## Problem box Estimating Ne from observed heterozygosity over time

Use the data provided in Table 3.5 to estimate N'e over four generations for each of the 10 replicate populations. Heterozygosity in the first generation was 0.5 in all populations since initial allele frequencies were p = q = 0.5. Does the average estimate of N'e better match what is expected for a fluctuating population of 100-10-50-100?

There are an array of methods that have been employed to estimate effective population size from genetic data using various estimators of the variance and inbreeding effective population sizes. Table 3.6 provides some estimates of the ratio of the effective population size to the census size. A general conclusion is that the effective population size is often one-tenth or less, sometimes much less, of the census population size. See Waples (1989) for more details on estimating effective population size from changes in allele frequency through time. In addition, the effective population size can be estimated with gametic disequilibrium (equation 2.31; Waples 1991; Slatkin 1994), heterozygote excess in small populations of self-incompatible individuals due to random allele-frequency differences between populations of male and female breeders (Balloux 2004), and gene diversity of DNA sequences or other molecular marker loci.

### Breeding effective population size

Up to this point, an implicit assumption has been that a population is an easily recognized and discrete entity. In species where individuals are more or less continuously distributed over large areas, there are no obvious physical or geographic boundaries that define populations. Instead, populations can be defined by average mating and dispersal patterns among individuals that result in limits to the movement of gametes each generation. Based on the size of the breeding and dispersal area there is the breeding effective population size, which is particularly suitable for populations where individuals may occur relatively uniformly over large areas and not form discrete aggregations. Imagine a large, continuous plant population that covers many hectares (plants are a good example since they stay in the same place over time, but the concept applies to all organisms). Now imagine examining all of the successful mating events for many individuals. The distances of mating

Table 3.6 Estimates of the ratio of effective to census population size wide range of estimation methods and assumptions.

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