Dynamics Fridays Talk: Long term demographics depend on early stochastic dynamics in growing populations
Speaker: Jeffrey Philippson, Simons Center, NCBS
Venue: Simons Centre Ground Floor, NCBS
It is well known that demographic fluctuations play a crucial role in the evolutionary dynamics of small populations. In growing systems, stochastic effects have traditionally been neglected, since exponential growth rapidly gives rise to large populations that exhibit deterministic dynamics. Here we demonstrate that stochastic effects while the population remains small can have far-reaching consequences, with critical dependence of demographic outcomes on birth and mutation rates. Using stochastic simulations, we adapt a well-known model for the evolution of cooperation based on the iterated prisoner’s dilemma to include growth via frequency-dependent selection. A comparison with the deterministic model shows that, contrary to widely held belief, the effects of stochasticity can impede the establishment of a cooperative population. Surprisingly, the deterministic dynamics of the eventual population carry echoes of the early demographics in spite of the randomizing effects of stochasticity. The correlation between pre- and post-growth demographics exhibits a subtle dependence on mutation rate, explained in terms of the underlying attractors. Frequency-dependent competition due to resource limitation carry through the effects of early stochastic dynamics to ultimate population size.