A mathematical contribution to the study of orientation of organisms

Patlak, Clifford S.

doi:10.1007/bf02476435

Cited by 54 publications

(16 citation statements)

References 23 publications

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“…In the long‐term, however, the distribution of turn angles becomes uniformly distributed as the influence of the initial movement direction disappears (Benhamou 2006). Hence, correlated random walks are useful for modelling the forward persistence propensity characteristic of most animal movements (Patlak 1953a; Bovet & Benhamou 1988).…”

Section: Mechanistic Home Range Models: the Random Walk Approachmentioning

confidence: 99%

Are there general mechanisms of animal home range behaviour? A review and prospects for future research

Börger¹,

Dalziel²,

Fryxell³

2008

Ecology Letters

596

522

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Home range behaviour is a common pattern of space use, having fundamental consequences for ecological processes. However, a general mechanistic explanation is still lacking. Research is split into three separate areas of inquiry -movement models based on random walks, individual-based models based on optimal foraging theory, and a statistical modelling approach -which have developed without much productive contact. Here we review recent advances in modelling home range behaviour, focusing particularly on the problem of identifying mechanisms that lead to the emergence of stable home ranges from unbounded movement paths. We discuss the issue of spatiotemporal scale, which is rarely considered in modelling studies, as well as highlighting the need to consider more closely the dynamical nature of home ranges. Recent methodological and theoretical advances may soon lead to a unified approach, however, conceptually unifying our understanding of linkages among home range behaviour and ecological or evolutionary processes.

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Section: Mechanistic Home Range Models: the Random Walk Approachmentioning

confidence: 99%

Are there general mechanisms of animal home range behaviour? A review and prospects for future research

Börger¹,

Dalziel²,

Fryxell³

2008

Ecology Letters

596

522

View full text Add to dashboard Cite

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“…One is by a directed orientation reaction (taxis), in which the direction of motion of the organism is influenced by the stimulus. The other method of orientation is an undirected locomotory reaction (kinesis) in which the average speed or the average rate of turning of the organism, but not the direction in which it moves, are dependent on the stimulus [8], [29], [30]. In the diffusive version, there is no directional information that would orient the trajectories of the animals, and the standard BW model takes accordingly for granted that speed, turning rates and reorientation decisions are constant parameters over the field (or at least that they are isotropic since they do not depend on the heading of the animal).…”

Section: Introductionmentioning

confidence: 99%

How Do Ants Make Sense of Gravity? A Boltzmann Walker Analysis of Lasius niger Trajectories on Various Inclines

et al. 2013

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The goal of this study is to describe accurately how the directional information given by support inclinations affects the ant Lasius niger motion in terms of a behavioral decision. To this end, we have tracked the spontaneous motion of 345 ants walking on a 0.5×0.5 m plane canvas, which was tilted with 5 various inclinations by rad ( data points). At the population scale, support inclination favors dispersal along uphill and downhill directions. An ant's decision making process is modeled using a version of the Boltzmann Walker model, which describes an ant's random walk as a series of straight segments separated by reorientation events, and was extended to take directional influence into account. From the data segmented accordingly ( segments), this extension allows us to test separately how average speed, segments lengths and reorientation decisions are affected by support inclination and current walking direction of the ant. We found that support inclination had a major effect on average speed, which appeared approximately three times slower on the incline. However, we found no effect of the walking direction on speed. Contrastingly, we found that ants tend to walk longer in the same direction when they move uphill or downhill, and also that they preferentially adopt new uphill or downhill headings at turning points. We conclude that ants continuously adapt their decision making about where to go, and how long to persist in the same direction, depending on how they are aligned with the line of maximum declivity gradient. Hence, their behavioral decision process appears to combine klinokinesis with geomenotaxis. The extended Boltzmann Walker model parameterized by these effects gives a fair account of the directional dispersal of ants on inclines.

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“…He derived a suitable Fokker-Planck-type equation characterizing the particles' movement and used this stochastic model to analyze klino-kinesis [13]. However, his model ignores the adaptation process which plays a vital role in the description given by Ullyott and Fraenkel and Gunn.…”

Section: Klino-kinesis In the D Lacteummentioning

confidence: 98%