Trends and Paradoxes of Competitive Evolution in the Predation Mechanism

Author:

Sanchez-Palencia Evariste1,Aziz-Alaoui M. A.2ORCID

Affiliation:

1. Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, 75005 Paris, France

2. Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

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.

Publisher

MDPI AG

Reference22 articles.

1. Sanchez-Palencia, E., and Françoise, J.-P. (2022). Dialectique Dans les Sciences et Systèmes Dynamiques, Le Temps des Cerises.

2. Murray, J.D. (2002). Mathematical Biology I: An Introduction, Springer. Interdisciplinary Applied Mathematics.

3. Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type-II schemes;Daher;Appl. Math. Lett.,2003

4. The functional response of invertebrate predators to prey density;Holling;Mem. Entomol. Soc. Can.,1966

5. On transient processes in attractors in biological evolution;Lherminier;Electron. J. Differ. Equ.,2015

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