Dynamic Selection Systems and Replicator Equations
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The dynamic replicator equation is inferred from a generalized Kolmogorov-type dynamic system that is called selection system. This way, both systems have the same dimension. The main result shows that the replicator equation is in a certain sense equivalent to a selection system of lower dimension. Corollaries demonstrating connections with known results are also presented. The equations are interpreted as models of biological evolution on different time scales. Hence, the results show a link between ecology and evolution at least on the level of mathematical models.
KeywordsSelection System Game Dynamic Dynamic Replicator Replicator Equation Forward Jump
This research was supported by the grant No. GAP201/10/1032 of the Czech Grant Agency.
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