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Stability Properties of Underdominance in Finite Subdivided Populations

DOI: 10.1371/journal.pcbi.1002260

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In isolated populations underdominance leads to bistable evolutionary dynamics: below a certain mutant allele frequency the wildtype succeeds. Above this point, the potentially underdominant mutant allele fixes. In subdivided populations with gene flow there can be stable states with coexistence of wildtypes and mutants: polymorphism can be maintained because of a migration-selection equilibrium, i.e., selection against rare recent immigrant alleles that tend to be heterozygous. We focus on the stochastic evolutionary dynamics of systems where demographic fluctuations in the coupled populations are the main source of internal noise. We discuss the influence of fitness, migration rate, and the relative sizes of two interacting populations on the mean extinction times of a group of potentially underdominant mutant alleles. We classify realistic initial conditions according to their impact on the stochastic extinction process. Even in small populations, where demographic fluctuations are large, stability properties predicted from deterministic dynamics show remarkable robustness. Fixation of the mutant allele becomes unlikely but the time to its extinction can be long.


[1]  Fisher RA (1922) On the dominance ratio. Proc Roy Soc Edinburgh 42: 321–341.
[2]  Wright S (1931) Evolution in Mendelian populations. Genetics 16: 97–159.
[3]  Haldane JBS (1927) A mathematical theory of natural and artificial selection. Part V. Selection and mutation. Proc Camb Philol Soc 23: 838–844.
[4]  Hartl DL, Clark AG (1997) Principles of Population Genetics. 3rd edition. Sunderland, MA: Sinauer Associates, Inc.
[5]  Li CC (1955) The stability of an equilibrium and the average fitness of a population. Am Nat 89: 281–295.
[6]  Weibull J (1995) Evolutionary Game Theory. Cambridge, MA: MIT Press.
[7]  Hofbauer J, Sigmund K (1998) Evolutionary Games and Population Dynamics. Cambridge, UK: Cambridge University Press.
[8]  Skyrms B (2003) The Stag-Hunt Game and the Evolution of Social Structure. Cambridge, UK: Cambridge University Press.
[9]  Gintis H (2000) Game Theory Evolving. Princeton, NJ: Princeton University Press.
[10]  Traulsen A, Reed FA (2011) From genes to games: Cooperation and cyclic dominance in meiotic drive. J Theor Biol. E-pub ahead of print. doi:10.1016/j.jtbi.2011.04.032.
[11]  Lande R (1979) Effective deme sizes during long term evolution estimated from rates of chromosomal rearrangments. Evolution 33: 234–251.
[12]  Nachman MW, Searle JB (1995) Why is the house mouse karyotype so variable? Trends Ecol Evol 10: 397–402.
[13]  Rieseberg LH (2001) Chromosomal rearrangements and speciation. Trends Ecol Evol 16: 351–358.
[14]  Wright S (1941) On the probability of fixation of reciprocal translocations. Am Nat 75: 513–522.
[15]  Bengtsson BO, Bodmer WF (1976) On the increase of chromosome mutations under random mating. Theor Pop Biol 9: 260–281.
[16]  Snell GD (1946) An analysis of translocations in the mouse. Genetics 31: 157–180.
[17]  Barton NH, De Cara MAR (2009) The evolution of strong reproductive isolation. Evolution 63: 1171–1190.
[18]  Eppstein MJ, Payne JL, Goodnight CJ (2009) Underdominance, multiscale interactions, and selforganizing barriers to gene flow. J Artificial Ev App 2009: 725049.
[19]  Davis S, Bax N, Grewe P (2001) Engineered underdominance allows efficient and economical introgression of traits into pest populations. J Theor Biol 7: 83–98.
[20]  Magori K, Gould F (2006) Genetically engineered underdominance for manipulation of pest populations: a deterministic model. Genetics 172: 2613–2620.
[21]  Davison A, Chiba S, Barton NH, Clarke B (2005) Speciation and gene ow between snails of opposite chirality. PLoS Biol 3: 1559–1571.
[22]  Haldane JBS (1942) Selection against heterozygosis in man. Ann Eugenics 11: 333–340.
