Abstract
Natural selection favours phenotypes that match prevailing ecological conditions. A rapid process of adaptation is therefore required in changing environments. Maternal effects can facilitate such responses, but it is currently poorly understood under which circumstances maternal effects may accelerate or slow down the rate of phenotypic evolution. Here, we use a quantitative genetic model, including phenotypic plasticity and maternal effects, to suggest that the relationship between fitness and phenotypic variance plays an important role. Intuitive expectations that positive maternal effects are beneficial are supported following an extreme environmental shift, but, if too strong, that shift can also generate oscillatory dynamics that overshoot the optimal phenotype. In a stable environment, negative maternal effects that slow phenotypic evolution actually minimize variance around the optimum phenotype and thus maximize population mean fitness.