The Selection Gradient of an Infinite-Dimensional Trait

The selection gradient is of central importance in evolutionary biology because it quantifies the forces of directional selection acting on a trait. Lande has shown that the selection gradient can be computed as the vector gradient of the log mean fitness when the trait is normally distributed. Using the framework of Gaussian processes and reproducing kernel Hilbert spaces, a rigorous definition is developed for the selection gradient of an infinitedimensional trait. Lande’s result is then extended to this case.