Long-Term Correlated Response, Interpopulation Covariation, and Interspecific Allometry

A model of long-term correlated evolution of multiple quantitative characters is analyzed, which partitions selection into two components: one stabilizing and the other directional. The model assumes that the stabilizing component is less variable than the directional component among populations. The major result is that, within a population, the responses of characters to selection in the short term differ qualitatively from those in the long term. In the short term, the responses depend on genetic correlations between characters, but in the long term they are only determined by the fitness functions of stabilizing and directional selection, independent of genetic and phenotypic correlations. Treating the stabilizing component as a constant and assuming the directional component to vary among populations, I present formulas for the interpopulation covariation and interspecific allometry, which are functions of the intensity matrix of stabilizing selection. Particular attention is paid to the relationship between intra- and interpopulation correlations.