Optimal stopover decisions under wind influence: the effects of correlated winds

Wind speed and direction have a significant effect on a flying bird's ground speed. Migrants are therefore expected to be sensitive to wind conditions and this should have consequences for optimal strategies of stopover and refuelling. Based on an earlier model of time-minimizing migration which includes wind condition, we investigate the consequences of the temporal correlation of wind conditions. Day-to-day changes in wind conditions are modelled with a two-state Markov process and an expression for the expected speed of migration is derived. The policy of the migrants is described by two parameters: a day t(g) when the birds start to leave whenever favourable conditions occur and a later day t(b)when they leave even in unfavourable winds. The model predicts that in most cases departures should be close to the date which is predicted by a wind-free deterministic model and that the birds should never leave without wind assistance. Only if the probability that the condition remains the same on the following day is close to 1 should the birds leave even in unfavourable conditions shortly after the deterministic optimal date. If the transition matrix is highly asymmetrical, i.e. if it is very probable that unfavourable conditions remain and that favourable conditions will change into unfavourable, then the birds are predicted to start using good winds several days before the deterministic optimal date. An analysis of six years of wind data from two sites in Sweden shows that wind directions on successive days are in fact correlated in all years.