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. 2020 Nov 11;10:19508. doi: 10.1038/s41598-020-75684-4

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Population response when the genomic error rate can evolve to the ESS. (a) Fitness for different genomic error rates. It attains the maximum when $x = 0.1$ , which is the evolutionarily stable value. The other parameters are $u = 0.2$ , $k = 1.8$ , $m_{0} = 10$ , $f_{0} = 0.044$ , $q = 1.1$ , and $n = 5$ . (b) The evolutionarily stable value of genomic error rate $x^{*}$ . The horizontal axis represents $u$ , noncancerous mortality. The parameters are the same as in (a) unless specified otherwise. (c) Total cancerous mortality $M_{C}$ . The curve labeled as "before adaptation" indicates $M_{C}$ if the genomic error rate is fixed: $x = 0.1$ (the ESS value under $u = 0.2$ ), which is the same as that in Fig. 2a. The curve labeled as "after adaptation" indicates $M_{C}$ if the genomic error rate $x$ is equal to the ESS value corresponding to $u$ in the horizontal axis (shown in Fig. 4b). Note that the two curves cross each other at $u = 0.2$ . (d) Mean longevity $\bar{T}$ . The curve labeled as "before adaption" is $\bar{T}$ when $x = 0.1$ , which is the same as that in Fig. 2b. The curve labeled as "after adaptation" is $\bar{T}$ when $x$ is the ESS value corresponding to $u$ , given in the horizontal axis. (e) Age-specific mortality due to cancer $g_{C} (a)$ . The curve labeled as "before adaptation" is the one when $u = 0.2$ and $x = 0.1$ . When the noncancerous mortality is reduced to $u = 0.0667$ , the curve remains the same. The curve labeled as "after adaptation" is the one for $x = 0.0507$ , which is the ESS value under $u = 0.0667$ . (f) The relative fraction of cancer mortality at each age $a$ , $g_{C} (a) / (g_{C} (a) + g_{N} (a))$ . The curve labeled as I is the one in the original population, in which $u = 0.2$ and $x = 0.1$ (the ESS value). The curve labeled as II and "before adaptation" is the one when the noncancerous mortality is reduced to $u = 0.0667$ , without changing $x$ . The curve labeled as III and "after adaptation" is the one in which the genomic error rate evolves to the ESS value $x = 0.0507$ under $u = 0.0667$ . The curve III is lower than the other curves. Parameters are the same as in (a), unless specified otherwise.