The relative importance of social information use for population abundance in group-living and non-grouping prey

Predator-prey relationships are fundamental components of ecosystem functioning, within which the spatial consequences of prey social organization can alter predation rates. Group-living (GL) species are known to exploit inadvertent social information (ISI) that facilitates population persistence under predation risk. Still, the extent to which non-grouping (NG) prey can benefit from similar processes is unknown. Here we built an individual-based model to explore and compare the population-level consequences of ISI use in GL and NG prey. We differentiated between GL and NG prey only by the presence or absence of social attraction toward conspecifics that drives individual movement patterns. We found that the extent of the benefits of socially acquired predator information in NG highly depends on the prey's ability to detect nearby predators, prey density and the occurrence of false alarms. Conversely, even moderate probabilities of ISI use and predator detection can lead to maximal population-level benefits in GL prey. This theoretical work provides additional insights into the conditions under which ISI use can facilitate population persistence irrespective of prey social organisation.

Harmonic radar tracking of individual melon flies, Zeugodacus cucurbitae, in Hawaii: Determining movement parameters in cage and field settings

Tephritid fruit flies, such as the melon fly, Zeugodacus cucurbitae, are major horticultural pests worldwide and pose invasion risks due primarily to international trade. Determining movement parameters for fruit flies is critical to effective surveillance and control strategies, from setting quarantine boundaries after incursions to development of agent-based models for management. While mark-release-recapture, flight mills, and visual observations have been used to study tephritid movement, none of these techniques give a full picture of fruit fly movement in nature. Tracking tagged flies offers an alternative method which has the potential to observe individual fly movements in the field, mirroring studies conducted by ecologists on larger animals. In this study, harmonic radar (HR) tags were fabricated using superelastic nitinol wire which is light (tags weighed less than 1 mg), flexible, and does not tangle. Flight tests with wild melon flies showed no obvious adverse effects of HR tag attachment. Subsequent experiments successfully tracked HR tagged flies in large field cages, a papaya field, and open parkland. Unexpectedly, a majority of tagged flies showed strong flight directional biases with these biases varying between flies, similar to what has been observed in the migratory butterfly Pieris brassicae. In field cage experiments, 30 of the 36 flies observed (83%) showed directionally biased flights while similar biases were observed in roughly half the flies tracked in a papaya field. Turning angles from both cage and field experiments were non-random and indicate a strong bias toward continued “forward” movement. At least some of the observed direction bias can be explained by wind direction with a correlation observed between collective melon fly flight directions in field cage, papaya field, and open field experiments. However, individual mean flight directions coincided with the observed wind direction for only 9 out of the 25 flies in the cage experiment and half of the flies in the papaya field, suggesting wind is unlikely to be the only factor affecting flight direction. Individual flight distances (meters per flight) differed between the field cage, papaya field, and open field experiments with longer mean step-distances observed in the open field. Data on flight directionality and step-distances determined in this study might assist in the development of more effective control and better parametrize models of pest tephritid fruit fly movement.

Social information-mediated population dynamics in non-grouping prey

Abstract

Inadvertent social information (ISI) use, i.e., the exploitation of social cues including the presence and behaviour of others, has been predicted to mediate population-level processes even in the absence of cohesive grouping. However, we know little about how such effects may arise when the prey population lacks social structure beyond the spatiotemporal autocorrelation originating from the random movement of individuals. In this study, we built an individual-based model where predator avoidance behaviour could spread among randomly moving prey through the network of nearby observers. We qualitatively assessed how ISI use may affect prey population size when cue detection was associated with different probabilities and fitness costs, and characterised the structural properties of the emerging detection networks that would provide pathways for information spread in prey. We found that ISI use was among the most influential model parameters affecting prey abundance and increased equilibrium population sizes in most examined scenarios. Moreover, it could substantially contribute to population survival under high predation pressure, but this effect strongly depended on the level of predator detection ability. When prey exploited social cues in the presence of high predation risk, the observed detection networks consisted of a large number of connected components with small sizes and small ego networks; this resulted in efficient information spread among connected individuals in the detection networks. Our study provides hypothetical mechanisms about how temporary local densities may allow information diffusion about predation threats among conspecifics and facilitate population stability and persistence in non-grouping animals.

