Fixation of a rare advantageous alleles: Modes
of genetic speciation
(N = 50, q = 0.01; W0 =
0.5, W1 = 0.4, W2
= 1; 1,000
replicates)
Advantageous alleles arise occasionally in
a population by new mutation. Even with a major selective
advantage, most such variants never become common, and
disappear in a few generation. This is because a rare
advantageous recessive allele B rarely occurs in BB
genotypes, where the fitness advantage
would make a difference. Further, because a
single new mutant allele occurs at an initial f(B)
= 1/2N, random loss by genetic
drift has greater influence than the selective
advantage. Rarely, and depending on population size and the
degree of selective advantage, such an allele may drift to a
critical frequency, at which point the selective advantage
drives it rapidly to fixation.
In the example shown, a single new
variant occurs in a population of 50 (with 100
alleles) at f(B) = (1)/(2)(50) = 0.01.
The BB genotype has a two-fold selective advantage
over AA; the new variant has lower fitness in
heterozygous combination AB. Among 1,000 replicates,
in almost all f(B)
0 without reaching a threshold value of f(B) ~
0.2, (20 copies of the new variant). As f(B) →
0.2, f(BB) = 0.22 x 50 = 2,
that is, an expectation of two BB individuals in
the population. Thereafter, selection causes f(B) to
increase rapidly, reaching fixation between t = 18 ~ 48
generations in five populations, while the variant in the
other 995 populations has been lost.
Peripatric speciation by fixation of
new alleles in small populations on the periphery of a
large population, where the alleles confer selective
advantage in the new adaptive environment, is one mode
of allopatric speciation. It can be seen in
island populations separated from a mainland, where
conditions on the island different greatly from each
other and from the mainland. Darwin's Finches or the
different forms of tortoises among the Galapagos Islands
may be an example.
HOMEWORK:
Use the WriFish MatLab
program to repeat the simulation above. Are the
same results obtained every time? Is there a critical value
of W2 with respect to W1 for routine
fixation of ca. one population in a thousand (what is the
ratio)? Is heterozygote disadvantage (W1 < W0
<< W2) critical to the model (try W1
= 0.3, 0.4, & 0.5)? Adjust N and q to
correspond to one variant in 5 or 500 individuals: can the
same phenomenon be achieved?
Figure & Text
material © 2024 by Steven M.
Carr