Long-term evolution of multilocus traits. (English) Zbl 0851.92009
Summary: We analyze monomorphic equilibria of long-term evolution for one or two continuous traits, controlled by an arbitrary number of autosomal loci and subject to constant viability selection. It turns out that fitness maximization always obtains at long term equilibria, but in the case of two traits, linkage determines the precise nature of the fitness measure that is maximized. We then consider local convergence to long term equilibria, for two multilocus traits subject to either constant or frequency dependent selection. From a model of long-term dynamics near an equilibrium we derive a criterion of local long-term stability for 2-dimensional equilibria. It turns out that mutation can be a decisive factor for stability.
Keywords:
asymmetric conflicts; adaptive dynamics; continuous stability; evolutionary stability; population genetics; monomorphic equilibria; long-term evolution; continuous traits; autosomal loci; constant viability selection; fitness maximization; linkage; local convergence to long term equilibria; multilocus traits; local long-term stability; 2-dimensional equilibria; mutationReferences:
| [1] | Cavalli-Sforza, L. L., Feldman, M. W.: Darwinian selection and ”altruism”. Theor. Pop. Biol.14, 268–280 (1978) · Zbl 0432.92017 · doi:10.1016/0040-5809(78)90028-X |
| [2] | Charlesworth, B.: Evolution in age-structured populations. (Cambridge Stud. Math. Biol. 1) Cambridge: Cambridge University Press 1980 · Zbl 0449.92011 |
| [3] | Christiansen, F. B.: Natural selection related to the biotic environment. In: Jayakar, S. D., Zonta, L. (eds) Evolution and the genetics of populations (Atti Ass. Genet. Ital. suppl. vol. 29), pp. 85–102. Radova: Litografia La Photograph 1984 |
| [4] | Christiansen, F. B.: Frequency dependence and competition. Phil. Trans. R. Soc. Lond. B319, 587–600 (1988) · doi:10.1098/rstb.1988.0067 |
| [5] | Christiansen, F. B.: On conditions for evolutionary stability for a continuously varying character. Amer. Nat.138, 37–50 (1991) · doi:10.1086/285203 |
| [6] | Cohen, D.: Optimizing reproduction in a randomly varying environment. J. Theor. Biol.12, 119–129 (1966) · doi:10.1016/0022-5193(66)90188-3 |
| [7] | Cole, L. C.: The population consequences of life history phenomena. Quart. Rev. Biol.29, 103–137 (1954) · doi:10.1086/400074 |
| [8] | Dieckmann, U., Law, R.: The dynamical theory of coevolution: A derivation from stochastic ecological processes. J. Math. Biol.34, 579–612 (1996) · Zbl 0845.92013 · doi:10.1007/BF02409751 |
| [9] | Eshel, I.: Evolutionary and continuous stability. J. Theor. Biol.108, 99–111 (1983) · doi:10.1016/0022-5193(83)90201-1 |
| [10] | Eshel, I.: Game theory and population dynamics in complex genetical systems: The role of sex in short term and long term evolution. In: Selten, R. (ed) Game equilibrium models I: Evolution and game dynamics, pp. 6–28. Berlin: Springer 1991 · Zbl 0733.92012 |
| [11] | Eshel, I.: On the changing concept of population stability as a reflection of a changing problematics in the quantitative theory of evolution. J. Math. Biol.34, 485–510 (1996) · Zbl 0851.92011 · doi:10.1007/BF02409747 |
| [12] | Eshel, I., Feldman, M. W.: On evolutionary genetic stability of the sex ratio. Theor. Pop. Biol.21, 430–439 (1982) · Zbl 0491.92012 · doi:10.1016/0040-5809(82)90028-4 |
| [13] | Eshel, I., Feldman, M. W.: Initial increase of new mutants and some continuity properties of ESS in two-locus systems. Amer. Nat.124, 631–640 (1984) · doi:10.1086/284303 |
| [14] | Eshel, I., Motro, U.: Kin selection and strong evolutionary stability of mutual help. Theor. Pop. Biol.19, 420–433 (1980) · Zbl 0473.92014 · doi:10.1016/0040-5809(81)90029-0 |
