The red-backed vole lives in the Grand Teton Mountains of Wyoming. For 25 years

Question

The red-backed vole lives in the Grand Teton Mountains of Wyoming. For 25 years severe periodic fluctuations in the vole population have negatively correlated with precipitation levels. The allele frequency of the r allele originally was 0.8. Heavy rainfalls have resulted in a drop in the red-backed voles, but not gray voles. Red-backed voles are produced by the rr allele combination, gray voles are produced by either Rr or RR genotypes. Following heavy rainfalls the fitness level of the red-backed voles drops to 0.4, while the fitness of the gray voles remains at 1.

What is the mean population fitness?

What will the allele frequencies in the population be after one generation of natural selection?

Graph the changing allele frequencies of the Grand Teton vole population over 10 years of heavy rainfall.

Explanation / Answer

To calculate the mean population fitness, first take the Hardy-Weinberg equation and multiply each frequency of the genotype with the fitness of the genotype

Here

q=0.8

p=1-0.8

   =0.2

According to Hardy-Weinberg equilibrium

p2+2pq+q2=1

Mean fitness= 1x(0.2)2 +1x2x0.8x0.2+0.4x(0.8)2 (here we have multiplied the genotype frequency with the fitness of respective genotypes.

=0.04+0.32+0.25

=0.6

Mean population fitness(W) =0.6

Allele frequency after one generation(q')=

q'=q2Waa/W+pqWAa/W

=(0.8)2 0.4/0.6+0.8x0.2(1/0.6)

=0.68

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