Genotype-phenotype maps for gene networks: from evolution to computation

One of the most fundamental and least understood elements of evolution is the mapping between genotype and phenotype. Recent work on genotype-phenotype (GP) maps suggests that these maps show properties which may have important evolutionary implications. These properties include a skewed distribution of genotypes over phenotypes, linear scaling between phenotype robustness and the logarithm of phenotype frequency, and a positive correlation between phenotype robustness and evolvability. However, most of these properties have only been studied for self-assembling systems, such as protein complexes or RNA folding. In this thesis, we ask ourselves if these properties are more general. First, we apply tools from algorithmic information theory to a wide class of inputoutput maps, of which GP maps are a subset. We find that these maps show a strong bias towards simple phenotypes, a pattern known as simplicity bias. We also define a matrix map of tunable complexity, with which we can study the conditions under which simplicity bias is present. Next, we investigate multiple models of GP maps for gene regulatory networks (GRNs). These include Boolean threshold networks, where we fix the strength of gene interactions, while varying the network topology, as well as systems of differential equations, where we fix the network topology while varying interaction strengths. For both modelling frameworks, the GRN GP maps exhibit all the structural properties found in the literature, as well as simplicity bias. We also find that the number of genotypes mapping to the wild-type phenotypes for various GRNs is unusually large, and argue that this is evidence that the structure of the GP map plays an important role in determining evolutionary outcomes. Finally, we return to more general input-output maps, and show that in addition to simplicity bias these maps also present randomness deficiency, that is, their output spectrum is less complex than expected. We argue that this additional property combines with simplicity bias in GP maps, and more generally, in input-output maps, and suggest a general trend towards simplicity in nature.