Question

An autosomal gene is segregating two alleles, R and r, with respective frequencies 0.3 and 0.7. If mating is random, what are the expected frequencies of the genotypes? Now suppose that every individual in the population mates with a sibling. What will the genotype frequencies be among the offspring? Suppose instead that every individual mates with a first cousin. What will the genotype frequencies be among their offspring? Finally, suppose that after many generations of random mating, every individual in the population reproduces by self- fertilization. What will the genotype frequencies be among the offspring of this kind of inbreeding?

Answer 1

Given figures:

Frequency of allele R (p) = 0.3

Frequency of allele r (q) = 0.7

Hardy weinberg equations:

1 = p + q

1 = p^2 + 2pq + q^2

i) If mating is random,

Frequency of RR (p^2) = 0.3 *0.3 = 0.09

Frequency of Rr (2pq) = 2 * 0.3 * 0.7 = 0.42

Frequency of rr (q^2) = 0.7 * 0.7 = 0.49

0.09 + 0.42 +0.49 = 1

Mating between siblings, mating with first cousin and self fertilization are non random matings. Non random matings do not change the frequency of alleles. But it will change the frequency of genotypes. Non random matings (inbreeding) increases the number of homozygotes and decreases the number of heterozygotes. Inbreeding coeffictient (F) is the probaility that an individual have two identical alleles (Homozygous)

ii) Mating between siblings

Inbreading coefficient (F) for the offspring resulting from the mating between siblings = 1/4

Frequency of RR = p^2 + Fpq = 0.09 + (1/4 * 0.3 * 0.7 ) = 0.1425

Frequency of Rr = 2pq - 2pqF = 0.42 - ( 2* 0.3 * 0.7 * 1/4) = 0.42 - 0.105 = 0.315

Frequency of rr = q^2 + Fpq = 0.49 + (1/4 * 0.3 * 0.7) = 0.5425

0.1425 + 0.315 + 0.5425 = 1

iii) Mating with first cousin

Inbreeding cofficient (F) for the offspring resulting from the mating with first cousin = 1/16

Frequency of RR = p^2 + Fpq = 0.09 + (1/16 * 0.3 * 0.7) = 0.103

Frequency of Rr = 2pq - 2pqF = 0.42 - (2 *0.3 * 0.7 * 1/16) = 0.42 - 0.026 = 0.394

Frequency of rr = q^2 + Fpq = 0.49 + (1/16 * 0.3 * 0.7 ) = 0.503

0.103 +0.394 + 0.503 = 1

iv) Self Fertilization

Inbreeding coeffcient (F) for the offspring resulting from self fertilization = 1/2

Frequency of RR = p^2 + Fpq = 0.09 + (1/2 * 0.3 *0.7) = 0.9 + 0.105 = 0.195

Frequency of Rr = 2pq - 2pqF = 0.42 - (2 *0.3 *0.7 *1/2) = 0.42 - 0.21 = 0.21

Frequency of rr = q^2 + Fpq = 0.49 + 1/2 * 0.3 *0.7 = 0.49 + 0.105 = 0.595

0.195 +0.21 + 0.595 = 1