After Wright (1951) developed F-statistics he went on to demonstrate that there is a simple relationship between the genetic divergence of two populations, measured as FST, and the amount of gene flow between them, which is given as:
where Ne is the effective size of each population and m is the migration rate between populations, and therefore Nem is the number of breeding adults that are migrants. From Equation 4.8 we can calculate Nem as:
In the scarlet tiger moth example that was given earlier in this chapter, the FST value for the two populations was 0.009. This would translate into a very high indirect estimate of gene flow since Nem = (1/0.009 — 1)/4 = 27.5 individuals migrating between the two populations each generation.
Nem is a popular method for estimating gene flow from genetic data, in part because of the ease with which it can be calculated. There are, however, several problems associated with estimates of Nem. For one thing, it is based on what is known as the island model of population structure. This model assumes no selection or mutation and an infinite number of populations, all of which are the same size and have an equal probability of exchanging migrants. Nem also assumes that populations are in migration-drift equilibrium, which occurs when the increase in genetic differentiation caused by drift is equal to the decrease in genetic differentiation caused by gene flow. Populations reach equilibrium only when population sizes and migration rates remain more or less constant; equilibrium is therefore negated by a number of demographic processes, including recent range expansions, habitat fragmentation, and population bottlenecks.
The extent to which a lack of migration-drift equilibrium can influence Nem estimates was illustrated by a study of the pond-dwelling whirligig beetle Dineutus assimilis. Gene flow estimates based on FST values were compared with dispersal estimates that were based on mark--recapture. Four sites within a few kilometres of each other yielded an average FST estimate of 0.0949, which translated into an average Nem value of 2.12. However, the mark--recapture study showed that up to eight immigrants arrived at a pond in a single season. An explanation for these contradictory results emerged after a closer investigation showed that regular bottlenecks were occurring within the ponds. These bottlenecks would accelerate genetic drift and thus prevent the populations from reaching migration--drift equilibrium. As a result, FST values would be inflated, which would lead to a corresponding reduction in Nem. Since the ecology of this species meant that a high proportion of immigrants were likely to reproduce in their new populations (i.e. dispersal and gene flow should be comparable), a lack of equilibrium provided the most plausible explanation for the discrepancy between Nem and direct dispersal estimates in this study (Nurnberger and Harrison, 1995).
There has been an ongoing debate in the literature over just how useful Nem values are as estimates of gene flow. On the one hand, Nem values in numerous studies are comparable with direct estimates of dispersal. A meta-analysis of 230 studies of phytophagous (plant-feeding) insects revealed estimates of Nem that generally agreed with direct estimates of dispersal that were based on mark-recapture studies or observations of new colonizations, since highly vagile species showed higher levels of gene flow (Nem) than sedentary species (Peterson and Denno, 1998b). Similar findings were obtained in another meta-analysis, this time based on 333 species of vertebrates and invertebrates from terrestrial, freshwater and marine habitats (Bohonak, 1999). Nevertheless, the FST values between populations are influenced by factors other than gene flow, and the unrealistic assumptions of the island model of population structure upon which Nem estimates are based mean that they should be interpreted with caution (Whitlock and McCauley, 1999).
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