Quantitative and Qualitative Dynamics of Interacting Populations

What is it about?

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”. This paper has also dealt with the topic of the qualitative dynamics of populations, which depend on evolutionary phenomena that, by modifying the phenotypes, favor adaptation to the new conditions of survival and modify the birth and extinction rates. Models have been presented to analyse the qualitative dynamics and to show how this can alter, even drastically, the quantitative dynamics.

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Why is it important?

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 which 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.

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