Bet-hedging strategies in expanding populations
Fig 4
The bet-hedging region is expanded for range expansions in spatially varying environments compared to temporally varying environments.
A) Optimal strategy α* as a function of the parameters for spatially varying environments in the limit ks → 0, Eq (9). White lines mark the limits of the bet-hedging region. The limit for which the strategy α = 1 is optimal in temporally fluctuating environments for k → 0 is also shown (gray line) for comparison. B) The velocity obtained by numerical integration of Eq (5) for sa = 0.25, ss = 1, sb = 2 (corresponding to the blue dot of panel A) and different values of kS shown in the figure legend. Light and dark gray lines correspond to the analytical limits for temporally varying environments, vM(k → 0) = (va(α) + vb(α))/2, and , respectively. The red curve is the analytical solution for a spatially fluctuating environment with kS → 0, see Eq (9). Note that in this case, the asymptotic mean velocity does not increase monotonically with kS but is maximal at kS ≈ 0.1.