A dynamic model for the ideal-free distribution as a partial differential equation
A dynamic model for the ideal-free distribution as a partial differential equation
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DOI：
10.1016/j.tpb.2004.09.002
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发表时间：
2005-03-01
影响因子：
1.4
通讯作者：
Cosner, C
中科院分区：
文献类型：
--
作者：
Cosner, C
理解生态学和种群动力学中的空间效应的主要方法之一是使用分析模型。一些类型的空间效应分析模型，例如基于偏微分方程组或积分核的扩散模型，可以捕捉到瞬时行为，并且可以很容易地扩展到考虑种群动力学。另一些理论，如由岛屿生物地理学理论衍生的理想自由分布或物种-面积关系，只提供了对生物或物种分布的平衡描述，而不描述动态过程。本文的目的是建立一类基于偏微分方程的模型，其平衡点是连续空间中一类无理想分布集的解。一个动机是制定一个理想自由分布的动态版本，它可以与其他类型的动态模型进行比较或合并到其他类型的动态模型中，如反应扩散系统。另一个动机是展示理想自由分布的全局预测如何从关于局部扩散行为的简单假设中产生。主要结果是利用与菲克扩散定律有关的思想，或者通过取离散模型的连续统极限来推导偏微分方程解，并验证在适当的假设下，这些偏微分方程解趋于满足理想自由分布的平衡点。(C)2004 Elsevier Inc.保留所有权利。
One of the major approaches to understanding spatial effects in ecology and population dynamics is the use of analytic models. Some types of analytic models for spatial effects, such as dispersal models based on partial differential equations or integral kernels, can capture transient behavior and can be easily extended to incorporate population dynamics. Others, such as the ideal-free distribution or the species-area relationship derived from island biogeography theory, only provide equilibrium descriptions of the distribution of organisms or species but do not describe dynamic processes. The goal of this paper is to formulate a class of models based on partial differential equations whose equilibria are solutions to a version of the ideal-free distribution set in continuous space. One motivation is to formulate a dynamic version of the ideal-free distribution which can be compared with or incorporated into other sorts of dynamic models such as reaction-diffusion systems. Another motivation is to show how the global predictions of the ideal-free distribution can arise from simple assumptions about local dispersal behavior. The main results are derivations of partial differential equations using ideas related to Fick's law for diffusion, and alternatively by taking a continuum limit of a discrete model, and a verification that under appropriate hypotheses the solutions to those partial differential equations approach equilibria that satisfy the ideal-free distribution. (C) 2004 Elsevier Inc. All rights reserved.