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Section: New Results

Effect of environment on population dynamics

Participants : Islam Boussaada, Silviu Niculescu, Jun-Xiu Chen [Nothestern University] , Sette Diop [L2S, CentraleSupélec] , Xu-Guang Li [Nothestern University] , Paul Raynaud de Fitte [LMRS, Université de Rouen Normandie] , Safia Slimani [LMRS, Université de Rouen Normandie] , Sami Tliba [L2S, CentraleSupélec] .

Competition in population dynamics is often considered to be governed by predator-prey models. In particular, Lotka-Volterra models are intensively used in this context.

A modified version of a prey-predator system with Leslie-Gower and Holling type II functional responses incorporating a refuge for preys is studied in [27]. Such a refuge substantially complicates the dynamics of the system. We study the local and global dynamics and the existence of limit-cycles. We also investigate conditions for extinction or existence of a stationary distribution, in the case of a stochastic perturbation of the system.

Most of the reported Lotka-Volterra examples have at most one stability interval for the delay parameters. Furthermore, the existing methods fall short in treating more general case studies. Inspired by some recent results for analyzing the stability of time-delay systems, this paper focuses on a deeper characterization of the stability of Lotka-Volterra systems w.r.t. the delay parameters. In [58], we introduced the recently-proposed frequency-sweeping approach to study the complete stability problem for a broad class of linearized Lotka-Volterra systems. As a result, the whole stability delay-set is analytically determined. Moreover, as a significant byproduct of the proposed approach, some Lotka-Volterra examples are found to have multiple stability delay-intervals. In some situations, a longer maturation period of species is helpful for the stability of a population system.

In another context, the effect of environment on yeast population dynamics is studied in [28]. In presence of oxygen cells usually adopt efficient metabolism in order to maximize energy production yield in poor diet. If nutrient resource increases, a metabolic shift from efficient metabolism (respiration) to inefficient metabolism (fermentation) is reflecting a minimal cost principle of living systems to optimize fitness. This is known as the Crabtree/Warburg effect. A model that describes the population dynamics of cells and the input growth condition is established. Proof of principle has been constructed using a battery of growth experiments on Crabtree-positive yeasts–Saccharomyces under various conditions of glucose in aerobic and micro-aerobic conditions. General cell growth model estimating metabolic shift has been constructed based on an Auto-Regressive approach.