Collective formation of territories in scent-marking animal population

While a great deal of studies have been devoted to explain the emerging patterns observed in schools of fish and flocks of birds, there exist many other animal collective movement phenomena where alignment does not play a role. One important example is the formation of animal territories, a form a spatial segregation relatively common in mammals. When the mechanism of territorial exclusion occurs via marks deposited on the terrain, one talks about stigmergy, a form of environment-mediated interaction often encountered in social insect societies. To study these stigmergic systems in mammals I have introduced the so-called territorial random walk model consisting of a collection of discrete random walkers that (scent) mark any lattice site they visit. As deposited marks remain active for a finite amount of time, each walker retreats upon encountering an active foreign scent. The emerging spatio-temporal dynamics of the system is analysed both at the meso and micro-scale.

At the meso-scale the scented territories can be quite rich. Short-lived marks produce rapidly morphing and highly mobile territories, while long-lived marks yield slow territories with a narrowly defined shape distribution. More importantly the full dependence in territory mobility as a function of the time for which individual marks remain active is accompanied by a liquid-hexatic-solid transition akin to the Kosterlitz-Thouless melting scenario, the first ecological model to predict such a transition.

At the micro-scale, and when population density is sufficiently large, I introduce localized walls to mimic the sharp (retreat) interaction when an animal encounters a foreign scent. A mean-field approximation then allows to represent via a Fokker-Planck formalism an animal roaming within neighbouring territorial boundaries whose movement statistics is subdiffusive and constrained by a spring whose equilibrium length makes the territory size equal to the inverse of the population density. Application of this approximate analytic model to movement data from a red fox population in Bristol, UK, is also shown.

If time allows, I will mention about an algorithmic implementation in the context of territorial searching robots.

References

[1] A. Heiblum-Robles and L. Giuggioli, Phase transitions in stigmergic territorial systems, accepted.

[2] L. Giuggioli, I. Ayre, A. Heiblum Robles and G.A. Kaminka, From ants to birds: a novel bio-inspired approach to on-line area coverage, in Groß R et al. (eds) Distributed Autonomous Robotic Systems, Springer Proceedings in Advanced Robotics, vol 6, pp. 31-43 (2018).

[3] L. Giuggioli and V.M. Kenkre, Consequences of animal interactions on their dynamics: emergence of home ranges and territoriality, Move. Ecol. 2(1), 20 (2014).

[4] L. Giuggioli, J.R. Potts, D.I. Rubenstein and S.A. Levin, Stigmergy, collective actions and animal social spacing, Proc. Natl. Acad. Sci. USA 110(42):16904-9 (2013).

[5] J.R. Potts, S. Harris and L. Giuggioli, Quantifying behavioral changes in territorial animals caused by sudden population declines, Am. Nat. 182:e73-e82 (2013).

[6] L. Giuggioli, J.R. Potts and S. Harris, Predicting oscillatory dynamics in the movement of territorial animals, J. Roy. Soc. Interface 9(72):1529-43 (2012).

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[8] L. Giuggioli, J.R. Potts and S. Harris, Brownian walkers within subdiffusing territorial boundaries, Phys. Rev. E 83:061138/1-11 (2011).

[9] L. Giuggioli, J.R. Potts and S. Harris, Animal interactions and the emergence of territoriality, PLoS Comp. Biol. 7(3):e1002008/1-9 (2011).