种群数学模型的基本性质

种群数学模型的建立有赖于对生物背景的各种似是而非的假设，然而，在建模过程中，这些假定常常容易得到不当的结合和表达，常常些关于生物背景的清晰而明确的假设被不适当地处理或者甚至被抛开，事实上，即使是某些赫赫有名的种群数学模型也难以完全避免这种缺陷，这一点在我们本文中提及并讨论，要使得所建立的模型在逻辑上可信正确。我们必须确保关于其背景的各种假设得到的始终如一和恰如其分的协调组合。本本文中，我们测试了由Arditi和Michalski在1996年提出的几条建模标准，对于斑块模型，我们在他们的基础上增加了一条模型。我们同时在单种群的其他特殊情形方面的建方面增列了一些重要的标准。按照Arditi和Mchalski的标准以及其他著名的生物建模假定，我们建立了一些有意义的三维捕食－食饵种群模型（比率依赖型），我们还讨论了种群各种振动现象的建模。

Basic Properties of Mathematical Population Models

Mathematical population models are constructed based on plausible explicit and implicit biological assumptions. While it is easy to incorporate explicit assumptions correctly in the models, those implicit ones are often ill treated or forgotten. Indeed, this happens to some well known models in the literature and examples of such will be mentioned and discussed. For a model to be logically credible, we must do our best to ensure that all assumptions are incorporated correctly and consistently. To this end, we exam a simple set of criteria proposed by Arditi and Michalski in 1996. For patchy models, we add an additional criterion to their list. We also add some important criteria in other specific situations and comment on modelling of single species growths. Following criteria of Arditi and Michalski and other well accepted biological assumptions, we introduce some interesting three dimensional predator-dependent (ratio-dependent) population models. We also discuss various aspects of modelling population fluctuations.