The Dynamics of Interactive Population Models

现有的分析植物和动物种群的人口统计学的数学方法不包括性别之间的相互作用。通常有一种默认的假设，即种群中有足够的雄性使所有成熟雌性受精，因此种群的动态由成熟雌性的丰度决定(这种假设被称为“雌性优势”)。人们现在知道，这一假设并不是普遍适用的，最近的研究表明，将性别纳入人口统计模型可能会产生复杂的、迄今意想不到的动态模式。这项研究将使用为研究非线性动力系统而开发的数学方法来研究这些模式。要研究的模型将包括男性和女性的年龄或体型类别，以及相同性别但不同年龄的个体之间争夺配偶的可能性。包括交配过程的不同模式、可选择的交配策略以及发育性变化的可能性(在某些植物和动物群体中已知的现象)的影响将被讨论。这一结果将对理解和管理种群具有重要意义，在这种种群中，雄性和雌性的相互作用是种群动态的重要决定因素。它们也可能适用于人类人口统计分析。

Available mathematical methods for analyzing the demography of plant and animal populations do not include the interactions of the sexes. The tacit assumption is usually made that the population contains sufficient males to fertilize all mature females, so that the dynamics of the population are determined by the abundance of the latter (this assumption is referred to as "female dominance"). This assumption is now known not to be universally true, and recent work has shown that including the sexes in demographic models can produce complicated and heretofore unexpected patterns of dynamics. This research will investigate these patterns, using mathematical methods developed for the study of nonlinear dynamical systems. The models to be studied will include age or size classes of both males and females, and the possibility of competition for mates among individuals of the same sex but different ages. The effects of including different models of the mating process, alternative mating strategies, and the possibility of developmental sex change (a known phenomenon in some groups of plants and animals) will be addressed. The results will have implications for the understanding and management of populations in which the interaction of males and females is an important determinant of population dynamics. They may also be applicable to human demographic analysis.