Evolvability and robustness: A paradox restored

Evolvability and robustness are crucial for the origin and maintenance of complex organisms, but may not be simultaneously achievable as robust traits are also hard to change. Andreas Wagner has proposed a solution to this paradox by arguing that the many-to-few aspect of genotype-phenotype maps creates neutral networks of genotypes coding for the same phenotype. Phenotypes with large networks are genetically robust, but they may also have more neighboring phenotypes and thus higher evolvability. In this paper, we explore the generality of this idea by sampling large numbers of random genotype-phenotype maps for Boolean genotypes and phenotypes. We show that there is indeed a preponderance of positive correlations between the evolvability and robustness of phenotypes within a genotype-phenotype map, but also that there are negative correlations between average evolvability and robustness across maps. We interpret this as predicting a positive correlation across the phenotypic states of a character, but a negative correlation across characters. We also argue that evolvability and robustness tend to be negatively correlated when phenotypes are measured on ordinal or higher scale types. We conclude that Wagner's conjecture of a positive relation between robustness and evolvability is based on strict and somewhat unrealistic biological assumptions.