SURFACE: detecting convergent evolution from comparative data by fitting Ornstein‐Uhlenbeck models with stepwise Akaike Information Criterion

Abstract

Summary1. We present a method, 'SURFACE', that uses the Ornstein-Uhlenbeck stabilizing selection model to identify cases of convergent evolution using only continuous phenotypic characters and a phylogenetic tree. 2. SURFACE uses stepwise Akaike Information Criterion first to locate regime shifts on a tree, then to identify whether shifts are towards convergent regimes. Simulations can be used to test the hypothesis that a clade contains more convergence than expected by chance. 3. We demonstrate the method with an application to Hawaiian Tetragnatha spiders, and present numerical simulations showing that the method has desirable statistical properties given data for multiple traits. 4. The R package surface is available as open source software from the Comprehensive R Archive Network.

Convergence in Multispecies Interactions

“…With sufficient data, recently developed methods for mapping trait evolution onto phylogenies [78] or for quantifying the strength of convergent evolution [79] might emerge as useful resources for identifying and measuring convergent interactions. However, to use these tools, one set of interacting partners must be redefined as a trait of interest or measure of diversity.…”

Convergence across a continent: adaptive diversification in a recent radiation of Australian lizards

“…Similarly, the three littoral species are joined with the arboreal regime because the difference in hindlimb length alone is not significant enough to identify a separate adaptive peak. Previous simulation analyses have confirmed that SURFACE performs well with datasets that include multiple convergent traits, but instances of convergence were not always identified with single (convergent) traits [43]. Thus, even though these two rock and three littoral species significantly differ along specific trait axes from arboreal types, they have not been diagnosed as distinct.…”

“…We fitted a single rate BM model (BM1) and OU models with either a single optimum for all species (OU1) or with multiple optima, but single rates of selection (a) and stochastic motion around all optima (s 2 ). Secondly, we evaluated whether independent lineages converged on similar phenotypic optima by using a comparative approach implemented in R. SURFACE [43] uses a stepwise corrected AICc (Akaike's information criterion corrected for sample size) approach to fit Hansen models and evaluates the most optimal set of evolutionary regimes and regime shifts. SURFACE analyses consist of two distinct phases; a 'forward' phase during which regime shifts are added to the tree and a 'backward' phase during which shifts towards the same peaks are identified and collapsed.…”

“…43), suggesting that there is more than one phenotypic optimum for traits that strongly load on PC1. The estimated optima were found within the values realized for the extant species (electronic supplementary material, table S4), indicating that the model is a realistic description of current morphological patterns and is not negatively biased by factors of uncertainty such as potentially spurious ancestral state reconstruction.…”

Genome of the Tasmanian tiger provides insights into the evolution and demography of an extinct marsupial carnivore

“…Under this approach, convergence is implied when two or more taxa have evolved to be more similar to one another than their ancestors were to each other 23 . Unlike other convergence methods like SURFACE 68 , which identify convergent shifts in selective regimes among lineages, C 1 -C 3 measure the increase in phenotypic similarity between taxa compared to that between the most divergent species in their lineages, without assuming an adaptive process. Therefore, the more dissimilar the ancestor and the more similar the descendants, the greater the strength of the convergence.…”