[23]  Curtis CF (1968) Possible use of translocations to fix desirable genes in insect pest populations. Nature 218: 368–369.
[24]  Karlin S, McGregor J (1972) Application of method of small parameters to multi-niche population genetic model. Theor Pop Biol 3: 186–209.
[25]  Karlin S, McGregor J (1972) Polymorphisms for genetic and ecological systems with weak coupling. Theo Pop Biol 3: 210–238.
[26]  Altrock PM, Traulsen A, Reeves RG, Reed FA (2010) Using underdominance to bi-stably transform local populations. J Theor Biol 267: 62–75.
[27]  Clark T (2002) Mosquitoes minus malaria. Nature 419: 429–430.
[28]  Pinto J, Donnelly MJ, Sousa CA, Malta-Vacas J, Gil V, et al. (2003) An island within an island: genetic differentiation of anopheles gambiae in S?o Tomé, West Africa, and its relevance to malaria vector control. Heredity 91: 407–414.
[29]  Marshall JC, Pinto J, Charlwood JD, Gentile G, Santolamazza F, et al. (2008) Exploring the origin and degree of genetic isolation of anopheles gambiae from the islands of S?o Tomé and Príncipe, potential sites for testing transgenic-based vector control. Evol Appl 1: 631–644.
[30]  Warner RE (1968) The role of introduced diseases in the extinction of the endemic Hawaiian avifauna. Condor 70: 101–120.
[31]  Ewens WJ (2004) Mathematical Population Genetics. 2nd edition. New York: Springer.
[32]  Moran PAP (1962) The Statistical Processes of Evolutionary Theory. Oxford: Clarendon Press.
[33]  Goel N, Richter-Dyn N (1974) Stochastic Models in Biology. New York: Academic Press.
[34]  Nowak MA, Sasaki A, Taylor C, Fudenberg D (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature 428: 646–650.
[35]  Taylor C, Fudenberg D, Sasaki A, Nowak MA (2004) Evolutionary game dynamics in finite populations. Bull Math Biol 66: 1621–1644.
[36]  Nowak MA (2006) Evolutionary Dynamics. Cambridge, MA: Harvard University Press.
[37]  Karlin S, Taylor HMA (1975) A First Course in Stochastic Processe. 2nd edition. London: Academic Press.
[38]  Redner S (2001) A Guide to First-Passage Processes. Cambridge, UK: Cambridge University Press.
[39]  Antal T, Scheuring I (2006) Fixation of strategies for an evolutionary game in finite populations. Bull Math Biol 68: 1923–1944.
[40]  Altrock PM, Gokhale CS, Traulsen A (2010) Stochastic slowdown in evolutionary processes. Phys Rev E 82: 011925.
[41]  Traulsen A, Pacheco JM, Imhof LA (2006) Stochasticity and evolutionary stability. Phys Rev E 74: 021905.
[42]  McInnis DO, Lance DR, Jackson CG (1996) Behavioral resistance to the sterile insect technique by mediterranean fruit y (diptera: tephritidae) in Hawaii. Ann Entomol Soc Am 89: 739–744.
[43]  Charlat S, Hornett EA, Fullard JH, Davies N, Roderick GK, et al. (2007) Extraordinary ux in sex ratio. Science 317: 214.
[44]  Soans AB, Pimentel D, Soans JS (1974) Evolution of reproductive isolation in allopatric and sympatric populations. Am Nat 108: 117–124.
[45]  Bataille A, Cunningham AA, Cede?o V, Cruz M, Eastwood G, et al. (2009) Evidence for regular ongoing introductions of mosquito disease vectors into the Galápagos Islands. Proc R Soc B 276: 3769–3775.
[46]  Ito J, Ghosh A, Moreira LA, Wimmer EA, Jacobs-Lorena M (2002) Transgenic anopheline mosquitoes impaired in transmission of a malaria parasite. Nature 417: 452–455.
[47]  Kokoza V, Ahmed A, Woon Shin S, Okafor N, Zou Z, et al. (2010) Blocking of plasmodium transmission by cooperative action of Cecropin A and Defensin A in transgenic aedes aegypti mosquitoes. Proc Nat Acad Sci USA 107: 8111–8116.
[48]  Woodworth BL, Atkinson CT, LaPointe DA, Hart PJ, Spiegel CS, et al. (2005) Host population persistence in the face of introduced vector-borne diseases: Hawaii amakihi and avian malaria. Proc Nat Acad Sci USA 102: 1531–1536.
[49]  Boussy IA (1988) A Drosophila model of improving the fitness of translocations for genetic control. Theor Appl Genet 76: 627–639.


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