Question

Question 3 [20 marks]
Defining heterozygosity, H, as the probability that two sequences randomly sampled from a population are different, for a diploid species with a population size of N = 1000 individuals and initial heterozygosity H₀ = 0.5

1. What will the heterozygosity be after 100 generations? [3 marks]
2. How many generations will it take to reduce the heterozygosity by half? [3 marks]
3. With a neutral mutation rate of u = 10^-9, what is the equilibrium value of heterozygosity? [3 marks]
4. What is the rate of substitution with the above mutation rate? Explain. [5 marks]
5. If, for beneficial mutation A1 the selection coefficient is s = 0.01, what is the
   probability of substitution for a new beneficial mutation? [3 marks]
6. If, for deleterious mutation A2 the selection coefficient is s = 0.001, what is the probability of substitution for a new deleterious mutation? [3 marks]

Answer 1

First you need to remember that heterozygosity will loss gradually after generations. In this case you should apply the next equation to estimate the heterozygosity in 100 generations (Ht) using the initial heterozygosity The equilibrium value of heterozygosity is given by Hardy-Weinberg equation: p2 + 2pq + q2-1 Where heterozygosity is 2N Under one way mutation, you need to calculate how a mutation of u 109 would affect the (0.9)100 x 0.5 0.000013 heterozygosity equilibrium (pq) To calculate how many generations take to reduce heterozygosity by half, you need to calculate de number of generations (t) of the previous equation using 0.25 (Half of 0.5) as Ht 0.510- 0.9 + Ln(Ho) 2N T 1.38 Approximately 2 generations to reduce in a half the initial -0.1-0.6 1.9 heterozygosity