Ontogenetic Sequence Analysis: using parsimony to characterize developmental sequences and sequence polymorphism.

Ontogenetic sequences are a pervasive aspect of development and are used extensively by biologists for intra- and interspecific comparisons. A tacit assumption behind most such analyses is that sequence is largely invariant within a species. However, recent embryological and experimental work emphasizes that ontogenetic sequences can be variable and that sequence polymorphism may be far more prevalent than is generally realized. We present a method that uses parsimony algorithms to map hierarchic developmental patterns that capture variability within a sample. This technique for discovering and formalizing sequences is called the "Ontogenetic Sequence Analysis" (OSA). Results of OSA include formalized diagrams of reticulating networks, describe all most parsimonious sequences, and can be used to develop statistics and metrics for comparison of both intraspecific and interspecific sequence variation. The method is tested with examples of human postnatal skeletal ossification, comprising a time-calibrated data set of human hand and wrist epiphyseal unions, and a longitudinal data set of human wrist ossification. Results illustrate the validity of the method for discovering sequence patterns and for predicting morphologies not represented in analytic samples. OSA demonstrates the potential and challenges of incorporating ontogenetic sequences of morphological information into evolutionary analyses.