Probabilistic bias in genotype-phenotype maps

Among the most fundamental features shared by all organisms is the mapping of information encoded in genotypes (genetic material) to generate phenotypes (biological structures, functions, and traits). Hence, elucidating the structure of genotype-phenotype (GP) maps is important for understanding evolution and biology. While it is known that often GP maps are highly degenerate with many different genotypes adopting the same phenotype, the distribution of genotypes over phenotypes is less well studied. In this thesis we investigate the question of the distribution of genotypes over phenotypes, or put differently the distribution of neutral set sizes (NSS), where a neutral set is the collection of all genotypes in a GP map which map to the same phenotype. We focus on examining phenotypic bias in GP maps, where some phenotypes have disproportionally large NSS as compared to others. We find phenotypic bias to be ubiquitous in the broad range of GP maps that we analyse, from the genetic code up to molecular RNA to a model of neuronal connections, and hence we hypothesise bias to be a common property of GP maps. Further, we also consider the implications that this bias has for evolutionary outcomes, and we argue that bias is a significant influencing factor in determining evolutionary outcomes. Finally, we propose a method to predict a phenotype's NSS via estimating the phenotype's structural complexity, without using detailed knowledge about the specifics of the relevant GP map. We achieve this via a novel application of algorithmic information theory and especially Levin's coding theorem.