Significance statement

The exploitation of inadvertently produced social cues may not only modify individual behaviour but also fundamentally influence population dynamics and species interactions. Using an individual-based model, we investigated how the detection and spread of adaptive antipredator behaviour may cascade to changes in the demographic performance of randomly moving (i.e., non-grouping) prey. We found that social information use contributed to population stability and persistence by reducing predation-related per capita mortality and raising equilibrium population sizes when predator detection ability reached a sufficient level. We also showed that temporary detection networks had structural properties that allowed efficient information spread among prey under high predation pressure. Our work represents a general modelling approach that could be adapted to specific predator-prey systems and scrutinise how temporary local densities allow dynamic information diffusion about predation threats and facilitate population stability in non-grouping animals.

Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

BACKGROUND

Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps.

METHODS

We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency.

RESULTS

We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion.

CONCLUSION

Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Walking behaviour in the ground beetle, Poecilus cupreus: dispersal potential, intermittency and individual variation

Dispersal is a key ecological process affecting community dynamics and the maintenance of populations. There is increasing awareness of the need to understand individual dispersal potential to better inform population-level dispersal, allowing more accurate models of the spread of invasive and beneficial insects, aiding crop and pest management strategies. Here, fine-scale movements of Poecilus cupreus, an important agricultural carabid predator, were recorded using a locomotion compensator and key movement characteristics were quantified. Net displacement increased more rapidly than predicted by a simple correlated random walk model with near ballistic behaviour observed. Individuals displayed a latent ability to head on a constant bearing for protracted time periods, despite no clear evidence of a population level global orientation bias. Intermittent bouts of movement and non-movement were observed, with both the frequency and duration of bouts of movement varying at the inter- and intra-individual level. Variation in movement behaviour was observed at both the inter- and intra- individual level. Analysis suggests that individuals have the potential to rapidly disperse over a wider area than predicted by simple movement models parametrised at the population level. This highlights the importance of considering the role of individual variation when analysing movement and attempting to predict dispersal distances.

Flight Burst Duration as an Indicator of Flight Ability and Physical Fitness in Two Species of Tephritid Fruit Flies

We introduce a method to quantify flight ability and physical fitness of individual fruit flies which we term 'Flight Burst Duration' (FBD). This consisted of tethering individual insects by the dorsal thorax using a vacuum and measuring the length of time the insect beats its wings while suspended off a surface. Consecutive measurements with Bactrocera dorsalis Hendel (Dipera: Tephritidae) and Zeugodacus cucurbitae Coquillett (Diptera: Tephritidae) in the same day and across days indicated that a single measurement was sufficient, and that FBD was consistent and repeatable. Insects under stress from starvation displayed shorter FBD over time, and we suggest that the measure also relates to the physical condition or survival fitness of the individual. Though somewhat laborious and time-consuming, we propose that FBD can be useful for research studies requiring individual-level phenome data and for obtaining estimates quality and dispersive movement for insects.

Path Meander of Male Codling Moths (Cydia pomonella) Foraging for Sex Pheromone Plumes: Field Validation of a Novel Method for Quantifying Path Meander of Random Movers Developed Using Computer Simulations

Simple Summary

Measures of insect movement patterns are key to understanding how insects forage for resources and mating opportunities in their environment. Directly observing large numbers of these small organisms can be extremely challenging, especially for flying insects in low light conditions such as codling moth (Cydia pomonella), a key pest of apple. Here we provide a novel approach to indirectly measure the path meander of randomly moving organisms. Computer simulations were used to simulate insect movement across a wide range of possible movement patterns, measured in circular standard deviation (c.s.d.) of turn angles between track segments. For each c.s.d., the pattern of catch across a rectangular grid of traps was plotted and the resulting exponential decay constant (k) of the fitted lines were used to generate a standard curve describing this linear relationship. Using this standard curve, field data from target organisms caught in the described trapping grid can reveal the pattern of movement employed by these movers. Here we have demonstrated methodology for indirect measure of the movement patterns employed by random walkers such as C. pomonella. While we employed codling moth as our model system, we suggest this approach could prove useful in a wide range of other systems.

