Evolutionary Accessibility of Mutational Pathways

Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection (‘fitness’), measured values over all possible combinations of a set of mutations yield a fitness landscape that determines which mutational states can be reached from a given initial genotype. Understanding the accessibility properties of fitness landscapes is conceptually important in answering questions about the predictability and repeatability of evolutionary adaptation. Here we theoretically investigate accessibility of the globally optimal state on a wide variety of model landscapes, including landscapes with tunable ruggedness as well as neutral ‘holey’ landscapes. We define a mutational pathway to be accessible if it contains the minimal number of mutations required to reach the target genotype, and if fitness increases in each mutational step. Under this definition accessibility is high, in the sense that at least one accessible pathway exists with a substantial probability that approaches unity as the dimensionality of the fitness landscape (set by the number of mutational loci) becomes large. At the same time the number of alternative accessible pathways grows without bounds. We test the model predictions against an empirical 8-locus fitness landscape obtained for the filamentous fungus Aspergillus niger. By analyzing subgraphs of the full landscape containing different subsets of mutations, we are able to probe the mutational distance scale in the empirical data. The predicted effect of high accessibility is supported by the empirical data and is very robust, which we argue reflects the generic topology of sequence spaces. Together with the restrictive assumptions that lie in our definition of accessibility, this implies that the globally optimal configuration should be accessible to genome wide evolution, but the repeatability of evolutionary trajectories is limited owing to the presence of a large number of alternative mutational pathways. Author Summary: Fitness landscapes describe the fitness of related genotypes in a given environment, and can be used to identify which mutational steps lead towards higher fitness under particular evolutionary scenarios. The structure of a fitness landscape results from the way mutations interact in determining fitness, and can be smooth when mutations have multiplicative effect or rugged when interactions are strong and of opposite sign. Little is known about the structure of real fitness landscapes. Here, we study the evolutionary accessibility of fitness landscapes by using various landscape models with tunable ruggedness, and compare the results with an empirical fitness landscape involving eight marker mutations in the fungus Aspergillus niger. We ask how many mutational pathways from a low-fitness to the globally optimal genotype are accessible by natural selection in the sense that each step increases fitness. We find that for all landscapes with lower than maximal ruggedness the number of accessible pathways increases with increases of the number of loci involved, despite decreases in the accessibility for each pathway individually. We also find that models with intermediate ruggedness describe the A. niger data best.