Electronic Journal of Differential Equations (Nov 2015)
Remarks and examples on transient processes and attractors in biological evolution
Abstract
We present a model for the competition of two biological entities into the same species (polyphasie, clonal/sex, cancerous cells), the first one with a birth ratio higher than the second when the resources are abundant, whereas the situation is reversed for scarce resources. The first one rapidly exhausts the resources, improving growth of the second, leading to a auto-sustained cyclic process (ESS = Evolutionary Stable Strategy). We use known models of population dynamics for three agents: two phases asexual and sexual (for instance) of the same species and one of resources. The main feature of the model (for certain values of the parameters) is the very long and entangled transient process, which involves a long period where one of the forms is practically absent, before emerging again to join a stable cycle which implies preservation of both forms. This model should throw some light on the biological problem of the maintenance of sexuality in competition with asexual clones, as well as on the alternated fast growth versus latency in cancer tumors.