Biology 280/545: Fun with p & q

Background: Freeman and Herron: Chapter 5

Outline:

I. Mutation

II. Selection

III. Selection on dominant vs. recessive alleles

IV. Mutation-selection balance

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I. Mutation:

A. Remember the Mutationists?

B. Mutation as an evolutionary force

a. Assume a population at time, or generation, t=0 (t₀):

To start:

frequency of A₁ = p₀, frequency of A₂ = q₀,

and mutation rate of A₁àA₂ = µ

The frequency of A₁ in the next generation:

C. How fast does mutation change allele frequencies?

II. Now let’s add selection:

A. Selection Coefficients and Fitness

Fitness:

Selection coefficient:

	A1A1	A1A2	A2A2
Average # of progeny per individual	2	1.8	1
Relative reproductive efficiency (fitness)
Selection coefficient

2. Adding Selection to Hardy-Weinberg

Let w₁₁ = fitness of A₁A₁ genotype; w₁₂ = fitness of A₁A₂ ; w₂₂ = fitness of A₂A₂

	A1A1	A1A2	A2A2	Total
Genotypic Frequency before selection	p^2	2pq	q^2	1
Genotypic Frequency after selection	p^2w11	2pq w12	q^2 w22
Normalized Genotypic frequency after selection				1

What is the new frequency of the A₁ allele?

When does selection stop?

Answer: When Dp = 0

Allele A₁ is selected to be fixed when:

Allele A₂ is selected to be fixed when:

A genetic polymorphism (both A₁ and A₂ existing at intermediate frequencies) is selected for when:

Hence, a genetic polymorphism is selected for when the heterozygote is most fit:

Heterozygote advantage = heterosis

We can wave the math magic wand and get

where s is selection against AA and t is selection against aa)

Why is this interesting?

Solve for equilibrium (where Dq = 0) and you get:

p = 0 or q =0 or

III. Selection on dominant vs. recessive alleles

A. Selection against a recessive allele

One gene, 2 alleles: A, A₂: A₁ is dominant over A₂

w₁₁ = w₁₂ = 1

w₂₂ =1-s

Put these values in the equation from above:

.

algebra

.

B. Selection against a dominant allele

One gene, 2 alleles: A₁, A₂: A₁ is recessive to A₂

w₁₁ = 1

w₁₂ = w₂₂ =1-s

Put these values in the equation from above:

algebra

.

C. Frequency dependent selection

IV. Mutation-selection Balance