Genotype-phenotype (GP) maps specify how the random mutations that change genotypes generate variation by altering phenotypes, which, in turn, can trigger selection. Many GP maps share the following general properties: 1) The total number of genotypes is much larger than the number of selectable phenotypes; 2) Neutral exploration changes the variation that is accessible to the population; 3) The distribution of phenotype frequencies , with the number of genotypes mapping onto phenotype , is highly biased: the majority of genotypes map to only a small minority of the phenotypes. Here we explore how these properties affect the evolutionary dynamics of haploid Wright-Fisher models that are coupled to a random GP map or to a more complex RNA sequence to secondary structure map. For both maps the probability of a mutation leading to a phenotype scales to first order as , although for the RNA map there are further correlations as well. By using mean-field theory, supported by computer simulations, we show that the discovery time of a phenotype similarly scales to first order as for a wide range of population sizes and mutation rates in both the monomorphic and polymorphic regimes. These differences in the rate at which variation arises can vary over many orders of magnitude. Phenotypic variation with a larger is therefore be much more likely to arise than variation with a small . We show, using the RNA model, that frequent phenotypes (with larger ) can fix in a population even when alternative, but less frequent, phenotypes with much higher fitness are potentially accessible. In other words, if the fittest never ‘arrive’ on the timescales of evolutionary change, then they can't fix. We call this highly non-ergodic effect the ‘arrival of the frequent’.

Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps—a model for RNA secondary structure, the HP model for protein tertiary structure, and the Polyomino model for protein quaternary structure—to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain genotypes mapping to the same phenotype than in the random null model. Such neutral correlations can be quantified by the robustness to mutations, which can be many orders of magnitude larger than that of the null model, and crucially, above the critical threshold for the formation of large neutral networks of mutationally connected genotypes which enhance the capacity for the exploration of phenotypic novelty. Thus neutral correlations increase evolvability. We also study non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.

The prevalence of neutral mutations implies that biological systems typically have many more genotypes than phenotypes. But, can the way that genotypes are distributed over phenotypes determine evolutionary outcomes? Answering such questions is difficult, in part because the number of genotypes can be hyper-astronomically large. By solving the genotype-phenotype (GP) map for RNA secondary structure (SS) for systems up to length L ¼ 126 nucleotides (where the set of all possible RNA strands would weigh more than the mass of the visible universe), we show that the GP map strongly constrains the evolution of non-coding RNA (ncRNA). Simple random sampling over genotypes predicts the distribution of properties such as the mutational robustness or the number of stems per SS found in naturally occurring ncRNA with surprising accuracy. Because we ignore natural selection, this strikingly close correspondence with the mapping suggests that structures allowing for functionality are easily discovered, despite the enormous size of the genetic spaces. The mapping is extremely biased: the majority of genotypes map to an exponentially small portion of the morphospace of all biophysically possible structures. Such strong constraints provide a nonadaptive explanation for the convergent evolution of structures such as the hammerhead ribozyme. These results present a particularly clear example of bias in the arrival of variation strongly shaping evolutionary outcomes and may be relevant to Mayr's distinction between proximate and ultimate causes in evolutionary biology.

Oral administration of drug products is a strict requirement in many medical indications. Therefore, bioavailability prediction models are of high importance for prioritization of compound candidates in the drug discovery process. However, oral exposure and bioavailability are difficult to predict, as they are the result of various highly complex factors and/or processes influenced by the physicochemical properties of a compound, such as solubility, lipophilicity, or charge state, as well as by interactions with the organism, for instance, metabolism or membrane permeation. In this study, we assess whether it is possible to predict intravenous (iv) or oral drug exposure and oral bioavailability in rats. As input parameters, we use (i) six experimentally determined in vitro and physicochemical endpoints, namely, membrane permeation, free fraction, metabolic stability, solubility, pK a value, and lipophilicity; (ii) the outputs of six in silico absorption, distribution, metabolism, and excretion models trained on the same endpoints, or (iii) the chemical structure encoded as fingerprints or simplified molecular input line entry system strings. The underlying data set for the models is an unprecedented collection of almost 1900 data points with high-quality in vivo experiments performed in rats. We find that drug exposure after iv administration can be predicted similarly well using hybrid models with in vitro-or in silico-predicted endpoints as inputs, with fold change errors (FCE) of 2.28 and 2.08, respectively. The FCEs for exposure after oral administration are higher, and here, the prediction from in vitro inputs performs significantly better in comparison to in silico-based models with FCEs of 3.49 and 2.40, respectively, most probably reflecting the higher complexity of oral bioavailability. Simplifying the prediction task to a binary alert for low oral bioavailability, based only on chemical structure, we achieve accuracy and precision close to 70%.

In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space-namely, that networks of genomes encoding the same phenotype may not be connected by single mutational moves. We use the folding of RNA sequences into secondary structures as a model genotype -phenotype map and explore the neutral spaces corresponding to networks of genotypes with the same phenotype. In most of these networks, we find that it is not possible to connect all genotypes to one another by single point mutations. Instead, a network for a phenotypic structure with n bonds typically fragments into at least 2 n neutral components, often of similar size. While components of the same network generate the same phenotype, they show important variations in their properties, most strikingly in their evolvability and mutational robustness. This heterogeneity implies contingency in the evolutionary process.