Figure 2.

Hypothetical example of our approach for examining distances and vectors of expected and observed divergence among groups, to test for the potential imprint of past history on convergence. The black square represents the mean of species in the focal group that still have the ancestral ecology. The white square represents the mean of species of the focal group that have the novel ecology, and the white circle is the mean of non-focal species that have the same ecology as the focal group with the novel ecology. Hence, similar colour represents similar ecology and similar shape represents close phylogenetic relatedness. D_obs, D_env, D_proj, D_exp and θ are as described in the text. An effect of history would be indicated by a much shorter D_obs than D_exp, whereas convergence would be indicated by a smaller D_env than D_obs and a small θ. Note that only two traits are shown in this example for visual clarity, but this approach can be applied in any n-dimensional trait space.