Territorial behaviour of buzzards versus random matrix spacing distributions. (21st January 2021)

• Record Type: Journal Article
• Authors: Akemann, Gernot; Baake, Michael; Chakarov, Nayden; Krüger, Oliver; Mielke, Adam; Ottensmann, Meinolf; Werdehausen, Rebecca
• Is Part Of: Journal of theoretical biology. Volume 509(2021)
• Publication Date: 2021-01-21
• Subjects: Territorial behaviour -- Common buzzard -- Nearest neighbour spacing distribution -- Population density dependence -- Random matrices; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2020.110475
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: We propose a first large-scale analysis of the two-dimensional spatial statistics that quantifies the repulsive behaviour of a bird of prey, the Common buzzard, as a function of its time dependent population. The wealth of 20 years of data allows us to compare the spacings between next and next-to-nearest nests of buzzards using methods from spatial statistics, that have so far seen little application to biological systems. The two-dimensional spacing distributions derived from non-Hermitian random matrices are tailored to give a universal description of the repulsive behaviour amongst particles. Its generalisation to a Coulomb gas system, that includes the uncorrelated Poisson case, allows us to perform a one-parameter fit to the spacings between nests. This quantifies the effect of the observed population increase on the correlation length between these very territorial birds. Abstract: 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.