Optimal avian migration: A dynamic model of fuel stores and site use

Abstract

Birds migrating between widely separated wintering and breeding grounds may choose among a number of potential stopover sites by using different itineraries. Our aim is to predict the optimal migration schedule in terms of (1) rates of fuel deposition, (2) departure fuel loads and (3) stopover site use, when only a handful of such sites are available. We assume that reproductive success depends on the date and fuel load at arrival on the breeding grounds. On migration, the birds face a trade-off between gaining fuel and avoiding predation. To allow the optimal decision at any given moment to depend on the fuel load and the location of the bird, as well as on unpredictability in conditions, we employed stochastic dynamic programming. This technique assumes that the birds know the probability distribution of conditions in all sites, but not the particular realization they will encounter. We examined the consequences of varying aspects of the model, like (1) the shape of the relationship between arrival date and fitness, (2) the presence of stochasticity in fuel deposition rates and wind conditions, and (3) the nature of predation (i.e. whether predation risk depends on the fuel load of the birds or their feeding intensity).

Optimal fuel deposition rates are predicted to be constant if there are either only predation risks of maintaining stores or only risks of acquiring fuel stores. If only fuel acquisition is risky, fuel deposition rates can be below maximum, especially if there also is an intermediate best arrival time at the breeding ground. The fuel deposition rate at a site then depends not just on the site's quality but on the qualities of all visited sites. In contrast, rates of fuel deposition are not constant if both the acquisition and the maintenance of fuel stores carry risk. Optimal departure fuel loads are just enough to reach the next site if the environment is deterministic and are simply set by the energetic cost of covering the distance. As with time-minimizing models, more fuel than necessary to reach a site is only deposited under very restricted circumstances. Such overloads are more likely to be deposited if either fuel gains or expenditure are stochastic. The size of overloads is then determined by the variance in fuel gain at the target site and the worst possible conditions during flight. Site use is modified by differences in predation risk between sites and differences in fuel deposition rates. An expression derived to predict site use under time minimization provides a good approximation in state-dependent models. In some cases, the possibility of starvation may influence optimal decisions, even when the probability of starvation under the optimal policy is low. This effect of starvation has also been found in other contexts.