Skalski Garrick T, Gilliam James F
Program in Biomathematics and Department of Zoology, North Carolina State University, Raleigh, North Carolina 27695-7617, USA.
Am Nat. 2003 Mar;161(3):441-58. doi: 10.1086/367592.
We develop a general theory of organism movement in heterogeneous populations that can explain the leptokurtic movement distributions commonly measured in nature. We describe population heterogeneity in a state-structured framework, employing advection-diffusion as the fundamental movement process of individuals occupying different movement states. Our general analysis shows that population heterogeneity in movement behavior can be defined as the existence of different movement states and among-individual variability in the time individuals spend in these states. A presentation of moment-based metrics of movement illustrates the role of these attributes in general dispersal processes. We also present a special case of the general theory: a model population composed of individuals occupying one of two movement states with linear transitions, or exchange, between the two states. This two-state "exchange model" can be viewed as a correlated random walk and provides a generalization of the telegraph equation. By exploiting the main result of our general analysis, we characterize the exchange model by deriving moment-based metrics of its movement process and identifying an analytical representation of the model's time-dependent solution. Our results provide general and specific theoretical explanations for empirical patterns in organism movement; the results also provide conceptual and analytical bases for extending diffusion-based dispersal theory in several directions, thereby facilitating mechanistic links between individual behavior and spatial population dynamics.
我们建立了一个关于异质种群中生物体运动的通用理论，该理论能够解释自然界中常见的尖峰态运动分布。我们在一个状态结构框架中描述种群异质性，采用平流扩散作为处于不同运动状态个体的基本运动过程。我们的一般分析表明，运动行为中的种群异质性可定义为不同运动状态的存在以及个体在这些状态中所花费时间的个体间变异性。基于矩的运动度量的展示说明了这些属性在一般扩散过程中的作用。我们还给出了该通用理论的一个特殊情况：一个由占据两种运动状态之一的个体组成的模型种群，这两种状态之间存在线性转换或交换。这个双态“交换模型”可被视为一种相关随机游走，并提供了电报方程的一种推广。通过利用我们一般分析的主要结果，我们通过推导其运动过程的基于矩的度量并确定模型时间相关解的解析表示来刻画交换模型。我们的结果为生物体运动中的经验模式提供了一般和具体的理论解释；这些结果还为在多个方向扩展基于扩散的扩散理论提供了概念和分析基础，从而促进个体行为与空间种群动态之间的机制联系。
