Data from: Testing for independence between evolutionary processes

Evolutionary events co-occurring along phylogenetic trees usually point to
complex adaptive phenomena, sometimes implicating epistasis. While a
number of methods have been developed to account for co-occurrence of
events on the same internal or external branch of an evolutionary tree,
there is a need to account for the larger diversity of possible relative
positions of events in a tree. Here we propose a method to quantify to
what extent two or more evolutionary events are associated on a
phylogenetic tree. The method is applicable to any discrete character,
like substitutions within a coding sequence or gains/losses of a
biological function. Our method uses a general approach to statistically
test for significant associations between events along the tree, which
encompasses both events inseparable on the same branch, and events
genealogically ordered on different branches. It assumes that the
phylogeny and themapping of branches is known without errors. We address
this problem from the statistical viewpoint by a linear algebra
representation of the localization of the evolutionary events on the
tree.We compute the full probability distribution of the number of paired
events occurring in the same branch or in different branches of the tree,
under a null model of independence where each type of event occurs at a
constant rate uniformly inthephylogenetic tree. The strengths
andweaknesses of themethodare assessed via simulations;we then apply the
method to explore the loss of cell motility in intracellular pathogens.