The insular body size trends for different vertebrate families are compared. Certain groups such as lagomorphs, bats, artiodactyls, elephants, foxes, raccoons, snakes, and teiid and lacertid lizards are habitually represented by relatively smaller forms on islands. On the other hand, cricetid rodents, iguanid lizards, tortoises, and bears often have races with larger body sizes on islands. Contrary to conventional niche theoretic concepts, in many instances knowledge of the body sizes of some of these animals' insular and mainland competitors does not help explain the difference in that species body size in the 2 places. To account for these divergent size changes I examine optimum body size models that use as the optimization criterion the net energy gained by an organism over a given time period. These models predict that increases in the mean amount of available food should lead to evolutionary increases in body size, but only if body size is not tightly constrained by additional physical or biotic factors: such additional factors might be important if a change in body size alters an animal's effectiveness in finding or handling preferred food items or increases competition with its neighbors. Next using arguments derived from simple non—age—structured 2 species predator—prey models, the availability of food for a given consumer species at equilibrium is compared in theoretical island and mainland situations. Because islands usually contain fewer competitors and the insular physical environment is often more moderate, food availability for colonists is initially expected to be high. On the other hand, as the population grows resources will become depleted. Further, the loss of many predator species on islands may allow consumer densities to increase to such an extent that at equilibrium food may become relatively more limiting for consumers on islands than on the mainland. Whether the supply to demand ratio (S:D) of consumers for their food is ultimately greater or lower will depend on the relative magnitude of these various factors. Within this framework, a necessary condition for island S:D ratios to be greater than on the mainland is that the consumers maintain individual feeding territories. For animals whose body sizes are not tightly bound within narrow limits by physical or competitive restraints, an increase in S:D should lead to an evolutionary increase in body size. Accordingly, a good association is found between the presence or absence of territoriality and the direction of the insular body size shift in a number of different vertebrate groups. Yet there are exceptions which fall into 2 categories: First, if a species' mainland predators preferentially take larger individuals, selection favoring small size may override selection based on optimizing energy input. Such may have been the case for the now extinct mainland relatives of certain giant relictual insular reptiles. Secondly, an animal's body size may be tightly constrained by physical or competitive factors. The body size of island foxes, rattlesnakes, and some lizards appears to be primarily adjusted to the competitive milieu along typical niche theoretic lines. That is, body size may be predicted quite well from knowing the size class of competitors which are absent from an island or from differences in the species' prey—size distribution between island and mainland sites.