Population Genetics. Matthew B. Hamilton
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Figure 2.22 The decay of gametic disequilibrium (D) over time with random mating (s = 0) and three levels of self‐fertilization. Initially, there are only coupling (P11 = P22 = ½) and no repulsion gametes (P12 = P21 = 0). Self‐fertilization slows the decay of gametic disequilibrium appreciably even when there is free recombination because double heterozygote genotypes are infrequent.
Population size
It is possible to observe gametic disequilibrium just by chance in small populations or small samples of gametes. Recombination itself is a random process in terms of where crossing over events occur in the genome. As shown in the Appendix, estimates are more likely to approach their true values as larger samples are taken. This applies to mating patterns and the number of gametes that contribute to surviving progeny in biological populations. If only a few individuals mate (even at random) or only a few gametes found the next generation, then this is a small “sample” of possible gametes that could deviate from independent segregation just by chance. When the chance effects due to population size and recombination are in equilibrium, the effects of population size can be summarized approximately by
(2.40)
where Ne is the genetic effective population size and c is the recombination fraction per generation (Hill and Robertson 1968; Ohta and Kimura 1969a, b; the basis of this type of equation is derived in Chapter 4). As shown in Figure 2.23, when the product of Ne and c is small, chance sampling contributes to maintaining some gametic disequilibrium since only a few gametes contribute to the next generation when Ne is small and genetic drift is strong, or only a few recombinant gametes exist when c is small. The lesson is that D as we have used it in this section assumes a large population size (similar to Hardy–Weinberg) so that actual gamete frequencies approach those expected based on allele frequencies, an assumption that is not met in actual populations to some degree because they are finite. Strong growth in population size over time can also alter the rate of decay of gametic disequilibrium compared to that seen in a population of constant size through time (Pritchard and Przeworski 2001; Rogers 2014).
Figure 2.23 Expected levels of the squared gametic disequilibrium correlation (ρ2) due to the combination of finite effective population size (Ne) and recombination at rate (c). Gametic disequilibrium is greater when fewer recombinant haplotypes are produced each generation (small c), the population is small causing haplotype frequencies to fluctuate by chance (small Ne), or if both factors are acting in combination (small Nec).
Interact box 2.4 Estimating genotypic disequilibrium
In practice, the recombination fraction for two loci can be measured by crossing a double heterozygote with a double homozygote and then counting the recombinant gametes. However, this basic experiment cannot be carried out unless individuals can be mated in controlled crosses, excluding many, if not most, species. For two diploid loci, disequilibrium can occur between loci at two alleles positioned on the same chromosome, as well as between loci at two alleles positioned on different chromosomes (Weir 1996). With observed genotype data from pairs of loci where the phase of alleles or gamete organization is unknown, these latter two types of between‐locus disequilibrium cannot be distinguished but they can be considered together as genotypic disequilibrium (Rogers and Huff 2009).
An approximate means to test for gametic equilibrium is to examine the joint frequencies of genotypes at pairs of loci. If there is independent segregation at the two loci, then the genotypes observed at one locus should be independent of the genotypes at the other locus. Such contingency table tests are commonly employed to determine whether genotypes at one locus are independent of genotypes at another locus.
Contingency table tests involve tabulating counts of all genotypes for pairs of loci. In Table 2.14, genotypes observed at two microsatellite loci (AC25‐6#10 and AT150‐2#4) within a single population (the Choptank River) of the fish Morone saxatilis are given. The genotypes of 50 individuals are tabulated with alleles at each locus are represented with numbers. For example, there were 15 fishes that had a 22 homozygous genotype for locus AC25‐6#10 and also had a 44 homozygous genotype for locus AT150‐2#4. This joint frequency of homozygous genotypes is unlikely if genotypes at the two loci are independent, in which case the counts should be distributed randomly with respect to genotypes.
In the striped bass case shown here, null alleles (microsatellite alleles that are present in the genome but not reliably amplified by PCR) are probably the cause of fewer than expected heterozygotes that lead to a non‐random joint distribution of genotypes (Brown et al. 2005). Thus, the perception of gametic disequilibrium can be due to technical limitations of genotyping techniques in addition to population genetic processes such as reduced recombination (or linkage), self‐fertilization, consanguineous mating, and mixing of diverged populations that cause actual gametic disequilibrium.
Genepop on the Web can be used to construct genotype count tables for pairs of loci and carry out statistical tests that compare observed to those expected by chance. Instructions on how to use Genepop and an example of striped bass microsatellite genotype data set in the Genepop format are available on the text website along with a link to the Genepop site.
Table 2.14 Joint counts of genotype frequencies observed at two microsatellite loci in the fish Morone saxatilis . Alleles at each locus are indicated by numbers (e.g. 12 is a heterozygote and 22 is a homozygote).
| Genotype at locus AC25‐6#10 | ||
|---|---|---|
| Genotype at locus AT150‐2#4 | 12 |
22
|