Question

You are a wildlife biologist in charge of managing a population of Spotted Owls in Glacier National Park. There are a total of 800 owls in the population. Your records indicate that last generation 50 owls died before reproducing due to a lethal recessive genetic disorder. How many owls are likely to die in the next generation due to this affliction. You may answer this in words, as a formula or numerically.

Answer 1

Initial population = 800

Of this 800, fifty individuals are homozygous for lethal allele.  

As per Hardy Weinberg Equilibrium, sum total of all allelic frequencies is equal to 1. Let p and q be the frequencies of non lethal(dominant ) and lethal (recessive ) alleles respectively.

So, p + q = 1

(p + q)^2 = 1

p^2 + 2pq + q^2 = 1, here, p^2, 2pq and q^2 are the frequencies of homozygous dominant, heterozygous and homozygous recessive respectively.

We know the frequency of homozygous recessive lethal genotype, i.e., q^2 = 50÷800

q^2 = 0.0625  

Therefore, q = square root of 0.0625 = 0.25

Since, p+ q = 1; p = 1- 0.25

p = 0.75

So frequency of homozygous dominant non lethal genotype = p^2 = 0.75*0.75 = 0.5625

Hence, number of individuals that are homozygous dominant = 0.5625 * 800 = 450

The number of heterozygous individuals = 2pq * 800 = 300

We know that 50 individuals die before next generation due to homozygous lethal genetic make up. Hence, total number of individuals become 750. The allelic frequency also changes. The new allelic frequencies are as follows:

p' = [(2*number of homozygous dominant )+(heterozygous individual)]÷(2*Total number of individuals)

p' = (2*450 + 300)÷ (2* 750) = 0.8

Here, p' is the new allelic frequency of dominant non lethal allele. Since homozygous dominant has 2 dominant alleles and the heterozygotes have 1 dominant allele, the total number of dominant alleles in the population is the sum of the number of heterozygotes and two times the number of homozygous dominant. The total number of allele is two times the total number of individuals.

q' be the new frequency of recessive lethal allele.

Since, p' + q' = 1, q' = 1 - 0.8 = 0.2

This means that new allelic frequencies after the loss of 50 homozygous recessive individuals is:

p' = 0.8 and q' = 0.2

This population (of 750 individuals) upon mating to make the next generation, will contribute to the following frequencies for each genotype:

Frequency of homozygous dominant in next generation = p'^2 = p' * p' = 0.8 * 0.8 = 0.64

This means that number of homozygous dominant individuals in the next generation = 0.64 times the total number of individuals having reproductive capacity in the previous generation (This is under the assumption that each individual having reproductive capacity in a population will contribute to one offspring in the next generation).

The number of homozygous dominant in next generation = 0.64 * 750 = 480

Number of heterozygous individuals in next generation = 2p'q' * 750 = 240

Number of homozygous recessive (die off) = q'^2 * 750 = 30

Hence, number of individuals that die in the next generation due to the homozygous recessive allele is 30 Owls.