Engen S, Saether B E
J Theor Biol. 1985 Nov 21;117(2):277-89. doi: 10.1016/s0022-5193(85)80222-8.
A model for the joint evolution of a secondary sexual male trait Z and a female mating preference Y is discussed. Recurrence relations for the moments of (Z, Y) are given under the assumption that the traits are binormally distributed. It is shown that female preference for a male character can lead to an equilibrium distribution of the male trait with non-zero variances. The conditions under which the distribution is stable, are given. Unstable situations, in which a continued exaggeration of the male trait occurs, are described. It is demonstrated that the effect of sexual selection on the evolution of the male trait depends on the intensity of natural selection, i.e. the effect of the sexual selection increases when the intensity of natural selection is reduced. The effect of the female preference on the male trait also increases with increasing availability of males. This provides a link to several ecological conditions which have generally been known to be correlated with the degree of sexual selection. Furthermore, it is demonstrated that perturbations away from the equilibrium may cause rapid evolution of the male character, eventually leading to speciation.
本文讨论了雄性第二性征Z和雌性交配偏好Y的联合进化模型。在性状呈双正态分布的假设下，给出了(Z, Y)矩的递归关系。结果表明，雌性对雄性特征的偏好可导致雄性性状具有非零方差的平衡分布，并给出了该分布稳定的条件。文中描述了雄性性状持续夸张的不稳定情况。研究表明，性选择对雄性性状进化的影响取决于自然选择的强度，即当自然选择强度降低时，性选择的影响会增加。雌性偏好对雄性性状的影响也随着雄性可获得性的增加而增加。这为一些通常已知与性选择程度相关的生态条件提供了联系。此外，研究表明，偏离平衡的扰动可能导致雄性性状的快速进化，最终导致物种形成。
