Question

The survival to sexual maturity rates for genotypes A1A1, A1A2, and A2A2 are 90%, 85%, & 75%, and their fecundities are 50, 55, and 70 offspring, respectively.

a. what are the absolute fitnesses (W) of these genotypes?

b. Using A1A1 as the fitness reference, what are the genotype’s relative fitnesses (w)?

c. If the frequency of the A2 allele is p = 0.5, what will be its frequency one generation later?

Answer 1

1. Absolute fitness = number of offspring * survival rate

Absolute fitness for A1A1 genotype = 50*90% = 50*0.9 = 45.00

Absolute fitness for A1A2 genotype = 85*55% = 85*0.55 = 46.75

Absolute fitness for A2A2 genotype = 75*70% = 75*0.7 = 52.50

2. Relative fitness = absolute fitness / absolute fitness of a reference genotype

Here the reference genotype is A1A1 having absolute fitness 45.00

Relative fitness for A1A1 genotype = 45.0/45.00 = 1.00

Relative fitness for A1A2 genotype = 46.75/45.00 = 1.04

Relative fitness for A2A2 genotype = 52.50/45.00 = 1.17

3. If the mating is random, mixing of the gametes are random. We don’t need to consider their parental origin.

In this generation, A2 allele = p = 0.5

thus, A1 allele = q = 1 - 0.5 = 0.5

So, the population have 50% gametes with A1 allele and 50 % gametes with A2 allele. Therefore in both sperms and eggs the proportions of these two alleles are same (0.5 A1 allele and 0.5 A2 allele).

Therefore,

The probability of A1 sperm mating A1 egg is 0.5*0.5 = 0.25

The probability of A1 sperm mating A2 egg is 0.5*0.5 = 0.25

The probability of A2 sperm mating A1 egg is 0.5*0.5 = 0.25

The probability of A2 sperm mating A2 egg is 0.5*0.5 = 0.25

Therefore A1A1 = 0.25, A1A2= 0.25+0.25= 0.50, A2A2= 0.25

Frequency of A2 allele in next generation is A2A2 + ½ A1A2 = 0.25+ ½ 0.50 = 0.25 + 0.25 = 0.5

Kindly revert if you have any query.