Alex Hening, Department of Mathematics, Tufts Universy
The competitive exclusion principle in stochastic environments
The competitive exclusion principle states in its simplest form that a number of species competing for a smaller number of resources cannot coexist. Nevertheless, in nature there are many instances where this is not true. One example is Hutchinson's 'paradox of the plankton'. This is an instance where a large number of phytoplankton species coexist while competing for a very limited number of resources. Both experimental and theoretical studies have shown that in some instances temporal fluctuations of the environment can facilitate coexistence. Hutchinson conjectured that one can get coexistence because nonequilibrium conditions would make it possible for different species to be favored by the environment at different times. In this talk I will look at how random environmental fluctuations interact with competitive exclusion. I will showcase models given by stochastic differential equations and piecewise deterministic Markov processes. In particular, I will show that, contrary to Hutchinson's explanation, one can switch between two environments in which the same species is favored and still get coexistence.