Matthew B. Hamilton - Population Genetics

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 Webcan 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).

Mendel's experiments with peas lead him to hypothesize particulate inheritance with independent segregation of alleles within loci and independent assortment of multiple loci.

Expected genotype frequencies predicted by the Hardy–Weinberg equation (for any number of alleles) show that Mendelian inheritance should lead constant allele frequencies across generations. This prediction has a large set of assumptions about the absence of many population genetic processes. Hardy–Weinberg expected genotype frequencies therefore serve as a null model used as a standard of reference.

The null model of Hardy–Weinberg expected genotype frequencies can be tested directly or assumed to be approximately true in order to test other hypotheses about Mendelian inheritance.

The fixation index (F) measures departures from Hardy–Weinberg expected genotype frequencies (excess or deficit of heterozygotes) that can be caused by patterns of mating.

Mating among relatives or consanguineous mating causes changes in genotype frequencies (specifically a decrease in heterozygosity) but usually no changes in allele frequencies.

Mating among relatives is a process that increases the autozygosity or chance that alleles descended from a common ancestor are found together in a diploid genotype.

The coancestry coefficient gives the probability that an allele sampled from each of two individuals is identical by descent, defining relatedness between individuals.

The fixation index, the coancestry coefficient, and autozygosity are all interrelated measures of changes in genotype frequencies due to consanguineous mating.

Mating among relatives alters mean phenotypes because homozygosity increases.

An increase in homozygosity leads to inbreeding depression, which ultimately is caused by overdominance (heterozygote advantage) or dominance (deleterious recessive alleles).

The gametic disequilibrium parameter (D) and its correlation version (ρ) measure the degree of association of alleles paired at two loci compared with random pairing. Gametic disequilibrium is broken down by recombination, decaying by the maximum of 50% per generation when loci experience free recombination.

A wide variety of population genetic processes – natural selection, chance, admixture of populations, mating system, and mutation – can maintain and increase gametic disequilibrium even between loci without physical linkage to reduce recombination.

For a detailed history of Gregor Mendel's research in the context of early theories of heredity as well as the analysis of Mendel's results by subsequent generations of scientists, see:

1 Orel, V. (1996). Gregor Mendel: The First Geneticist. Oxford: Oxford University Press.For perspectives on whether or not Gregor Mendel may have fudged his data, see a set of articles published together:

2 Myers, J.R. (2004). An alternative possibility for seed coat color determination in Mendel's experiment. Genetics 166: 1137.

3 Novitiski, C.E. (2004). Revision of Fisher's analysis of Mendel's garden pea experiments. Genetics 166: 1139–1140.

4 Novitiski, E. (2004). On Fisher's criticism of Mendel's results with the garden pea. Genetics 166: 1133–1136.More on the history of GH Hardy's contributions to expected genotype frequencies is explained in:

5 Edwards, A.W.F. (2008). G. H. Hardy (1908) and Hardy–Weinberg equilibrium. Genetics 179: 1143–1150.For a brief biography of Reginald Punnett and his work on expected genotype frequencies, see:

6 Edwards, A.W.F. (2012). Reginald Crundall Punnett: first Arthur Balfour professor of genetics, Cambridge, 1912. Genetics 192: 3–13.To learn more about the short tandem repeat (STR) genetic marker loci used in forensic investigation, consult:

7 Butler, J.M. (2006). Genetics and genomics of core short tandem repeat loci used in human identity testing. Journal of Forensic Sciences 51: 253–265.To learn more about the Mendelian genetics of the ABO blood group, see the brief history:

8 Crow, J.F. (1993). Felix Bernstein and the first human marker locus. Genetics 133: 4–7.Genomic sequence data has provided new insights on the classical concept of coancestry and relatedness through explicit tracing of DNA segments that are identical by descent. Consult this review to learn more:

9 Speed, D. and Balding, D.J. (2015). Relatedness in the post‐genomic era: is it still useful? Nature Reviews Genetics 16 (1): 33–44.For more detail on ways to estimate gametic disequilibrium and its applications, consult: