Modeling colonization rates over time: Generating null models and testing model adequacy in phylogenetic analyses of species assemblages.

A central theme connecting macroevolutionary processes to macroecological patterns is the shaping of regional biodiversity over time through speciation, extinction, migration, and range shifts. The use of phylogenies to explore the dynamics of diversification due to variation in speciation and extinction rates has been well-developed and there are established methods for inferring speciation times from phylogenies and generating its null distributions (as represented by node heights on molecular phylogenies). But inferring colonization events from phylogenies is more challenging. Unlike speciation events, represented by nodes, colonization events could occur at any point along a branch connecting species in the assemblage to the regional pool. We account for uncertainty in identification of colonization lineages and timing of colonization events by using an efficient analytical solution to inferring the distribution of colonization times from an assemblage phylogeny. Using the same solution, we efficiently derive the null distribution of colonization times, which provides us with a general approach to testing the adequacy of a model to describe colonization events into the assemblage. We illustrate this approach by demonstrating how the movement of squamate lineages into Madagascar has been uneven over time, peaking in the early Cenozoic when ocean conditions favored colonization.