Analyzing developmental sequences within a phylogenetic framework.

Heterochrony is important as a potential mechanism of evolutionary change. However, the analysis of developmental timing data within a phylogenetic framework to identify important shifts has proven difficult. In particular, analytical problems with sequence (event) heterochrony revolve around the lack of an absolute time frame in development to allow standardization of timing data across species. An important breakthrough in this regard is the method of "event-pairing," which compares the relative timing of developmental events in a pairwise fashion. The resulting event-pair-encoded data can be mapped onto a phylogeny, which can provide important biological information. However, event-paired data are cumbersome to work with and lack a rigorous quantitative framework under which to analyze them. Critically, the otherwise advantageous relativity of event-pairing prevents an assessment of whether one or both events in a single event-pair have changed position during evolutionary history. Building on the method of event-pairing, we describe a protocol whereby event-pair transformations along a given branch are analyzed en bloc. Our method of "event-pair cracking" thereby allows developmental timing data to be analyzed quantitatively within a phylogenetic framework to infer key heterochronic shifts. We demonstrate the utility of event-pair cracking through a worked example and show how it provides a set of desired features identified by previous authors.