| [15] | Eshel, I., Sansone, E.: Parent-offspring conflict over the sex-ratio in a diploid population with different investment in male and in female offspring. Amer. Nat.138, 954–972 (1991) · doi:10.1086/285262 |
| [16] | Eshel, I., Sansone, E.: Parent-offspring conflict over sex ratio. II. Offspring response to parental manipulation. Amer. Nat.143, 987–1006 (1994) · doi:10.1086/285645 |
| [17] | Ewens, W. J.: Mean fitness increases when fitnesses are additive. Nature221, 1076 (1969) · doi:10.1038/2211076a0 |
| [18] | Ewens, W. J.: Mathematical population genetics (Blomathematics 9). Berlin Heidelberg New York: Springer 1979 · Zbl 0422.92011 |
| [19] | Feldman, M. W., Ayala, F. J., Bengtsson, B., Brückner, D., Crozier, R. H., Vogel, C., Williams, G. C., Wrangham, R. W.: Genetics and social behavior group report. In: Markl, H. (ed) Evolution of social behavior: Hypotheses and empirical tests (Dahlem Konferenzen 1980), pp. 221–232. Weinheim: Verlag Chemie GmbH 1980 |
| [20] | Fenchel, T. M., Christiansen, F. B.: Selection and interspecific competition. In: Christiansen, F. B., Fenchel, T. M. (eds) Measuring selection in natural populations (Lect. Notes Biomath. vol. 19), pp. 477–498. Berlin Heidelberg New York: Springer 1977 · Zbl 0349.00028 |
| [21] | Fisher, R. A.: The possible modifications of the response of the wild type to recurrent mutation. Amer. Nat.62, 115–226 (1928) · doi:10.1086/280193 |
| [22] | Fisher, R. A.: The genetical theory of natural selection. New York: Dover 1958 · JFM 56.1106.13 |
| [23] | Gould, S. J., Lewontin, R. C.: The spandrels of San Marco and the panglossian paradigm: A critique of the adaptationist programme. Proc. R. Soc. B205, 581–598 (1979) · doi:10.1098/rspb.1979.0086 |
| [24] | Galdane, J. B. S.: The cost of natural selection. J. Genet.55, 511–524 (1957) · doi:10.1007/BF02984069 |
| [25] | Haldane, J. S. B., Jayakar, S.D.: Polymorphism due to selection of varying direction. J. Genet.58, 237–242 (1963) · Zbl 0114.11302 · doi:10.1007/BF02986143 |
| [26] | Hamilton, W. D.: The genetical evolution of social behavior. J. Theor. Biol.7, 1–52 (1964) · doi:10.1016/0022-5193(64)90038-4 |
| [27] | Hamilton, W. D.: Extraordinary sex ratios. Science156, 477–488 (1967) · doi:10.1126/science.156.3774.477 |
| [28] | Hamilton, W. D.: Selfish and spiteful behaviour in an evolutionary model. Nature228, 1218–1220 (1970) · doi:10.1038/2281218a0 |
| [29] | Hammerstein, P., Selten, R.: Evolutionary game theory. In: Aumann, R. J., Hart, S. (eds) Handbook of game theory with economic applications Amsterdam: North-Holland 1993 |
| [30] | Hofbauer, J., Sigmund, K.: Adaptive dynamics and evolutionary stability. Appl. Math. Lett.3, 75–79 (1990) · Zbl 0709.92015 · doi:10.1016/0893-9659(90)90051-C |
| [31] | Karlin, S.: Selection with many loci and possible relations to quantitative genetics. In: Pollak, E., Kempthorne, O., Bailey, T. (eds). Proc. Int. Conf. Quant. Gen., pp. 207–226. Ames: Iowa State University Press 1977 |
| [32] | Karlin, S., Lieberman, U.: Random temporal variation in selection intensities: Case of large population size. Theor. Pop. Biol.6, 355–382 (1974) · Zbl 0289.92025 · doi:10.1016/0040-5809(74)90016-1 |
| [33] | Karlin, S., O’Donald, P.: Some population genetic models combining sexual selection with assortative mating. Heredity41, 165–174 (1978) · doi:10.1038/hdy.1978.85 |
| [34] | Lessard, S.: Evolutionary stability: one concept, several meanings. Theor. Pop. Biol.37, 159–170 (1990) · Zbl 0692.92016 · doi:10.1016/0040-5809(90)90033-R |
| [35] | Levins, R.: Evolution in changing environments (Mon. Pop. Biol. 2). Princeton: Princeton University Press 1968 |
| [36] | Lewontin, R. C.: The genetic basis of evolutionary change. New York: Columbia University Press 1974 |
