Search space topology, algorithmic information theory and biological evolution

Dr Ard Louis

Evolutionary dynamics are driven by the interplay of random mutations, which change genotypes and thus generate variation, and selection, which favours fitter phenotypes. While Darwinian selection acting on existing variation is relatively well understood, the rate at which selectable variation arises in the first place remains a wide open question. Nevertheless, for many systems that can be approximately solved (including RNA secondary structure, and simple models of protein folding, protein quaternary structure, gene regulatory networks and development), the topologies of the genotype-phenotype (G-P) mappings exhibit strong biases in favour of certain phenotypes (variation) over others. If these G-P maps are interpreted as information processing systems, where the information in the genotype encodes the algorithm to produce the phenotype, then powerful results from algorithmic information theory (AIT) suggest that such exponential biases may be the norm rather than the exception.

By combining this perspective from AIT with the high-dimensional nature of evolutionary search, accurate approximations for evolutionary dynamics can be derived. Furthermore, this new picture suggests that the distribution of Darwin's "endless forms most beautiful" may be profoundly influenced by effects such as 1) The arrival of the frequent: certain types of variation are exponentially more likely to arise than others, so that more frequently arising phenotypes with lower fitness are much more likely to fix than less frequent phenotypes with higher fitness, and 2) Simplicity bias: G-P map topologies favour the spontaneous emergence of higher symmetry and/or more modular structures.