On modeling metapopulation processes

Three paradigms of cognition of the world are presented: Laplacian determinism (“Laplace's demon”), stochasticism and chaos-self-organization (uncertainty in the dynamics of the behavior of wildlife objects). The formation of the mathematical theory of population dynamics within these three paradigms is discussed. A metapopulation is a spatially structured population that persists over time as a set of spatially separated, local, interacting populations with limited settlement between them. The principle of migration is the main mechanism that distinguishes the theory of metapopulations from the standard theory of population dynamics, which analyzes mortality and fertility within a single population. The compromise between competition and colonization allows competing species to coexist in a heterogeneous environment. Quantitative approaches make it possible to take into account other mechanisms and more general spatial variations. Stochastic and deterministic models of the dynamics of metapopulations are discussed. They are point model (parameters change only in one variable), diffuse one (taking into account the diffusion exchange between two habitats identical in their ecological characteristics) and agent-based models (based on the individual behavior of agent-objects and operating with parameter values averaged for a group of similar objects), etc. The main properties of individual agents are: “intelligence” (learnability), location in time and space (a certain “habitat” is set), and the presence of a life goal.