Quiescence wins: The Discovery Of Slowness

Abstract

We investigate the evolution of quiescence within the framework of Adaptive Dynamics for an SIQS (Susceptible - Infected - Quiescent) model with constant environment. In the first part of the paper, the competition of two strains which have the same basic fitness (same reproduction number) but different timing in quiescence is analyzed. Thereto, the complexity of the model is reduced: By a time scale argument, we approximate the SQIS model by an SIS model under the assumption of rapid switching between I and Q. Furthermore, using dimension reduction methods for the van Kampen expansion of the models, we replace the multi-dimensional SDE by an effective one dimensional SDE on the center manifold of the models. Finally, the fixation probabilities of the strains are derived. In the second part of the paper, we use concepts from adaptive dynamics to analyze the stochastic random walk on the trait space. We find that quiescence is favored by intrinsic stochastic effects. In the end, a more intuitive explanation is added to the mathematical arguments. The analysis suggests a new paradigm for the evolution of quiescence in parasites: In the present context, quiescence is not a bed-hedging strategy to escape detrimental conditions in a fluctuating environment, but a simple and efficient method to continuously control and slow down the time scale of life-history traits. It turns out that evolution favors slowness, with the analysis suggesting that this effect may be widespread in systems where species interact only indirectly through competition for resources.