On the impossibility of coexistence of infinitely many strategies.

@article{Gyllenberg2005OnTI,
  title={On the impossibility of coexistence of infinitely many strategies.},
  author={Mats Gyllenberg and G{\'e}za Mesz{\'e}na},
  journal={Journal of mathematical biology},
  year={2005},
  volume={50 2},
  pages={133-60}
}
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… CONTINUE READING