Phenotypic Integration Without Modularity: Testing Hypotheses About the Distribution of Pleiotropic Quantitative Trait Loci in a Continuous Space

Abstract

Theories of phenotypic integration have relied heavily on the concept of modularity in order to model the ways in which traits in an organism correlate and covary. Recent investigations suggest that, while some functional and developmental processes may be morphologically and ontogenetically localized, and thus modular in a developmental sense, there is a great deal of overlap among these influences on patterns of integration in the adult form. This can result in blurry boundaries between hypothesized modules constructed to test hypotheses about phenotypic integration. This investigation tests hypotheses about the contribution of pleiotropic quantitative trait loci (QTL) to phenotypic integration in the mouse mandible without using a priori categorical hypotheses about which traits constitute a module. We ask two main questions: (1) Are the effects of pleiotropic QTL localized to highly correlated traits or more spread out among traits than one might expect by chance? (2) Does the pattern of trait influence when all pleiotropic QTL are considered together deviate from what we might expect if QTL affect traits without regard for the correlations among traits? We find that a large proportion of pleiotropic QTL affect traits that are more highly correlated than we expect by chance with the remainder having effects that are distributed as if by chance. Furthermore, the overall distribution of the effects of pleiotropic QTL differs significantly from the null distribution of no association between pleiotropic effects on traits and correlations among traits. The main modular hypothesis used by earlier studies often does not predict the distribution of sets of traits sharing a common QTL. These results suggest that there is a clear tendency for pleiotropic effects of QTL to be localized but that the localization may be best thought of as occurring in a continuous space rather being clustered in discrete modules.