Disadvantages of Preferential Dispersals in Fluctuating Environments

The evolution of a bet-hedging system is an important problem in fluctuating environments. However, the adaptability of preferential dispersal is not yet known. We have investigated preferential and random dispersals in bet-hedging systems using a discrete-time stochastic matrix model, in which each site fluctuates between good and bad environments with a temporal correlation. To explore the optimal migration pattern, an analytical estimation of the total growth was derived by mean-field approximation. We clarified the effect of the time correlation of environments and found that the preference for fertile sites is disadvantageous when transportation among sites has a cost or when the sensitivity of preference is superlinear.