Tip-based metrics
The estimated node states were used to calculate three tip-based metrics of trait evolution. The transition rates (TR) of the species swere calculated as:
\begin{equation} TRs=\ \frac{t}{N}\nonumber \\ \end{equation}
where t is the number of transitions of trait states detected at the nodes that a species underwent from the phylogeny root to the tip, and N is the total number of nodes, counting from the tip to the root. A value equal to 1 indicates that the species presented as many character-state transitions as possible given its evolutionary history, whereas a value equal to 0 indicates that there were no transitions – the tip and the ancestral character-state remained the same (Fig. 1).
Stasis Time (ST) of the species s was calculated as:
\begin{equation} \text{ST}_{s}=\max{\ \{L_{i},\ldots,L_{N}\}}\ \text{if}\ L_{i}\in A_{i}=a\nonumber \\ \end{equation}
where L is the branch length value from node i to N that have the trait-state A similar to the tip trait-state a . Stasis time (ST) examines evidence for character retention over time (Fig. 1). The metric consists in determining, across the whole phylogeny, the maximum value of branch length between two nodes with mapped trait A similar to the tip trait a . This can be seen in Fig. 1, where species 3 is currently an insectivore, having recently transitioned from a plant-eater diet. Its lineage had a longer time as an insect-eater from node 2 to the 3 than between any other nodes. Thus, the longer stasis time as an insect-eater is that one embracing the branches predating the time as a plant-eater.
Finally, Last Transition Time (LT) of the species s was calculated as:
\begin{equation} \text{LT}_{s}=\sum_{i=1}^{min\{N,\ \text{\ L}_{i}\ \notin\text{\ A}_{i}\ =\ a\}}L_{i}\nonumber \\ \end{equation}
where branch lengths L are summed from node i to Nhaving a trait A similar to the tip trait a . The sum stops when the trait A of the node i differs from the tip traiti =1. Last transition time indicates when the current tip trait became fixed. The values of LT will exceed ST because the former consists of a sum of more recent branch lengths with trait a , whereas the latter is the maximum branch length between two nodes with trait a . R code with the tip-based metrics we develop here can be found in the GitHub of the first author.