Reversible phenotypic plasticity with continuous adaptation

We introduce a novel model for continuous reversible phenotypic plasticity. The model includes a one-dimensional environmental gradient, and we describe performance of an organism as a function of the environmental state by a Gaussian tolerance curve. Organisms are assumed to adapt their tolerance curve after a change of the environmental state. We present a general framework for calculating the genotype fitness if such adaptations happen in a continuous manner and apply the model to a periodically changing environment. Significant differences of our model with previous models for plasticity are the continuity of adaptation, the presence of intermediate phenotypes, that the duration of transformations depends on their extent, fewer restrictions on the distribution of the environment, and a higher robustness with respect to assumptions about environmental fluctuations. Further, we show that continuous reversible plasticity is beneficial mainly when environmental changes occur slow enough so that fully developed phenotypes can be exhibited. Finally we discuss how the model framework can be generalized to a wide variety of biological scenarios from areas that include population dynamics, evolution of environmental tolerance and physiology.