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

Potts JR, Lewis MA - Proc. Biol. Sci. (2014)

Bottom Line: At the population level, animals often segregate into distinct territorial areas.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, , Edmonton, , Alberta, Canada , T6G 2G1, Department of Biological Sciences, University of Alberta, , Edmonton, , Alberta, Canada , T6G 2G1.

ABSTRACT
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.

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Related in: MedlinePlus

Using individual-based territoriality models to extract scent longevity fromlocation data. Location data can be fitted to the analytic model of [34] using the methods of[19] to giveinformation about the territory border movement, K, theanimal's intrinsic diffusion constant, D, and thepopulation density ρ. Analysis of the IBM from[17] then gives auniversal curve K =αDexp(−βDρTAS)[19], which can beused, together with the information on K,D and ρ, to obtain an estimateof the active scent time, TAS.
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RSPB20140231F3: Using individual-based territoriality models to extract scent longevity fromlocation data. Location data can be fitted to the analytic model of [34] using the methods of[19] to giveinformation about the territory border movement, K, theanimal's intrinsic diffusion constant, D, and thepopulation density ρ. Analysis of the IBM from[17] then gives auniversal curve K =αDexp(−βDρTAS)[19], which can beused, together with the information on K,D and ρ, to obtain an estimateof the active scent time, TAS.

Mentions: However, there turns out to be a ‘parameter collapse’ of the simulationoutput to a universal curve relating the generalized diffusion constant of theterritory border, K, to a dimensionless input parameterZ, so that for particular constants α andβ reported in reference [33] in one-dimension and [19] in two-dimensions. Here, in one-dimension and in two-dimensions, whereρ is the population density and D is theintrinsic diffusion constant of the animal. This enables users of this modellingapproach to extract the active scent time from details of the border movement that,in turn, can be extracted from movement data via the approximate analytic model(figure 3). Figure 3.


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

Potts JR, Lewis MA - Proc. Biol. Sci. (2014)

Using individual-based territoriality models to extract scent longevity fromlocation data. Location data can be fitted to the analytic model of [34] using the methods of[19] to giveinformation about the territory border movement, K, theanimal's intrinsic diffusion constant, D, and thepopulation density ρ. Analysis of the IBM from[17] then gives auniversal curve K =αDexp(−βDρTAS)[19], which can beused, together with the information on K,D and ρ, to obtain an estimateof the active scent time, TAS.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4043092&req=5

RSPB20140231F3: Using individual-based territoriality models to extract scent longevity fromlocation data. Location data can be fitted to the analytic model of [34] using the methods of[19] to giveinformation about the territory border movement, K, theanimal's intrinsic diffusion constant, D, and thepopulation density ρ. Analysis of the IBM from[17] then gives auniversal curve K =αDexp(−βDρTAS)[19], which can beused, together with the information on K,D and ρ, to obtain an estimateof the active scent time, TAS.
Mentions: However, there turns out to be a ‘parameter collapse’ of the simulationoutput to a universal curve relating the generalized diffusion constant of theterritory border, K, to a dimensionless input parameterZ, so that for particular constants α andβ reported in reference [33] in one-dimension and [19] in two-dimensions. Here, in one-dimension and in two-dimensions, whereρ is the population density and D is theintrinsic diffusion constant of the animal. This enables users of this modellingapproach to extract the active scent time from details of the border movement that,in turn, can be extracted from movement data via the approximate analytic model(figure 3). Figure 3.

Bottom Line: At the population level, animals often segregate into distinct territorial areas.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, , Edmonton, , Alberta, Canada , T6G 2G1, Department of Biological Sciences, University of Alberta, , Edmonton, , Alberta, Canada , T6G 2G1.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus