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Effective Parameters in Population Genetic Models with Class Structure

Many parameters of a population such as the total number of individuals or migration rates between subpopulations cannot be measured directly by experiments. Therefore, population geneticists estimate them by fitting a mathematical model to available data. A general problem in this approach is that the estimates often deviate from the real values. This is not only due to statistical errors but also due to idealizations of the underlying models. The value of a parameter that accounts for the pattern of data under the idealized assumptions is usually called the ‘effective’ value of the parameter. By definition, the effective value is not the real value as the ideal model scenario is hardly ever met in reality. Among a variety of effective parameter values, the effective population size ( N e ), which measures the intensity of genetic drift, has been playing a central role since Wright’s (1931) seminal work. Less acknowledged but possibly equally important is the concept of the effective migration rate ( m e ), which quantifies gene flow (Bengtsson 1985). Effective parameter values are key characteristics of a population, and it is of primary importance to predict how they deviate from real values under various non-ideal situations. The presentation gives an overview over the effective migration rate and how it relates to other effective parameters. First, I discuss scenarios where genetic influx into a population does not correspond to the real migration rate ( m ) of individuals, due to class structure within the population (e.g., different age, sex, allelic composition, infection status). The ratio m e / m is called the gene flow factor, and represents the degree of gene flow modification in such situations. Second, I discuss the example where both gene flow and genetic drift is modified by cytoplasmic sex ratio distorters, and demonstrate that the allele frequency distributions are beautifully described by both m e and N e . Finally, it is shown how the effective migration rate relates to the effective recombination rate ( r e ). Examples are presented that show how r e can be used to analyze and compare different sym- and parapatric models of speciation.