A 2017 computational study of the Avida digital-organism system (Fortuna, Zaman, Ofria and Wagner) mapped the genotypes of self-replicating computer programs to the sets of Boolean logic operations they perform, and found a two-level relationship between phenotypic complexity and evolvability: individual genotypes with more complex phenotypes are more likely to produce novel phenotypes by single mutations (higher genotypic evolvability), yet more complex phenotypes are encoded by fewer genotypes, are less robust, and are less phenotypically evolvable at the genotype-network level. The authors stated that this relationship had not been reported for any natural system, and called for systematic comparisons of different genotype–phenotype maps to identify those that are most evolvable, with implications for designing evolvable artificial and synthetic-biological systems. It remains unknown whether natural biological genotype–phenotype maps exhibit this relationship, and which GP-map architectures maximize evolvability.

Background

A genotype–phenotype map (GP map) is the correspondence between all possible genetic variants (genotypes) of a system and the traits or functions they produce (phenotypes). GP maps have been characterized for molecules such as RNA (sequences mapping to secondary structures) and proteins (sequences mapping to folds or functions), for metabolic networks, and for artificial systems. Across these very different maps, several regularities recur: most genotypes are non-viable or encode no functional phenotype; phenotypes differ enormously in how many genotypes encode them (phenotypic bias or rarity); and genotypes with the same phenotype form genotype networks — sets of sequences connected by single-point mutations that preserve the phenotype — which populations can drift along while remaining functional. Two properties of these networks are central here. Mutational robustness is the fraction of a genotype's one-mutant neighbors that preserve its phenotype. Evolvability, the capacity to produce novel phenotypes, comes in two flavors: genotypic evolvability is the number of distinct novel phenotypes reachable from one genotype by single point mutations, while phenotypic evolvability refers to the diversity of phenotypes accessible from the genotype network as a whole, which is shaped by how many genotypes encode the phenotype and how those genotypes are distributed in sequence space. Avida is a widely used artificial-life platform in which digital organisms are self-replicating computer programs whose genome is a circular sequence of instructions from a 26-instruction alphabet; organisms take binary numbers as environmental input and can perform Boolean logic operations on them, so a phenotype is naturally defined as the set of logic operations a genome performs, and phenotypic complexity as the number of such operations. Fortuna, Zaman, Ofria and Wagner (2017) exhaustively characterized this GP map and found: complex phenotypes (more logic operations) are encoded by fewer genotypes; transitions between phenotypes by single mutations are highly asymmetric, so complex phenotypes are harder to reach and typically require intermediates of lower complexity; genotypes with complex phenotypes have higher genotypic evolvability (their one-mutant neighbors express more novel phenotypes) but lower robustness; and because complex phenotypes are rare, their phenotypic evolvability is lower. These results connect to earlier work on phenotypic bias in molecular GP maps, such as Schaper and Louis's (2014) demonstration that bias in a GP map alone can steer evolving populations toward frequent phenotypes. The 2017 study ends with two explicitly unresolved directions. First, the complexity–evolvability relationship had, in the authors' words, not been reported for any natural system, and they argued that if natural GP maps show the same pattern, two predictions follow: mutations in an evolving population whose members have a complex phenotype should be more likely to create novel phenotypes, and on long evolutionary time scales the phenotypic diversity reachable from complex phenotypes should be lower than for simple ones. Second, they proposed that future studies systematically compare different GP maps — varying genetic languages, instruction sets, or biological mapping rules — to identify those that are most evolvable, with insights for designing evolvable synthetic biological systems. Whether these organizational principles of the Avida GP map hold for natural biological GP maps, and which GP-map architectures maximize evolvability, is the open problem this task addresses.

Problem Statement

Determine whether natural biological genotype–phenotype maps exhibit the same two-level relationship between phenotypic complexity, robustness, and evolvability that Fortuna et al. (2017) found in the Avida digital-organism GP map — namely that (i) individual genotypes encoding more complex phenotypes have higher genotypic evolvability (more of their one-mutant neighbors express novel phenotypes) while being less mutationally robust, and (ii) more complex phenotypes are encoded by fewer genotypes and therefore have lower phenotypic evolvability — by testing, in one or more natural biological GP maps (such as RNA sequences to structures or functions, protein sequences to functional phenotypes, or regulatory genotypes to expression phenotypes), the two predictions stated in the source: first, that mutations in an evolving population whose members have a complex phenotype are more likely to create novel phenotypes; and second, that on long evolutionary time scales the phenotypic diversity accessible from complex phenotypes is lower than from simpler ones. This requires an explicit, justified operationalization of phenotypic complexity in the natural system studied; this operationalization must be fixed a priori and must not be defined in terms of mutational robustness, genotypic evolvability, phenotypic evolvability, or phenotype-encoding genotype counts. In addition to the two evolvability predictions, the validation must measure, for complex versus simple phenotypes, mutational robustness and the number of genotypes encoding each phenotype. The companion objective, jointly serving the same goal of establishing which GP-map properties drive evolvability, is to systematically compare different GP map architectures — varying genetic languages, instruction sets, or biological mapping rules — under consistent metrics (phenotypic bias, genotype-network size, robustness, genotypic and phenotypic evolvability), and thereby identify which architectures maximize evolvability and yield design principles for evolvable artificial and synthetic-biological systems. The comparison must cover the Avida map together with at least two additional GP-map architectures — RNA sequences to secondary structures, protein sequences to folds or functions, regulatory genotypes to expression phenotypes, or metabolic networks — under a single consistent set of definitions for the metrics listed above, and must report the evolvability ordering for genotypic evolvability and for phenotypic evolvability. The natural-system validation must test every component of the relationship stated above (the two predictions together with mutational robustness and phenotype-encoding genotype counts).

