Introduction
A little over 30 years ago Waples and Teel reported a remarkable
pattern in genetic samples of Pacific Coast salmon:
In nine wild populations sampled in two different years, only 8
percent of allele frequency comparisons between years showed differences
that were statistically significant - only a little more than what you’d
expect given that they used a 5 percent threshold to determine
statistical significance.
In eight of nine hatchery populations, on the other hand, the
proportion of statisticaly significant changes ranged from 22-63
percent. Only in one was the fraction of statisticaly significant
changes similar to that in wild populations.
Their paper goes beyond simply noting that conservationists need to
monitor the genetic impact of hatchery populations on wild populations.
They construct a relatively simple model to explore the magnitude of
allele frequency changes you’d expect to see as a result of genetic
drift and they extend it to see whether natural selection in the
hatchery environment could account for the large number of allele
frequency changes observed there.
Problem #2
This project will be different from any of the lab exercises you’ve
done so far. I’m not going to ask you to analyze any data, and I’m not going to
ask you to run any simulations. Instead, I want you to read Waples and Teel
carefully and use what you’ve learned about how genetic drift and
natural selection interact to answer the following questions. I’m not
looking for lengthy answers - a paragraph, maybe two, for each will be
sufficient. What I’m looking for is that you can can apply what you’ve
learned to evaluate research done by a pair of very talented population
geneticists.
Waples and Teel argue that “Temporally spaced samples will on
average differ more than independent binomial samples drawn from the
same population…” (p. 149).
Waples and Teel show that the average magnitude of allele
frequency change drops at year 4 and increases from there.
Waples and Teel note that the fraction of significant tests for
comparisons of allele frequencies between samples taken at different
times depends neither on the sample size, \(S\), nor the effective number of breeders,
\(N_b\),, but on the ratio
\(S/N_b\) (see Figure 4,
p. 149).
Waples and Teel used the following set of fitnesses in their
simulation to study the effect of selection:
\(1\) |
\(1 - s\) |
\(1 - 2s\) |
- They note that \(s > 0.2\) would
be necessary for 36 percent of allele frequency comparisons to be
statistically significant after 4 years (Figure 5, p. 151). I agree that
this magnitude of selection is unrealistic. They did not note that small
populations show a higher proportion of significant tests than larger
ones unless \(s\) is very large.
Questions
Why will independent samples from the same population taken at
different times differ more, on average, than independent samples from
the same population taken at the same time?
What might explain the drop at year 4 and the increase from
there.
Why does the fraction of significant tests become so large when
the sample size is large relative to the effective number of breeders,
i.e., when \(S/N_b\) is large?
Given what you know about drift and selection, why do you think
there are fewer significant changes in allele frequency detected when
populations are large than when they are small?
If you were extending this simulation study, do you think it
would be more useful to (a) calculate the fraction of allele frequency
comparisons that show statisticaly significant differences between time
periods or (b) study how the mean and variance of allele frequency
differences changes over time?
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