We present a stochastic dynamic programming model of the contribution of stored food to winter survival. Using the acorn woodpecker (Melanerpes formicivorus) as a model organism, we demonstrate that a hoard of small energetic value can impart considerable improvement in the probability of surviving the winter and so improve fitness. With this model we hope to resolve Koenig and Mumme's paradox, that acorn woodpeckers expend much time and effort to create and maintain hoards of acorns which provide no more than 16% of their energetic needs over the period in which they are used. We further demonstrate that the contribution of hoarded acorns to survival depends on the variability in foraging outcome, independently of the energetic value of the hoard in absolute terms. We point out that the results apply in principle to all hoarding animals and suggest a number of further elaborations of the model.
