Random walk models in biology

By Edward A. Codling, Michael J. Plank, S. Benhamou. Journal of the Royal Society Interface, 2008

1,444 citations recorded by the source corpus.

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/e5ccc6a56d3a4d83fc9f03990e051bf27a9e2183

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Citations in the corpus

Predicting monarch butterfly (Danaus plexippus) movement and egg-laying with a spatially-explicit agent-based model: The role of monarch perceptual range and spatial memory (2018, background): “Correlated random walk algorithms are reasonable for modeling animal movement (Jones, 1977; Karieva and Shigesada, 1983; Zalucki, 1983; Bovet and Benhamou, 1988; Turchin, 1998) in some situations and especially in homogeneous environments (Codling et al., 2008; Smouse et al., 2010).”
Integrated step selection analysis: bridging the gap between resource selection and animal movement (2015, methodology): “tatistical (phenomenological) RSAs and mathematical (mechanistic) RW models (Potts et al. 2014b), models that form the backbone of much of the existing body of theory in the field of animal movement (Codling et al. 2008; Fagan & Calabrese 2014; Benhamou 2014) . In this paper we outline a -based ”
Air pollutants degrade floral scents and increase insect foraging times (2016, methodology): “Random walk models are frequently used to represent the foraging behavior of animals 157 (Codling et al., 2008).”
Random walks and diffusion on networks (2016, background): “ic motivation from an application (e.g., a Pac-Man-like \hungry RW" [81] has been used as a model for chemotaxis in a porous medium), are often inspired by applications, such as animal movement [10, 12] or nancial markets [21], and one can nd discussions of dierent avors of RWs in Refs. [4, 34,”
Active Brownian particles (2012, background): “This so-called “run & tumble” motion has been successfully modelled by a random walk approach [31,62], where usually constant speed and Poissonian distribution of reorientation events is assumed.”
Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions. (2012, background): “The class of building blocks that we consider for the state-dependent process Zt comprises correlated and biased random walks (CRWs and BRWs, respectively), as well as walks that are both correlated and biased (BCRWs); see Codling et al. (2008) and Appendix C for more details.”
Establishing the link between habitat selection and animal population dynamics (2015, background): “…and Lucas 1970) has opened the debate about the implications of competition for the distribution of conspecifics, movement ecology (Turchin 1998, Codling et al. 2008, Schick et al. 2008) has created useful abstractions to describe how organisms navigate their environment, behavioral ecology…”
Movement ecology of amphibians: A missing component for understanding population declines (2014, background): “At the most basic level, this type of movement is common in animals that are not responsive to environmental features and which are not employing spatial memory or navigational mechanisms during movement (Codling et al., 2008; Haefner and Crist, 1994).”
Indices of movement behaviour: conceptual background, effects of scale and location errors (2010, methodology): “As MSD should scale linearly with time or path length for purely diffusive paths, super-diffusive movements have MSD increasing with a power exponent between 1 and 2 (CODLING et al. 2008).”