A Theoretical Investigation of the Fat Reserves and Mortality Levels of Small Birds in Winter

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We assume that the fat levels of a small bird in winter reflect a tradeoff between starvation and predation. This tradeoff is formalized by finding the level of fat that minimizes total mortality (starvation plus predation) in a given environment. A bird is characterised in terms of its level of energy reserves. The bird starves if these reserves fall to zero. In general, the probability that the bird is killed by a predator increases with increasing reserves. We consider two models. In both at each time unit during a day a bird can choose, as a function of its reserves, to forage or to rest. In the forage vs rest model there is only one foraging option. In the foraging intensity model the bird can choose from a range of options, where options with a high energetic gain also incur a high predation risk. We find the optimal level of reserves for various environments, together with the resulting levels of starvation and predation. Unless food availability is very high, an improvement in overall availability results in a decrease in the mean reserves at dusk (MRD); in the foraging intensity model there is also a trend towards choosing safer foraging options with lower mean gains. An increase in variability, either as a result of a decreased probability of finding food or an increase in interruptions of foraging, increases MRD. The increase in reserves is not sufficient to prevent an increase in starvation. As a result, reserves and starvation can be positively correlated across environmental conditions. The level of starvation tends to be lower than the level of predation, but the ratio of starvation to predation tends to increase as conditions become worse. In the middle of winter, the days are short and the nights are long and cold. The optimal response to a decrease in daylength involves an increase in both dawn and dusk levels of reserves. This pattern is also found when overnight expenditure increases but daylength is constant. In this context we show that when temperatures are very low, a small saving in energy can result in a substantial increase in survival probability. The relevance of this result for evaluating the importance of hypothermia is discussed.