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 seem 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?
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 seem 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 © 2021 by Steven M. Carr