa are common only on the floating
allochthonous debris and garbage that accumulates at the eastern end, by the
drain, and rather rare elsewhere.
And a third is the summer maximum temperatures, which can be
brutal. The City of North Charleston also
installed a couple fountain pumps during those renovations a few years ago, but
during the hot months, I feel certain that all aerobic life must be confined to
the top centimeter or two of the pond.
And concentrated at the eastern end.
All those stipulations registered, I had no problem
collecting several hundred Physa at the Quarterman Park Duck Pond in the spring
of 2009. I knelt on the walkway at the
eastern end of the pond and hand-plucked Physa off the floating debris. Or sometimes I found it easier to wash higher
concentrations of snails off large sticks and bread bags into my bucket. The entire sample didn’t take more than 30
minutes to collect.
And in the fall of 2009, the students enrolled in my three
sections of Genetics Lab 305L estimated gene frequencies at three loci in 93 of
them. And ditto for another N = 93 in
the spring of 2010. And I went back to
the Duck Pond to fetch more.
This went on for seven years, from 2009 to 2015. The actual date of the sampling varied a bit
from year to year, depending on the density of the snail population, which in
turn, seemed to vary with the weather. I
could always find at least a few Physa in the Duck Pond – any day, 12 months
per year. But to collect the hundreds I
needed annually, I needed a bloom.
After a few years of experience, I began to notice a
relationship between Physa blooms and the blooming of the azaleas. In the Charleston area, as I am sure
elsewhere, azaleas bloom in response to a pulse of warmth and sunshine – the
stronger the pulse, the more brilliant the display. The bloom typically takes place in March here
and lasts for several weeks. My annual observations
suggested that the Physa bloom at the Quarterman Park Duck Pond typically
commenced around the week the azaleas dropped their flowers – in early to
mid-April. The population typically
expanded through May, contracted in June, and died back almost entirely in the
summer.
The only exception happened in 2012, when no Physa bloom
occurred at all. The spring of 2012 was
exceptionally hot in Charleston – the mean March temperature (65.3 degrees F)
the second-highest value in the 80-year record of the National Weather
Service. I was never able to make a
collection that year. I visited the pond
every couple weeks from March to July, and could always find a few snails, but
never in the quantity that would prompt me to get on my knees and start washing
bread bags into buckets.
So I was relieved of my duties at the College of Charleston
in February of 2016, and ultimately banned from campus for a Woodrow Wilson
quote [8], bringing my study to an end with the 2015 field season. The paper reporting the results obtained by
myself and my team of 540 undergraduates was published early last year in
Ecology and Evolution, citation from Note [9] below.
I should thank my good friend and former student Dr. John
Robinson for putting me onto a really excellent freeware resource called “NeEstimator,”
developed by Chi Do and colleagues [10].
The software calculates effective population size using both allelic
frequency variance (which are called “two-sample methods”) and gametic phase
disequilibrium (“one-sample methods”).
All the statistics and other gory details are available in my paper.
The bottom line turned out to be that Ne for the Physa
population at the Quarterman Park Duck Pond was infinite in 2009 and 2010, dipped
in 2011 to somewhere around Ne = 100, dipped again between 2011 and 2013 to
around Ne = 50, popped up to around Ne = 200 in 2014, and then rebounded to
infinite again in 2015. These results
are remarkably consistent across both my one-sample and the two-sample
analyses, which are independent, and really tend to strengthen their mutual
credibility.
I suppose the first explanation that might occur to one would
be a population bottleneck in the 2012 year.
But bottleneck effects are notoriously long-lasting… once allelic
diversity is lost, it takes many, many generations to regain it.
I think the key factor in the volatility of Ne demonstrated
in this study may be cryptic population
subdivision. In retrospect, the
striking dip in apparent population census size I observed in 2012 may have
been localized at the east end of the pond, and its subsequent recovery due
to immigration from elsewhere within a Physa population subdivided by distance.
Some of the most influential studies of population
subdivision published ever 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 [11]. Could freshwater gastropod populations
perceive their environments much differently than Cepaea?
At minimum, these results should be received as a cautionary
tale by those researchers, including yours truly, a sinner, who would represent
the evolutionary relationships between populations by single samples, even as
large as 200, even with multiple polymorphic loci, collected from single sites
at single dates.
And as for the practice of sampling individual genes from individual
snails from individual populations to represent an entire biological species? That’s just plain White-House-stupid.
Notes
[1] I know that garden peas are self-pollinating. Give me this one, for the sake of the
example, OK? Geeze, you must have really
irritated your tenth-grade biology teacher.
[2] And I also realize that, because of dominance, you’d
have to assume HWE to get gene frequencies at the seed color locus in garden
peas. Doggone it, now you’re beginning
to piss me off.
[3] See the introduction section of my paper from note [9]
below for the references.
[4] From 1983 into the mid-1990s, I only taught one section
per semester – perhaps 15 students. But
the number of lab sections I taught per semester increased from two to three in
the latter half of my career, as my lecture sections were assigned to adjunct
faculty more sensitive to the self-esteem of the customers.
[5] My first-favorite Physa population inhabits the pond at
Charles Towne Landing State Park. See:
[7] Dillon, R.T., and A.R. Wethington (1994) Inheritance at
five loci in the freshwater snail, Physa heterostropha. Biochemical Genetics
32:75-82. [PDF]
[9] Dillon, R. T. (2018) Volatility in the effective size of
a freshwater gastropod population.
Ecology and Evolution 8: 2746 - 2751.
[https://doi.org/10.1002/ece3.3912]
[PDF]
[10] Do, C., Waples, R., Peel, D., Macbeth, G., Tillett, B.,
& Ovenden, J. (2014) NeEstimator v2:
Re-implementation of software for the estimation of contemporary effective
population size (Ne) from genetic data. Molecular Ecology Resources, 14,
209–214. https://doi.org/10.1111/1755-0998.12157
[11] Cain, A. J. & Currey, J. D. (1963) Area effects in
Cepaea. Phil. Trans. R. Soc. London Series B 246: 1-81. Cain, A. J. & Currey, J. D. (1968) Studies on Cepaea
III: Ecogenetics of a population of Cepaea nemoralis (L) subject to strong area
effects. Phil. Trans. R. Soc. London
Series B: 253, 447-482. Ochman, H., J. S. Jones & R. K. Selander (1983)
Molecular area effects in Cepaea. PNAS
80: 4189 – 4193.