Genetics - A. V. Sivolob 2008

Population Genetics
Factors of the Dynamics of Population Genetic Structure
Inbreeding

Inbreeding—mating between genetically related individuals—is a violation of panmixia. Like Genetic Drift, it increases population homozygosity; however, unlike drift, allele frequencies remain unchanged.

Several types of such mating are distinguished depending on the degree of genetic relatedness between mates. The very term "inbreeding" (breeding "within") originated in animal husbandry, where it referred to mating within a single line, such as brother $\times$ sister, etc. The closest form of inbreeding is self-Fertilization.

To assess the intensity of inbreeding, the so-called inbreeding coefficient $F$ is used, which represents the probability that both alleles at a given Gene locus in an individual's genotype are identical by descent. Let us consider a pedigree involving a brother $\times$ sister mating (Fig. 8.8).

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Fig. 8.8. Brother $\times$ sister mating. Inbred individual Д is homozygous for the allele a₂, both copies of which are identical by descent.

All participants in this pedigree are homozygotes for the recessive allele a. All copies of this allele in individuals А and Б are identical, but they were inherited from different ancestors and have different origins. Assigning them numbers for convenience, we can trace their fate in the offspring. Individuals В and Г have different sets of alleles, but they share one in common (a₂). It is precisely this allele that is present in the genotype of Д in a double dose—these are two replica copies of the same allele that was originally present in the genotype of А. Thus, Д is a homozygote for alleles that are not only identical, but also share an identical origin.

The probability that А will transmit the allele a₂ to both offspring В and Г equals 1/2 $\times$ 1/2 = 1/4. Similarly, the probability that В and Г will simultaneously transmit this allele to offspring Д is 1/2 $\times$ 1/2 = 1/4. The overall probability that two copies of a₂ will be passed from А to Д equals (1/2)⁴ = 1/16. Since in this pedigree any of the four variants of allele a can be passed to Д in a double dose, the probability that Д will be a homozygote for alleles identical by descent is $F$ = 4 $\times$ (1/2)⁴ = 1/4.

During self-fertilization, $F$ = 1/2: this means that the proportion of heterozygotes in each successive generation will be halved compared to the preceding one, and after $t$ generations, the proportion of heterozygotes will be (1/2)^t.

In general terms, under inbreeding, the proportion of homozygotes will increase at the expense of heterozygotes:

(p² + pqF) + 2 pq(1 - F) + (q² + pqF) = 1.

The value of $F$ can range from 0 to 1. Substituting $F$ = 0 into the last formula yields the Hardy-Weinberg equation for panmictic populations: p² + 2pq + q² = 1. A value of $F$ = 1 indicates the complete absence of heterozygotes in the population, while the frequencies of genotypes АА and аа will equal the frequencies of alleles А and а, respectively.

A population can reach this state over a certain number of generations—the closer the inbreeding, the faster it occurs. Meanwhile, allele frequencies remain unchanged. Therefore, the primary consequence of inbreeding for population Structure is an increase in the proportion of homozygotes. Consequently, the probability of homozygosity for recessive alleles (including lethal or disease-causing ones) also increases, leading to what is known as inbreeding depression.

Nevertheless, some animal and plant species that reproduce via self-fertilization remain entirely viable. If a population undergoes inbreeding over many generations, "deleterious" recessive alleles are purged from it through Selection (discussed below), meaning the population becomes homozygous for "beneficial" alleles. In this way, inbreeding is frequently utilized in breeding programs to obtain plants and animals with desired traits.

Since inbreeding (in the absence of selection) does not alter allele frequencies, the genetic Variability of an inbred population is often assessed using expected heterozygosity—the proportion of individuals that would be heterozygous According to the Hardy-Weinberg equation (2pq for a two-allele locus). Thus, for self-pollinating plants, actual heterozygosity may be very low, but the population can exhibit considerable genetic variability, with expected heterozygosity serving as its measure. Typically, expected heterozygosity is averaged across several studied loci.