On Relationships Among Various Types of Population Models
On Relationships Among Various Types of Population Models
复制标题
论各类人口模型之间的关系
DOI：
10.1086/282816
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发表时间：
1973
期刊：
影响因子：
--
通讯作者：
R. May
中科院分区：
文献类型：
--
作者：
R. May
相互作用物种群落的数学模型通常试图将种群增长率与各种种间和种内相互作用联系起来。如果出生是一个连续的过程，那么人口以连续的方式增长，结果是一个微分方程组;相反，如果世代是离散的，那么人口增长是一个离散的过程，结果是一个差分方程组。对应于任何特定的微分方程系统是一个类似的差分方程系统，它体现了相同的生物学假设，除了时间是离散的，而不是连续的变量。我明确的任何这样的对模型的稳定性之间的关系，显示在什么意义上的差分方程系统中的人口往往是不太稳定的比那些在微分方程模型。虽然这一点基本上是老生常谈，但它的一些含义似乎没有得到广泛的理解。通过说明的方式，对一些特定模型的方面进行了详细的评论（例如，Lotka-Volterra; Nicholson-Bailey）.
Mathematical models for communities of interacting species usually seek to relate the population growth rates to the various inter- and intraspecific interactions. If birth is a continuous process, so that the populations grow in a continuous manner, one ends up with a system of differential equations; conversely, if generations are discrete, so that population growth is a discrete process, the result is a system of difference equations. Corresponding to any particular differential equation system is an analogous difference equation system, which embodies identical biological assumptions except that time is a discrete rather than a continuous variable. I make explicit the relation between the stability properties of any such pair of models, showing in precisely what sense the populations in the difference equation system tend to be less stable than those in the differential equation model. Although this point is basically a commonplace one, some of its implications do not seem to be widely appreciated. By way of illustration, detailed comments are made about aspects of some particular models (e.g., Lotka-Volterra; Nicholson-Bailey).