A simple model captures key characteristics of biological non-deterministic genotype-phenotype maps

By connecting genotypic mutations to the higher-level phenotypes relevant for selection, genotype-phenotype (GP) maps play a key role in evolution. GP maps are typically investigated using computational models of biophysical phenotypes (for example, RNA secondary structures and simplified models of protein tertiary and quaternary structures), but GP map concepts are relevant beyond these specific models. While there has been significant progress in quantifying GP map properties and their evolutionary implications, this is largely limited to the simplest case, where each genotype corresponds to a single, categorical phenotype. Here, I turn to a more realistic, but also more complex, non-deterministic (ND) treatment, meaning that each genotype generates an ensemble of phenotypes. To provide a tool for tackling the additional complexity of ND GP maps, this paper identifies a tuneable synthetic model that produces an ND GP map reproducing central features of biophysical ND GP maps: phenotypic bias, genetic correlations, a tradeoff between genotypic robustness and evolvability and a non-negative trend between phenotypic robustness and evolvability. These features are reproduced for several alternative models combining additive genotype dependencies with non-linearities, suggesting that few ingredients are needed for these shared features to appear. Moreover, the synthetic ND GP map may be useful as a conceptually and computationally simpler model for addressing open questions about ND GP maps: for simulations linking GP map properties to evolutionary implications, for the development of sampling methods for ND GP maps and for extrapolations.Author summary: Genotype-phenotype maps connect genotypic mutations to their phenotypic effect, and are thus important for modelling evolution. Many realistic models of such maps are non-deterministic, meaning that each genotype corresponds to an ensemble of phenotypes rather than to a single, categorical phenotype. This non-determinism, combined with the high number of possible genotypes, means that genotype-phenotype maps are huge datasets, and thus complex to build, to analyse and to use in evolutionary models. To provide a tool for tackling this complexity, I show that a simple model produces a non-deterministic genotype-phenotype map that – despite its simplicity - mirrors important shared features of genotype-phenotype maps derived from biophysical models. Thus, this model is highly suitable as a tool for addressing open questions about non-deterministic genotype-phenotype maps. Moreover, I consider modified versions of the simple model, finding that several of them reproduce the shared features of biophysical genotype-phenotype maps. This implies that, rather than being special properties of biophysical models, these shared features easily emerge from few ingredients.