title: Surviving evolutionary escape on complex genotype-phenotype networks.
abstract: We study the problem of evolutionary escape and survival of cell populations with a genotype-phenotype structure. We refer to evolutionary escape as the process where a cell of a given ill-adapted population to reach a well-adapted phenotype. Similarly, survival refers to the dynamics of the population once the escape phenotype has been reached. The aim of this paper is to analyse the influence of topological properties associated to robustness and evolvability on the probability of escape and on the probability of survival. 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 exploit the separation of time scales introduced by the the difference in reproductive ratios between the ill-adapted phenotypes and the escape phenotype. 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. We exploit this separation of time scales to analyse the topological factors which determine escape and survival probabilities. We show that, while the escape probability depends on the degree of escape phenotype, the probability of survival is essentially determined by its robustness, measured in terms of a weighted clustering coefficient.
authors.affiliation: Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra, 08193, Barcelona, Spain. esther1987@gmail.com.|Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain. esther1987@gmail.com.
authors.forename: Esther
authors.initials: E
authors.lastname: Ibáñez-Marcelo
authors.affiliation: Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra, 08193, Barcelona, Spain. talarcon@crm.cat.|Departament de Matemàtiques, Universitat Atonòma de Barcelona, Bellaterra, 08193, Barcelona, Spain. talarcon@crm.cat.
authors.forename: Tomás
authors.initials: T
authors.lastname: Alarcón
mesh_terms: D000818:Animals; D005075:Biological Evolution; D002470:Cell Survival / Q000235:genetics / Q000502:physiology; D019295:Computational Biology; D056726:Genetic Association Studies; D005838:Genotype; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009154:Mutation; D010641:Phenotype; D011157:Population Dynamics; D012641:Selection, Genetic
keywords: Evolutionary escape; Genotype–phenotype map; Local weighted clustering; Survival probability