Self-fertilization

Self-fertilization is the most extreme form of inbreeding possible, and it is characteristic of many flowering plants and some hermaphroditic animals, including freshwater snails.¹ It's not too hard to figure out what the consequences of self-fertilization will be without doing any algebra.

• All progeny of homozygotes are themselves homozygous.

• Half of the progeny of heterozygotes are heterozygous and half are homozygous.

So you might expect that the frequency of heterozygotes would be halved every generation, and you'd be right. To see why, consider the following mating table:

		Offsrping genotype
Mating	frequency	$A_1A_1$	$A_1A_2$	$A_2A_2$
$A_1A_1 \times A_1A_1$	$x_{11}$	1	0	0
$A_1A_2 \times A_1A_2$	$x_{12}$	$\frac{1}{4}$	$\frac{1}{2}$	$\frac{1}{4}$
$A_2A_2 \times A_2A_2$	$x_{22}$	0	0	1

Using the same technique we used to derive the Hardy-Weinberg principle, we can calculate the frequency of the different offspring genotypes from the above table.

$$x_{11}' = x_{11} + x_{12}/4$$ (1)

$$x_{12}' = x_{12}/2$$ (2)

$$x_{22}' = x_{22} + x_{12}/4$$ (3)

I use the $'$ to indicate the next generation. Notice that in making this caclulation I assume that all other conditions associated with Hardy-Weinberg apply (meiosis is fair, no differences among genotypes in probability of survival, no input of new genetic material, etc.). We can also calculate the frequency of the $A_1$ allele among offspring, namely

$$p' = x_{11}' + x_{12}'/2$$ (4)

$$= x_{11} + x_{12}/4 + x_{12} /4$$ (5)

$$= x_{11} + x_{12}/2$$ (6)

$$= p$$ (7)

These equations illustrate two very important principles that are true with any system of strict inbreeding:

1. Inbreeding does not cause allele frequencies to change, but it will generally cause genotype frequencies to change.

2. Inbreeding reduces the frequency of heterozygotes relative to Hardy-Weinberg expectations. It need not eliminate heterozygotes entirely, but it is guaranteed to reduce their frequency.
   • Suppose we have a population of hermaphrodites in which $x_{12} = 0.5$ and we subject it to strict self-fertilization. Assuming that inbred progeny are as likely to survive and reproduce as outbred progeny, $x_{12} < 0.01$ in six generations and $x_{12} < 0.0005$ in ten generations.