Box 1 Which measure of genetic diversity?
Expected heterozygosity (HE, gene diversity) was the preferred measure of within-population diversity among the studies we reviewed (see also Vucetich & Waite 2003), although most studies reported trends in alternate measures such as the proportion of loci polymorphic (PLP) and the average number of alleles per locus (A). These three measures are obviously interrelated. However, theoretical studies have suggested that A is likely to be reduced by stochastic processes, including those that occur at range limits, to a greater extent than HE (Nei et al. 1975). This is because rare alleles, which influence the estimate of A but have a lesser effect on HE, are readily lost during founder events, population bottlenecks and sporadic fluctuations in population size, which may occur more commonly towards range edges. Some empirical studies have even documented contrasting patterns of geographical variation for HE vs. A (e.g. Cwynar & MacDonald 1987; Comps et al. 2001). However, our survey suggests that on the whole, various measures of diversity usually exhibit parallel patterns of geographical variation, at least in the context of comparisons between central and peripheral populations. Among the 54 studies that reported both HE and A, differences between central and peripheral populations were usually in the same direction for both parameters (87.0% of studies); hence there was a strong and significant association between the results based on HE and those based on A (2 × 2 χ2 = 20.19, P < 0.0001). This is also supported by the figures below. The proportional difference in A between central vs. peripheral populations [i.e. (C–P)/C] correlated positively with the proportional difference in HE among both the 35 studies that assayed allozymes polymorphisms (left panel) and the 15 studies that assayed variation at microsatellite loci (right panel).
However, we found some evidence that the processes reducing diversity at range limits affect A more strongly than HE. A higher proportion of studies found the expected difference in A (83.3%) than in HE (74.1%). When central populations exhibited higher HE, they almost always (97.5% of the time) had higher A (n = 40 studies); but when central populations had higher A (n = 45), HE was the same or lower than for peripheral populations in 13.3% of cases. The expected difference in A was found in 43.9% of 14 studies where the difference in HE was not detected. Our analysis must, however, be interpreted with caution because very few of the studies estimated A using rarefaction to reduce the effect of variation in sample size among populations (Petit et al. 1998; see also Comps et al. 2001; Coyer et al. 2004; Hoffman & Blouin 2004; Johansson et al. 2006; Böhme et al. 2007).
Box 2 Controlling for geographical dispersion when testing for variation in genetic distance among populations
Hamilton & Eckert (2007) compared the level of genetic differentiation between a sample of nine disjunct populations of the perennial plant Geum triflorum (Rosaceae) isolated on alvar habitat in the eastern Great Lakes region of North America to 16 populations sampled from prairie habitat throughout the core of the species’ distribution in midwestern Canada and the USA. Differentiation among populations was measured by based on differentiation in allele size phenotypes at five microsatellite loci (G. triflorum is an allohexaploid, so phenotypic measures of differentiation were used). They contrasted differentiation between peripheral (P) alvar population pairs and central (C) prairie population pairs by comparing the regressions of pairwise on geographical distance. Because central populations were sampled over a broader geographical range than peripheral populations, only pairs of central populations within the range of geographical distances between peripheral population pairs were analyzed. To compare differentiation while controlling for geographical distance between populations, randomization tests were used to evaluate the differences in the slope and the y intercept of the regressions of over geographical distance.
Pairwise increased with geographical distance within peripheral (r = +0.36, P = 0.03) and central regions (r = +0.56, P < 0.0001). The slope of the regression did not differ between regions (P = 0.29), but the intercept was higher for peripheral populations (P = 0.007). The increase in genetic differentiation with geographical distance was similar between regions, but peripheral populations were more differentiated at all distances. Pairwise was also more variable for peripheral population pairs across all distances. The variance in the residuals from the regressions was greater for peripheral than central comparisons (P < 0.0001).
Differentiation may be higher among disjunct than among central populations due to a simple extension of a common pattern of isolation by distance. However, peripheral populations of G. triflorum were more differentiated from each other than were central populations, even after isolation by distance was accounted for, and the variability in differentiation was greater for peripheral populations. This is consistent with a more continuous distribution of G. triflorum in the prairie region. The central populations sampled occurred in a landscape containing many other populations of G. triflorum (of which only a fraction were sampled), whereas peripheral populations were restricted to patches of alvar habitat that were few and far between. As the isolation of populations increases, genetic drift becomes more influential than gene flow, and the differentiation among populations is expected to become greater and more variable. The nature of the landscape matrix separating populations may combine with geographical isolation to influence the pattern of genetic differentiation.
Box 3 Comparing genetic differentiation among populations when diversity within populations varies geographically
The level of genetic differentiation among populations is widely measured by FST or its analogue GST as the proportion of total genetic diversity (HT) distributed among populations as opposed to within populations (HS): GST = (HT – HS)/HT, where HS is the average heterozygosity within populations at Hardy–Weinberg equilibrium and HT is the expected heterozygosity of all populations pooled. However, as Hedrick (1999, 2005) points out, the magnitude of GST is strongly influenced by the amount of genetic diversity, especially when individual populations maintain many alleles at the marker loci used. The problem arises because GST measures the amount of variation among populations (HT – HS) relative to the total variation (HT), without taking account of the identity of the alleles involved. As a result, both HS and HT can approach 1, even if different populations maintain different alleles. Hence the difference between HT and HS and, in turn GST, will be underestimated.
This problem complicates comparisons of population differentiation between genes with different levels of polymorphism (Hedrick 2005), such as allozymes vs. the more highly variable microsatellites (which have increasingly found use in studies of geographical variation in population genetic structure). This problem also applies to comparisons between geographical regions that may differ in HS and/or HT. In the case of comparisons of central vs. marginal populations, the degree of differentiation as measured by GST will be underestimated for central populations if, as expected, central populations tend to contain more genetic diversity (i.e. higher HS) than peripheral populations.
Hedrick (2005) suggests controlling for variation in HS and HT by scaling GST by the maximum possible value (GST(Max)) given the level of polymorphism, where GST(Max) = (1 – HS)/(1 + HS). It follows from this that central populations, given that they are likely to have higher values of HS than peripheral populations, will have lower values of GST(Max) and potentially lower overall GST, regardless of the level of population differentiation. A corrected should therefore be calculated as GST/GST(Max). Given that this approach was introduced relatively recently, none of the studies we reviewed had corrected GST before comparing the level of genetic differentiation for central vs. peripheral populations. Our analyses may possibly overestimate the difference in differentiation of peripheral vs. central populations, especially for studies using highly polymorphic markers. Post-hoc calculation of is possible, but only in the rare instances where authors reported HS and HT for individual loci and central and peripheral populations separately (two of 134 studies) or population-level allele frequencies (21 studies). Our analyses of differentiation must be interpreted with due caution.