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  • 1 Istituto di Genetica Biochimica ed Evoluzionistica, Consiglio Nazionale delle Ricerche, Pavia, Italy Via Abbiategrasso 207, 27100 Pavia, Italy
  • | 2 Department of Biology, University of Maryland College Park, Md., USA
  • | 3 Department of Ecology and Evolutionary Biology - Department of Mathematics, University of Tennessee Knoxville, Tenn., USA
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We analyze the long-term evolution of a continuous trait subject to frequency-dependent disruptive selection, and controlled by a single diploid, additive locus. Our simple selection model is a mathematical approximation to many complex systems of ecological interactions resulting in disruptive selection, like, for example, scramble competition and habitat heterogeneity. A polymorphism of two specific alleles at equal frequencies is the unique long-term equilibrium, or ESS, of this system. We then study the evolution of direct assortative mating for the selected trait, through mutations of small effect at modifier loci controlling the degree of assortment. The mating process is described by a model that allows for possible costs of assortment. Unless the cost of assortment is too high, strength of assortment always increases in populations where mating is random or weakly assortative, and also in populations that already practice very strong assortative mating. However, even if it has no cost, assortment can increase continuously from random mating to complete isolation, resulting in sympatric speciation, only if selection is sufficiently strong. In fact, only a modest degree of assortment, corresponding to a continuously stable ESS, can be attained from random mating, when selection intensity is below a certain threshold.

  • Maynard Smith, J. (1966): Sympatric speciation. Amer. Nat.100:637-650.

    'Sympatric speciation ' () 100 Amer. Nat. : 637 -650.

  • Abrams, P. A., Matsuda, H. and Harada, Y. (1993): Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol.7:465-487.

    'Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits ' () 7 Evol. Ecol. : 465 -487.

    • Search Google Scholar
  • Bodmer, W. F. (1965): Differential fertility in population genetics models. Genetics51:411-424.

    'Differential fertility in population genetics models ' () 51 Genetics : 411 -424.

  • Butlin, R. (1987): Speciation by reinforcement. Trends Ecol. Evolut.2:8-13.

    'Speciation by reinforcement ' () 2 Trends Ecol. Evolut. : 8 -13.

  • Charnov, E. L. (1982): The Theory of Sex Allocation. Princeton University Press, Princeton, N. J., U.S.A.

    The Theory of Sex Allocation , ().

  • Christiansen, F. B. (1991): On conditions for evolutionary stability for a continuously varying character. Amer. Nat.138:37-50.

    'On conditions for evolutionary stability for a continuously varying character ' () 138 Amer. Nat. : 37 -50.

    • Search Google Scholar
  • Asmussen, M. A. and Basnayake, E. (1990): Frequency-dependent selection: the high potential for permanent genetic variation in the diallelic, pairwise interaction model. Genetics125:215-230.

    'Frequency-dependent selection: the high potential for permanent genetic variation in the diallelic, pairwise interaction model ' () 125 Genetics : 215 -230.

    • Search Google Scholar
  • Christiansen, F. B. and Loeschcke, V. (1980): Evolution and intraspecific exploitative competition I. One-locus theory for small additive gene effects. Theor. Popul. Biol.18: 297-313.

    'Evolution and intraspecific exploitative competition I. One-locus theory for small additive gene effects ' () 18 Theor. Popul. Biol. : 297 -313.

    • Search Google Scholar
  • Clarke, B. C. (1979): The evolution of genetic diversity. Proc. R. Soc. Lond. B 205:453-474.

    'The evolution of genetic diversity ' () 205 Proc. R. Soc. Lond. B : 453 -474.

  • Cockerham, C. C., Burrows, P. M., Young, S. S. and Prout, T. (1972): Frequency-dependent selection in randomly mating populations. Amer. Nat.106:493-515.

    'Frequency-dependent selection in randomly mating populations ' () 106 Amer. Nat. : 493 -515.

    • Search Google Scholar
  • Cody, M. L. (1974): Competition and the Structure of Bird Communities. Princeton University Press, Princeton, N. J., U.S.A.

    Competition and the Structure of Bird Communities , ().

  • Dieckmann, U. and Doebeli, M. (1999): On the origin of species by sympatric speciation. Nature400:354-357.

