New tools for studying integration and modularity.

The study of phenotypic integration concerns the modular nature of organismal phenotypes. The concept provides a rationale for why certain subsets of phenotypic traits show particularly high levels of association over development and/or evolution. The techniques detailed in this report facilitate the generation and testing of hypotheses of phenotypic integration and trait interaction. The approach advocated for exploring patterns of interaction among traits is based on the statistical notion of conditional independence, incorporated in a technique known as graphical modeling. The use of graphical models is illustrated with an application to a well-known biological dataset of fowl skeletal measurements, previously analyzed by Sewall Wright. A definition of phenotypic modularity is given, based on a notion of mutual information, which provides a consistent criterion for recognizing and delimiting integrated subsets of traits and which can be related to standard models of multivariate selection.