Abstract

Measures of path meander are highly relevant to studies of optimal foraging by animals. However, directly recording paths of small animals such as insects can be difficult because of small size or crepuscular activity. Computer simulations of correlated random walkers demonstrated that the rates of decay in captures across a rectangular grid of traps when movers were released at its corner can be used to produce calibration curves for quantifying path meander indirectly. Simulations using spatial parameters matching those previously documented for male codling moths (Cydia pomonella (L.)) foraging for female pheromone plumes in the field predicted that meander, as measured in circular standard deviation (c.s.d.) of turn angles between track segments, should be ca. 50° and 30° when the target population density is high vs. low, respectively. Thus, if optimized, the mean value measured for C. pomonella populations encountering an unknown target density should fall between these limits. We recorded decay in C. pomonella catch across a 5 × 5 grid of pheromone-baited traps each separated by 15 m on 39 occasions where batches of ca. 800 males were released 10 m outside the corner of trapping grids arranged in five large Michigan apple orchards. This decay constant was translated into mean c.s.d value for path meander using the standard curve generated by the computer simulations. The measured decay constant for C. pomonella males was negative 0.99 ± 0.02 (S.E.M.), which translates to a path meander of 37 ± 2° c.s.d. Thus, the measured path meander of 37° fell between the 50° and 30° values optimal for dense and sparse populations, respectively. In addition to providing a rare documented example of optimal foraging for odor plumes, this research offers proof-of-concept for a novel approach to quantifying path meander of movers that could prove useful across diverse taxa.

Lévy like patterns in the small-scale movements of marsupials in an unfamiliar and risky environment

We investigate the movement patterns of three different Neotropical marsupials in an unfamiliar and risky environment. Animals are released in a matrix from which they try to reach a patch of forest. Their movements, performed on a small spacial scale, are best approximated by Lévy flights. Patterns of oriented and non-oriented individuals - with forest patches within or beyond their perceptual range - differ only slightly in the value of their exponents. These facts suggest that, for these species, the appearance of Lévy flights is the product of animals innate behaviour that emerges spontaneously, as a neutral characteristic proper of a default movement mode for alerted animals.

Navigational efficiency in a biased and correlated random walk model of individual animal movement

Understanding how an individual animal is able to navigate through its environment is a key question in movement ecology that can give insight into observed movement patterns and the mechanisms behind them. Efficiency of navigation is important for behavioral processes at a range of different spatio-temporal scales, including foraging and migration. Random walk models provide a standard framework for modeling individual animal movement and navigation. Here we consider a vector-weighted biased and correlated random walk (BCRW) model for directed movement (taxis), where external navigation cues are balanced with forward persistence. We derive a mathematical approximation of the expected navigational efficiency for any BCRW of this form and confirm the model predictions using simulations. We demonstrate how the navigational efficiency is related to the weighting given to forward persistence and external navigation cues, and highlight the counter-intuitive result that for low (but realistic) levels of error on forward persistence, a higher navigational efficiency is achieved by giving more weighting to this indirect navigation cue rather than direct navigational cues. We discuss and interpret the relevance of these results for understanding animal movement and navigation strategies.

Movement Path Tortuosity in Free Ambulation: Relationships to Age and Brain Disease

Ambulation is defined by duration, distance traversed, number and size of directional changes, and the interval separating successive movement episodes; more complex measures of ambulation can be created by aggregating these features. This review article of published findings defines random changes in direction during movement as "movement path tortuosity" and relates tortuosity to the understanding of cognitive impairments of persons of all ages. Path tortuosity is quantified by subjecting tracking data to fractal analysis, specifically Fractal Dimension (Fractal D), which ranges from a value of 1 when the movement path is perfectly straight to a value of 2 when the movement path is random, resembling the "drunkard's walk." The review elucidates the mathematical assumptions underlying Fractal D, its use in the analysis of movements of free ranging animals, and its application to the study of cognitive impairment and the prediction of falls in older adults. We conclude Fractal D offers a reliable, valid, sensitive, and easily interpreted real-time longitudinal measure of unrestricted movement path tortuosity unaffected by mobility aid use.

