Trends and Paradoxes of Competitive Evolution in the Predation Mechanism

Evariste Sanchez-Palencia and M. A. Aziz-Alaoui ()
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Evariste Sanchez-Palencia: Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, 75005 Paris, France
M. A. Aziz-Alaoui: Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

Mathematics, 2024, vol. 12, issue 7, 1-17

Abstract: We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey and predators). We then develop the mathematical theory that enables us to understand the causality involved, and we identify a trend towards the emergence of the functional predation mechanism as such (and not of populations of the species involved). The realization of this trend only takes place when the conditions for it are offered by the hazards proposed to successive competitive choices. The logical structure of this trend is similar to that of the “tendency of rate of profit to fall” in certain economic models.

Keywords: predator–prey interactions; Hopf bifurcation; limit cycle; evolutionary trend; evolutionary ecology; emergence of efficiency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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