Artículos de revistas
A Nonsmooth Two-sex Population Model
Registro en:
Mathematical Biosciences. Elsevier Inc., v. 253, n. 1, p. 1 - 10, 2014.
255564
10.1016/j.mbs.2014.03.015
2-s2.0-84900870987
Autor
Garibaldi E.
Sobottka M.
Institución
Resumen
This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose parameters are the secondary sex ratio (the ratio of males to females at time of birth), inter-, intra- and outer-gender competitions, fertility and mortality rates and a mating function. For the case where there is no inter-gender competition and the mortality rates are negligible with respect to the density-dependent mortality, using geometrical techniques, we analyze the singularities and the basin of attraction of the system, determining the relationships between the parameters for which the system presents an equilibrium point. In particular, we describe conditions on the secondary sex ratio and discuss the role of the average number of female sexual partners of each male for the conservation of a two-sex species. © 2014 Elsevier Inc. 253 1 1 10 Charnov, E.L., (1982) The Theory of Sex Allocation, , Princeton University Press, New Jersey Castillo-Chavez, C., Huang, W., The logistic equation revisited: the two-sex case (1995) Math. Biosci., 128, p. 299 Fisher, R.A., (1930) The Genetical Theory of Natural Selection, , Clarendon Press, Oxford Fredrickson, A.G., A mathematical theory of age structure in sexual populations: random mating and monogamous marriage models (1971) Math. Biosci., 10, p. 117 Le Galliard, J.F., Fitze, P.S., Ferrière, R., Clobert, J., Sex ratio bias, male aggression, and population collapse in lizards (2005) Proc. Nat. Acad. Sci. U.S.A., 102, p. 18231 Garibaldi, E., Sobottka, M., Average sex ratio and population maintenance cost (2011) SIAM J. Appl. Math., 71, p. 1009 Goodman, L.A., Population growth of the sexes (1953) Biometrics, 9, p. 212 Grayson, K.L., De Lisle, S.P., Jackson, J.E., Black, S.J., Crespi, E.J., Behavioral and physiological female responses to male sex ratio bias in a pond-breeding amphibian (2012) Front. Zool., 9, p. 1 Hadeler, K.P., Waldstätter, R., Wörz-Busekros, A., Models for pair formation in bisexual populations (1988) J. Math. Biol., 26, p. 635 Hamilton, W.D., Extraordinary sex ratios (1967) Science, 156, p. 477 Hesketh, T., Xing, Z.W., Abnormal sex ratios in human populations: causes and consequences (2006) Proc. Nat. Acad. Sci. U.S.A., 103, p. 13271 Hoppensteadt, F., (1975) Mathematical Theory of Populations: Demographics, Genetics and Epidemics, , SIAM, Philadelphia Kendall, D.G., Stochastic processes and population growth (1949) J. R. Stat. Soc. Ser. B Methodol., 11, p. 230 Melin, J., Does distribution theory contain means for extending Poincaré-Bendixon theory? (2004) J. Math. Anal. Appl., 303, p. 81 Michler, S.P.M., Nicolaus, M., Ubels, R., van der Velde, M., Both, C., Tinbergen, J.M., Komdeur, J., Do sex-specific densities affect local survival of free-ranging great tits? (2011) Behav. Ecol., 22, p. 869 Ranta, E., Kaitala, V., Lindström, J., Sex in space: population dynamic consequences (1999) Proc. R. Soc. Lond. Ser. B: Biol. Sci., 266, p. 1155 Rosen, K.H., Mathematical models for polygamous mating systems (1983) Math. Model., 4, p. 27 Trivers, R.L., Willard, D.E., Natural selection of parental ability to vary the sex ratio of offspring (1973) Science, 179, p. 90 Yang, K., Milner, F., The logistic, two-sex, age-structured population model (2009) J. Biol. Dyn., 3, p. 252 Yellin, J., Samuelson, P.A., A dynamical model for human population (1974) Proc. Nat. Acad. Sci. U.S.A., 71, p. 2813