Evolution with complex selection and transmission

Inheritance is the key factor making biological evolution possible. Despite this central role, transmission is often bundled into the simplifying assumptions of evolutionary models, making it difficult to see how changes in the patterns of transmission influence evolutionary dynamics. We present a mathematical formalism for studying phenotypic evolution, under any selection regime and with any transmission rules, that clearly delineates the roles played by transmission, selection, and interactions between the two.\n\nTo illustrate the approach, we derive models in which heritability and and fitness are influenced by the same environmental factors - producing a covariation between selection and transmission. By itself, variation in heritability does not influence directional evolution. However, we show that any covariation between heritability and selection can have a sub-stantial effect on trait evolution. Moderate differences in heritability between environments can lead to organisms adapting much more to environments with higher heritability, and can pull a population off of an \"adaptive peak\". When habitat preference is allowed to evolve as well, variation in heritability between environments can lead to organisms exclusively using the environment in which heritability is highest. This effect is most pronounced when initial habitat selection is weak.