Characterizing and mitigating confounding by unreplicated evolutionary events in phylogenetic regression

When researchers want to test for a direct effect of one attribute on another using interspecific data, they need to account for the confounding influence of other attributes that have phylogenetic structure. Accordingly, a suite of approaches have been developed for this purpose, mostly notably the use of phylogenetic regression. However, it has been shown that such methods can be misled by evolutionary events with large effects. We suggest that one widely-applicable solution to this problem can be found by borrowing both from the statistical genetics literature and by digging into the past of phylogenetic comparative methods. In conventional phylogenetic regression, the phylogenetic variance-covariance matrix is included as a random-effect term; here, we argue that it can be advantageous to also include the leading eigenvectors of this matrix as fixed effects. Building on the recent results of Schraiber et al. (2024), we use mathematical analysis and simulations to show under which scenarios this hybrid strategy is effective. We develop a novel approach for visualizing the contributions of different branches of the phylogeny to the eigenvectors of the variance-covariance matrix. We also illustrate how quantile-quantile plots can be used to assess whether the phylogenetic structure has been effectively controlled. We then apply the mixed approach to investigate the co-evolution of gene expression levels of different genes across the phylogeny of cichlid fishes; we show that including the leading eigenvectors likely reduces the false positive rate. To facilitate the use of our visualization approach and of including eigenvectors in phylogenetic regression models, we present a new R package called EIGER. We argue that the approaches we explore here can both help address the statistical problems that arise from large, historical events and more generally, provide richer insights into the nature of phylogenetic confounding.