Evolution of Stochastic Switching Rates in Asymmetric Fitness Landscapes

Abstract

Uncertain environments pose a tremendous challenge to populations: The selective pressures imposed by the environment can change so rapidly that adaptation by mutation alone would be too slow. One solution to this problem is given by the phenomenon of stochastic phenotype switching, which causes genetically uniform populations to be phenotypically heterogenous. Stochastic phenotype switching has been observed in numerous microbial species and is generally assumed to be an adaptive bet-hedging strategy to anticipate future environmental change. We use an explicit population genetic model to investigate the evolutionary dynamics of phenotypic switching rates. We find that whether or not stochastic switching is an adaptive strategy is highly contingent upon the fitness landscape given by the changing environment. Unless selection is very strong, asymmetric fitness landscapes-where the cost of being maladapted is not identical in all environments-strongly select against stochastic switching. We further observe a threshold phenomenon that causes switching rates to be either relatively high or completely absent, but rarely intermediate. Our finding that marginal changes in selection pressures can cause fundamentally different evolutionary outcomes is important in a wide range of fields concerned with microbial bet hedging.

The role of migration in the evolution of phenotypic switching

“…Increasing the variability parameter c (i.e. increasing the variance in waiting time) decreases the evolutionarily stable switching rate, which can then be orders of magnitude less than 1/n, consistent with previous results in the absence of spatial heterogeneity [15]. As the migration rate increases, the evolutionarily stable switching rate first decreases.…”

“…Figure 3a illustrates the difference between results for the symmetric regime above (all selection coefficients equal) and this regime, in which higher migration rates select for higher switching rates. Consistent with single-deme theoretical results [15,16], asymmetry often leads to the evolution of zero mutation rate when the migration rate is low. As the level of asymmetry in selection within demes increases, the curves change from dipping to monotonically increasing with migration.…”

“…However, Salathé et al [15] and Liberman et al [16] showed that evolutionarily stable switching rates became close to zero as the variability in temporal fluctuations increased, or if fitness costs were asymmetric between the two environments. Including the potential for non-random phenotypic switching, Kussell & Leibler [17] found that costly sensing was favoured in rapidly changing environments, while pure stochastic switching was favoured in slowly changing environments.…”

The evolutionary advantage of heritable phenotypic heterogeneity

“…This uninvadable switching rate is an evolutionary stable strategy (ESS) in an infinite population 60 . Further studies confirmed these results and also generalized them to include both environmental and spatial fluctuations in selection 40,54,61 . Most of these studies, however, consider the dynamics of mutation rates in infinite populations, and they do not explore the evolutionary fate of a new mutation in a finite population subject to demographic stochasticity.…”

“…Previous study of partly heritable phenotypic variation has been pursued in an infinite population 6,40,53,54 , with the notable exception of work by ref. 55 studied bet-hedging against rare events, whose analysis involved considering a single environmental change.…”