The concept of territoriality proposed by E. Odum was used in this study. The territories were determined that were occupied by individuals of specific animal species and the notion "territory of individual" was proposed. The territories of individuals for different representatives of aquatic animals, including fish, were calculated and their relationships with mass and energy potential of animals were established. The territories of individuals and home ranges were compared in invertebrates and vertebrates. It was shown that for the entire animal world the relationship of these areas and mass can be described by a power equation with the exponent indistinguishable from 1. It was established on the example of zooplankton and zoobenthos communities that animal species with a larger size obtain advantage in the oligotrophic water bodies, since when the territories of individuals increase, they are capable of obtaining the necessary amount of food objects at their low density in such conditions. On the contrary, in the eutrophic water bodies, smaller animals have advantage, since they are capable of obtaining the necessary amount of food at a small home range and high density of food objects. A hypothesis was put forward that large and largest aquatic animals can occur in sea and oceanic waters not only because these are huge water basin, but also because these waters are, on the most part of territories, less productive, as compared to continental water bodies. In these conditions, the animals have to hunt over big territories for the necessary amount of food to be obtained and only large animals are able to do this.