Wagner (2008) resolved the apparent paradox between mutational robustness and evolvability by distinguishing the genotype level from the phenotype level in the RNA sequence-to-secondary-structure map: genotype robustness antagonizes evolvability, while phenotype robustness promotes it. The paper itself left three linked open questions that jointly define whether this phenotype-level paradigm holds for life in general: (i) there is no reliable and tractable method to estimate phenotype frequencies — the fraction of genotype space mapping to a given phenotype — for biologically important phenotypes, so their robustness and evolvability cannot currently be quantified; (ii) the positive association between phenotype-level robustness and phenotype-level evolvability is established only for RNA secondary structure and must be tested in other systems such as regulatory circuits, proteins, metabolic networks, and whole-organism phenotypes; (iii) it is unresolved whether high phenotypic evolvability is an adaptation in its own right or a by-product of selection for other properties such as mutational robustness or thermodynamic stability. Later literature has partially advanced all three fronts — Monte Carlo and free-energy-based estimators and generative models for RNA phenotype abundances, demonstrations of the robustness–evolvability association across regulatory, metabolic, genetic-code, and empirical molecular maps together with a monotonicity theorem for random maps, and evidence for the by-product, direct-selection, and second-order-selection routes to evolvability — but no external evidence closes any of the three questions at its stated generality, and the origin question in particular is explicitly framed as open in the most recent reviews.

Background

A genotype is the heritable information encoding a biological system (for example, an RNA sequence of nucleotides), while a phenotype is any observable characteristic it produces (for example, the two-dimensional folded shape, or secondary structure, that the RNA adopts). A genotype–phenotype (GP) map assigns genotypes to phenotypes. Because many different sequences can fold to the same structure, such maps are many-to-one. Mutational robustness is the ability of a system to maintain its phenotype despite mutation; evolvability is its ability to produce heritable, potentially adaptive phenotypic variation. These two properties appear paradoxical — robustness suppresses variation, evolvability produces it. The set of genotypes sharing a phenotype is called a neutral set or genotype network (the graph in which such genotypes are nodes, joined when they differ by a single small mutation). The phenotype frequency ff is the fraction of all possible genotypes that map to a phenotype; it sets the size of that phenotype's genotype network and hence, in aggregate, its robustness. Wagner (2008) showed in the RNA secondary-structure map that a genotype's robustness and its evolvability are antagonistically related, whereas a phenotype's robustness and evolvability are positively related: phenotypes realized by many genotypes have larger genotype networks and access more distinct alternative phenotypes in the mutational neighborhoods of those networks. Finite populations drifting on a large network therefore accumulate genotypic diversity and access more phenotypic variation. In the same paper's discussion, three obstacles to generalizing this resolution were identified. First, the phenotype-level quantities are defined in terms of phenotype frequencies, and genotype spaces grow astronomically (an RNA of length nn has 4n4^n sequences), so no reliable, tractable method existed to estimate ff for most biologically important phenotypes — molecular or higher-level. Second, the positive association had been demonstrated only for RNA secondary structure; regulatory circuits, proteins, metabolic networks, and whole-organism phenotypes had not been tested. Third, the analysis was static: it did not address which evolutionary forces produce high phenotypic evolvability — whether evolvability is an adaptation in its own right, or a by-product of selection for other properties such as mutational robustness or thermodynamic stability, which are themselves positively associated. The three questions form one scientific program: to establish the phenotype-level robustness–evolvability paradigm as a general, measurable, and evolutionarily explained principle, rather than an RNA-specific observation.

Problem Statement

The overarching objective is to complete the phenotype-level account of robustness and evolvability that Wagner (2008) established for RNA secondary structure — to measure it, establish its generality, and explain its evolutionary origin. Specifically: (1) Develop reliable and tractable methods to estimate phenotype frequencies — the fraction of a vast genotype space whose members map to a given phenotype — so that the mutational robustness and evolvability of biologically important molecular and higher-level phenotypes (RNAs, proteins, regulatory circuits, metabolic networks, whole-organism phenotypes) can actually be quantified rather than assumed. (2) Determine whether the positive association between phenotype-level robustness and phenotype-level evolvability found for RNA secondary structure holds in these other biological systems — that is, whether phenotypes realized by many genotypes are systematically more evolvable because larger genotype networks grant access to more phenotypic variety in their mutational neighborhoods — including empirical natural systems and complex, continuously varying traits, not only idealized computational maps. (3) Determine the evolutionary origin of high phenotypic evolvability: to what extent it is an adaptation in its own right (selected directly, or via second-order selection — selection that favors a property such as future adaptive potential rather than immediate fitness) and to what extent a by-product of selection for other properties such as mutational robustness or thermodynamic stability. The three questions are jointly linked: measurement (1) supplies the quantities that generality claims (2) are about, and both constrain which selective forces could plausibly produce the pattern (3). All three parts are required, and the phenotype classes named in (1) are illustrative of the required breadth rather than an exhaustive checklist. The program's scope is therefore: (1) a reliable and tractable phenotype-frequency estimator extending beyond RNA secondary structure, for at least one further molecular class and at least one higher-level or whole-organism class; (2) the robustness–evolvability association established for that same breadth; and (3) the evolutionary origin of high evolvability settled for that same breadth for each of the three routes named in (3) — direct selection, second-order selection, and by-product.

