BACKGROUND Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness… (More)
Heterochrony has become a central organizing concept relating development and evolution. Unfortunately, the standard definition of heterochrony--evolutionary change in the rate or timing of developmental processes--is so broad as to apply to any case of phenotypic evolution. Conversely, the standard classes of heterochrony only accurately describe a small… (More)
The development of most phenotypic traits involves complex interactions between many underlying factors, both genetic and environmental. To study the evolution of such processes, a set of mathematical relationships is derived that describe how selection acts to change the distribution of genetic variation given arbitrarily complex developmental interactions… (More)
Statistical associations between phenotypic traits often result from shared developmental processes and include both covariation between the trait values and more complex associations between higher moments of the joint distribution of traits. In this article, an analytical technique for calculating the covariance between traits is presented on the basis of… (More)
BACKGROUND Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration,… (More)
Species selection, differential rates of speciation or extinction resulting from species level characters, is often invoked as the main mechanism of macroevolution that is not simply an extension of microevolutionary processes. So long as we are careful in defining "species", the logic of species selection is sound. This does not mean, however, that this… (More)
Note: This is a book chapter that will have embedded in it a Box explaining the geometry of phenotype landscapes. The text for the Box, which includes Figures 1 and 2, is at the end of the manuscript.