Invasion in multi-type populations: the role of phenotypic robustness and fluctuations

We study the invasion dynamics of a mutant population characterized by an increased phenotypic variability with respect to the incumbent population, with an emphasis on the effects of increased phenotypic robustness and fluctuations induced by small system size. This model is based on recent experimental and theoretical results which hint at the possibility that inactivation of certain genes, either by the effect of mutations or by pharmacological intervention, leads to the liberation of cryptic genetic variation which, in turn, produces a host of new phenotypic variants. We present a theoretical framework based on the so-called evolutionary formalism where the population dynamics can be analysed in terms of a suitably defined entropy function. This analytical framework allows us to ascertain the effect that increased phenotypic robustness of the new phenotypes has on the invasion probability and show that increased phenotypic robustness improves the fixation probability of the mutant population. The stochastic effects due to small population size are evaluated by means of numerical simulations. Our results are discussed in the light of recent results concerning the effect of diversity on the progression from a premalignant condition, such as the Barret's esophagus, to a fully developed tumour.