A thousand empirical adaptive landscapes and their navigability

The adaptive landscape is an iconic metaphor that pervades evolutionary biology. It was mostly applied in theoretical models until recent years, when empirical data began to allow partial landscape reconstructions. Here, we exhaustively analyse 1,137 complete landscapes from 129 eukaryotic species, each describing the binding affinity of a transcription factor to all possible short DNA sequences. We find that the navigability of these landscapes through single mutations is intermediate to that of additive and shuffled null models, suggesting that binding affinity—and thereby gene expression—is readily fine-tuned via mutations in transcription factor binding sites. The landscapes have few peaks that vary in their accessibility and in the number of sequences they contain. Binding sites in the mouse genome are enriched in sequences found in the peaks of especially navigable landscapes and the genetic diversity of binding sites in yeast increases with the number of sequences in a peak. Our findings suggest that landscape navigability may have contributed to the enormous success of transcriptional regulation as a source of evolutionary adaptations and innovations. An adaptive landscape is a mapping from a high-dimensional space of genotypes onto fitness or some other related quantitative phenotype, which defines the ‘elevation’ of each coordinate in genotype space 1 . Evolution can be viewed as a hill-climbing process in an adaptive landscape, where populations tend to move towards peaks as a consequence of natural selection. The ruggedness of an adaptive landscape has important evolutionary consequences, particularly for the evolution of sex, reproductive isolation and mutational robustness, and for the predictability of evolution 2 . An adaptive landscape that is smooth and single peaked does not pose any obstacle to evolutionary exploration. It is therefore highly navigable, in that it is possible to reach the global peak via positive selection through a series of small mutations that only move ‘uphill’. In contrast, a rugged landscape can block the approach to the highest peak by entrapping populations on local suboptimal peaks 3 . We know very little about the navigability of empirical adaptive landscapes, largely due to the incompleteness of the landscapes that have been constructed to date. With few exceptions 4,5 , these landscapes were built by assaying the phenotypes of only a small number of mutations in all possible combinations within a single wild-type background 2 . These studies have helped form our intuition about the structure and navigability of empirical adaptive landscapes, but their conclusions are limited by the fact that they describe only a minute fraction of any complete landscape. An additional caveat of earlier studies is their focus on just one or a few landscapes, which limits the generality of their findings. To study the navigability of a large number of complete, empirical adaptive landscapes, we consider data that describe the binding affinity of a transcription factor (TF)—a sequence-specific DNA-binding protein that helps regulate gene expression—to all possible DNA sequences (TF binding sites) of eight nucleotides in length. TFs are fundamental mediators of gene expression and are involved in numerous evolutionary innovations 6 . Their regulatory effect can be modulated via mutations in TF binding sites, which may alter a TF’s affinity for a site and thereby affect gene expression 7,​8,​9 . We describe the mapping of DNA sequence to binding affinity as an adaptive landscape, where we can study selection for TF binding. This is a common approach for exploring the evolution of TF binding sites 10,​11,​12,​13,​14 , other protein–DNA interactions 4,15,16 and protein–RNA interactions 17 . In this context, adaptive evolution is an exploration of sequence space that attempts to optimize the capacity of a sequence to bind a particular TF