Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 7 (1), 15519

Critical Mutation Rate Has an Exponential Dependence on Population Size for Eukaryotic-length Genomes With Crossover

Affiliations

Critical Mutation Rate Has an Exponential Dependence on Population Size for Eukaryotic-length Genomes With Crossover

Elizabeth Aston et al. Sci Rep.

Abstract

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness ("flattest"). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction.

Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1
Two-peak fitness landscape with one narrow peak of high fitness (peak 0), and one broader peak of lower fitness (peak 1). Each step on the x axis represents a single base mutation. Diagram adapted from Wilke.
Figure 2
Figure 2
CMR when the simulation model was run for one gene with sequence lengths of 30 up to 150,000 bp (shown in the legend) for population sizes 10 up to 1,000. Peak 0 had a radius of 2 and peak 1 a radius of 5. The Hamming distance between the peaks was 10. The exponential lines were obtained by curve-fitting using R with a least squares method. Error bars are not plotted, but are small, for instance 9.37×1003 (9.317×10039.423×1003, 95% confidence interval) and 1.84×1006 (1.834×10061.846×1006, 95% confidence interval) for uppermost (30 bp) and lowest (150,000 bp) points (population size 900) respectively.
Figure 3
Figure 3
CMR plotted against population size for varying values of scale parameter S. Population size was varied from 10 up to 1,000 and each individual consisted of 1 gene of 1,000 bp in length. Peak 0 and 1 were given a radius of 2 and 5 respectively, while the distance between their peaks was set to 10. (a) CMR plotted for population sizes 10 up to 1,000. The radius of the peaks was initially set to 2 and 5 for peak 0 and 1 respectively, with the distance between the top of the peaks set to 10. These values were then scaled by parameter S (shown in the legend). The exponential lines were obtained by curve-fitting using R with a least squares method. Error bars are not plotted, but are small, for instance 8.66×1004 (8.621×10048.699×1004, 95% confidence interval) and 2.75×1004 (2.740×10042.760×1004, 95% confidence interval) for uppermost (S = 10) and lowest (S = 1) points (population size 900) respectively. (b) CMR plotted for varying values of S when population size is 1,000.
Figure 4
Figure 4
(a) CMR plotted for varying number of crossovers. The number of crossover events per reproduction is given in the legend. The exponential lines were obtained by curve-fitting using R with a least squares method. Error bars are not plotted, but are small, for instance 3.91×1003 (3.866×10033.954×1003, 95% confidence interval) and 2.75×1004 (2.740×10042.760×1004, 95% confidence interval) for uppermost (5 crossovers) and lowest (1 crossover) points (population size 900) respectively. (b) CMR plotted for varying number of chromosomes. The number of chromosomes each gene was split into is given in the legend. The exponential lines were obtained by curve-fitting using R with a least squares method. Error bars are not plotted, but are small, for instance 4.73×1003 (4.703×10034.757×1003, 95% confidence interval) and 2.75×1004 (2.740×10042.760×1004, 95% confidence interval) for uppermost (10 chromosomes) and lowest (1 chromosome) points (population size 900) respectively. Population size was varied from 10 up to 1,000 and each individual consisted of 1 gene of 1,000 bp in length. Peak 0 had a radius of 2 and peak 1 a radius of 5. The Hamming distance between the peaks was 10. The number of crossovers per reproduction was increased from 1 (as per previous experiments) to 5, as per the legend in (a). The number of chromosomes per gene (given in the legend) was increased from 1 (as per previous experiments) to 10, as per the legend in (b).
Figure 5
Figure 5
CMR plotted alongside gene number for varying population sizes. Data are shown for population sizes 10 to 80 with results plotted on a log log scale. Peak 0 had a radius of 2 and peak 1 a radius of 5. The Hamming distance between the peaks was 10. Gene length was kept constant at 1,000, while gene number was doubled from 1 up to 8,192. The corresponding quadratic lines were obtained by curve-fitting using R. Error bars are not plotted, but are small, for instance 5.26×1008 (4.100×10086.400×1008, 95% confidence interval) and 1.25×1007 (1.000×10071.500×1007, 95% confidence interval) for uppermost (population size 80) and lowest (population size 10) points (gene number 8192) respectively. A line representing 1/L, where L is gene length, is plotted for reference. Population sizes shown represent the steep part of the curve in Fig. 2 before it levels out. Population size 10 was also run with 25,000 genes, the correct range for the plant A. thaliana. Gene length was set to 1,000 bp to match the other runs or 2,000 bp to bring it closer to A. thaliana’s gene length. For reference, the range of per base mutation rates from Table 1 is shown for A. thaliana, Caenorhabditis elegans (nematode worm), Drosophila melanogaster (fruit fly), and humans (with gene number estimates from,, and respectively).

Similar articles

See all similar articles

References

    1. Masel J, Trotter MV. Robustness and evolvability. Trends in Genetics. 2010;26:406–414. doi: 10.1016/j.tig.2010.06.002. - DOI - PMC - PubMed
    1. Orr HA. The population genetics of beneficial mutations. Philosophical Transactions of the Royal Society B. 2010;365:1195–1201. doi: 10.1098/rstb.2009.0282. - DOI - PMC - PubMed
    1. Wilke CO, Wang JL, Ofria C, Lenski RE, Adami C. Evolution of digital organisms at high mutation rates leads to survival of the flattest. Nature. 2001;412:331–333. doi: 10.1038/35085569. - DOI - PubMed
    1. Wilke CO. Quasispecies theory in the context of population genetics. BMC Evolutionary Biology. 2005;5:44. doi: 10.1186/1471-2148-5-44. - DOI - PMC - PubMed
    1. Sardanyés J, Elena SF, Solé RV. Simple quasispecies models for the survival-of-the-flattest effect: The role of space. Journal of Theoretical Biology. 2008;250:560–568. doi: 10.1016/j.jtbi.2007.10.027. - DOI - PubMed
Feedback