Fig. 1

Two examples of the coevolution score computation for a pair of genes (left and right trees in each panel). A an example with all disjoint close pairs. B An example with an unresolved polytomy “bush,” in which all individuals present are close pairs with each other. The vertical dashed lines indicate the distance cutoffs used to determine close pairs. Filled squares indicate presence of a gene, empty squares indicate its absence. Dashed boxes indicate individuals that are in close pairs with each other. In both A and B, there is exactly one close pair of individuals (in red) that is polymorphic for both genes, indicating recent gain/loss, so only that close pair contributes to the score. The genes differ in the same way (the top red individual has neither gene, the bottom red individual has both), so this contributes to the positive score for the gene pair. In A, the single close pair contributes a value of 1 to the positive score. In B, this close pair is part of a bush of \({4 \atopwithdelims ()2} = 6\) close pairs, so it contributes only \(\frac{1}{6}\) to the positive score. The more ancient event that produced the difference between the top clade (where both genes are present in all individuals) and the bottom clade (where both genes are mostly absent) does not contribute to the score. Note that our method does not actually use the trees, only which pairs of individuals are closely related