    'On the origin of species by sympatric speciation ' () 400 Nature : 354 -357.

  • Dobzhansky, T. (1940): Speciation as a stage in evolutionary divergence. Amer. Nat.74:312-321.

    'Speciation as a stage in evolutionary divergence ' () 74 Amer. Nat. : 312 -321.

  • Doebeli, M. (1996): A quantitative genetic competition model for sympatric speciation. J. Evol. Biol.9:893-909.

    'A quantitative genetic competition model for sympatric speciation ' () 9 J. Evol. Biol. : 893 -909.

    • Search Google Scholar
  • Doebeli, M. and Dieckmann, U. (2000): Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Amer. Nat.156:S77-S101.

    'Evolutionary branching and sympatric speciation caused by different types of ecological interactions ' () 156 Amer. Nat. : S77 -S101.

    • Search Google Scholar
  • Eshel, I. (1983): Evolutionary and continuous stability. J. Theor. Biol.103:99-111.

    'Evolutionary and continuous stability ' () 103 J. Theor. Biol. : 99 -111.

  • Eshel, I. and Motro, U. (1981): Kin selection and strong evolutionary stability of mutual help. Theor. Popul. Biol.21:430-439.

    'Kin selection and strong evolutionary stability of mutual help ' () 21 Theor. Popul. Biol. : 430 -439.

    • Search Google Scholar
  • Eshel, I., Motro, U. and Sansone, E. (1997): Continuous stability and evolutionary convergence. J. Theor. Biol.185:333-343.

    'Continuous stability and evolutionary convergence ' () 185 J. Theor. Biol. : 333 -343.

  • Felsenstein, J. (1981): Skepticism towards Santa Rosalia, or why are there so few kinds on animals? Evolution35:124-138.

    'Skepticism towards Santa Rosalia, or why are there so few kinds on animals ' () 35 Evolution : 124 -138.

    • Search Google Scholar
  • Gantmacher, F. R. (1960): The Theory of Matrices. Vol. II. Chelsea Pub. Co., New York.

    The Theory of Matrices , ().

  • Gavrilets, S. (1998): One-locus two-allele models with maternal (parental) selection. Genetics149:1147-1152.

    'One-locus two-allele models with maternal (parental) selection ' () 149 Genetics : 1147 -1152.

    • Search Google Scholar
  • Gavrilets, S. and Boake, C. R. B. (1998): On the evolution of premating isolation after a founder event. Amer. Nat.152:706-716

    'On the evolution of premating isolation after a founder event ' () 152 Amer. Nat. : 706 -716.

    • Search Google Scholar
  • Metz, J. A. J., Geritz, S. A. H., Meszena, G., Jacobs, F. J. A. and van Heerwaarden, J. S. (1996): Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In van Strien, S. J. and Verdyan Lunel, S. M. (EDS): Stochastic and Spatial Structures of Dynamical Systems. North Holland, Amsterdam, The Netherlands, pp. 183-231.

    Stochastic and Spatial Structures of Dynamical Systems , () 183 -231.

  • Nayfeh, A. H. (1981): Introduction to Perturbation Techniques. John Wiley and Sons, New York, U.S.A.

    Introduction to Perturbation Techniques , ().

  • Taylor, P. D. (1989): Evolutionary stability in one-parameter models under weak selection. Theor. Popul. Biol.36: 125-143.

    'Evolutionary stability in one-parameter models under weak selection ' () 36 Theor. Popul. Biol. : 125 -143.

    • Search Google Scholar
  • Udovic, D. (1980): Frequency-dependent selection, disruptive selection, and the evolution of reproductive isolation. Amer. Nat.116:621-641.

    'Frequency-dependent selection, disruptive selection, and the evolution of reproductive isolation ' () 116 Amer. Nat. : 621 -641.

    • Search Google Scholar
  • Uyenoyama, M. K. and Bengtsson, B. O. (1982): Towards a genetic theory for the evolution of the sex ratio. III. Parental and sibling control of brood investment ratio under partial sib mating. Theor. Popul. Biol.22:43-68.

    'Towards a genetic theory for the evolution of the sex ratio. III. Parental and sibling control of brood investment ratio under partial sib mating ' () 22 Theor. Popul. Biol. : 43 -68.

