Finite population size
Sewall Wright (1889 – 1988)
Two important effects of finite population size
Genetic Drift
Inbreeding
Progeny from mating between two heterozygotes
Aa x Aa
|
Possible
genotypes of two offspring
|
Probability
|
Allele
frequencies
|
|
|
|
|
A
|
a
|
AA and AA
|
(1/4)(1/4)
=
|
1/16
|
1.00
|
0.00
|
aa and aa
|
(1/4)(1/4)
=
|
1/16
|
0.00
|
1.00
|
AA and aa
|
2(1/4)(1/4) =
|
2/16
|
0.50
|
0.50
|
Aa and Aa
|
(2/4)(2/4)
=
|
4/16
|
0.50
|
0.50
|
AA and Aa
|
2(1/4)(2/4) =
|
4/16
|
0.75
|
0.25
|
aa and Aa
|
2(1/4)(2/4) =
|
4/16
|
0.25
|
0.75
|
When is drift important?
Founder event
Bottlenecking
Captive population
Founder event example
Rubus alceifolius
(Asian bramble)
Native to mainland East Asia (e.g. Viet
Nam)
Introduced to Oceanic Islands
(e.g. Réunion)
Study by Amsellem L., et al. 2000. Mol. Ecol.
9: 443-455
Réunion
Viet Nam
Bottleneck example
Northern
Elephant Seal (Mirounga angustirostis)
Hunted
almost to extinction
By 1890,
fewer than 20 animals
Population
now numbers more than 150,000
Captive population (hypothetical example)
Concepts
Identity by descent
Coalescence time
Problem
The western tussuck moth (Orgyia vetusta) is an annual moth that feeds on
the yellow bush lupine, Lupinus arboreus. The population overwinters
as eggs, which hatch in the early spring.
Larvae feed for about a month and then metamorphose into adults, which
quickly mate. The females oviposit (lay eggs) on the lupine bushes and the adults
subsequently die, so that there is only one generation per year. Larvae feed voraciously, and when populations
are dense, they defoliate and kill entire patches of lupine.
Suppose you are studying a population of moths at Bodega Marine
Reserve. During your study, the Fast and Slow allozymes at the pgi locus have been at
Hardy-Weinberg Equilibrium with p = freq(Fast) = q = freq(Slow).
After the El Niño rains of 1998, the moth
population exploded and defoliated all the lupines on the Reserve. When you returned in 1999, despite extensive
searching with multiple black light stations over several weeks, you find only
one moth. You have reason to believe
that there was no selection on this locus during this extreme population
bottleneck (i.e. mortality was random with respect to genotype at this
locus).
1.
What is the allele frequency in
the 1999 generation?
2.
What is the probability that the
population lost a pgi
allele in this bottleneck?
3.
If the population had declined to
only three individuals (N = 3), what
would the allele frequency be?
4.
In that case, what would be the
probability that the population had lost a pgi allele in the bottleneck?
5.
Can you come up with a general
equation that predicts the probability that a large population will lose one of
the two alleles at a locus (become monomorphic) when
it drops to any small size N?
Homework
Use this genetic drift model to
observe outcome of drift
1.
Choose a pair of allele
frequencies (p = freq(A), q
= freq(a)) to examine (remember, p + q = 1)
2.
Key in this frequency
3.
Set population size to 100
individuals
4.
Set run time to 200 generations
5.
Run model
6.
Record final allele frequencies
7.
Run model with same allele
frequencies for 10 runs
8.
Imagine that you are observing
evolution by drift in 10 replicate small populations. Use your results to test whether the mean
allele frequencies averaged over the 10 populations
equal p and q.
9.
Among the runs in which one allele
fixes, calculate probability with which each allele fixes (e.g. 
).