Statistical analyses of developmental sequences: the craniofacial region in marsupial and placental mammals.

Heterochrony is most often thought to involve changes in the rate of development or maturation (rate changes). However, heterochrony can also involve changes in the timing of specific developmental events relative to other events (sequence changes). Sequence changes have received much less attention than have changes in developmental rates, in part because few methods exist for comparing developmental sequences. Here, we present two methods to statistically evaluate developmental sequence changes. First, Kendall's coefficient of concordance (W) is used to quantify overall similarity of developmental sequences in two or more groups of organisms, and second, ANOVA is used to identify the individual events that differ most in their relative developmental timing. Computer simulation is used to control for the nonindependence of species. We examine the sequence of developmental events in the craniofacial region of marsupial and placental mammals. We conclude that the most important differences in development in the two clades relate to the relative sequence of development of the central nervous system and somatic elements of the craniofacial region. The rationale behind the methods and their limitations are discussed, and the results from this study are compared with a previous analysis.