Adaptation of a quantitative trait to a moving optimum

We investigate adaptive evolution of a quantitative trait tinder stabilizing selection with a moving optimum. We characterize three regimes, depending on whether (1) the beneficial mutation rate, (2) the fixation time, or (3) the rate of environmental change is the limiting factor for adaptation. If the environment is rate limiting, mutations with a small phenotypic effect are prefered over large mutations, in contrast to standard theory.