A simple model captures key characteristics of biological non-deterministic genotype-phenotype maps
Nora S. Martin
Abstract
By connecting genotypic mutations to the higher-level phenotypes relevant for selection, genotype-phenotype (GP) maps play a key role in evolution. GP maps are typically investigated using computational models of biophysical phenotypes (for example, RNA secondary structures and simplified models of protein tertiary and quaternary structures), but GP map concepts are relevant beyond these specific models. While there has been significant progress in quantifying GP map properties and their evolutionary implications, this is largely limited to the simplest case, where each genotype corresponds to a single, categorical phenotype.
Introduction
Variation through random mutations is a central component of models of evolutionary processes [3]. Since variation at the phenotypic level is produced by mutations on the genotypic level, a genotype-phenotype (GP) map is needed to model variation quantitatively. GP maps can be characterised by a set of quantitative features [4] such as phenotypic frequencies and evolvabilities.
Methods
4.1. RNA GP map
For each RNA genotype of length L = 12 nucleotides, the Boltzmann ensemble of secondary structures was computed using the ViennaRNA package [12] (version 2.7.0): first, a list was generated with all secondary structures whose base pairs are compatible with the genotype g. Then, the free energy of each structure p was calculated with the eval_structure function in ViennaRNA’s Python bindings.
Results
2.1. Defining a simple synthetic ND GP map
To produce an ND GP map, the synthetic model needs to map a genotype , i.e., a sequence of characters from a fixed alphabet, to an ensemble of phenotypes, given by a valid probability distribution (i.e., non-negative ensemble frequencies summing to one).
Discussion
While many realistic genotype-phenotype (GP) maps are non-deterministic (ND), our understanding of such maps is much less developed than that of simpler GP maps without ND, where every genotype maps to a single categorical phenotype. Here, I build a foundation for a more systematic understanding of ND GP maps by showing that a simple, tuneable non-biological model of an ND GP map reproduces key features of three biophysical ND GP maps (RNA secondary structure, lattice protein model, Polyomino self-assembly model): phenotypic bias, genetic correlations, a tradeoff between genotypic robustness and evolvability and a non-negative trend between phenotypic robustness and evolvability.
Acknowledgments
I thank M. Giraud for helpful comments.
Citation: Martin NS (2026) A simple model captures key characteristics of biological non-deterministic genotype-phenotype maps. PLoS Comput Biol 22(5): e1014272. https://doi.org/10.1371/journal.pcbi.1014272
Editor: Alexandre V. Morozov, Rutgers University: Rutgers The State University of New Jersey, UNITED STATES OF AMERICA
Received: July 26, 2025; Accepted: April 27, 2026; Published: May 22, 2026
Copyright: © 2026 Nora S. Martin. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The code behind this analysis can be found at https://github.com/noramartin/simple_models.
Funding: I acknowledge support of the Spanish Ministry of Science and Innovation through the Centro de Excelencia Severo Ochoa (CEX2020-001049-S, MCIN/AEI/10.13039/501100011033), the EMBL partnership and the Generalitat de Catalunya through the CERCA programme. Research for this publication has been partially carried out in the Barcelona Collaboratorium for Modelling and Predictive Biology. This research is part of Grant JDC2022-049526-I funded by MCIN/AEI/10.13039/501100011033 and by European Union NextGenerationEU/PRTR. The funders played no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The author has declared that no competing interests exist.
