A random walk description of individual animal movement accounting for periods of rest

Tilles, Paulo F. C.; Petrovskii, Sergei; Natti, Paulo Laerte

doi:10.1098/rsos.160566

Cited by 18 publications

(17 citation statements)

References 38 publications

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“…10–100 sec for various insect species) are common and they are observed both in natural environments and under controlled laboratory conditions 34 , 55 – 57 . Good understanding of the uninterrupted movement is therefore required; once its properties are revealed and analyzed, it can be upscaled to include intermittency 58 .…”

Section: Model and Methodsmentioning

confidence: 99%

A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

Tilles

Petrovskii

Natti

2017

Sci Rep

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Patterns of individual animal movement attracted considerable attention over the last two decades. In particular, question as to whether animal movement is predominantly diffusive or superdiffusive has been a focus of discussion and controversy. We consider this problem using a theory of stochastic motion based on the Langevin equation with non-Wiener stochastic forcing that originates in animal’s response to environmental noise. We show that diffusive and superdiffusive types of motion are inherent parts of the same general movement process that arises as interplay between the force exerted by animals (essentially, by animal’s muscles) and the environmental drag. The movement is superballistic with the mean square displacement growing with time as at the beginning and eventually slowing down to the diffusive spread . We show that the duration of the superballistic and superdiffusive stages can be long depending on the properties of the environmental noise and the intensity of drag. Our findings demonstrate theoretically how the movement pattern that includes diffusive and superdiffusive/superballistic motion arises naturally as a result of the interplay between the dissipative properties of the environment and the animal’s biological traits such as the body mass, typical movement velocity and the typical duration of uninterrupted movement.

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Section: Model and Methodsmentioning

confidence: 99%

A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

Tilles

Petrovskii

Natti

2017

Sci Rep

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“…In the Bayesian‐like approach, the parameters were obtained from (positive) Gaussian distributions to slightly account for bird diversity. Alternatives to this function can be drawn in directions including those that may impact (a) short‐ and long‐distance movements, such as bird diversity in biology and ecology, health status and infection dynamics (van Gils et al, ; McKay & Hoye, ), and (b) the kind of motions to account for non‐isotropic movements in the dispersion or more complex motions, such as anomalous diffusion or Levy walks (Lewis, Maini, & Petrovskii, ; Tilles, Petrovskii, & Natti, ), which allows for taking into account landscape heterogeneity and correlations in motions. Both (a) and (b) lead to complexifying the density g ( ρ | τ ) which, to be constructed, requires having and knowing how to couple information on the epidemiology of avian influenza and the mechanisms and modes of movement of diverse birds in various landscapes.…”

Section: Resultsmentioning

confidence: 99%

Fireworks‐like surveillance approach: The case of HPAI H5N1 in wild birds in Europe

Pereira

Artois

Bicout

2019

Transbound Emerg Dis

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Highly pathogenic avian influenza (HPAI) risk management requires efficient surveillance of the infection in wild birds for early warning purposes. In this study, our aim was to describe the spread of continent‐wide infection cases using a fireworks model and therefore improve current surveillance systems. The fireworks model is a metaphor illustrating the spread of HPAI as a point source epizootic. The approach is based on early detection of the outbreak seeds (sparks from the fireworks) and uses a predictive model of the probability of the occurrence of new cases following a seed introduction; this then determines the spatiotemporal perimeter for intense surveillance investigations. For a case study, we used surveillance data on HPAI H5N1 in wild birds across Europe between 2005 and 2010 to describe the outbreaks and determine the success of the case detection used to inform management of the disease. The fireworks description assumes simultaneous introductions of ‘seeds’ of cases, which then ‘explode’ in local foci but do not merge into a progressive disease wave. This model fits the data well. Using this predictive approach for HPAI cases in EU countries, we found that the investigation radius needed to achieve a detection level of 90% of new cases after an outbreak ranged from 10 km to more than 300 km, depending on the outbreak pattern. Based on these findings, the fireworks approach can be a valuable method for identifying the perimeters and risk areas to be targeted for enhanced surveillance. The rationale of the fireworks approach is quite generic and can easily be adapted to different situations and contexts.

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“…We will focus on the case Q = P, and therefore p = q. The periodic case, including the case when S is a periodic sequence in (9), can be handled also by the topological Markov chain method explained in the previous section. However, the method described below is more direct to find s and r. Let us consider that the size of P is equal to k > 0 and that S is periodic.…”

Section: Unique Critical Orbitmentioning

confidence: 99%

“…The computational tractability and mathematical simplicity are stressed as main advantages of the referred methods, and the authors apply the models to changing behavior of the animals and to multiple animal movement description.Until recently there remains some academic debate with respect to the stochastic nature of animal movement and the appropriate length probability distribution in the characterization of animal movements, in particular, regarding the importance or not of the Levy walk type. See, for example References [8,9].The objective of the present paper is to develop a model, introduced in Reference [10], which simulate and classify different types of trajectories using a very simple iterated map of the interval-a cubic map f b,d , depending on two parameters b, d ∈ [−1, 1]. The map f b,d produce the displacements in each Cartesian coordinate through iteration.…”

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confidence: 99%

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Kinematics in Biology: Symbolic Dynamics Approach

Ramos

2020

Mathematics

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Motion in biology is studied through a descriptive geometrical method. We consider a deterministic discrete dynamical system used to simulate and classify a variety of types of movements which can be seen as templates and building blocks of more complex trajectories. The dynamical system is determined by the iteration of a bimodal interval map dependent on two parameters, up to scaling, generalizing a previous work. The characterization of the trajectories uses the classifying tools from symbolic dynamics-kneading sequences, topological entropy and growth number. We consider also the isentropic trajectories, trajectories with constant topological entropy, which are related with the possible existence of a constant drift. We introduce the concepts of pure and mixed bimodal trajectories which give much more flexibility to the model, maintaining it simple. We discuss several procedures that may allow the use of the model to characterize empirical data.The methods used vary, ranging from pure stochastic, see for example the survey [1], machine learning or mechanistic approaches. An important reference in this last direction of study is Reference [2], where a conceptual framework for movement in ecology is proposed. Their approach is general and includes certain components which determine the movement path. Three of these components regard the individual and are: internal state, motion capacity and navigation capacity. A fourth component, corresponding to the external factors, represents aspects of the abiotic and biotic environment which affect the movement.In Reference [3], the authors review literature on the agent based modeling approach allowing to incorporate in simulations characteristics of animal behavior and the interaction with different environments. Other methods are introduced and developed in References [4][5][6]. For example, state space models appropriate to deal with biological and statistical features of satellite tracking data and different methodologies of collecting data using statistically robust methods. The state-space framework considers the internal state of the animal as a possible state variable which influence the displacement, therefore allowing the transition between behavior states or modes, within the model. This is important for the observed type of trajectory, since the animal may be migrating, searching for water, foraging, exploring, and these types of behavior produce distinct types of trajectories.In Reference [7], the authors refer to alternative methods for modeling animal trajectories with hidden Markov models, where the modeling is based on existing non-observable states which are governed by some probability distributions, for example, Markov chains. The authors discuss these methods comparing them with the state-space model approach. The computational tractability and mathematical simplicity are stressed as main advantages of the referred methods, and the authors apply the models to changing behavior of the animals and to multiple animal movement description.Until recently...

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A random walk description of individual animal movement accounting for periods of rest

Cited by 18 publications

References 38 publications

A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

Fireworks‐like surveillance approach: The case of HPAI H5N1 in wild birds in Europe

Kinematics in Biology: Symbolic Dynamics Approach

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