Fundamental Insights into the Random Movement of Animals from a Single Distance‐Related Statistic
Fundamental Insights into the Random Movement of Animals from a Single Distance‐Related Statistic
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从单一距离相关统计数据对动物随机运动的基本见解
作者：
Pierre Nouvellet;Jonathan P. Bacon;D. Waxman
动物运动的统计理论通常基于随机行走模型，其中运动以离散的步骤发生并在离散的时间发生。在这些方法中描述动物运动所需的分布的多样性（即，角度、离散步长和时间的分布）具有不能简单地解开的影响，因此它们不能被明确地确定。在这里，我们提出了一个连续的动物运动的数学公式。在这个新的框架中，它表明，一个单一的时间依赖的距离统计量，均方位移，可以直接测量或数学建模，是这样的随机行走的一个中心决定因素，并封装有关动物运动的统计特性的关键信息。这里提出的模型和方法不仅可以确定以前被视为动物运动的独立方面，如方向角变化的分布，而且，由于新强调的均方位移，它们可能会开辟一系列新的问题，动物运动和相关现象。本文的研究结果直接应用于法老蚁的觅食行为，观察结果与理论结果非常吻合。
Statistical theories of animal movement have often been based on models of random walks, where movements take place in discrete steps and occur at discrete times. The multiplicity of distributions required in these approaches to describe animal movement (i.e., the distributions of angles, discrete steps, and times) have effects that cannot be simply disentangled, and hence they cannot be unambiguously determined. Here we present a mathematical formulation of continuous animal movements. In this new framework, it is shown that a single time‐dependent distance statistic, the mean square displacement, which may be directly measured or mathematically modeled, is a central determinant of such random walks and encapsulates key information about the statistical properties of animal movements. The model and methodology presented here not only allow the determination of what were previously viewed as independent aspects of animal movements, such as the distribution of angular changes in direction, but also, because of the new emphasis on the mean square displacement, they may open up a new set of questions concerning animal movement and related phenomena. The results established in this work are directly applied to the foraging behavior of Pharaoh’s ants, and very close agreement is found between observation and theory.