Fixation of a rare advantageous variant: Modes
of genetic speciation
(N = 50, q = 0.01; W0 =
0.5, W1 = 0.4, W2
= 1; 1,000
replicates)
Occasionally, new advantageous allelic variants
arise in a population by new mutation. Despite even a major
selective advantage, most such variants never become common,
and typically disappear in a few generation. This is
because, when rare, (1) a recessive allele B rarely
occurs in BB genotypes where the fitness advantage
makes a difference, and (2) genetic drift of a
single new mutant allele that occurs at an initial f(B)
= 1/2N 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 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 f(B) ~ 0.2, that is, 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