Zagórski, Marcin PIST Austria ; Burda, Zdzisław; Wacław, Bartłomiej
Evolutionary pathways describe trajectories of biological evolution in the space of different variants of organisms (genotypes). The probability of existence and the number of evolutionary pathways that lead from a given genotype to a better-adapted genotype are important measures of accessibility of local fitness optima and the reproducibility of evolution. Both quantities have been studied in simple mathematical models where genotypes are represented as binary sequences of two types of basic units, and the network of permitted mutations between the genotypes is a hypercube graph. However, it is unclear how these results translate to the biologically relevant case in which genotypes are represented by sequences of more than two units, for example four nucleotides (DNA) or 20 amino acids (proteins), and the mutational graph is not the hypercube. Here we investigate accessibility of the best-adapted genotype in the general case of K > 2 units. Using computer generated and experimental fitness landscapes we show that accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences. The increase in accessibility comes from the increase in the number of indirect trajectories exploited by evolution for higher K. As one of the consequences, the fraction of genotypes that are accessible increases by three orders of magnitude when the number of units K increases from 2 to 16 for landscapes of size N ∼ 106genotypes. This suggests that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.
PLoS Computational Biology
MZ acknowledges the Polish National Science Centre grant no. DEC-2012/07/N/NZ2/00107. BW was supported by the Scottish Government/Royal Society of Edinburgh Personal Research Fellowship. We thank Marjon de Vos and Oliver Martin for critically reading the manuscript.
Zagórski MP, Burda Z, Wacław B. Beyond the hypercube evolutionary accessibility of fitness landscapes with realistic mutational networks. PLoS Computational Biology. 2016;12(12). doi:10.1371/journal.pcbi.1005218
Zagórski, M. P., Burda, Z., & Wacław, B. (2016). Beyond the hypercube evolutionary accessibility of fitness landscapes with realistic mutational networks. PLoS Computational Biology, 12(12). https://doi.org/10.1371/journal.pcbi.1005218
Zagórski, Marcin P, Zdzisław Burda, and Bartłomiej Wacław. “Beyond the Hypercube Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks.” PLoS Computational Biology 12, no. 12 (2016). https://doi.org/10.1371/journal.pcbi.1005218.
M. P. Zagórski, Z. Burda, and B. Wacław, “Beyond the hypercube evolutionary accessibility of fitness landscapes with realistic mutational networks,” PLoS Computational Biology, vol. 12, no. 12, 2016.
Zagórski MP, Burda Z, Wacław B. 2016. Beyond the hypercube evolutionary accessibility of fitness landscapes with realistic mutational networks. PLoS Computational Biology. 12(12).
Zagórski, Marcin P., et al. “Beyond the Hypercube Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks.” PLoS Computational Biology, vol. 12, no. 12, e1005218, Public Library of Science, 2016, doi:10.1371/journal.pcbi.1005218.
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