Adaptive source search in a gradient field

Most existing source search algorithms suffer from a high travel cost, and few of them have been analyzed in performance in noisy environments where local basins are presented. In this paper, the theseus gradient search (TGS) is proposed to effectively overcome local basins in search. Analytical performances of TGS and the gradient ascend with correlated random walk (GACRW), which is a variant of correlated random walk, are derived and compared. A gradient field model is proposed as an analytical tool that makes it feasible to analyze the performances. The analytical average searching costs of GACRW and TGS are obtained for the first time for this class of algorithms in the environments with local basins. The costs, expressed as functions of searching space size, local basin size, and local basin number are confirmed by simulation results. The performances of GACRW, TGS, and two chemotaxis algorithms are compared in the gradient field and a scenario of indoor radio source search in a hallway driven by real data of signal strengths. The results illustrate that GACRW and TGS are robust to noisy gradients and are more competitive than the chemotaxis-based algorithms in real applications. Both analytical and simulation results indicate that in the presence of local basins, TGS almost always costs the lowest.

Field Estimates of Attraction of Ceratitis capitata to Trimedlure and Bactrocera dorsalis (Diptera: Tephritidae) to Methyl Eugenol in Varying Environments

Measuring and modeling the attractiveness of semiochemical-baited traps is of significant importance to detection, delimitation, and control of invasive pests. Here, we describe the results of field mark-release-recapture experiments with Ceratitis capitata (Wiedemann) and Bactrocera dorsalis (Hendel) to estimate the relationship between distance from a trap baited with trimedlure and methyl eugenol, respectively, and probability of capture for a receptive male insect. Experiments were conducted using a grid of traps with a central release point at two sites on Hawaii Island, a Macadamia orchard on the East side of the island and a lava field on the West side. We found that for B. dorsalis and methyl eugenol there is a 65% probability of capture at ∼36 m from a single trap, regardless of habitat. For C. capitata, we found a 65% probability of capture at a distance of ∼14 m from a single trap in the orchard and 7 m in the lava field. We also present results on the spatial and temporal pattern of recaptures. The attraction data are analyzed via a hyperbolic secant-based capture probability model.

A computer model of insect traps in a landscape

Attractant-based trap networks are important elements of invasive insect detection, pest control, and basic research programs. We present a landscape-level, spatially explicit model of trap networks, focused on detection, that incorporates variable attractiveness of traps and a movement model for insect dispersion. We describe the model and validate its behavior using field trap data on networks targeting two species, Ceratitis capitata and Anoplophora glabripennis. Our model will assist efforts to optimize trap networks by 1) introducing an accessible and realistic mathematical characterization of the operation of a single trap that lends itself easily to parametrization via field experiments and 2) allowing direct quantification and comparison of sensitivity between trap networks. Results from the two case studies indicate that the relationship between number of traps and their spatial distribution and capture probability under the model is qualitatively dependent on the attractiveness of the traps, a result with important practical consequences.

Modelling foraging movements of diving predators: a theoretical study exploring the effect of heterogeneous landscapes on foraging efficiency

Foraging in the marine environment presents particular challenges for air-breathing predators. Information about prey capture rates, the strategies that diving predators use to maximise prey encounter rates and foraging success are still largely unknown and difficult to observe. As well, with the growing awareness of potential climate change impacts and the increasing interest in the development of renewable sources it is unknown how the foraging activity of diving predators such as seabirds will respond to both the presence of underwater structures and the potential corresponding changes in prey distributions. Motivated by this issue we developed a theoretical model to gain general understanding of how the foraging efficiency of diving predators may vary according to landscape structure and foraging strategy. Our theoretical model highlights that animal movements, intervals between prey capture and foraging efficiency are likely to critically depend on the distribution of the prey resource and the size and distribution of introduced underwater structures. For multiple prey loaders, changes in prey distribution affected the searching time necessary to catch a set amount of prey which in turn affected the foraging efficiency. The spatial aggregation of prey around small devices (∼ 9 × 9 m) created a valuable habitat for a successful foraging activity resulting in shorter intervals between prey captures and higher foraging efficiency. The presence of large devices (∼ 24 × 24 m) however represented an obstacle for predator movement, thus increasing the intervals between prey captures. In contrast, for single prey loaders the introduction of spatial aggregation of the resources did not represent an advantage suggesting that their foraging efficiency is more strongly affected by other factors such as the timing to find the first prey item which was found to occur faster in the presence of large devices. The development of this theoretical model represents a useful starting point to understand the energetic reasons for a range of potential predator responses to spatial heterogeneity and environmental uncertainties in terms of search behaviour and predator-prey interactions. We highlight future directions that integrated empirical and modelling studies should take to improve our ability to predict how diving predators will be impacted by the deployment of manmade structures in the marine environment.

