The comparative analysis of lineage-pair traits.

For many questions in ecology and evolution, the most relevant data to consider are attributes of lineage pairs. Comparative tests for causal relationships among traits like 'diet niche overlap', 'divergence time', and 'strength of reproductive isolation (RI)' - measured for pairwise combinations of related species or populations - have led to several groundbreaking insights, but the correct statistical approach for these analyses has never been clear. Lineage-pair traits are non-independent, but unlike the expected covariance among species' traits, which is captured by a phylogenetic covariance matrix arising from a given model, the expected covariance among lineage-pair traits has not been explicitly formulated. Analyses of pairwise-defined data have thus employed untested workarounds for non-independence rather than direct models of lineage-pair covariance, with consequences that are unexplored. Here, we consider how evolutionary relatedness among taxa translates into non-independence among taxonomic pairs. We develop models by which phylogenetic signal in an underlying character generates covariance among pairs in a lineage-pair trait. We incorporate the resulting lineage-pair covariance matrices into modified versions of phylogenetic generalized least squares and a new phylogenetic beta regression for bounded response variables. Both outperform previous approaches in simulation tests. We find that a common heuristic method, node averaging, imparts a greater cost to model performance than does the non-independence it was designed to correct. We re-analyze two empirical datasets to find dramatic improvements in model fit and, in the case of avian hybridization data, an even stronger relationship between pair age and RI than is revealed from uncorrected analysis. We finally present a new tool, the R package phylopairs, that allows empiricists to test relationships among pairwise-defined variables in a way that is statistically robust and more straightforward to implement.