Question

In a population of snow hares, 1 out of 5,000 hares are born with a dark-haired coat, which is a recessive phenotype. A decadal study showed that the relative fitness (w) of these individuals was 0.1. What mutation rate would be needed to maintain this phenotype? If the mutation rate is actually ~1.0 x 10-8, how could the occurrence of this genotype best be explained?

Answer 1

Given, 1 out of 5,000 hares are born with a dark-haired coat, which is a recessive phenotype, relative fitness of recessive phenotype = 0.1

So, frequency of recessive phenotype (q2) = 1/5000 = 0.0002

So, frequency of recessive allele (q) = =

Now, mutation selection balance needs to occur to maintain this phenotype in the population in this frequency where loss of deleterious allele will equal to the generation of new recessive allele due to mutation.

Now, selection co-efficient = 1 - relative fitness = 1 - 0.1 = 0.9

Now, = where, = equilibrium allele frequency, = mutation rate, s = selection co-efficient

According to the question, = , s = 0.9

So, mutation rate () = ()2 x s = 0.0002 x 0.9 = 0.00018

Now, actual mutation rate is ~1 x 10-8 that is much lower than our calculated mutation rate. Thus, we observed higher frequency of recessive allele than the expected value. So, there must be some gene flow (From outside recessive allele came in the population through migration) which resulted in the increased allele frequency.