    • Search Google Scholar
  • Wilson, D. S. and Turelli, M. (1986): Stable underdomi-nance and the evolutionary invasion of empty niches. Amer. Nat.127:835-850.

    'Stable underdomi-nance and the evolutionary invasion of empty niches ' () 127 Amer. Nat. : 835 -850.

    • Search Google Scholar
  • Geritz, S. A. H., Kisdi, E., Meszena, G. and Metz, J. A. J. (1998): Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol.12:35-57.

    'Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree ' () 12 Evol. Ecol. : 35 -57.

    • Search Google Scholar
  • Geritz, S. A. H., Van der Meijden, E. and Metz, J. A. J. (1999): Evolutionary dynamics of seed size and seedling competitive ability. Theor. Popul. Biol.55:324-343.

    'Evolutionary dynamics of seed size and seedling competitive ability ' () 55 Theor. Popul. Biol. : 324 -343.

    • Search Google Scholar
  • Geritz, S. A. H. and Kisdi, E. (2000): Adaptive dynamics in diploid, sexual populations and the evolution of reproductive isolation. Proc. R. Soc. Lond. B267:1671-1678.

    'Adaptive dynamics in diploid, sexual populations and the evolution of reproductive isolation ' () 267 Proc. R. Soc. Lond. B : 1671 -1678.

    • Search Google Scholar
  • Hadeler, K. P. and Liberman, U. (1975): Selection models with fertility differences. J. Theor. Biol.2:19-32.

    'Selection models with fertility differences ' () 2 J. Theor. Biol. : 19 -32.

  • Howard, D. J. (1993): Reinforcement: origin, dynamics and fate of an evolutionary hypothesis. In Harrison, R. G. (ED.): Hybrid zones and the evolutionary process. Oxford Univ. Press, New York, pp. 46-69.

    Hybrid zones and the evolutionary process , () 46 -69.

  • Hutchinson, G. E. (1959): Homage to Santa Rosalia or why are there so many kinds of animals? Amer. Nat.93: 145-159.

    'Homage to Santa Rosalia or why are there so many kinds of animals ' () 93 Amer. Nat. : 145 -159.

    • Search Google Scholar
  • Karlin, S. and Lessard, S. (1986): Sex Ratio Evolution. Princeton University Press, Princeton, N. J., U.S.A.

    Sex Ratio Evolution , ().

  • Kisdi, E. (1999): Evolutionary branching under asymmetric competition. J. Theor. Biol.197:149-162.

    'Evolutionary branching under asymmetric competition ' () 197 J. Theor. Biol. : 149 -162.

  • Kisdi, E. and Geritz, S. A. H. (1999): Adaptive dynamics in allele space: evolution of genetic polymorphism by small mutations in a heterogeneous environment. Evolution53: 993-1008.

    'Adaptive dynamics in allele space: evolution of genetic polymorphism by small mutations in a heterogeneous environment ' () 53 Evolution : 993 -1008.

    • Search Google Scholar
  • Kondrashov, A. S. (1986): Multilocus model of sympatric speciation. III. Computer simulations. Theor. Popul. Biol.29:1-15.

    'Multilocus model of sympatric speciation. III. Computer simulations ' () 29 Theor. Popul. Biol. : 1 -15.

    • Search Google Scholar
  • Kondrashov, A. S. and Kondrashov, F. A. (1999): Interactions among quantitative traits in the course of sympatric speciation. Nature400:351-354.

    'Interactions among quantitative traits in the course of sympatric speciation ' () 400 Nature : 351 -354.

    • Search Google Scholar
  • Lande, R. (1981): Models of speciation by sexual selection on polygenic traits. Proc. Natl. Acad. Set USA78:3721-3725.

    'Models of speciation by sexual selection on polygenic traits ' () 78 Proc. Natl. Acad. Set USA : 3721 -3725.

    • Search Google Scholar
  • MacArthur, R. (1972): Geographical Ecology. Harper and Row, New York, U.S.A.

    Geographical Ecology , ().

Selection
Language English
Year of
Foundation
2001
Publication
Programme
ceased
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 1585-1931 (Print)
ISSN 1588-287X (Online)