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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.

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Figure 1: Adaptive landscapes of TF binding affinity.
Figure 2: The navigability of adaptive landscapes of TF binding affinity.
Figure 3: In vivo binding site abundance correlates with landscape navigability.
Figure 4: Gene expression increases along accessible mutational paths and reflects landscape topography.
Figure 5: Global peak breadth influences the diversity of TF binding sites in the yeast genome.


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J.A.-R. and J.L.P. acknowledge support through the Forschungskredit program of the University of Zurich (grant numbers FK-14-076 and K-74301-04-01). J.L.P. acknowledges additional support through the Ambizione program of the Swiss National Science Foundation. A.W. acknowledges support through the Swiss National Science Foundation (grant 31003A_146137) and the University Priority Research Program in Evolutionary Biology at the University of Zurich. We thank S. Bratulic, F. Khalid, A. Moya, Y. Schaerli and M. Toll-Riera for discussions and helpful comments on this manuscript.

Author information




J.A.-R., J.L.P. and A.W. designed the research. J.A.-R. and J.L.P. performed the research. J.A.-R., J.L.P. and A.W. analysed the data and wrote the paper.

Corresponding author

Correspondence to Andreas Wagner.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Figures 1–33; Supplementary Analyses, Results and Discussion (PDF 1981 kb)

Supplementary Table 1

Information about the 1,137 transcription factors and their landscapes. (XLSX 212 kb)

Supplementary Table 2

Sources for the DNase I hypersensitive regions, footprints, and RNA-seq data for the 14 cell and tissue types analysed in this study.Sources for the DNase I hypersensitive regions, footprints, and RNA-seq data for the 14 cell and tissue types analysed in this study. (XLSX 10 kb)

Supplementary Table 3

Spearman’s rank correlations between peak accessibility and the abundance of the highest-affinity site in DNase I footprints for the 14 cell and tissue types, in addition to Wilcoxon rank-sum tests comparing binding site abundance amongst single-peaked and multi-peaked landscapes. (XLSX 54 kb)

Supplementary Table 4

Spearman’s rank correlations between peak accessibility and the abundance of the highest-affinity site in DNase hypersensitive regions for 14 murine cell and tissue types, after having removed the DNase I footprints, in addition to Wilcoxon rank-sum tests comparing binding site abundance in the same hypersensitive regions amongst single-peaked and multi-peaked landscapes. (XLSX 57 kb)

Supplementary Table 5

Analysis of covariance (ANCOVA) and its underlying assumptions. (XLSX 53 kb)

Supplementary Table 6

Partial Spearman’s rank correlations with binding affinity between peak accessibility and the abundance of the highest-affinity site in DNase I footprints for the 14 cell and tissue types. (XLSX 41 kb)

Supplementary Table 7

Partial Spearman’s rank correlations with PWM information content between peak accessibility and the abundance of the highest-affinity site in DNase I footprints for 14 murine cell and tissue types. (XLSX 51 kb)

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Aguilar-Rodríguez, J., Payne, J. & Wagner, A. A thousand empirical adaptive landscapes and their navigability. Nat Ecol Evol 1, 0045 (2017).

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