## Interact box Continentisland model of gene flow

PopGene.S2 contains a module to simulate the continent-island model of gene flow. In PopGene. S2 click on the Gene Flow and Subdivision menu and then select Continent-Island model of migration. The simulation window allows you to set allele frequencies in the island and continent, the rate at which island alleles are replaced by continent alleles (or the migration rate) and the number of generations to simulate. Enter the parameters of pC = 0.9, pI = 0.1, m = 0.1, and 100 generations to run. Before clicking the OK button, predict the equilibrium allele frequency in the island population.

Keeping the same values for initial allele frequencies, try a series of values of the migration rate to see how it affects time to equilibrium. Click the Clear Screen button to clear the graph window. Increase the Generations to run to 300. Run the simulation with m = 0.1, m = 0.05, m = 0.001, and m = 0.001 without clearing the graph window. This should give a plot with four blue lines (one for each value of the migration rate). What is the relationship between the migration rate and time to equilibrium?

to converge on the same allele frequency depends on the proportion of continent individuals moving to the island each generation. In contrast, the difference in allele frequencies between the island and continent does not alter the time to equilibrium for a given migration rate (see Fig. 4.13). This occurs since the rate of change in the island allele frequency is determined by the difference in allele frequencies. Greater differences lead to greater rates of change toward the continent allele frequency. Thus, the continent-island model shows that the process of gene flow alone is capable of bringing populations to the same allele frequency. Identical allele frequencies between or among populations is really a lack of population structure or panmixia. So the continent-island can be thought of as a demonstration that gene flow acting in the absence of other processes will eventually result in panmixia.

### Two-island model

One simple adjustment to the continent-island model is to consider the two subpopulations as being equal in size, removing the assumption that one population (the continent) serves as an unchanging source of migrants. The model then represents gene flow between two islands which can each exhibit changes in allele frequency over time. The switch to a two-island model also allows an independent rate of gene flow for each subpopulation, m1 and m2. Using reasoning similar to that for the continent-island model, the allele frequency in a subpopulation one generation in the future is the sum of the allele frequency in the proportion of individuals that do not migrate (1 - m)

plus the allele frequency in the immigrants. Assuming that m1 = m2 = m, the allele frequency in either subpopulation is

where p = —2. The allele frequency in the migrants is now the average of the two subpopulations rather than just a constant like the continent allele frequency. This happens because both subpopulations receive immigrants so the allele frequencies of each subpopulation are approaching the allele frequency in the total population as gene flow mixes the subpopulations. Similar to the result for the continent-island model, the allele frequency in either of the two islands is

after t generations have elapsed. Figure 4.14 shows allele frequencies in the two-island model over time. When the rates of gene flow are not equal then the

P1m2 + P2m1

average allele frequency is p = ——2-2—-, or the m1 + m2

gene-flow-weighted average of the allele frequencies in the two subpopulations. When m1 ^ m2 the equilibrium allele frequencies will be closer to the initial allele frequency of the subpopulation with the lower migration rate. This happens because the subpopulation with the lower migration rate experiences less immigration and remains closer to its initial allele frequency, yet it supplies migrants to the other subpopulation. As seen in Fig. 4.14, the time to equilibrium

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