Figure 1.

The geometry of selected mutations in Fisher’s fitness landscape for various complexities of the phenotypic space. The left panel represents an isotropic landscape with n = 3. The log-fitness isocline in the phenotypic space is a sphere centered at the origin $\left(\log \right[W\left[z\right]]=-{\Sigma }_{i=1}^n{z}_i^2)$. The vertical axis is the main axis of selection. The ancestral strain and the optimum are shown as black points. A beneficial mutation is shown as a plain arrow. The geometry of the mutation is characterized by the norm ||z|| and by the angle between the mutations and the main axis of selection θ. On the right panel, the distribution of these quantities is shown for complexities n = 3, n = 10, n = 100. The mutational variance σ_mut was normalized such that the expected norm is the same for all complexities. At higher complexities, mutations tend to be almost orthogonal to the main axis of selection (θ → π/2) and to exhibit very little variation in their norm.