Bounding phenotype transition probabilities via conditional complexity

Abstract

By linking genetic sequences to phenotypic traits, genotype-phenotype maps represent a key layer in biological organisation. Their structure modulates the effects of genetic mutations, shaping evolutionary outcomes. Recent work based on algorithmic information theory introduced an upper bound on the likelihood of a random genetic mutation causing a transition between two phenotypes, using only the conditional complexity between them. Here we evaluate how well this bound works for a range of biologically relevant genotype-phenotype maps, including a differential equation model for circadian rhythm, a matrix-multiplication model of gene regulatory networks, a developmental model of tooth morphologies for ringed seals, a polyomino-tile shape model of biological self-assembly, and the HP lattice protein model. By assessing three levels of predictive performance, we find that the bound provides meaningful estimates of transition probabilities across these complex systems. These results suggest that transition probabilities can be predicted to some degree directly from the phenotypes themselves, without needing detailed knowledge of the underlying genotype-phenotype map. This offers a powerful approach for understanding evolutionary dynamics in complex biological systems.