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Andy M Reynolds
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ABSTRACT: For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented 'moves'. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.
Journal of The Royal Society Interface 12/2010; 7(53):1753-8. · 4.40 Impact Factor
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ABSTRACT: It has long been recognized that chemotaxis is the primary means by which nematodes locate host plants. Nonetheless, chemotaxis has received scant attention. We show that chemotaxis is predicted to take nematodes to a source of a chemo-attractant via the shortest possible routes through the labyrinth of air-filled or water-filled channels within a soil through which the attractant diffuses. There are just two provisos: (i) all of the channels through which the attractant diffuses are accessible to the nematodes and (ii) nematodes can resolve all chemical gradients no matter how small. Previously, this remarkable consequence of chemotaxis had gone unnoticed. The predictions are supported by experimental studies of the movement patterns of the root-knot nematodes Meloidogyne incognita and Meloidogyne graminicola in modified Y-chamber olfactometers filled with Pluronic gel. By providing two routes to a source of the attractant, one long and one short, our experiments, the first to demonstrate the routes taken by nematodes to plant roots, serve to test our predictions. Our data show that nematodes take the most direct route to their preferred hosts (as predicted) but often take the longest route towards poor hosts. We hypothesize that a complex of repellent and attractant chemicals influences the interaction between nematodes and their hosts.
Journal of The Royal Society Interface 09/2010; 8(57):568-77. · 4.40 Impact Factor
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ABSTRACT: Migratory insects flying at high altitude at night often show a degree of common alignment, sometimes with quite small angular dispersions around the mean. The observed orientation directions are often close to the downwind direction and this would seemingly be adaptive in that large insects could add their self-propelled speed to the wind speed, thus maximising their displacement in a given time. There are increasing indications that high-altitude orientation may be maintained by some intrinsic property of the wind rather than by visual perception of relative ground movement. Therefore, we first examined whether migrating insects could deduce the mean wind direction from the turbulent fluctuations in temperature. Within the atmospheric boundary-layer, temperature records show characteristic ramp-cliff structures, and insects flying downwind would move through these ramps whilst those flying crosswind would not. However, analysis of vertical-looking radar data on the common orientations of nocturnally migrating insects in the UK produced no evidence that the migrants actually use temperature ramps as orientation cues. This suggests that insects rely on turbulent velocity and acceleration cues, and refocuses attention on how these can be detected, especially as small-scale turbulence is usually held to be directionally invariant (isotropic). In the second part of the paper we present a theoretical analysis and simulations showing that velocity fluctuations and accelerations felt by an insect are predicted to be anisotropic even when the small-scale turbulence (measured at a fixed point or along the trajectory of a fluid-particle) is isotropic. Our results thus provide further evidence that insects do indeed use turbulent velocity and acceleration cues as indicators of the mean wind direction.
PLoS ONE 01/2010; 5(12):e15758. · 4.09 Impact Factor
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ABSTRACT: Studies made with both entomological and meteorological radars over the last 40 years have frequently reported the occurrence of insect layers, and that the individuals forming these layers often show a considerable degree of uniformity in their headings--behaviour known as 'common orientation'. The environmental cues used by nocturnal migrants to select and maintain common headings, while flying in low illumination levels at great heights above the ground, and the adaptive benefits of this behaviour have long remained a mystery. Here we show how a wind-mediated mechanism accounts for the common orientation patterns of 'medium-sized' nocturnal insects. Our theory posits a mechanism by which migrants are able to align themselves with the direction of the flow using a turbulence cue, thus adding their air speed to the wind speed and significantly increasing their migration distance. Our mechanism also predicts that insects flying in the Northern Hemisphere will typically be offset to the right of the mean wind line when the atmosphere is stably stratified, with the Ekman spiral in full effect. We report on the first evidence for such offsets, and show that they have significant implications for the accurate prediction of the flight trajectories of migrating nocturnal insects.
Proceedings of the Royal Society B: Biological Sciences 11/2009; 277(1682):765-72. · 5.41 Impact Factor
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ABSTRACT: Apart from being notorious outbreak pests, locusts are of interest because of their expression of density-dependent "phase polyphenism." In this remarkable form of phenotypic plasticity, changes in local population density generate distinct solitarious and gregarious phases that differ in behavior, physiology, and appearance. A hallmark of phase polyphenism in outbreak species is the transition from solitary living to group formation and subsequent mass movement in migratory bands or swarms, yet there has been no convincing general explanation for the evolution of these density-dependent switches in spatial distribution. Using a model from "percolation theory", we show that it would be highly detrimental for locust individuals to continue indefinitely in a dispersed spatial distribution as their population densities increase. Switching to an extremely clumped distribution is advantageous because it disrupts the connectivity of predators' food-patch networks. Thus, selection pressure from predators has probably been an important factor underlying the initial evolution of conditional switches between "dispersed" and strongly aggregative behavior, which will also affect outbreak dynamics. Although group formation is the best alternative for high-density populations, it brings its own set of severe problems, resulting in secondary selection for many of the traits seen in gregarious-phase individuals.