References

  1. Wagner A. Robustness and evolvability: a paradox resolved. Proceedings of the Royal Society B 275:91–100 (2008). doi:10.1098/rspb.2007.1137, https://doi.org/10.1098/rspb.2007.1137
  2. Jörg T, Martin OC, Wagner A. Neutral network sizes of biological RNA molecules can be computed and are not atypically small. BMC Bioinformatics 9:464 (2008). doi:10.1186/1471-2105-9-464, https://doi.org/10.1186/1471-2105-9-464
  3. Manrubia S, Cuesta JA. Distribution of genotype network sizes in sequence-to-structure genotype-phenotype maps. Journal of the Royal Society Interface 14:20160976 (2017). doi:10.1098/rsif.2016.0976, https://doi.org/10.1098/rsif.2016.0976
  4. Martin NS, Ahnert SE. Fast free-energy-based neutral set size estimates for the RNA genotype-phenotype map. Journal of the Royal Society Interface 19:20220072 (2022). doi:10.1098/rsif.2022.0072, https://doi.org/10.1098/rsif.2022.0072
  5. Schaper S, Louis AA. The arrival of the frequent: how bias in genotype-phenotype maps can steer populations to local optima. PLoS ONE 9:e86635 (2014). doi:10.1371/journal.pone.0086635, https://doi.org/10.1371/journal.pone.0086635
  6. Lambert CN, Opuu V, Calvanese F, Pavlinova P, Zamponi F, Hayden EJ, Weigt M, Smerlak M, Nghe P. Exploring the space of self-reproducing ribozymes using generative models. Nature Communications 16:7836 (2025). doi:10.1038/s41467-025-63151-5, https://doi.org/10.1038/s41467-025-63151-5
  7. Payne JL, Moore JH, Wagner A. Robustness, evolvability, and the logic of genetic regulation. Artificial Life 20:111–126 (2014). doi:10.1162/artl_a_00099, https://doi.org/10.1162/artl_a_00099
  8. Aguilar-Rodríguez J, Peel L, Stella M, Wagner A, Payne JL. The architecture of an empirical genotype-phenotype map. Evolution 72:1242–1260 (2018). doi:10.1111/evo.13487, https://doi.org/10.1111/evo.13487
  9. Wei X, Zhang J. Why phenotype robustness promotes phenotype evolvability. Genome Biology and Evolution 9:3509–3515 (2017). doi:10.1093/gbe/evx264, https://doi.org/10.1093/gbe/evx264
  10. Catalán P, Wagner A, Manrubia S, Cuesta JA. Adding levels of complexity enhances robustness and evolvability in a multilevel genotype-phenotype map. Journal of the Royal Society Interface 15:20170516 (2018). doi:10.1098/rsif.2017.0516, https://doi.org/10.1098/rsif.2017.0516
  11. Fortuna MA, Zaman L, Ofria C, Wagner A. The genotype-phenotype map of an evolving digital organism. PLoS Computational Biology 13:e1005414 (2017). doi:10.1371/journal.pcbi.1005414, https://doi.org/10.1371/journal.pcbi.1005414
  12. Rozhoňová H, Martí-Gómez C, McCandlish DM, Payne JL. Robust genetic codes enhance protein evolvability. PLoS Biology 22:e3002594 (2024). doi:10.1371/journal.pbio.3002594, https://doi.org/10.1371/journal.pbio.3002594
  13. Hardy NB. How does robustness affect evolvability? Evolution 79:1996–2006 (2025). doi:10.1093/evolut/qpaf116, https://doi.org/10.1093/evolut/qpaf116
  14. Hardy NB. The robustness and evolvability of continuously varying traits. Evolution 80:1532–1541 (2026). doi:10.1093/evolut/qpag082, https://doi.org/10.1093/evolut/qpag082
  15. Bloom JD, Labthavikul ST, Otey CR, Arnold FH. Protein stability promotes evolvability. Proceedings of the National Academy of Sciences USA 103:5869–5874 (2006). doi:10.1073/pnas.0510098103, https://doi.org/10.1073/pnas.0510098103
  16. Draghi JA, Parsons TL, Wagner GP, Plotkin JB. Mutational robustness can facilitate adaptation. Nature 463:353–355 (2010). doi:10.1038/nature08694, https://doi.org/10.1038/nature08694
  17. Hayden EJ, Ferrada E, Wagner A. Cryptic genetic variation promotes rapid evolutionary adaptation in an RNA enzyme. Nature 474:92–95 (2011). doi:10.1038/nature10083, https://doi.org/10.1038/nature10083
  18. Woods RJ, Barrick JE, Cooper TF, Shrestha U, Kauth MR, Lenski RE. Second-order selection for evolvability in a large Escherichia coli population. Science 331:1433–1436 (2011). doi:10.1126/science.1198914, https://doi.org/10.1126/science.1198914
  19. Pavlicev M, Cheverud JM, Wagner GP. Evolution of adaptive phenotypic variation patterns by direct selection for evolvability. Proceedings of the Royal Society B 278:1903–1912 (2011). doi:10.1098/rspb.2010.2113, https://doi.org/10.1098/rspb.2010.2113
  20. Karve S, Dasmeh P, Zheng J, Wagner A. Low protein expression enhances phenotypic evolvability by intensifying selection on folding stability. Nature Ecology & Evolution 6:1155–1164 (2022). doi:10.1038/s41559-022-01797-w, https://doi.org/10.1038/s41559-022-01797-w
  21. Wagner A. Adaptive evolvability through direct selection instead of indirect, second-order selection. Journal of Experimental Zoology Part B 338:395–404 (2022). doi:10.1002/jez.b.23071, https://doi.org/10.1002/jez.b.23071
  22. Payne JL, Wagner A. The causes of evolvability and their evolution. Nature Reviews Genetics 20:24–38 (2019). doi:10.1038/s41576-018-0069-z, https://doi.org/10.1038/s41576-018-0069-z
  23. Kharma N, Bédard-Couture R. Robustness and evolvability: Revisited, redefined and applied. BioSystems 246:105281 (2024). doi:10.1016/j.biosystems.2024.105281, https://doi.org/10.1016/j.biosystems.2024.105281