Models of Optimal Size for Solitary Predators

Models are presented which predict an optimal size, defined as that size which takes the least amount of time to satisfy its energy requirements, for several types of predators: I-predators which expend no time or energy in food search alone and which pursue their prey over varying distances; II-predators which expend time and energy while searching for items but none in pursuit; IIa and IIb-predators which expend time and energy both in search and pursuit. All predators are assumed to expend time and energy in handling and swallowing prey. In the simplest models considered, equations are constructed which combine to produce three major properties: (a) larger predators expend more energy in pursuing an item over a given distance than do smaller ones; (b) for most prey items, larger animals expend less time and for somewhat fewer items less energy in handling and swallowing than do smaller predators; (c) time and to a lesser extent energy lost while searching between two items are often not very different for differently sized predators, but to a large degree are homeostatically controlled by varying the range of acceptable items. The kinds of predictions and how these vary with parameters describing feeding efficiency and size-abundance distributions of available prey are summarized for these simple models in Table 3. Some of the ways in which more complicated models, produced by varying the above three properties, might change these predictions are specified. Several of the more interesting predictions consistent with existing data are (examples in parentheses): 1. For the same-sized predators, variance in home-range size should be greater in animals which are efficient pursuers (Accipiter) than less efficient pursuers (Buteo), whereas variance in food-size range should be greatest for the latter group. 2. As predators (Anolis lizards) become smaller, size distributions of prey consumed should become more and more similar, until a further decrease in size involves no further reduction in average prey size, even if available prey sizes are equinumerous. 3. Predators (Accipiter, some Carnivora) which pursue their prey over large distances should eat a mean prey-size larger in comparison with their own bulk than should less wide-ranging predators. 4. Distributions of prey sizes eaten by predators from a uniform size-abundance distribution of available prey should be more negatively skewed if the predator pursues its prey over greater distances (perch, pike) or is relatively large than if the predator pursues its prey less (carp, bleak, bream) or is relatively small. 5. Animals which spend a large portion of their feeding time pursuing (Accipiter, Falco) should more often be markedly sexually dimorphic in size than those which do not (warblers and to a lesser degree Buteo). 6. Small insectivorous poikilotherms (Anolis) should more often be markedly sexually dimorphic in size when solitary than small insectivorous homeotherms (flycatchers). 7. Rather than classical character displacement, a lowering of the sizes of both resident and invading species (Anolis, Uta) should occur, even if the invader is smaller than the resident, if species are generalized with respect to food size or if food is relatively scarce. 8. The degree of sexual dimorphism in size (Anolis) and size difference between species (many birds) should often be greater the larger the species.