The home range fractal: From random walk to memory-dependent space use

Gautestad, Arild O.; Mysterud, Iver

doi:10.1016/j.ecocom.2009.11.005

Cited by 29 publications

(60 citation statements)

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“…It has clearly created a counterproductive distance between these complementary approaches. A more explicit statistical mechanical approach may bridge the two traditions, for example by paying closer attention to a broader range of the qualitative differences between a scale-specific and a scale-free process and the importance of observational scale [14,16].…”

Section: Discussionmentioning

confidence: 99%

“…Not only has the traditional approach towards testing for log -log linearity based on equation (1.1) (regression analysis) been questioned and more sophisticated statistical methods advocated (in particular, the Akaike model approach), but even these advanced approaches have been cast in doubt for some parameter range of b [29]. Thus, some alternative protocols for distinguishing between these processes from a statistical mechanical perspective, by studying fractal properties of space use, have been proposed [16,34].…”

Section: Scaling and Memorymentioning

confidence: 99%

“…The result is a self-organized home range (an emergent property of site fidelity) with fractal properties [33]. Contrary to LW, the scaling and memory aspects are implemented under a postulate of parallel processing over a continuum of process rates (see below) rather than assuming Markov compliance at a specific temporal unit scale t for the simulations [14,16]. Thus, power-law compliance is explained as an emergent property from a complex cognitive process, which may be mimicked in statistical mechanical terms by the MRW model design.…”

Section: Scaling and Memorymentioning

confidence: 99%

“…Reynolds & Rhodes [12] and Viswanathan et al [13]. However, it has been argued that theoretical progress in the context of vertebrate space use also depends on a realistic implementation of the memory aspect of movement [9][10][11], including a statistical mechanical system description in this regard [14][15][16]. Thus, on the one hand, the scaling property observed in real GPS data over some scale range [13,17,18]-even if the power-law fit has been questioned for some of the datasets [19,20]-requires a deeper understanding of the processes behind the emergence of scale-free movement.…”

Section: Introductionmentioning

confidence: 99%

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Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion

Gautestad

2012

J. R. Soc. Interface.

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Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.

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Section: Discussionmentioning

confidence: 99%

Section: Scaling and Memorymentioning

confidence: 99%

Section: Scaling and Memorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion

Gautestad

2012

J. R. Soc. Interface.

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“…A ratio is scale-free, but the actual processes as they are defined here are not. There are several scales involved: D in the context of a diffusion process regards dispersal distance squared divided by time, thus both space-and timescales are involved (Gautestad and Mysterud, 2010). Due to the implicit scale of the grid cells (unit size) relative to unit time increment, D is a dimensionless number in the present model.…”

Section: Limitations and Simplifications Of The Methodsmentioning

confidence: 99%

The effects of marine protected areas over time and species' dispersal potential: a quantitative conservation conflict attempt

Moustakas¹

2016

Web Ecol.

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Abstract. Protected areas are an important conservation measure. However, there are controversial findings regarding whether closed areas are beneficial for species and habitat conservation as well as for harvesting. Species dispersal is acknowledged as a key factor for the design and impacts of protected areas. A series of agent-based models using random diffusion to model fish dispersal were run before and after habitat protection. All results were normalized without the protected habitat in each scenario to detect the relative difference after protecting an area, all else being equal. Model outputs were compared with published data regarding the impacts over time of MPAs on fish biomass. In addition, data on species' dispersal potential in terms of kilometres per year are compared with model outputs. Results show that fish landings of species with short dispersal rates will take longer to reach the levels from before the Marine Protected Areas (MPAs) were established than landings of species with long dispersal rates. Further, the establishment of an MPA generates a higher relative population source within the MPA for species with low dispersal abilities than for species with high dispersal abilities. Results derived here show that there exists a feasible win-win scenario that maximizes both fish biomass and fish catches.

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2013

Spatial Simulation

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The home range fractal: From random walk to memory-dependent space use

Cited by 29 publications

References 50 publications

Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion

Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion

The effects of marine protected areas over time and species' dispersal potential: a quantitative conservation conflict attempt

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