## Parallelism between drift and inbreeding

• Autozygosity due to sampling in a finite gamete population.

• The relationship between the fixation index (F) and heterozygosity (H).

• Decline in heterozygosity over time due to genetic drift.

• Heterozygosity in island and mainland populations.

The chapter up to this point has focused on population size and genetic drift. This section will demonstrate that finite population size can also be thought of as a form of inbreeding. In large populations with random mating, chance biparental inbreeding is unlikely to occur often. However, in small populations the chance of mating with a relative is larger since the number of possible mates is limited. As populations get smaller, the probability of chance matings between related individuals should increase. Genetic drift also occurs due to finite population size. Therefore, genetic drift and the tendency for inbreeding are interrelated phenomena connected to the size of a population. Both have the result of increasing the homozygosity in a population over time.

Before we can reach the goal of showing that genetic drift and inbreeding are really equivalent genetic processes, it is necessary to develop a bit of conceptual machinery. In Chapter 2, autozygosity was defined as the probability that two alleles are identical by descent and demonstrated using a pedigree. We now need to revisit the autozygosity from the perspective of a finite population. Figure 3.18 shows three possible ways that alleles could be sampled from a finite population of gametes when constructing diploid genotypes. This gamete population meets Wright-Fisher assumptions with the exception that it is finite and contains alleles that are identical in state but are not identical by descent. To make offspring in the next generation, alleles are sampled with replacement from the population of 2N gametes. What is the probability that two alleles in a genotype in the next generation are identical by descent? Given that one allele has been sampled, say an A1 allele, what is the probability of sampling the same allele on the next draw? Since there is only one copy of this allele in gamete population, there is only one of the 2N alleles

Ancestral population of 2N gametes

Ancestral population of 2N gametes

Autozygous Allozygous Allozygous and homozygous and heterozygous and homozygous

Autozygous Allozygous Allozygous and homozygous and heterozygous and homozygous

Possible genotypes in next generation when sampling with replacement

Figure 3.18 Autozygosity and allozygosity in a finite population where identity by descent is related to the size of the population. Finite populations accumulate genotypes containing alleles identical by descent through random sampling in a manner akin to mating among relatives. In this example, alleles in the ancestral gamete pool identical in state are not identical by descent. Sampling of alleles takes place to form the diploid genotypes of the next generation. By chance, the same allele can be sampled twice to form an autozygous genotype with probability . The chance of not sampling

2Ne the same allele twice is the probability of all other outcomes or 1 - Autozygous genotypes must be homozygous but allozy g ous genotypes can be either homozygous or heterozygous.

that are the same. Therefore the chances of sampling the same allele to make a genotype are-, which

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