A general framework for the analysis of phenotypic trajectories in evolutionary studies.

Many evolutionary studies require an understanding of phenotypic change. However, while analyses of phenotypic variation across pairs of evolutionary levels (populations or time steps) are well established, methods for testing hypotheses that compare evolutionary sequences across multiple levels are less developed. Here we describe a general analytical procedure for quantifying and comparing patterns of phenotypic evolution. The phenotypic evolution of a lineage is defined as a trajectory across a set of evolutionary levels in a multivariate phenotype space. Attributes of these trajectories (their size, direction, and shape), are quantified, and statistically compared across pairs of taxa, and a summary statistic is used to determine the extent to which patterns of phenotypic evolution are concordant across multiple taxa. This approach provides a direct quantitative description of how patterns of phenotypic evolution differ, as well as a statistical assessment of the degree of repeatability in the evolutionary responses to selection among taxa. We describe how this approach can quantify phenotypic trajectories from many ecological and evolutionary processes, whose data encode multivariate characterizations of the phenotype, including: phenotypic plasticity, ecological selection, ontogeny and growth, local adaptation, and biomechanics. We illustrate the approach by examining the phenotypic evolution of several fossil lineages of Globorotalia.