  The two-dimensional Coulomb gas is a one-parameter family of random point
processes, depending on the inverse temperature $\beta$. Based on previous
work, it is proposed as a simple statistical measure to quantify the intra- and
interspecies repulsion among three different highly territorial birds of prey.
Using data from the area of the Teutoburger Wald over 20 years, we fit the
nearest and next-to-nearest neighbour spacing distributions between the
respective nests of Goshawk, Eagle Owl and the previously examined Common
Buzzard to $\beta$ of the Coulomb gas. Within each species, the repulsion
measured in this way deviates significantly from the Poisson process of
independent points in the plane. In contrast, the repulsion amongst each of two
species is found to be considerably lower and closer to Poisson.
Methodologically we investigate the influence of the terrain, of a shorter
interaction range given by the two-dimensional Yukawa interaction, and the
statistical independence of the time moving average we use for the yearly
ensembles of occupied nests. We also check that an artificial random
displacement of the original nest positions of the order of the mean level
spacing quickly destroys the repulsion measured by $\beta> 0$. A simple,
approximate analytical expression for the nearest neighbour spacing
distribution derived from non-Hermitian random matrix theory proves to be very
useful.
