Territorial behaviour of buzzards versus random matrix spacing distributions

The nearest and next-to-nearest neighbour spacings between buzzard nests in the Teutoburger Wald around Bielefeld, as gathered in the years 2000--2019, are compared with Ginibre random matrix ensembles as well as the Poisson spacing distribution in two dimensions. Our goal is a phenomenological description of some structural aspects in the territorial behaviour of these birds. To capture intermediate spacings between Ginibre and Poisson, we also compare to numerically generated two-dimensional Coulomb gases at different temperatures, which interpolate between the two. We find a stronger repulsion between nearest neighbours than between next-to-nearest ones, for more than the first half of the observed period. The increase of the absolute density of nests observed in that area over the monitored period of time leads to an increase of repulsion among neighbouring nests. Central to our approach is the use of well-established ideas from universal spatial structures, which suggest to employ a family of interpolating distributions with only one free parameter that parametrises the repulsion and that correlates well with the concepts from population ecology.