References

  1. Fortuna MA, Zaman L, Ofria C, Wagner A (2017). The genotype-phenotype map of an evolving digital organism. PLOS Computational Biology 13(2): e1005414. doi:10.1371/journal.pcbi.1005414, https://doi.org/10.1371/journal.pcbi.1005414 (primary source)
  2. Schaper S, Louis AA (2014). The Arrival of the Frequent: How Bias in Genotype-Phenotype Maps Can Steer Populations to Local Optima. PLoS ONE 9(1): e86635. doi:10.1371/journal.pone.0086635, https://doi.org/10.1371/journal.pone.0086635
  3. Catalán P, Wagner A, Manrubia S, Cuesta JA (2018). Adding levels of complexity enhances robustness and evolvability in a multilevel genotype–phenotype map. Journal of the Royal Society Interface 15: 20170516. doi:10.1098/rsif.2017.0516, https://doi.org/10.1098/rsif.2017.0516
  4. Schweizer G, Wagner A (2020). Genotype networks of 80 quantitative Arabidopsis thaliana phenotypes reveal phenotypic evolvability despite pervasive epistasis. PLOS Computational Biology 16(9): e1008082. doi:10.1371/journal.pcbi.1008082, https://doi.org/10.1371/journal.pcbi.1008082
  5. Manrubia S, Cuesta JA, Aguirre J, Ahnert SE, Altenberg L, Cano AV, Catalán P, Diaz-Uriarte R, Elena SF, García-Martín JA, Hogeweg P, Khatri BS, Krug J, Louis AA, Martin NS, Payne JL, Tarnowski MJ, Weiß M (2021). From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics. Physics of Life Reviews. doi:10.1016/j.plrev.2021.03.004, https://doi.org/10.1016/j.plrev.2021.03.004
  6. Wright AH, Laue CL (2021). Evolvability and complexity properties of the digital circuit genotype-phenotype map. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2021). doi:10.1145/3449639.3459393, https://doi.org/10.1145/3449639.3459393
  7. Kumawat B, Zaman L (2021). Architecture of the Genotype-Phenotype Map and the Coevolution of Complexity. ALIFE 2021: The 2021 Conference on Artificial Life. doi:10.1162/isal_a_00386, https://doi.org/10.1162/isal_a_00386
  8. Milano N, Nolfi S (2022). Phenotypic complexity and evolvability in evolving robots. Frontiers in Robotics and AI 9: 994485. doi:10.3389/frobt.2022.994485, https://doi.org/10.3389/frobt.2022.994485
  9. Fortuna MA (2022). The phenotypic plasticity of an evolving digital organism. Royal Society Open Science 9: 220852. doi:10.1098/rsos.220852, https://doi.org/10.1098/rsos.220852
  10. García-Galindo P, Ahnert SE, Martin NS (2023). The non-deterministic genotype–phenotype map of RNA secondary structure. Journal of the Royal Society Interface 20: 20230132. doi:10.1098/rsif.2023.0132, https://doi.org/10.1098/rsif.2023.0132
  11. Santos-Moreno J, Tasiudi E, Kusumawardhani H, Stelling J, Schaerli Y (2023). Robustness and innovation in synthetic genotype networks. Nature Communications 14. doi:10.1038/s41467-023-38033-3, https://doi.org/10.1038/s41467-023-38033-3
  12. Herrera-Álvarez S, Patton JEJ, Thornton JW (2025). The structure of an ancient genotype–phenotype map shaped the functional evolution of a protein family. Nature Ecology & Evolution. doi:10.1038/s41559-025-02777-6, https://doi.org/10.1038/s41559-025-02777-6
  13. Dingle K, Hagolani P, Zimm R, Umar M, O'Sullivan S, Louis A (2025). Bounding phenotype transition probabilities via conditional complexity. Journal of the Royal Society Interface 22: 20240916. doi:10.1098/rsif.2024.0916, https://doi.org/10.1098/rsif.2024.0916
  14. Kumawat B, Lalejini A, Acosta MM, Zaman L (2025). Evolution takes multiple paths to evolvability when facing environmental change. Proceedings of the National Academy of Sciences. doi:10.1073/pnas.2413930121, https://doi.org/10.1073/pnas.2413930121
  15. Lafuma F, Renvoisé É, Clavel J, Corfe IJ, Escarguel G (2025). Six million years of vole dental evolution shaped by tooth development. Proceedings of the National Academy of Sciences. doi:10.1073/pnas.2505624122, https://doi.org/10.1073/pnas.2505624122
  16. Martin NS (2026). A simple model captures key characteristics of biological non-deterministic genotype-phenotype maps. PLOS Computational Biology. doi:10.1371/journal.pcbi.1014272, https://doi.org/10.1371/journal.pcbi.1014272
  17. Manrubia S, Seoane LF, Cuesta JA (2026). The challenge of scale in molecular adaptation: Local searches in astronomical genotype networks. arXiv:2601.12005, https://arxiv.org/abs/2601.12005