Hubbell社区动力学模型的解析解
Analytic solution of Hubbell's model of local community dynamics
摘要：
最近的理论方法，以社区结构和动态显示，许多大规模的社区结构的功能（如种级分布和种面积关系）可以解释一个所谓的中性模型。使用这种方法，物种被认为是等效的，营养关系没有被明确考虑在内。在这里，我们提供了一个一般的分析解决方案，哈贝尔的生物多样性中性理论的本地社区模型重铸它作为一个瓮模型，即马尔可夫描述的状态和它们的过渡。固定和时间依赖的分布进行了分析。平稳分布-也称为零和多项式-以封闭形式给出。通过对主方程的展开，得到了时间依赖性的近似形式。近似分布的时间演化被证明是一个很好的代表性的真实的时间演化的参数值的大范围内。
英文摘要：
Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model i.e.a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution -- also called the zero-sum multinomial -- is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.
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