V) Maintenance of Polymorphism Under Selection (continued)

C. Recurrent recessive, deleterious mutation

F(A) = p dominant, not deleterious

F(a) = q recessive, deleterious

µ = mutation rate = F(A => a)

1. Decrease in F(a) due to selection:

(as before)

2. Increase in F(a) due to mutation:

Dq_m = µp

3. Equilibrium point where they exactly balance

= µp

Since this is basically a directional selection model we can assume the F(a) is very low and therefore is close to 1. The above equation then simplifies to:

pq²s = µp

Fast mutation = larger and slow mutation = smaller

D. Frequency Dependent Selection – the fitness of the genotype depends on the frequency of that genotype in the environment.

1. Negative Frequency Dependence:

Genotype AA Aa aa

Fitness s(1-p) 1 t(1-q)

E. Heterogenous Environment

1. Temporally Varying Selection

Genotype AA Aa aa

Fitness Spring 1.0 0.8 0.6

Fitness Fall 0.7 0.9 1.0

Average Overall 0.85 0.85 0.8

Mean Relative 1.0 1.0 0.94

– no real equilibrium unless the fitness values are symmetrical across time or the heterozygote has highest mean relative fitness (marginal overdominance). Note the heterozygote does not, however, have to be overdominant in any single time.

2. Spatially varying selection

Genotype AA Aa aa

Fitness Niche 1 1.0 1.0 1 - s

Fitness Niche 2 1 - t 1 - t 1.0

– is a function of the magnitude of the selection coefficients and the area of each niche. An equilibrium is possible if the combination of the two results in a marginal overdominance.