Dynamic selection systems and replicator equations. (English) Zbl 1317.92057

Pospíšil, Zdeněk

AlSharawi, Ziyad (ed.) et al., Theory and applications of difference equations and discrete dynamical systems. ICDEA, Muscat, Oman, May 26–30, 2013. Berlin: Springer (ISBN 978-3-662-44139-8/hbk; 978-3-662-44140-4/ebook). Springer Proceedings in Mathematics & Statistics 102, 203-213 (2014).

Summary: 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.
For the entire collection see [Zbl 1297.39001].

MSC:

92D15	Problems related to evolution
92D40	Ecology

Keywords:

dynamic replicator equation; Kolmogorov-type dynamic system; selection system