Mathematical Biosciences and Engineering, 2014, 11(4): 841-875. doi: 10.3934/mbe.2014.11.841

Primary: 92D25, 92D15; Secondary: 34C60, 92B05.

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Effects of nutrient enrichment on coevolution of a stoichiometric producer-grazer system

1. School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024

A simple producer-grazer model based on adaptive evolution and ecological stoichiometry is proposed and well explored to examine the patterns and consequences of adaptive changes for the evolutionary trait (i.e., body size), and also to investigate the effect of nutrient enrichment on the coevolutin of the producer and the grazer. The analytical and numerical results indicate that this simple model predicts a wide range of evolutionary dynamics and that the total nutrient concentration in the ecosystem plays a pivotal role in determining the outcome of producer-grazer coevolution. Nutrient enrichment may yield evolutionary branching, trait cycles or sensitive dependence on the initial values, depending on how much nutrient is present in the ecosystem. In the absence of grazing, the lower nutrient density facilitates the continuously stable strategy while the higher nutrient density induces evolutionary branching. When the grazer is present, with the increasing of nutrient level, the evolutionary dynamics is very complicated. The evolutionary dynamics sequentially undergo continuously stable strategy, evolutionary branching, evolutionary cycle, and sensitive dependence on the initial values. Nutrient enrichment asserts not only stabilizing but also destabilizing impact on the evolutionary dynamics. The evolutionary dynamics potentially show the paradox of nutrient enrichment. This study well documents the interplay and co-effect of the ecological and evolutionary processes.
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