Current biology: CB 01/2009; 19(1):20-4. · 10.99 Impact Factor
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ABSTRACT: Seminal field studies led by C. G. Johnson in the 1940s and 1950s showed that aphid aerial density diminishes with height above the ground such that the linear regression coefficient, b, of log density on log height provides a single-parameter characterization of the vertical density profile. This coefficient decreases with increasing atmospheric stability, ranging from -0.27 for a fully convective boundary layer to -2.01 for a stable boundary layer. We combined a well-established Lagrangian stochastic model of atmospheric dispersal with simple models of aphid behaviour in order to account for the range of aerial density profiles. We show that these density distributions are consistent with the aphids producing just enough lift to become neutrally buoyant when they are in updraughts and ceasing to produce lift when they are in downdraughts. This active flight behaviour in a weak flier is thus distinctly different from the aerial dispersal of seeds and wingless arthropods, which is passive once these organisms have launched into the air. The novel findings from the model indicate that the epithet 'passive' often applied to the windborne migration of small winged insects is misleading and should be abandoned. The implications for the distances traversed by migrating aphids under various boundary-layer conditions are outlined.
Proceedings of the Royal Society B: Biological Sciences 10/2008; 276(1654):137-43. · 5.41 Impact Factor
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ABSTRACT: We monitored the movements of a starved model predator, the carabid beetle Pterostichus melanarius, in arenas containing test papers upon which beetles had previously walked and unexposed control papers. Significantly, beetles accumulated on the unexposed controls, indicating conspecific avoidance (i.e. behaviour designed to avoid locations previously traversed by individuals of the same species). This finding is novel and important because optimal Lévy-flight (scale-free) search patterns for the location of sparsely and randomly distributed prey resources can emerge from conspecific avoidance. This finding may account for the shortcomings of random-walk (scale-finite) models when used to predict large-scale movement and search patterns by extrapolating from observations made at small scales.
Animal Behaviour 01/2008; 76:585-591. · 3.49 Impact Factor
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ABSTRACT: We have solved a long-standing and seemingly paradoxical set of questions that relate to the conditions which govern spider ballooning. We show that observations of spider ballooning excursions are best explained by meteorological conditions which maximize dispersal. Dispersal is predicted to be most effective in terms of distance when the stability of the atmosphere is non-ideally convective and is less effective during purely convective or neutrally stable conditions. Ballooners are most likely to travel a few hundred metres, but dispersal distances of several hundred kilometres are possible.
Biology letters 07/2007; 3(3):237-40. · 3.76 Impact Factor
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ABSTRACT: During their trajectories in still air, fruit flies (Drosophila melanogaster) explore their landscape using a series of straight flight paths punctuated by rapid 90 degrees body-saccades [1]. Some saccades are triggered by visual expansion associated with collision avoidance. Yet many saccades are not triggered by visual cues, but rather appear spontaneously. Our analysis reveals that the control of these visually independent saccades and the flight intervals between them constitute an optimal scale-free active searching strategy. Two characteristics of mathematical optimality that are apparent during free-flight in Drosophila are inter-saccade interval lengths distributed according to an inverse square law, which does not vary across landscape scale, and 90 degrees saccade angles, which increase the likelihood that territory will be revisited and thereby reduce the likelihood that near-by targets will be missed. We also show that searching is intermittent, such that active searching phases randomly alternate with relocation phases. Behaviorally, this intermittency is reflected in frequently occurring short, slow speed inter-saccade intervals randomly alternating with rarer, longer, faster inter-saccade intervals. Searching patterns that scale similarly across orders of magnitude of length (i.e., scale-free) have been revealed in animals as diverse as microzooplankton, bumblebees, albatrosses, and spider monkeys, but these do not appear to be optimised with respect to turning angle, whereas Drosophila free-flight search does. Also, intermittent searching patterns, such as those reported here for Drosophila, have been observed in foragers such as planktivorous fish and ground foraging birds. Our results with freely flying Drosophila may constitute the first reported example of searching behaviour that is both scale-free and intermittent.
PLoS ONE 02/2007; 2(4):e354. · 4.09 Impact Factor
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ABSTRACT: A simple model in which immobilizing events are imposed onto otherwise free Brownian diffusion [R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000) and a recent adaptation due to S. Khan and A. M. Reynolds, Physica A 350, 183 (2005)] is shown to encapsulate the peculiar transport characteristics of individual cell receptors within plasma membranes observed in single-particle tracking (SPT) experiments. These characteristics include the occurrence of normal diffusion; non-Gaussian subdiffusion; confined diffusion; a superdiffusive mode of transport that is not due to flow of the membrane or molecular motor attachment; and the occurrence of transitions between these transport modes. Model predictions are shown to be in close agreement with a reanalysis of existing SPT data.
Physical Review E 05/2005; 71(4 Pt 1):041915. · 2.26 Impact Factor
