Quantitative and Qualitative Dynamics of Interacting Populations

Abstract

This research paper deals with the vast topic of population dynamics from both a quantitative view, the change in the number of individuals in a population, and a qualitative one, the variation or change in the phenotypes in evolutionary processes. In a broader sense, what regards the populations is also applicable to species. Quantitative dynamics are studied not only in an isolated population but also in the more interesting case of two or more populations interconnected in a simple trophic food chain in a prey–predator model, in the broadest sense of the term, thereby forming an ecosystem. However, the paper introduces the concept of ‘population control’. Two or more interconnected prey–predator populations regulate, in turn, their dynamics, even though unconsciously, exercising a control that has been defined as ‘natural’ and ‘endogenous’. The concept of ‘external’ control is also introduced, which is carried out by man through interventions aimed at increasing or reducing the size of one or more interconnected populations to arrive at minimum limits (populations of species in danger of extinction) or maximum ones (populations of invasive species) held to be advantageous to and congruous with the ecosystem. Also highlighted is the connection between qualitative and quantitative dynamics, in the sense that every mutation in the individuals of a population which increases the potency of the defence apparatus in prey, or the hunting apparatus in predators, necessarily modifies the rates of fecundity or extinction of that population, which necessarily affects the quantitative dynamics of all the interconnected populations. Taking as a basis, the Volterra–Lotka equations, Excel and Powersim simulations are presented for specific examples in which population dynamics is treated under the assumption of unlimited resources or resources that are limited but reproducible or limited until depletion. The case of environmental catastrophes that externally modify the dynamics of one or more populations is also touched upon. © 2018 John Wiley & Sons, Ltd.