I dont understand why a dominant beneficial allele might nev

I don\'t understand why a dominant, beneficial allele might never fix in a population completely?

Also,

Two genes A and B have relative fitnesses...

A1A1 = .7   A1A2=.7    A2A2=1

B1B1=1     B1B2= 1     B2B2= .8

What is the dominance coefficient (h)??

The answer is that for the A gene h=1 and for the B gene h=0. But how?? I\'ve tried to solve this problem many ways but just won\'t get the correct answer.

Solution

w: Relative fitness (survival and/or reproductive rate of a genotype relative to the maximum survival and/or reproductive rate of other genotypes in the population.)

w_Aa: Relative fitness of “Aa” genotype (heterozygote)

w_AA: Relative fitness of “AA” genotype (homozygote)

s: Selection coefficient (difference between relative fitness of both homozygote)

h: dominance coefficient / heterozygous effect

Formulas used

s = w_AA- w_aa (where w_AA is normalized to 1)

w_A1A2 = 1 – h * s

For “A” genes

Genotype

A1A1

A1A2

A2A2

Relative fitness

.7

.7

1

As A2A2 genotype has relative fitness of 1, it implies it has maximum survival

s_A = w_A2A2– w_A1A1 = 1 – 0.7 = 0.3

The dominance coefficient (h_A)

w_|A1A2 = 1 – h­_A * s_A

=> h­_A * s_A = 1 – 0.7 = 0.3

=> h­_A = 0.3 / 0.3 = 1

For “B” genes

Genotype

B1B1

B1B2

B2B2

Relative fitness

1

1

0.8

Both B1B1 & B1B2 genotypes have relative fitness of 1, it implies both have maximum survival

s_B = w_B1B1– w_B2B2 = 1 – 0.8 = 0.2

The dominance coefficient (h_B)

w_|B1B2 = 1 – h­_B * s_B

=> h_B * s_B = 1 – 1 = 0

=> h­_B = 0