On the impossibility of coexistence of infinitely many strategies |
| |
Authors: | Mats Gyllenberg Géza Meszéna |
| |
Institution: | (1) Department of Mathematics and Statistics, University of Helsinki, 20014 Helsinki, Finland;(2) Department of Biological Physics, Eötvös University, Pázmány Péter sétány 1A, 1117 Budapest, Hungary;(3) Collegium Budapest, Institute for Advanced Studies, Szentháromság tér 2, 1014 Budapest, Hungary |
| |
Abstract: | We investigate the possibility of coexistence of pure, inherited strategies belonging to a large set of potential strategies. We prove that under biologically relevant conditions every model allowing for coexistence of infinitely many strategies is structurally unstable. In particular, this is the case when the "interaction operator" which determines how the growth rate of a strategy depends on the strategy distribution of the population is compact. The interaction operator is not assumed to be linear. We investigate a Lotka-Volterra competition model with a linear interaction operator of convolution type separately because the convolution operator is not compact. For this model, we exclude the possibility of robust coexistence supported on the whole real line, or even on a set containing a limit point. Moreover, we exclude coexistence of an infinite set of equidistant strategies when the total population size is finite. On the other hand, for infinite populations it is possible to have robust coexistence in this case. These results are in line with the ecological concept of "limiting similarity" of coexisting species. We conclude that the mathematical structure of the ecological coexistence problem itself dictates the discreteness of the species. |
| |
Keywords: | Limiting similarity Ecological niche Regulated coexistence Lotka-Volterra competition model Physiologically structured populations Evolution of seed-size Structural stability |
本文献已被 PubMed SpringerLink 等数据库收录! |
|