Abstract
Territorial behaviour is an important part of the lives of many animals. Once a territory has been acquired, an animal may spend its entire life on it, and may have to repeatedly defend it from conspecifics. Some species make great investments in the defence of a territory, and this defence can be costly, in terms of time, energy and risk of injury. Time costs in particular have rarely been explicitly factored into such models. In this paper we consider a model of territorial defence which includes both population dynamic and time delay elements, building upon recent advances in time constraint models. Populations may divide into two distinct types, where one type makes no effort to control territories. We shall call this type nomads, and the other type territorials. Here the territory owners must divide their time between patrolling and foraging, and this balance is their only strategic decision. We show how to find the evolutionarily stable patrolling strategy and the population composition of territorials and nomads, and consider some examples demonstrating key situations. We see that both time constraints and population density pressure are crucial to influencing behaviour. In particular we find cases with both territorial individuals and nomads where a mixed, either pure or both pure patrolling strategies are evolutionarily stable. In different conditions either nomads or territorials can be absent, and indeed for a significant range of parameter combinations the population can exhibit tristability, with three distinct ecologically stable population compositions: with both nomads and territorials, only nomads or only territorials.
Highlights
Territory is the sociographical area that an animal defends against conspecifics (Adams 2001, Hinsch and Komdeur 2017, Owen-Smith 1977)
The model investigates the questions from the energetic aspect so that we focus on two factors mentioned in the introduction during the development of the model: time constraints and density dependence
In this paper we have considered a model of territorial behaviour, where territory owners must defend their territories from intruders who in turn wish to take over the territory
Summary
Territory is the sociographical area that an animal defends against conspecifics (Adams 2001, Hinsch and Komdeur 2017, Owen-Smith 1977). Broom and Ruxton (1998) developed a game-theoretic model of kleptoparasitism where individuals could strategically challenge for food, but where contests took time that could be spent searching (e.g. see Broom et al 2004, Broom and Rychtaˇr 2011) This model was fitted to a population of foraging gulls in Spencer and Broom (2018). The territorial interaction (that is the fight for the territory) decreases the fitness of both participants in the model introduced in the present article too, but this is considered through loss in intake (energy) and time. This presumption on mortality is realistic for several species.
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