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Territorial dynamics and stable home range formation for central place foragers.

Potts JR, Harris S, Giuggioli L - PLoS ONE (2012)

Bottom Line: Approximate analytic expressions for the animal's probability density function are derived.Comparisons are made with previous theoretical work modelling central place foragers with conspecific avoidance.Some insights into the mechanisms behind allometric scaling laws of animal space use are also given.

View Article: PubMed Central - PubMed

Affiliation: Bristol Centre for Complexity Sciences, University of Bristol, Bristol, United Kingdom. jonathan.potts.08@bristol.ac.uk

ABSTRACT
Uncovering the mechanisms behind territory formation is a fundamental problem in behavioural ecology. The broad nature of the underlying conspecific avoidance processes are well documented across a wide range of taxa. Scent marking in particular is common to a large range of terrestrial mammals and is known to be fundamental for communication. However, despite its importance, exact quantification of the time-scales over which scent cues and messages persist remains elusive. Recent work by the present authors has begun to shed light on this problem by modelling animals as random walkers with scent-mediated interaction processes. Territories emerge as dynamic objects that continually change shape and slowly move without settling to a fixed location. As a consequence, the utilisation distribution of such an animal results in a slowly increasing home range, as shown for urban foxes (Vulpes vulpes). For certain other species, however, home ranges reach a stable state. The present work shows that stable home ranges arise when, in addition to scent-mediated conspecific avoidance, each animal moves as a central place forager. That is, the animal's movement has a random aspect but is also biased towards a fixed location, such as a den or nest site. Dynamic territories emerge but the probability distribution of the territory border locations reaches a steady state, causing stable home ranges to emerge from the territorial dynamics. Approximate analytic expressions for the animal's probability density function are derived. A programme is given for using these expressions to quantify both the strength of the animal's movement bias towards the central place and the time-scale over which scent messages persist. Comparisons are made with previous theoretical work modelling central place foragers with conspecific avoidance. Some insights into the mechanisms behind allometric scaling laws of animal space use are also given.

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Simulation output for systems of territorial central place foragers.The dependence of the saturation mean square displacement (saturation MSD)  (resp. ) of the dimensionless territory border position  () on the dimensionless parameters  and  () from stochastic simulation output. The notation  denotes an ensemble average over stochastic simulations. The border movement is non-dimensionalised by dividing by , the average distance between central places of adjacent territories. Panel (a) shows output from 1D simulations and panel (b) from 2D simulations. The best-fit lines for the 2D plots are  for ,  for ,  for ,  for ,  for , and  for .
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pone-0034033-g001: Simulation output for systems of territorial central place foragers.The dependence of the saturation mean square displacement (saturation MSD) (resp. ) of the dimensionless territory border position () on the dimensionless parameters and () from stochastic simulation output. The notation denotes an ensemble average over stochastic simulations. The border movement is non-dimensionalised by dividing by , the average distance between central places of adjacent territories. Panel (a) shows output from 1D simulations and panel (b) from 2D simulations. The best-fit lines for the 2D plots are for , for , for , for , for , and for .

Mentions: For a fixed , the amount of border movement arises from the ratio of the active scent time to the diffusive time, which is in 1D or in 2D (figure 1). Increasing has the effect of reducing the animal's tendency to move into interstitial regions and claim extra territory. This causes the borders to move less on average as each animal keeps to a small core area well within its territory most of the time. Consequently, when plotting the MSD saturation value against or , we see that the curves for higher values of lie below those for lower values (figure 1).


Territorial dynamics and stable home range formation for central place foragers.

Potts JR, Harris S, Giuggioli L - PLoS ONE (2012)

Simulation output for systems of territorial central place foragers.The dependence of the saturation mean square displacement (saturation MSD)  (resp. ) of the dimensionless territory border position  () on the dimensionless parameters  and  () from stochastic simulation output. The notation  denotes an ensemble average over stochastic simulations. The border movement is non-dimensionalised by dividing by , the average distance between central places of adjacent territories. Panel (a) shows output from 1D simulations and panel (b) from 2D simulations. The best-fit lines for the 2D plots are  for ,  for ,  for ,  for ,  for , and  for .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3316599&req=5

pone-0034033-g001: Simulation output for systems of territorial central place foragers.The dependence of the saturation mean square displacement (saturation MSD) (resp. ) of the dimensionless territory border position () on the dimensionless parameters and () from stochastic simulation output. The notation denotes an ensemble average over stochastic simulations. The border movement is non-dimensionalised by dividing by , the average distance between central places of adjacent territories. Panel (a) shows output from 1D simulations and panel (b) from 2D simulations. The best-fit lines for the 2D plots are for , for , for , for , for , and for .
Mentions: For a fixed , the amount of border movement arises from the ratio of the active scent time to the diffusive time, which is in 1D or in 2D (figure 1). Increasing has the effect of reducing the animal's tendency to move into interstitial regions and claim extra territory. This causes the borders to move less on average as each animal keeps to a small core area well within its territory most of the time. Consequently, when plotting the MSD saturation value against or , we see that the curves for higher values of lie below those for lower values (figure 1).

Bottom Line: Approximate analytic expressions for the animal's probability density function are derived.Comparisons are made with previous theoretical work modelling central place foragers with conspecific avoidance.Some insights into the mechanisms behind allometric scaling laws of animal space use are also given.

View Article: PubMed Central - PubMed

Affiliation: Bristol Centre for Complexity Sciences, University of Bristol, Bristol, United Kingdom. jonathan.potts.08@bristol.ac.uk

ABSTRACT
Uncovering the mechanisms behind territory formation is a fundamental problem in behavioural ecology. The broad nature of the underlying conspecific avoidance processes are well documented across a wide range of taxa. Scent marking in particular is common to a large range of terrestrial mammals and is known to be fundamental for communication. However, despite its importance, exact quantification of the time-scales over which scent cues and messages persist remains elusive. Recent work by the present authors has begun to shed light on this problem by modelling animals as random walkers with scent-mediated interaction processes. Territories emerge as dynamic objects that continually change shape and slowly move without settling to a fixed location. As a consequence, the utilisation distribution of such an animal results in a slowly increasing home range, as shown for urban foxes (Vulpes vulpes). For certain other species, however, home ranges reach a stable state. The present work shows that stable home ranges arise when, in addition to scent-mediated conspecific avoidance, each animal moves as a central place forager. That is, the animal's movement has a random aspect but is also biased towards a fixed location, such as a den or nest site. Dynamic territories emerge but the probability distribution of the territory border locations reaches a steady state, causing stable home ranges to emerge from the territorial dynamics. Approximate analytic expressions for the animal's probability density function are derived. A programme is given for using these expressions to quantify both the strength of the animal's movement bias towards the central place and the time-scale over which scent messages persist. Comparisons are made with previous theoretical work modelling central place foragers with conspecific avoidance. Some insights into the mechanisms behind allometric scaling laws of animal space use are also given.

Show MeSH
Related in: MedlinePlus