Evolutionary escape on complex genotype–phenotype networks

• We perform a comparative analysis between escape on regular hypercube (H-graphs) and complex genotype–phenotype spaces (B-graphs).
• We find that the distribution of distances between phenotypes in B-graphs exhibits a much larger degree of heterogeneity than in H-graphs.
• This property causes heterogeneous behaviour in all results associated to the escape problem.
• Our main result is that the escape probability can be underestimated by assuming a regular hypercube genotype network.

We study the problem of evolutionary escape that is the process whereby a population under sudden changes in the selective pressures acting upon it try to evade extinction by evolving from previously well-adapted phenotypes to those that are favoured by the new selective pressure. We perform a comparative analysis between results obtained by modelling genotype space as a regular hypercube (H-graphs), which is the scenario considered in previous work on the subject, to those corresponding to a complex genotype–phenotype network (B-graphs). In order to analyse the properties of the escape process on both these graphs, we apply a general theory based on multi-type branching processes to compute the evolutionary dynamics and probability of escape. We show that the distribution of distances between phenotypes in B-graphs exhibits a much larger degree of heterogeneity than in H-graphs. This property, one of the main structural differences between both types of graphs, causes heterogeneous behaviour in all results associated to the escape problem. We further show that, due to the heterogeneity characterising escape on B-graphs, escape probability can be underestimated by assuming a regular hypercube genotype network, even if we compare phenotypes at the same distance in H-graphs. Similarly, it appears that the complex structure of B-graphs slows down the rate of escape.