"Effective" population size

Bocquet-Appel-Recent_Advances_in_Palaeodemography-9781402064234

Chapter 1 by J Hawks.

In the absence of selection, allele frequencies vary as a stochastic process. The parameters influencing this process are themselves demographic: population size and mating pattern. Ultimately, the rate of evolution of a population must be constrained by these parameters. This means that the observable genetic characteristics of populations are to some extent natural estimators of demographic characteristics. The relationship between the demographic parameters of a population and its genetic characteristics may in some cases be approximated by a single parameter: the “effective population size.” Effective population size refers the demographic complexity of some real population to the simplicity of some ideal population — in other words, it is a measure of the extent to which a natural population corresponds to some theoretical population model.

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The model-dependence of effective population size is rarely considered in analyses of molecular data. Ewens (2004) gives a good account of the problem:

Except in simple cases, the concept [of effective population size] is not directly related to the actual size of the population. For example, a population might have an actual size of 200 but, because of a distorted sex ratio, have an effective population size of only 25. This implies that some characteristic of the model describing this population, for example a leading eigenvalue, has the same numerical value as that of a Wright- Fisher model with a population size of 25. It would be more indicative of the concept if the adjective “effective” were replaced by “in some given respect Wright-Fisher model equivalent.” Misinterpretations of effective population size calculations frequently follow from a misunderstanding of this fact (Ewens, 2004, 37–38).

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The utility of effective population size comes from the fact that it concatenates many separate stochastic phenomena into a single parameter. As an example, a gene frequency is a single value, with a single degree of freedom. It is therefore sufficient to estimate only a single parameter. This approach obviously runs into trouble when more than one stochastic factor varies in the population.