“Predator-prey models with competition: the emergence of territoriality”

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Henri Berestycki and Alessandro Zilio (Mar 2019)

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This paper aims at understanding animal territories through a new predator-prey model with strong competition

A simulation of the model showing the distribution of prey (blue curves) and of two groups of rival predators (red curves) for different values of the predator competition strength. We see that as this parameter becomes larger (curves drawn with more solid colors) the two groups of predators separate and an interface between the territories emerges. At such interfaces prey become more abundant, eventually benefitting the overall size of the population of predators.
(Credit: Henri Berestycki)

What mechanisms lead certain animals like wolves to form well-separated territories? How are ant territories shaped? And what is the impact of territorial behavior on populations like coyotes? These are some of the questions that Henri Berestycki and Alessandro Zilio consider in a general framework in this article in which they propose a new and concise mathematical model for territoriality. Assuming only that predators and prey interact with the environment and with each other, they emphasize the role played by conspecific competitive behavior, that is between different packs of predators. They find this to be a key factor in the formation of territories. Indeed, strong competition between packs of predators leads to territorial segregation. More precisely, they find that, as the strength of competition becomes large, groups of predators divide the original region into subregions, each of which is occupied by only one group, thus forming territories. This model predicts certain shapes of territories that can be compared with observations. It also relates territory size to other ecological parameters. The findings match observations. By means of their model, the authors also consider the impact of strong competition on other relevant ecological indicators, such as the size of the overall predator population. They derive a rather counterintuitive consequence of strong competition and territoriality: in some situations, predators with territorial behaviors and very aggressive competition can sustain a larger population than identical predators would if they did not adopt a territorial behavior and did not fight. Indeed, the creation of territories leads to prey thriving at the interfaces of these territories that predators tend to avoid. Thus, the model highlights this buffer zone effect by providing a quantitative explanation.


We introduce a model aimed at shedding light on the emergence of territorial behaviors in predators and on the formation of packs. We consider the situation of predators competing for the same prey (or spatially distributed resource). We observe that strong competition between groups of predators leads to the formation of territories. At the edges of territories, prey concentrate and prosper, leading to a feedback loop in the population distribution of predators. We focus our attention on the effects of the segregation of the population of predators into competing, hostile packs on the overall size of the population of predators. We present some numerical simulations that allow us to describe our counter-intuitive and most important conclusion: lethal aggressiveness among hostile groups of predators may actually lead to an increase in their total population.

Modèles proie-prédateurs avec compétition : l’émergence de la territorialité

Nous introduisons un modèle qui se propose d’apporter un éclairage sur l’émergence de la territorialité et la formation de meutes chez certains prédateurs. Nous considérons des prédateurs en compétition pour la même proie (ou ressource distribuée spatialement). Nous montrons qu’une compétition très forte entre groupes de prédateurs conduit à la formation de territoires. Les proies se concentrent et prospèrent aux interfaces entre territoires, créant ainsi une boucle de rétroaction sur la distribution de la population des prédateurs. Nous étudions plus spécifiquement les effets de la ségrégation des prédateurs entre plusieurs groupes hostiles sur la taille totale de la population de prédateurs. Nous présentons des simulations numériques qui illustrent une de nos conclusions les plus importantes et contre-intuitive : une agressivité létale entre des groupes hostiles de prédateurs peut conduire à un accroissement de la population totale de prédateurs.