Phylogenies are a foundation for studies of phenotypic evolution, but sometimes phylogenetic reconstruction is poorly supported. To account for phylogenetic uncertainty, it is advisable to run comparative models on multiple phylogenetic tree replicates and model-average results. Additionally, Garamszegi and Mundry (2014) suggested using Akaike weights (w) when averaging comparative models, to down-weight inefficient models that likely use phylogenies with a poor fit to the data. However, this latter advice was rarely followed, and there are concerns that weighting by w might bias results due to over-weighting models where, by chance, phylogenetic inaccuracy increases the explanatory power of predictors. We assessed these concerns simulating correlated trait evolution followed by phylogenetic generalized least square (PGLS) regression models. We found that: (i) w is not associated with the explanatory power of predictors; (ii) w is instead associated with the phylogenetic signal of models; and (iii) weighting models by w does not bias results. Additionally, (iv) using phylogenetic trees from vertlife.org, we found only a marginal benefit of weighting by w. This is likely because most trees from vertlife.org are approximately equiprobable, as may happen for many phylogenetic trees obtained with phylogenomic approaches. Lastly, (v) using phylogenetic trees along a gradient of tree quality, we found a larger benefit of model-averaging weighted by w, which produced more accurate results than non-weighted model-averaging. We conclude that weighting comparative models by w is an unbiased method that can substantially improve comparative work results. However, benefits may often be minimal, when alternative trees are approximately equiprobable.
