## Interact box Heterozygosity and inbreeding over time in finite populations

Populus can be used to simulate genetic drift in a finite population and then track values of the inbreeding coefficient over time. In Populus, click on the Model menu and select Mendelian Genetics and then Inbreeding. A dialog box will open that has entry fields for the effective population size and the initial level of the inbreeding coefficient for a diallelic locus. You can also set the number of generations to run the simulation. To get started, set Population = 30, Initial Frequency = 0.0 and Generations = 120. A graph of the results will appear after entering the simulation parameter values. Despite the name, Initial Frequency is actually the initial level of inbreeding in the population. A value of zero means that the population is in Hardy-Weinberg equilibrium. Pressing the View button in the model dialog will generate a new data set and redraw the graph.

The graph will show three types of inbreeding coefficients. Ft is the "theoretical" inbreeding coefficient based on the decline in heterozygosity over time (equation 3.52) or Ft = 1 -

The other two lines are both based on the observed frequency of homozygous genotypes in the simulated population. Fa (the blue line) is the actual frequency of homozygous individuals in the population (often called F; outside of Populus). Ff (the green line) is the population homozygosity. Fa and Ff can be different because the individual homozygosity tracks the combined frequency of homozygotes for either allele while the population homozygosity tracks how close the population is to fixation or loss (global homozygosity). When the population homozygosity is one there can be only one homozygous genotype in the population.

Why do the individual and population homozygosity values fluctuate? Is the amount of fluctuation related to the population size? Although the graph does not show the heterozygosity over time, what would lines for the theoretical, and individual and population heterozygosities look like? Try graphing each of these quantities on paper for a given run based on the three inbreeding coefficients.

Table 3.3 Levels of heterozygosity found in island and mainland populations of the same species demonstrates that small population size has effects akin to inbreeding. Heterozygosity in island and mainland populations is compared using the effective inbreeding coefficient

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