Effect of Bottlenecks on heterozygosity (Chakraborty et al. 1975)

A population
bottleneck occurs when a large population undergoes a drastic
decrease in size. The
expected effect is a loss of variation, measured as decrease in
heterozygosity and loss of rare alleles. For example, if a
population is reduced to N = 2 individuals (one male and
one female), there will be a maximum of 4 alleles per locus, This
sample will almost certainly not represent the allele frequencies
in the pre-bottleneck population, and most or all of the rare
alleles in that population will not make it through the
bottleneck. In some cases, a rare allele that persists through
chance may generate a population with novel genetic
characteristics.

Chakraborty et al. (1975) modeled
bottleneck effects on heterozygosity for four combinations of size
(N_{0} = 2 or 10) and population
growth (r = 0.1 or 1.0, where r is the
reproductive rate, such that r=1 means the population is
doubling each generation). An initial H_{obs}
= 0.14 is assumed. In the mildest case, a bottleneck of N_{0}
= 10 followed by a doubling in population size each
generation (r = 1.0) has minimal impact on H_{obs}:
the initial sample of 2N = 20 alleles / locus is a
reasonable sample of the pre-bottleneck variation, and if N
doubles from 10 to 20, 40, 80, ..., 1,280 in the first eight
generations, very few alleles will be lost subsequently. The same
is true for a more severe bottleneck (N_{0} = 2):
although rare alleles are lost, if N doubles to 1,024
over ten generations, recovery is rapid. Only an extreme
bottleneck (N_{0}
= 2) with slow growth subsequently (r = 0.1)
has a severe impact on heterozygosity. Every generation in which N
remains < 10 is in effect another bottleneck.
Variation in all cases is recovered by new mutation: Note that the
time scale is logarithmic: the increase in heterozygosity over
time is actually a straight line as genetic diversity is restored
by mutation.