The effect of phenotypic plasticity on evolution in multipeaked fitness landscapes

When facing the challenge of developing an individual that best fits its environment, nature demonstrates an interesting combination of two fundamentally different adaptive mechanisms: genetic evolution and phenotypic plasticity. Following numerous computational models, it has become the accepted wisdom that lifetime acclimation (e.g. via learning) smooths the fitness landscape and consequently accelerates evolution. However, analytical studies, focusing on the effect of phenotypic plasticity on evolution in simple unimodal landscapes, have often found that learning hinders the evolutionary process rather than accelerating it. Here, we provide a general framework for studying the effect of plasticity on evolution in multipeaked landscapes and introduce a rigorous mathematical analysis of these dynamics. We show that the convergence rate of the evolutionary process in a given arbitrary one-dimensional fitness landscape is dominated by the largest descent (drawdown) in the landscape and provide numerical evidence to support an analogous dominance also in multidimensional landscapes. We consider several schemes of phenotypic plasticity and examine their effect on the landscape drawdown, identifying the conditions under which phenotypic plasticity is advantageous. The lack of such a drawdown in unimodal landscapes vs. its dominance in multipeaked landscapes accounts for the seemingly contradictory findings of previous studies.