Mathematical models of biological populations

Abstract

The study of development and interaction of biological species is an important direction of modern research. As one of the central parts of this study, mathematical modeling assists in understanding the behavior of populations and provides reliable forecasts and recommendations for sustainable policies and management. A variety of mathematical models of biological populations and their investigation techniques have been pretty well developed, but practice requires new models that consider, for instance, aftereffect and joint influence of different exogenous and endogenous factors. This chapter explores well-known population models that have become a foundation to contemporary models widely used in practice. Section 6.1 presents population models based on ordinary differential equations and basic elements of their analysis. Section 6.2 explores different types of interaction among species and offers a detailed analysis of predator-prey models. Section 6.3 discusses partial differential and integral models of population dynamics.