Institute of Theoretical Physics, University of Cologne, Köln, Germany.
PLoS Comput Biol. 2011 Aug;7(8):e1002134. doi: 10.1371/journal.pcbi.1002134. Epub 2011 Aug 18.
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.
不同突变的功能效应以非常复杂的方式组合起来，共同构成总效应。对于进化选择下的性状（适合度），在一组突变的所有可能组合上测量的值会产生一个适合度景观，该景观决定了从给定的初始基因型可以达到哪些突变状态。理解适合度景观的可达性属性在回答关于进化适应的可预测性和可重复性的问题方面具有概念上的重要性。在这里，我们从理论上研究了在各种模型景观上全局最优状态的可达性，包括可调节崎岖度的景观以及中性“空洞”景观。我们定义，如果一条突变途径包含到达目标基因型所需的最小突变数量，并且在每个突变步骤中适合度增加，那么该途径就是可达的。根据这个定义，可达性很高，至少有一种可达途径存在，而且随着适应景观的维度（由突变位点的数量决定）变得很大，这种可能性接近 1。同时，替代可达途径的数量呈无界增长。我们通过分析包含不同突变子集的完整景观的子图，将模型预测与从丝状真菌黑曲霉获得的 8 个基因座的实际适合度景观进行了比较。我们能够探测出实际数据中的突变距离尺度。高可达性的预测效果得到了实际数据的支持，而且非常稳健，我们认为这反映了序列空间的通用拓扑。与可达性定义中的限制假设一起，这意味着全局最优配置应该可以通过全基因组进化来实现，但由于存在大量替代的突变途径，进化轨迹的可重复性受到限制。
