Radcliffe J, Rass L
School of Mathematical Sciences, Queen Mary and Westfield College, University of London, UK.
Math Biosci. 1998 Aug 1;151(2):199-218. doi: 10.1016/s0025-5564(98)10011-1.
This paper considers complex models arising in sociobiology. These combine genetic and strategic aspects to model the effect of gene-linked strategies on the ability of individuals to survive to maturity, mate and produce offspring. Several important models considered in the literature are generalised and extended to incorporate a spatial aspect. Individuals are allowed to migrate. Contests, e.g. for food or amongst males for females, take place locally. The choice of the point at which the population structure is measured affects the complexity of the equations describing the system, although it is possible to utilise any point in the life cycle. For our spatial models the simplest approach is to measure the population structure immediately after migration. A saddle point method, developed by the authors, has previously been used to obtain results for simple discrete time spatial models. It is utilised here to obtain the speed of first spread of a new gene-linked strategy for the much more complex sociobiological models included in this paper. This demonstrates the wide-ranging applicability and power of the method.
本文考虑了社会生物学中出现的复杂模型。这些模型结合了遗传和策略方面，以模拟与基因相关的策略对个体存活至成熟、交配和繁殖后代能力的影响。文献中考虑的几个重要模型被推广和扩展，以纳入空间因素。允许个体迁移。竞争，例如为了食物或雄性之间为了雌性而进行的竞争，在局部发生。测量种群结构的时间点的选择会影响描述该系统的方程的复杂性，尽管在生命周期中的任何时间点进行测量都是可行的。对于我们的空间模型，最简单的方法是在迁移后立即测量种群结构。作者开发的一种鞍点方法，此前已用于获得简单离散时间空间模型的结果。在此，它被用于获得本文中包含的更为复杂的社会生物学模型中一种新的与基因相关的策略的首次传播速度。这证明了该方法广泛的适用性和强大的功能。
