Centre de Recerca Matemàtica
Evolutionary escape and surviving in populations with genotype-phenotype structure
We study the problem of evolutionary escape and survival for cell populations with genotype-phenotype map. Classical approaches, which do not consider populations with genotype-phenotype structure, have focused on the problem of estimating the probability of reaching a well-adapted (so-called escape) genotype from an ill-adapted one. This perspective implies that, once the escape genotype has been reached, the population survives with probability one. If genotype-phenotype structure is added to the picture, the situation is not quite so simple: genotype-phenotype structure provides a complex structure to the escape phenotype which, in particular, endows robustness to the escape phenotype, so that the dynamics of the system post-escape is not trivial. Furthermore, the consideration of a genotype-phenotype map introduces a complex topology in the genotype-phenotype network. In order to explore these issues, we formulate a population dynamics model, consisting of a multi-type time-continuous branching process, where types are associated to genotypes and their birth and death probabilities depend on the associated phenotype (non-escape or escape). We show that, within the setting associated to the escape problem, separation of time scales naturally arises and two dynamical regimes emerge: a fast-decaying regime associated to the escape process itself, and a slow regime which corresponds to the (survival) dynamics of the population once the escape phenotype has been reached (i.e., conditioned to escape). We exploit this separation of time scales to analyse the topological factors which determine escape and survival. In particular, the aim of this work is to analyse the influence of topological properties associated to robustness and evolvability on the probability of escape and on the probability of survival upon escape. We show that, while the escape probability depends on the size of the neutral network of the escape phenotype (i.e., its degree), the probability of survival is essentially determined by its robustness (i.e., the resilience of the escape phenotype against genetic mutations), measured in terms of a weighted clustering coefficient.