Assessing model fit in phylogeographical investigations: an example from the North American sandbar willow Salix melanopsis

Aim: Coalescent models enable the direct estimation of parameters with clear biological relevance (i.e. divergence time, migration rate and rate of expansion), but they have typically been applied to phylogeographical research without a priori assessment of their fit to the empirical system. Here we explore the extent to which phylogeographical inference can be misled by evaluating the fit of several population genetic models to empirical data collected from the sandbar willow, Salix melanopsis. Location: The Pacific Northwest mesic forest of North America. Methods: We collected sequence data from five loci in 145 individuals. We assessed model fit in: (1) models delimiting previously proposed races within S. melanopsis; (2) historical biogeographical models, each describing the timing and pattern of diversification; and (3) coalescent models that correspond to those implemented in popular software packages such as IMa, lamarc, and Migrate-n. Results: We found little evidence for previous hypotheses of cryptic races delimited by habitat type (mesic, lowland or subalpine); rather, our results suggested that these variants originated from the same source population. Historical biogeographical models demonstrate that S. melanopsis has recently expanded from a single refugial population, probably located in the northern Rocky Mountains. An analysis using approximate Bayesian computation indicated that the single population expansion model implemented in lamarc is a better fit to the data than multi-population models incorporating migration and/or divergence as implemented in Migrate-n and IMa, suggesting that the parameters estimated from the latter are potentially misleading for this system. Main conclusions: Our research highlights the importance of assessing model fit in addition to estimating parameters to understand evolutionary processes. Taken together, they allow us to infer the historical demography of S. melanopsis in a manner that is not biased by previous work in the system.