Fig. 1.

Fitness landscapes and CBN. Upper panels show schematic representations of three different fitness landscapes each including four mutations. Each vertex corresponds to a genotype, which is represented as a binary string and is color-coded according to its fitness. Each fitness landscape is arranged in five columns and each column contains all genotypes with the same number of mutations. The leftmost and the rightmost columns correspond, respectively, to the wild-type and the fully mutated genotype. There is an edge between a pair of genotypes if they differ in exactly one fitness-increasing mutation. A mutational pathway is comprised of a set of edges that connect the wild-type to the genotype with the highest fitness (i.e. the fully mutated one). In panel (a), all genotypes belonging to the same column have the same fitness and fitness increases monotonically from left to right. In this fitness landscape, all 4!=24 potential pathways are accessible with equal probability (minimum predictability). In panel (b), not all genotypes belonging to the same column have the same fitness, such that evolutionary trajectories are restricted: only five pathways are accessible with different probability (shown as different edge thickness) (intermediate predictability). In panel (c), only a single mutational pathway is accessible and predictability is maximal. Each network on the bottom (with green vertices and labeled by the mutation) represents a CBN, whose DAG encodes the order constraints. An edge $a\to b$ in the DAG means that mutation a must occur prior to mutation b. The graphs on the top are exactly the genotype lattices of the corresponding CBN models on the bottom