Optimal avian migration: A dynamic model of fuel stores and site use |
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Authors: | Thomas P Weber Bruno J Ens Alasdair I Houston |
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Institution: | (1) BBSRC/NERC Ecology and Behaviour Group, Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, UK;(2) Institute for Forestry and Nature Research (IBN-DLO), PO Box 167, 1790 AD Den Burg, Texel, The Netherlands;(3) School of Biological Sciences, University of Bristol, Woodland Road, Bristol, BS8 1UG, UK |
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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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | avian migration departure fuel loads fuel deposition rates stochastic dynamic programming stopover site use |
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