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Random walk models in biology
TLDR
The mathematical theory behind the simple random walk is introduced and how this relates to Brownian motion and diffusive processes in general and a reinforced random walk can be used to model movement where the individual changes its environment.
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How to reliably estimate the tortuosity of an animal's path: straightness, sinuosity, or fractal dimension?
  • S. Benhamou
  • Business
    Journal of theoretical biology
  • 21 July 2004
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How many animals really do the Lévy walk?
TLDR
Lévy walks are superdiffusive and scale-free random walks that have recently emerged as a new conceptual tool for modeling animal search paths and may be confounded with them because they present apparent move-length-heavy tail distributions and superdiffusivity.
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Dynamic Approach to Space and Habitat Use Based on Biased Random Bridges
  • S. Benhamou
  • Environmental Science
    PloS one
  • 26 January 2011
TLDR
The concept of a biased random (advective-diffusive) bridge (BRB) is introduced and the MKDE method is shown to be a practical means to estimate UDs based on simplified BRBs, which can approximate various movement types at short times from a given relocation.
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Animal movements in heterogeneous landscapes: identifying profitable places and homogeneous movement bouts.
TLDR
This work critically reviewed the few previously published methods to detect changes in movement behavior likely to occur when an animal enters a profitable place and designed a new, easy-to-use method based on the time spent in the vicinity of successive path locations.
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Memory keeps you at home: a mechanistic model for home range emergence
TLDR
This model is based on an animal tracking a dynamic resource landscape, using a biologically plausible two-part memory system, i.e. a reference- and a working-memory, and shows the potential for home-range behavior.
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Spatial analysis of animals' movements using a correlated random walk model*
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Efficiency of area-concentrated searching behaviour in a continuous patchy environment*
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Spatial memory and animal movement.
TLDR
This work draws together research from several disciplines to understand the relationship between animal memory and movement processes, and frames the problem in terms of the characteristics, costs and benefits of memory as outlined in psychology and neuroscience.
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Of scales and stationarity in animal movements.
  • S. Benhamou
  • Environmental Science
    Ecology letters
  • 1 March 2014
TLDR
This work proposes to build on stationarity (i.e. stability of statistical parameters) to develop a consistent theoretical framework in which animal movements are modelled as a generic composite multi-scale multi-mode random walk model.
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