Sampling animal movement paths causes turn autocorrelation

Animal movement models allow ecologists to study processes that operate over a wide range of scales. In order to study them, continuous movements of animals are translated into discrete data points, and then modelled as discrete models. This discretization can bias the representation of the movement path. This paper shows that discretizing correlated random movement paths creates a biased path by creating correlations between successive turning angles. The discretization also biases statistical tests for correlated random walks (CRW) and causes an overestimate in distances travelled; a correction is given for these biases. This effect suggests that there is a natural scale to CRWs, but that distance-discretized CRWs are in a sense, scale invariant. Perhaps a new null model for continuous movement paths is needed. Authors need to be aware of the biases caused by discretizing correlated random walks, and deal with them appropriately.

Adaptive collective decision-making in limited robot swarms without communication

In this work we investigate spatial collective decision-making in a swarm of microrobots, inspired by the thermotactic aggregation behavior of honeybees. The sensing and navigation capabilities of these robots are intentionally limited; no digital sensor data processing and no direct communication are allowed. In this way, we can approximate the features of smaller mesoscopic-scale systems and demonstrate that even such a limited swarm is nonetheless able to exhibit simple forms of intelligent and adaptive collective behavior.

Analysis of vertical distributions and effective flight layers of insects: three-dimensional simulation of flying insects and catch at trap heights

The mean height and standard deviation (SD) of flight is estimated for over 100 insect species from their catches on several trap heights reported in the literature. The iterative equations for calculating mean height and SD are presented. The mean flight height for 95% of the studies varied from 0.17 to 5.40 m, and the SD from 0.12 to 3.83 m. The relationship between SD and mean flight height (X) was SD = 0.711X(-0.7849), n = 123, R(2) = 0.63. In addition, the vertical trap catches were fit to normal distributions and analyzed for skew and kurtosis. The SD was used to calculate an effective flight layer used in transforming the spherical effective attraction radius (EAR) of pheromone-baited traps into a circular EAR(c) for use in two-dimensional encounter rate models of mass trapping and mating disruption using semiochemicals. The EAR/EAR(c) also serves to reveal the attractive strength and efficacy of putative pheromone blends. To determine the reliability of mean flight height and SD calculations from field trapping data, simulations of flying insects in three dimensions (3D) were performed. The simulations used an algorithm that caused individuals to roam freely at random but such that the population distributed vertically according to a normal distribution of specified mean and SD. Within this 3D arena, spherical traps were placed at various heights to determine the effects on catch and SD. The results indicate that data from previous field studies, when analyzed by the iterative equations, should provide good estimates of the population mean height and SD of flight.

Characteristic spatial and temporal scales unify models of animal movement

Animal movements have been modeled with diffusion at large scales and with more detailed movement models at smaller scales. We argue that the biologically relevant behavior of a wide class of movement models can be efficiently summarized with two parameters: the characteristic temporal and spatial scales of movement. We define these scales so that they describe movement behavior both at short scales (through the velocity autocorrelation function) and at long scales (through the diffusion coefficient). We derive these scales for two types of commonly used movement models: the discrete-step correlated random walk, with either constant or random step intervals, and the continuous-time correlated velocity model. For a given set of characteristic scales, the models produce very similar trajectories and encounter rates between moving searchers and stationary targets. Thus, we argue that characteristic scales provide a unifying currency that can be used to parameterize a wide range of ecological phenomena related to movement.

Truncated Lévy flights and agenda-based mobility are useful for the assessment of personal human exposure

Receptor-oriented approaches can assess the individual-specific exposure to air pollution. In such an individual-based model we analyse the impact of human mobility to the personal exposure that is perceived by individuals simulated in an exemplified urban area. The mobility models comprise random walk (reference point mobility, RPM), truncated Lévy flights (TLF), and agenda-based walk (RPMA). We describe and review the general concepts and provide an inter-comparison of these concepts. Stationary and ergodic behaviour are explained and applied as well as performance criteria for a comparative evaluation of the investigated algorithms. We find that none of the studied algorithm results in purely random trajectories. TLF and RPMA prove to be suitable for human mobility modelling, because they provide conditions for very individual-specific trajectories and exposure. Suggesting these models we demonstrate the plausibility of their results for exposure to air-borne benzene and the combined exposure to benzene and nonane.

