How do animal territories form and change? Lessons from 20 years of mechanistic modelling

Territory formation is ubiquitous throughout the animal kingdom. At the individual level, various behaviours attempt to exclude conspecifics from regions of space. At the population level, animals often segregate into distinct territorial areas. Consequently, it should be possible to derive territorial patterns from the underlying behavioural processes of animal movements and interactions. Such derivations are an important element in the development of an ecological theory that can predict the effects of changing conditions on territorial populations. Here, we review the approaches developed over the past 20 years or so, which go under the umbrella of 'mechanistic territorial models'. We detail the two main strands to this research: partial differential equations and individual-based approaches, showing what each has offered to our understanding of territoriality and how they can be unified. We explain how they are related to other approaches to studying territories and home ranges, and point towards possible future directions.