Territorial behaviour of buzzards versus random matrix spacing distributions

Akemann, Gernot; Baake, Michael; Chakarov, Nayden; Krüger, Oliver; Mielke, Adam; Ottensmann, Meinolf; Werdehausen, Rebecca

doi:10.1016/j.jtbi.2020.110475

Cited by 3 publications

(23 citation statements)

References 67 publications

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“…Two examples where 2D point processes have been applied in biology are the spatial distribution of trees (see [9] for a review) and the distribution of nests of birds of prey in space and time in our previous work [10]. Using data from [14][15][16] on the yearly locations of occupied nests of the common buzzard in an area of 300 km 2 in the Teutoburger Wald, Germany (see section 2.1), we have been able to draw the following conclusions.…”

Section: Introductionmentioning

confidence: 68%

“…This is reviewed in section 2.2, in particular a corresponding approximate surmise for the 2D NN spacing distribution valid for small values of β [27]; appendix B. These NN and NNN spacings were then used for fits as a function of β, for the spacing of eigenvalues of the Liouville operator of dissipative, boundary-driven systems in 2D [4], and in the yearly spacing distributions of nests of the common buzzard [10]. Here, each year represents a realisation of the ensemble, and we have taken averages over all years, or windows of time moving averages over several consecutive years, in order to be sensitive to the time dependence.…”

Section: J Stat Mech (2024) 053501mentioning

confidence: 99%

“…The goal of this article is to extend the analysis of a single species [10] to two further species, and to quantify their respective interactions. For the three species of competing birds of prey living in the observed area-the common buzzard, goshawk and eagle owl-annual data for the locations of their nests over the same area and period of time have been collected [14,16,31,32].…”

Section: J Stat Mech (2024) 053501mentioning

confidence: 99%

“…The study of the statistics of random point processes in one (1D) and two dimensions (2D) is a very active area of research, with many applications in physics and other sciences. Examples in 2D, on which we will focus here, include quantum optics [1], quantum chaos [2][3][4][5], condensed matter physics [6], statistics [7] and ecology [8][9][10]. The goal of such an analysis is to clarify, first, whether the points coming from experimental data or numerical simulations are independent or not, and if not to quantify their correlations.…”

Section: Introductionmentioning

confidence: 99%

“…Instead, our argument for using the spacing distribution of the 2D Coulomb gas is based on universality, as it has been observed to apply in several very different examples in physics: in dissipative quantum spin chains [2,4,5], the dissipative kicked rotor [2,3] and quantum chromodynamics with quark chemical potential [18]. This is of course a strong assumption for the biological system, but it has worked surprisingly well for the common buzzard [10]. Other authors make different strong mathematical assumptions when modelling point processes from biology; for example, that they are determinantal [7].…”

Section: Introductionmentioning

confidence: 99%

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Interactions between different birds of prey as a random point process

Akemann,

Chakarov,

Krüger

et al. 2024

J. Stat. Mech.

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The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. 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-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β 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 2D 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 β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.

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Section: Introductionmentioning

confidence: 68%

Section: J Stat Mech (2024) 053501mentioning

confidence: 99%

Section: J Stat Mech (2024) 053501mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Interactions between different birds of prey as a random point process

Akemann,

Chakarov,

Krüger

et al. 2024

J. Stat. Mech.

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Introduction

Hoppen

Jacobs²,

Trevisan³

2022

Locating Eigenvalues in Graphs

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Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at nonintegerβ

2022

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A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature β. For 2 × 2 matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective β eff (β ) in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of β. It reproduces the 2D Poisson distribution at β = 0 exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values β = 1.4 and β = 2.6 from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble.

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Territorial behaviour of buzzards versus random matrix spacing distributions

Cited by 3 publications

References 67 publications

Interactions between different birds of prey as a random point process

Interactions between different birds of prey as a random point process

Introduction

Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at nonintegerβ

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