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Evolutionary stability of minimal mutation rates in an evo-epidemiological model. (English) Zbl 1339.92056
Summary: We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.
MSC:
92D15 Problems related to evolution
92D30 Epidemiology
92D10 Genetics and epigenetics
Software:
deSolve; diffEq; R
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[1] Abrams, PA, Modelling the adaptive dynamics of traits involved in inter- and intraspecic interactions: an assessment of three methods, Ecol Lett, 4, 166-175, (2001)
[2] Alizon, S; Baalen, M, Emergence of a convex trade-off between transmission and virulence, Am Nat, 165, e155-e167, (2005)
[3] Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford
[4] Andre, JB; Hochberg, ME, Virulence evolution in emerging infectious diseases, Evolution, 59, 1406-1412, (2005)
[5] Bergstrom, CT; McElhany, P; Real, LA, Transmission bottlenecks as determinants of virulence in rapidly evolving pathogens, Proc Natl Acad Sci USA, 96, 5095-5100, (1999)
[6] Berngruber, TW; Froissart, R; Choisy, M; Gandon, S, Evolution of virulence in emerging epidemics, PLoS Pathog, 9, e1003,209, (2013)
[7] Bolker, BM; Grenfell, BT, Chaos and biological complexity in measles dynamics, Proc R Soc B, 251, 75-81, (1993)
[8] Bolker, BM; Nanda, A; Shah, D, Transient virulence of emerging pathogens, J R Soc Interface, 7, 811-822, (2010)
[9] Cushing, JM, Two species competition in a periodic environment, J Math Biol, 10, 385-400, (1980) · Zbl 0455.92012
[10] Day, T; Gandon, S, Applying population-genetic models in theoretical evolutionary epidemiology, Ecol Lett, 10, 876-888, (2007)
[11] Day, T; Proulx, S, A general theory for the evolutionary dynamics of virulence, Am Nat, 163, e40-e63, (2004)
[12] Drake, JW, A constant rate of spontaneous mutation in DNA-based microbes, PNAS, 88, 7160-7164, (1991)
[13] Drake, JW; Charlesworth, B; Charlesworth, D; Crow, JF, Rates of spontaneous mutation, Genetics, 148, 1667-1686, (1998)
[14] Fisher RA (1930) The genetical theory of natural selection. Clarendon, Oxford · JFM 56.1106.13
[15] Froissart R, Doumayrou J, Vuillaume F, Alizon S, Michalakis Y (2010) The virulence-transmission trade-off in vector-borne plant viruses: a review of (non-)existing studies. Philos Trans R Soc B Biol Sci 365(1548):1907-1918. doi:10.1098/rstb.2010.0068
[16] Herbeck, JT; Mittler, JE; Gottlieb, GS; Mullins, JI, An HIV epidemic model based on viral load dynamics: value in assessing empirical trends in HIV virulence and community viral load, PLoS Comput Biol, 10, e1003,673, (2014)
[17] Holmes, EC, What can we predict about viral evolution and emergence?, Curr Opin Virol, 3, 180-184, (2013)
[18] Johnson, T, Beneficial mutations, hitchhiking and the evolution of mutation rates in sexual populations, Genetics, 151, 1621-1631, (1999)
[19] Kimura, M, Optimum mutation rate and degree of dominance as determined by the principle of minimum genetic load, J Genet, 57, 21-34, (1960)
[20] Kimura, M, On the evolutionary adjustment of spontaneous mutation rates, Genet Res, 9, 23-34, (1967)
[21] Leigh, EG, Natural selection and mutability, Am Nat, 104, 301-305, (1970)
[22] Leigh, EG, The evolution of mutation rates, Genetics, 73, 1-18, (1973)
[23] Lloyd, AL, Estimating variability in models for recurrent epidemics: assessing the use of moment closure techniques, Theor Popul Biol, 65, 49-65, (2004) · Zbl 1105.92031
[24] Mollison, D, Dependence of epidemic and population velocities on basic parameters, Math Biosci, 107, 255-287, (1991) · Zbl 0743.92029
[25] Moran NA, Wernegreen JJ (2000) Lifestyle evolution in symbiotic bacteria: insights from genomics. Trends Ecol Evol 15(8):321-326. doi:10.1016/S0169-5347(00)01902-9
[26] Orr, HA, The rate of adaptation in asexuals, Genetics, 155, 961-968, (2000)
[27] Park, SC; Krug, J, Rate of adaptation in sexuals and asexuals: a solvable model of the Fisher-muller effect, Genetics, 195, 941-955, (2013)
[28] R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org/
[29] Regoes, RR; Hamblin, S; Tanaka, MM, Viral mutation rates: modelling the roles of within-host viral dynamics and the trade-off between replication fidelity and speed, Proc R Soc Lond B Biol Sci, 280, 2012-2047, (2013)
[30] Shirreff G, Pellis L, Laeyendecker O, Fraser C (2011) Transmission selects for HIV-1 strains of intermediate virulence: a modelling approach. PLoS Comput Biol 7(10):e1002185. doi:10.1371/journal.pcbi.1002185
[31] Sniegowski, PD; Gerrish, PJ; Johnson, T; Shaver, A, The evolution of mutation rates: separating causes from consequences, BioEssays, 22, 1057-1066, (2000)
[32] Soetaert K, Petzoldt T, Setzer RW (2010) Solving differential equations in R Package deSolve. J Stat Softw 33(9):1-25. http://www.jstatsoft.org/v33/i09
[33] Tilman D (1982) Resource competition and community structure. Princeton University Press, Princeton, NJ
[34] Turelli M, Barton NH (1994) Genetic and statistical analyses of strong selection on polygenic traits: what, me normal? Genetics 138(3):913-941
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