随机矩阵间距分布对秃鹰领地行为的影响
Territorial behaviour of buzzards versus random matrix spacing distributions
摘要：
更深入地了解动物在空间分布的过程对于基础生态学和应用生态学都至关重要。普通秃鹰（Buteo buteo）是一种高度攻击性的，领土性的猛禽，与其种内和种间竞争对手强烈相互作用。我们提出并使用随机矩阵理论来量化的强度和范围的排斥作为一个功能的秃鹰人口密度，从而提供了一种新的方法来模拟密度依赖。作为一个指标的领土行为，我们进行了大规模的分析，在一个地区的分布在$300$平方公里的Teutoburger森林，德国，收集了一段时间的$20$年。巢之间的最近的和下一个最近的邻居的间距分布相比，二维泊松分布，起源于不相关的随机变量，随机矩阵的复杂的特征值，这是强相关的，和这两个之间的二维库仑气体插值。一个参数的时间移动平均拟合揭示了一个显着增加的排斥相邻的巢之间，作为一个函数的绝对人口密度的增加，在监测的时间段内，从而证明了一个意想不到的，但简单的模型密度依赖的捕食者领土的间距。对于次近邻也得到类似的效果，尽管排斥力较弱，表明短程相互作用。我们的研究结果表明，随机矩阵理论可能是有用的人口生态学的背景下。
英文摘要：
A deeper understanding of the processes underlying the distribution of animals in space is crucial for both basic and applied ecology. The Common buzzard (Buteo buteo) is a highly aggressive, territorial bird of prey that interacts strongly with its intra- and interspecific competitors. We propose and use random matrix theory to quantify the strength and range of repulsion as a function of the buzzard population density, thus providing a novel approach to model density dependence. As an indicator of territorial behaviour, we perform a large-scale analysis of the distribution of buzzard nests in an area of $300$ square kilometres around the Teutoburger Wald, Germany, as gathered over a period of $20$ years. The nearest and next-to-nearest neighbour spacing distribution between nests is compared to the two-dimensional Poisson distribution, originating from uncorrelated random variables, to the complex eigenvalues of random matrices, which are strongly correlated, and to a two-dimensional Coulomb gas interpolating between these two. A one-parameter fit to a time-moving average reveals a significant increase of repulsion between neighbouring nests, as a function of the observed increase in absolute population density over the monitored period of time, thereby proving an unexpected yet simple model for density-dependent spacing of predator territories. A similar effect is obtained for next-to-nearest neighbours, albeit with weaker repulsion, indicating a short-range interaction. Our results show that random matrix theory might be useful in the context of population ecology.
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