Omn

random from the total population of d demes there is

a — chance they are from the same deme and a-

d d chance they are from different demes. Therefore, the average coalescence time for two lineages sampled at random from a subdivided population is

and equation 4.77 provides the average coalescence time for two lineages sampled from the same deme gives an expression for the pattern of population structure from the perspective of coalescence times (Slatkin 1991). Population structure can then be thought of as the difference in average coalescence times for a pair of lineages in the total population and a pair of lineages in a subpopulation.

In general, population subdivision is expected to increase the time required for lineages to coalesce to a single most recent common ancestor. When gene flow is limited, coalescent events within demes occur much as they would in an isolated panmictic population. However, the single ancestor for each deme must wait for a relatively rare migration event until two lineages in different demes can coalesce to a single ancestor. This tends to produce genealogical trees that have long branches connecting the individual ancestors of different demes. As rates of migration increase, the genealogical tree branch lengths approach the patterns expected in a single panmictic population of the same total size since migration events frequently move lineages among the demes.

Chapter 4 review

• Spatial and temporal separation of discrete subpopulations as well as isolation by distance in continuous populations both result in mating that is not random throughout a population. Without enough gene flow to maintain random mating (panmixia), genetic drift causes divergence of allele frequencies among subpopulations.

• Parentage analyses use genotypes of progeny and one known parent to infer the haplotype of the unknown parent. This unknown parent haplotype is then used to exclude possible parents from the pool of candidate parents. The power of this procedure to identify the true parent depends on the chance that a given haplotype will occur at random in a population.

• The Wahlund effect demonstrates that genetic variation can be stored as variance in allele frequencies among subpopulations or as hetero-zygosity within a panmictic population. Fusion of diverged subpopulations or subdivision of a panmictic population converts one type of genetic variation into the other type of genetic variation.

• FIS measures the average excess or deficit of heterozygous genotypes compared with random mating. FST measures the deficit of heterozygosity in subpopulations due to population structure compared to heterozygosity expected with panmixia. FIT measures the total excess or deficit of heterozygous genotypes due to both non-random mating within and allele-frequency divergence among subpopulations.

• Levels of gene flow can be measured by directly tracking parentage in contemporary populations (a direct estimate) or by measuring the pattern of allele-frequency differentiation among a set of subpopulations and then comparing the result to what is expected in an ideal standard such as the infinite island model (an indirect estimate).

• Genealogical trees in subdivided populations can be modeled with an exponentially distributed waiting time where the chance of migration and the chance of coalescence are combined.

• In two demes, the average time to coalescence for two lineages in the same deme is the total population size and is independent of the migration rate. For two lineages in different demes, the average time to coalescence gets longer as the number of demes increases and as the migration rate decreases, since two lineages can only coalesce when they are in the same deme.

• Population structure and limited gene flow lengthen the average coalescence time of two lineages sampled at random from the population compared to the average coalescence time of two lineages sampled from the same subpopulation.

Further reading

To learn more about the role that the plant Linanthus parryae played in the development of the theory of isolation by distance, as well as the personalities associated with competing interpretations of the spatial distributions of blue and white flower colors, see chapters 11 and 13 in

Provine WB. 1986. Sewall Wright and Evolutionary Biology. University of Chicago Press, Chicago, IL.

A review of probability theory for parentage assignment along with a detailed listing of available analysis software available can be found in

Jones AG and Ardren WR. 2003. Methods of parentage analysis in natural populations. Molecular Ecology 12: 2511-23.

An older yet still valuable review of concepts and empirical estimates of population structure and indirect estimates of gene flow can be found in

Slatkin M. 1985. Gene flow in natural populations. Annual Review of Ecology andSystematics 16: 393-430.

The impacts of population subdivision or isolate breaking on genotype frequencies is more complicated for loci with more than two alleles. For a treatment of this topic consult:

Li CC. 1969. Population subdivision with respect to multiple alleles. Annals of Human Genetics 33: 23-9.

A review of the conceptual bases and methodological approaches to estimation of population structure using analysis of variance can be found in

Weir BS. 1996. Genetic Data Analysis II. Sinauer Associates, Sunderland, MA.

A review of spatial patterns of genetic variation within and among populations, methods to measure spatial aspects of genetic variation, and discussion of the processes causing these patterns can be found in

Epperson BK. 2003. Geographical Genetics. Princeton University Press, Princeton, NJ.

A review of the impacts of population structure in the context of the coalescent model can be found in

Charlesworth B, Charlesworth D, and Barton NH. 2003. The effects of genetic and geographic structure on neutral variation. Annual Review of Ecology and Systematics 34: 99-125.

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