Evolutionary inferences from the analysis of exchangeability

Evolutionary inferences are usually based on statistical models that compare mean genotypes or phenotypes (or their frequencies) among populations. An alternative is to use the full distribution of genotypes and phenotypes to infer the "exchangeability" of individuals among populations. We illustrate this approach by using discriminant functions on principal components to classify individuals among paired lake and stream populations of threespine stickleback in each of six independent watersheds. Classification based on neutral and nonneutral microsatellite markers was highest to the population of origin and next highest to populations in the same watershed. These patterns are consistent with the influence of historical contingency (separate colonization of each watershed) and subsequent gene flow (within but not between watersheds). In comparison to this low genetic exchangeability, ecological (diet) and morphological (trophic and armor traits) exchangeability was relatively high-particularly among populations from similar habitats. These patterns reflect the role of natural selection in driving parallel adaptive changes when independent populations colonize similar habitats. Importantly, however, substantial nonparallelism was also evident. Our results show that analyses based on exchangeability can confirm inferences based on statistical analyses of means or frequencies, while also refining insights into the drivers of-and constraints on-evolutionary diversification.