Question

In a large plant population that reproduces by pollinator-assisted random mating (outcrossing), the frequencies of the genotypes GG, Gg and gg are 0.04, 0.32 and 0.64, respectively. Honey bees are under threat of decline. A loss of the bee pollinator forces the population to reproduce exclusively by self-fertilization. What will happen to the frequencies of the homozygous and heterozygous genotypes in this population after one generation of self-fertilization? If the same conditions continue to exist for many generations, what will eventually happen to the genotype frequencies at this locus? This is the snail example from class all over again. What happens to heterozygosity for any organism that self fertilizes? It is cut in half each generation.

Answer 1

Given:

Genotypic frequency of GG, Gg and gg plants are 0.04, 0.32 and 0.64 respectively.

f(GG) = 0.04

f(Gg) = 0.32

f(gg) = 0.64

The plants undergo self-fertilization, which means GG plants mate with GG, Gg plants mate with Gg plants and gg plants mate with gg plants.

GG and gg plants upon self-fertilization will produce GG and gg progeny respectively, i.e.homozygous plants will produce only the homozygous plants of same genotype.

​​​​​​On the other hand, self-fertilization of Gg individual will produce GG, Gg and gg plant progeny.

	G	g
G	GG	Gg
g	Gg	gg

Thus, a heterozygous plant, Gg will produce 1/4 GG, 1/2 Gg and 1/4 gg plants.

Genotypic frequencies after one generation of self-fertilization:

Frequency of Gg in next generation, Gg' will become half of its present frequency, f(Gg). On the other hand, frequency of GG and gg will increase each by one-fourth f(Gg).

Frequency of GG'

= f(GG) + (1/4) f(Gg)

=0.04 + ( 1/4 )×(0.32)

=0.04 + 0.08

=0.12

Frequency of Gg'

= (1/2) f(Gg)

=1/2 × (0.32)

= 0.16

Frequency of gg'

= f(gg) + (1/4) × f(Gg)

=0.64 + (1/4) ×0.32

=0.72

After one generation of self-fertilization, genotypic frequencies will become:

GG = 0.12 Gg = 0.16 gg = 0.72

If the same conditions remain for many generations, then eventually the population will consist entirely of homozygous individuals, and heterozygous ones would get eliminated.

​​​​​​Also, depending on genotypic fitness, one of the allele might get fixed in the population, leading to loss of the another allele.