MORPHOLOGICAL INTEGRATION AND MACROEVOLUTION: IS INTEGRATION THE CONVERSE OF MODULARITY?
The relationship between integration and modularity need not be fixed. Lack of equivalence and imperfect correlation can vary substantially because of
a) The geometry of organisms: the size and shape of body parts can differentially affect patterns of character connectivity. For homogeneous parts such as serial homologues, modularity may increase or decrease without change in integration. For heterogeneous parts, mismatches between inferred modularity and integration may be common.
b) The topology of morphospace: Intrinsic heterogeneities in morphospace structure can induce asymmetric transition probabilities. Changes in modularity or integration may not be reversible or equiprobable. Factorizations of echinoid morphospace suggest clear mismatches between regular and irregular echinoids in the large-scale evolution of modularity and of integration. Differences in dimensionality, ontogeny, and taxonomic structure help explain such mismatches.
c) Historical contingency: The relationship between integration and modularity is conditioned on which possible phenotypes have actually evolved, their location in morphospace, intrinsic origination and extinction probabilities, biogeographic and ecological factors, and the extent to which the history of occupation of morphospace is representative of its structure.