Hitchcock and Houston (1994) developed a model (based on acorn woodpecker data) in which hoarding substitutes for high levels of body fat. This model specifically considers the bet-hedging effect of stored food. Food acquisition can, on average, cover metabolic costs, but variation in foraging success means that dangerous deficits can accumulate. To hedge against this possibility, a bird must either maintain large body reserves, use its hoard, or both. The model predicts that moderate initial hoards can substantially increase fitness (i.e., survival). For example, a hoard equal to approximately 20% of total (100-day) energy requirements can, under realistic assumptions for the model parameters, increase the probability of survival from under 20% to 60%. The model also makes other predictions. First, predation, not starvation, will be the main cause of mortality. Second, birds will compensate for smaller hoards by maintaining higher body reserves. Thus, hoarding, under the model assumptions, mainly hedges against variation, resulting in lower predation risk. Hoarded supplies are not essential as an energy resource (unless the variation in food availability is very high). Hitchcock and Houston's model does not consider the cost of establishing a hoard, which one would have to consider in any complete analysis ofhoarding.
In more northern habitats than those inhabited by acorn woodpeckers, short-term variation in metabolic (thermoregulation) costs is likely to be at least as important as variation in food availability. Clark and Mangel (2000, section 5.4) discuss a model incorporating variable nocturnal costs [see equation (7.12)] and including hoard use. Its predictions are similar to those of Hitchcock and Houston (1994): relatively small hoards can increase fitness substantially in a fluctuating environment.
In a model with variable nighttime costs, Brodin (2000) showed that stored supplies hedged against variation, permitting hoarders to start each new day with small fat reserves. This model related to small birds such as parids in cold habitats and, unlike Hitchcock and Houston's model, incorporated hoarding. Throughout the winter, the model birds continued to store small amounts of food as insurance against unexpected variations (see section 7.4).
However, these and most other models ignore one important aspect of environmental stochasticity, the availability and use of information. For example, if the day provides no information about the demands of the coming night, the bird must store adequate body reserves at dusk to meet worst-case night costs. The bird will not use all of its reserves unless the worst-case conditions actually prevail. The phenomenon of winter fattening (see fig. 7.2)
suggests that animals do not posses perfect information about conditions in the nearest future. It is more realistic to assume that the current day's weather provides some (but not perfect) information about energy demands for the following night. In other words, current environmental "cues" influence the probability distribution of nightly costs, cn(t). Taking advantage of such cues might have strong fitness consequences, particularly for animals facing mass-dependent costs. Models of this situation could lead to novel, experimentally testable predictions.
McNamara et al. (1990) developed a dynamic model of optimal hoarding and fat regulation for the case ofephemeral hoards. Specifically, they assumed that a hoard can be built up and utilized later the same day, and that unused hoards disappear overnight. In spite of conservative assumptions (e.g., lack of mass-dependent predation risk and brief persistence of hoards), the optimal strategy involves the buildup and use ofdaily hoards. The main advantage of hoarding relative to immediate consumption is cost saving: consumed food increases metabolic costs, which daytime food storage can prevent. Secondarily, a hoard (built up in the morning) can hedge against lack of foraging success later in the day.
The model also predicted differences in foraging patterns between hoarders and nonhoarders. Since hoarders can rely on stored food, they can delay fat gain until late afternoon. Nonhoarders, on the other hand, face a more unpredictable access to food and must therefore start gaining fat earlier. So far, there is no empirical evidence for this prediction; on the contrary, hoarding species may even gain fat at a higher rate in the morning than nonhoarders (Lilliendahl 1997).
Changing three assumptions of McNamara and co-workers' model produces the pattern that Lilliendahl observed in the field (Brodin 2000; Pravosu-dov and Lucas 2001b). First, these revised models allow birds to leave caches overnight and retrieve them in the morning. Second, small fat reserves have little or no effect on predation risk (see section 7.4). Finally, the bird's scattered caches may be time-consuming to retrieve, decreasing the profitability of retrieval. Under these assumptions, hoarders can carry small overnight fat reserves. Ifthe morning weather is worse than expected, hoarders can retrieve caches, whereas similarly lean nonhoarders may starve. Since hoarders start the day with small reserves, they need to secure sufficient fat in the morning to hedge against uncertainty later in the day (fig. 7.9). After reaching a more secure level of reserves, they can afford to spend time on hoarding and other activities. This more secure level of reserves increases predation only slightly because it is relatively small (see fig. 7.4).
Lucas and Walter (1991) modeled hoarding strategies in Carolina chickadees (Poecile carolinensis). They listed four advantages of hoarding that earlier
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