  It has not been known whether preferential dispersal is adaptive in
fluctuating environments. We investigate the effect of preferential and random
dispersals in bet-hedging systems by using a discrete stochastic metapopulation
model, where each site fluctuates between good and bad environments with
temporal correlation. To explore the optimal migration pattern, an analytical
estimation of the total growth is derived by mean field approximation. We found
that the preference for fertile sites is disadvantageous when transportation
among sites has a cost or the sensitivity of preference is high.
