Four-Dimensional Discrete-time Lotka-Volterra Models with an Application to Ecology

Abstract: This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them has its own biological meaning, enabling more intuitive interpretation of biological conditions to the model . Moreover, the modified version is applicable to simulate a part of a large ecosystem, not only a closed predator-prey system with four species. An easy graphical method of analysis of the conditions on parameters ensuring long persistence under coexistence is presented. As an application, it is explained that a predator specie who feed on relatively small number of preys compared to the other predator species must be selective on the available preys in order for long persistence of the ecosystem. This may be regarded as a theoretical explanation of the existence of flush-pursuer birds, those who uses highly specialized hunting strategy and cross-adapts to the ecosystem relative to the ordinary bird species.