Hierarchical Fixation Indices in a finte Island model of population Structure

This simulation illustrates the evoluton of populations under variable mating patterns, levels of genetic drift, and levels of gene flow. The resulting patterns of genetic variation are measured as patterns of heterozygosity and fixation indices or F-statistics.

The simulation is based on an island model of gene flow (all subpopulations exchange gene flow as gametes at an equal rate) where there are a finite number of subpopulations, each of which is also finite. The locus has two alleles and mutation is absent.

The top two plots display the allele frequencies and heterozygosities over time for a small sample of populations (set by the "number of sample populations in plots:").

The bottom left plot displays the three heterozygosity measures (H_I, H_S, & H_T) over time for all populations. The bottom right plot displays the three fixation index measures (F_IS, F_ST, & F_IT) based on the three heterozygosity measures.

The heterozygosity measures are:

• H_I = the average observed heterozygosity within each subpopulation.
• H_S = the average of the expected heterozygosity within each population assuming random mating (2pq-bar).
• H_T = the expected heterozygosity of the total population based on average allele frequencies (2 x p-bar x q-bar).

The Fixation index measures are:

• F_IS = (H_S - H_I)/H_S
  The average difference between observed and Hardy-Weinberg expected heterozygosity within each subpopulation due to non-random mating.

• F_ST = (H_T - H_S)/H_T
  The difference between the average expected heterozygosity of subpopulations and the expected heterozygosity of the total population caused by subpopulation divergence in allele frequency.

• F_IT = (H_T - H_I)/H_T
  The average difference between observed heterozygosity within each subpopulation and the expected heterozygosity of the total population caused by both non-random mating and subpopulation divergence in allele frequency.

The simulation uses the coancestry coeffient (f) to construct a stochastic model of the mating system within subpopulations. The coancestry coeffient (f) ranges between +1 and -1. A value of zero indicates random mating, a positive value assortative mating, and a negative value disassortative mating. The coancestry coefficient determines the probability that two alleles in a genotype are identical by descent (e.g. frequency(AA) = p² + fpq) each generation.

For more background, see chapter 4 in Hamilton, MB. 2009. Population Genetics. Wiley-Blackwell.