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where FcSTlony is the expected allele frequency differentiation in newly established subpopulations, k is the number of diploid colonists, FST is the degree of allele frequency differentiation among the existing subpopulations, and ^ is the probability that the two alleles in a newly established population come from the same or different subpopulations (Whitlock & McCauley 1990). Colonization corresponds to the propagule pool for ^ = 1 (the chance of one that two founding alleles come from the same subpopulation) and the migrant pool for ^ = 0 (no chance that two founding alleles come from the same subpopulation so all alleles must come from different subpopulations). In the equation, all newly founded subpopulations have a chance of being established with alleles that are identical by descent due to sampling from the total population, hence the — term (see equation 3.47). For those subpopulations that are founded by individuals from a propagule pool (or 1), the chances of alleles being identical by descent and homozygous is greater to the degree that existing subpopulations are differentiated in their allele frequencies. With colonization from the propagule pool, newly founded populations inherit the average level of homozygosity of existing subpopulations plus some additional homozygosity due to sampling from a finite population. With colonization from the migrant pool (^ = 0), founding alleles are always drawn from a different subpopulation, so the heterozygosity is the same as the total population heterozygosity (2pq) except for sampling error from a finite number of founders.

The general conclusion is that extinction and recolonization can be an additional source of gene flow or an additional restriction on gene flow in meta-populations (Maruyama & Kimura 1980; Wade & McCauley 1988). Propagule pool colonization tends to increase overall population differentiation for all values of the number of diploid colonists (k). In contrast, the change in overall differentiation with the migrant model depends on the rate of gene flow among existing subpopulations. When the number of diploid colonists (k) exceeds twice the effective number of migrants (2Nem) then differentiation tends to decrease since colonization accomplishes additional mixing of alleles. Using newly established populations of the plant Silene alba, McCauley et al. (1995) estimated ^ between 0.73 and 0.89, suggesting that new populations do experience some additional sampling during their formation that increases population differentiation.

4.6 The impact of population structure on genealogical branching

• Event times with population subdivision.

• Sample configurations.

• Mean and variance of waiting time in two demes.

In structured populations with gene flow, lineages can move from deme to deme. In a retrospective view, two lineages sampled in the present can experience either coalescence or migration going back in time (Fig. 4.16). Determining the mean and variance of time to coalescence in structured populations will show the overall impact of population structure on genealogical trees. In particular, we would like to know whether population structure will alter the average and variance of the height of genealogical trees in comparison with the basic coalescent process in a single panmictic population. We will again utilize the properties of the exponential distribution to approximate the time to an event (see section 3.6).

Let's begin by thinking about the coalescent process when there is gene flow among several demes in terms of the bugs-in-a-box metaphor used to describe the basic coalescent process. With population subdivision the bugs are located in multiple boxes with each box representing a deme. Bugs move about within a box at random and eat each other, reducing their numbers. There is also the possibility of migration where a bug is chosen at random and moved to another box. If migration events are very rare, then the individual boxes have a good chance of being reduced to a single bug before a migrant bug enters or leaves the box. It will then take a long time for enough migration events to happen such that the entire group of boxes is reduced to a single bug. When migration events are common, migrant bugs move among the boxes frequently and the boxes are effectively interconnected. Therefore, there should be little or no time spent waiting for migration events as the bugs in all the boxes eat their way to a single bug.

Time Type of scale event

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