| [37] | Lewontin, R. C., Hubby, J. L.: A molecular approach to the study of genic heterozygosity in natural populations. II. Amount of variation and degree of heterozygosity in natural populations ofDrosophila pseudoobscura. Genetics54, 595–609 (1966) |
| [38] | Lieberman, U.: External stability and ESS: Criteria for initial increase of new mutant allele. J. Math. Biol.26 477–485 (1988) · Zbl 0713.92015 |
| [39] | MacArthur, R. H.: Some generalized theorems of natural selection. Proc. Natl. Acad. Sci. USA48, 1893–1897 (1962) · Zbl 0113.14002 · doi:10.1073/pnas.48.11.1893 |
| [40] | Matessi, C., Eshel, I.: Sex ratio in the social Hymenoptera: A population-genetics study of log-term evolution. Amer. Nat.139, 276–312 (1992) · doi:10.1086/285328 |
| [41] | Matessi, C., Gatto, M.: Does K-selection imply prudent predation? Theor. Pop. Biol.25, 347–363 (1984) · Zbl 0529.92023 · doi:10.1016/0040-5809(84)90014-5 |
| [42] | Matessi, C., Jayakar, S. D.: Conditions for the evolution of altruism under Darwinian selection. Theor. Pop. Biol.9, 360–387 (1976) · Zbl 0337.92009 · doi:10.1016/0040-5809(76)90053-8 |
| [43] | Matessi, C., Jayakar, S. D.: Coevolution of species in competition: A theoretical study. Proc. Natl. Acad. Sci. USA78, 1081–1084 (1981) · Zbl 0444.92016 · doi:10.1073/pnas.78.2.1081 |
| [44] | Maynard Smith, J.: Evolution and the theory of games. Cambridge: Cambridge University Press 1982 · Zbl 0526.90102 |
| [45] | Maynard Smith, J., Price, G. R.: The logic of animal conflict. Nature246, 15–18 (1973) · Zbl 1369.92134 · doi:10.1038/246015a0 |
| [46] | Metz, J. A. J., Geritz, S. A. H., Iwasa, Y., Meszena, G.: On the dynamical classification of evolutionarily singular strategies: I. Setting out the framework. Unpublished manuscript (1994) |
| [47] | Motro, U.: Avoiding inbreeding and sibling competition: Evolution of sexual dimorphism for dispersal. Amer. Nat.137, 108–115 (1991) · doi:10.1086/285148 |
| [48] | Motro, U.: Evolutionary and continuous stability in asymmetric games with continuous stratery sets: The parental investment conflict as an example. Amer. Nat.144, 229–241 (1994) · doi:10.1086/285672 |
| [49] | O’Donald, P.: Genetics models of sexual selection. Cambridge: Cambridge University Press 1980 |
| [50] | Parker, G. A., Maynard Smith, J.: Optimality theory in evolutionary biology. Nature348, 27–33 (1990) · doi:10.1038/348027a0 |
| [51] | Price, G. R.: Selection and covariance. Nature227, 520–521 (1970) · doi:10.1038/227520a0 |
| [52] | Roughgarden, J.: Resource partitioning among competing species: A coevolutionary approach. Theor. Pop. Biol.9, 388–424 (1976) · Zbl 0355.92015 · doi:10.1016/0040-5809(76)90054-X |
| [53] | Sibly, R. M., Calow, P.: Physiological ecology of animals. Oxford, London: Blackwell 1986 |
| [54] | Stearns, S. C.: Life-history tactics: A review of the ideas. Quart. Rev. Biol.51, 3–47 (1976) · doi:10.1086/409052 |
| [55] | Taylor, H. M., Gourley, R. S., Lawrence, C. E., Kaplan, R. S.: Natural selection of life history attributes: An analytical approach. Theor. Pop. Biol.5, 104–122 (1974) · Zbl 0289.92027 · doi:10.1016/0040-5809(74)90053-7 |
| [56] | Taylor, P. D.: Evolutionary stability in one-parameter models under weak selection. Theor. Pop. Biol.36, 125–143 (1989) · Zbl 0684.92014 · doi:10.1016/0040-5809(89)90025-7 |
| [57] | Taylor, P. D., Jonker, L. B.: Evolutionarily stable strategies and game dynamics. Math. Biosci.40, 145–156 (1978) · Zbl 0395.90118 · doi:10.1016/0025-5564(78)90077-9 |
| [58] | Wright, S.: Random drift and the shifting balance theory of evolution. In: Kojima, K. (ed) Mathematical topics in population genetics, pp. 1–31. Berlin Heidelberg New York: Springer 1970 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
