Pareto-optimal trade-off for phenotypic switching of populations in a stochastic environment

Abstract Finding optimal survival strategies of living systems embedded in fluctuating environments generally involves a balance between phenotypic diversification and sensing. If we neglect sensing mechanisms, it is known that slow, resp. fast, environmental transitions favor regime heterogeneous, homogeneous, response. We focus here on the simplest non-trivial case, i.e. two randomly switching phenotypes subjected to stochastically environments. The asymptotic (long term) growth rate this model was studied elsewhere; further expand these results by discussing finite time fluctuations. An exact expression for variance, alongside with approximations valid different regimes, are tested numerically details. Our simulations dynamics suggest close connection variance extinction probability, understood as risk population. Motivated an earlier trade-off analysis average capital Kelly’s gambling model, study present model. Despite considerable differences models, find similar curves (Pareto fronts), suggesting our conclusions robust, broadly applicable various fields ranging from biology/ecology economics.