Toward a theory of topopatric speciation: the role of genetic assortative mating

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOWe discuss a minimalist model of assortative mating for sexually reproducing haploid individuals with two biallelic loci. Assortativeness is introduced in the model by preventing mating between individuals whose alleles differ at both loci. Using methods of dynamical systems and population genetics we provide a full description of the evolution of the system for the case of very large populations. We derive the equations governing the evolution of haplotype frequencies and study the equilibrium solutions, stability, and speed of convergence to equilibrium. We find a constant of motion which allows us to introduce a geometrical construction that makes it straightforward to predict the fate of initial conditions. Finally, we discuss the consequences of this class of assortative mating models, including their possible extensions and implications for sympatric and topopatric speciation. © 2014 Elsevier B.V. All rights reserved.We discuss a minimalist model of assortative mating for sexually reproducing haploid individuals with two biallelic loci. Assortativeness is introduced in the model by preventing mating between individuals whose alleles differ at both loci. Using methods of dynamical systems and population genetics we provide a full description of the evolution of the system for the case of very large populations. We derive the equations governing the evolution of haplotype frequencies and study the equilibrium solutions, stability, and speed of convergence to equilibrium. We find a constant of motion which allows us to introduce a geometrical construction that makes it straightforward to predict the fate of initial conditions. Finally, we discuss the consequences of this class of assortative mating models, including their possible extensions and implications for sympatric and topopatric speciation.4093547FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO2009/11032-5302858/2011-0Coyne, J.A., Orr, H.A., (2004) Speciation, , first ed. Sinauer Associates, IncGavrilets, S., (2004) Fitness Landscapes and the Origin of Species (MPB-41), , Princeton University PressButlin, R.A., (2012) Trends Ecol. Evol., 27, p. 27Nosil, P., (2012) Ecological Speciation, , Oxford University Press OxfordNew YorkHiggs, P.G., Derrida, B., (1991) J. Phys. A., 24, p. 985Higgs, P.G., Derrida, B., (1992) J. Mol. Evol., 35, p. 454Kondrashov, A.S., Shpak, M., (1998) Proc. Soc. Lond R, 265, p. 2273Dieckmann, U., Doebeli, M., (1999) Nature, 400, p. 354Gavrilets, S., (1999) Am. Nat., 154, p. 1Hoelzer, G.A., Drewes, R., Meier, J., Doursat, R., (2008) PLoS Comput. Biol., 4, p. 1000126Doorn, G.S.V., Edelaar, P., Weissing, F.J., (2009) Science, 326, p. 1704Fitzpatrick, B.M., Fordyce, J.A., Gavrilets, S., (2009) J. Evol. Biol., 22, p. 2342De Aguiar, M.A.M., Baranger, M., Baptestini, E.M., Kaufman, L., Bar-Yam, Y., (2009) Nature, 460, p. 384Ashlock, D., Clare, E.L., Von Konigslow, T.E., Ashlock, W., (2010) J. Theoret. Biol., 264, p. 1202Kopp, M., (2010) BioEssays, 32, p. 564Melian, C.J., Vilas, C., Baldo, F., Gonzalez-Ortegon, E., Drake, P., Williams, R.J., (2011) Ad. Ecol. Res., 45, p. 225Desjardins-Proulx, P., Gravel, D., (2012) Am. Nat., 179, p. 137Wright, S., Isolation by distance (1943) Genetics., 28, p. 114Candolin, U., (2003) Biol. Rev., 78, p. 575Mallet, J., Meyer, A., Nosil, P., Feder, J.L., (2009) J. Evol. Biol., 22, p. 2332Rose, K., Gurewitz, E., Fox, C., (1990) Phys. Rev. Lett., 65, p. 945Holsinger, K.E., Lecture Notes in Population Genetics, , http://darwin.eeb.uconn.edu/eeb348/lecture-notes/book.pdfDieckmann, U., Doebeli, M., Metz, J.A.J., Tautz, D., (2012) Adaptive Speciation, , Cambridge University Press Cambridg