Movement analyses of wood cricket ( Nemobius sylvestris) (Orthoptera: Gryllidae)

Information on the dispersal ability of invertebrate species associated with woodland habitats is severely lacking. Therefore, a study was conducted examining the movement patterns of wood cricket (Nemobius sylvestris) (Orthoptera: Gryllidae) on the Isle of Wight, UK. Juvenile (i.e. nymphs) and adult wood crickets were released and observed over time within different ground surface substrates. Their movement paths were recorded and subsequently analysed using random walk models. Nymphs were found to move more slowly than adults did; and, when given a choice, both nymphs and adults showed a preference for moving through or over leaf litter compared to bare soil or grass. A correlated random walk (CRW) model accurately described the movement pattern of adult wood crickets through leaf litter, indicating a level of directional persistence in their movements. The estimated population spread through leaf litter for adults was 17.9 cm min-1. Movements of nymphs through leaf litter could not accurately be described by a random walk model, showing a change in their movement pattern over time from directed to more random movements. The estimated population spread through leaf litter for nymphs was 10.1 cm min-1. The results indicate that wood cricket adults can be considered as more powerful dispersers than nymphs; however, further analysis of how the insects move through natural heterogeneous environments at a range of spatio-temporal scales needs to be performed to provide a complete understanding of the dispersal ability of the species.

Inherent high correlation of individual motility enhances population dispersal in a heterotrophic, planktonic protist

Quantitative linkages between individual organism movements and the resulting population distributions are fundamental to understanding a wide range of ecological processes, including rates of reproduction, consumption, and mortality, as well as the spread of diseases and invasions. Typically, quantitative data are collected on either movement behaviors or population distributions, rarely both. This study combines empirical observations and model simulations to gain a mechanistic understanding and predictive ability of the linkages between both individual movement behaviors and population distributions of a single-celled planktonic herbivore. In the laboratory, microscopic 3D movements and macroscopic population distributions were simultaneously quantified in a 1L tank, using automated video- and image-analysis routines. The vertical velocity component of cell movements was extracted from the empirical data and used to motivate a series of correlated random walk models that predicted population distributions. Validation of the model predictions with empirical data was essential to distinguish amongst a number of theoretically plausible model formulations. All model predictions captured the essence of the population redistribution (mean upward drift) but only models assuming long correlation times (minute), captured the variance in population distribution. Models assuming correlation times of 8 minutes predicted the least deviation from the empirical observations. Autocorrelation analysis of the empirical data failed to identify a de-correlation time in the up to 30-second-long swimming trajectories. These minute-scale estimates are considerably greater than previous estimates of second-scale correlation times. Considerable cell-to-cell variation and behavioral heterogeneity were critical to these results. Strongly correlated random walkers were predicted to have significantly greater dispersal distances and more rapid encounters with remote targets (e.g. resource patches, predators) than weakly correlated random walkers. The tendency to disperse rapidly in the absence of aggregative stimuli has important ramifications for the ecology and biogeography of planktonic organisms that perform this kind of random walk.

Organism movement is fundamental to how organisms interact with each other and the environment. Such movements are also important on the population level and determine the spread of disease and invasion, reproduction, consumption, and mortality. Theoretical ecologists have sought to predict population dispersal rates, which are often hard to measure, from individual movement behaviors, which are often easier to measure. This problem has been non-trivial. This manuscript contributes seldom available, simultaneously measured movement behaviors and population distributions of a single celled planktonic organism. The empirical data are used to distinguish amongst a set of plausible theoretical modeling approaches to suggest that organism movements are highly correlated, meaning movement direction and speed is consistent over several minutes. Previous estimates suggested persistence only lasted several seconds. Minute-scale correlations result in much more rapid organism dispersal and greater dispersal distance, indicating that organisms encounter and impact a greater portion of their surrounding habitat than previously suspected.

Evaluation of human mobility models, for exposure to air pollutants

The subject of the present study is to find the best way of making a simulation model for the exposure assessment of mobile individuals. For that purpose we consider and apply several very different approaches to model movement patterns in a more or less random way and compare them in terms of the exposure resulting for the individuals. The models combine random movement with agenda-driven movement. We do not aim to involve all details of real conditions into the models, but explain and review the general concepts and provide an inter-comparison of these concepts. Stationary and ergodic behaviour are explained and applied as well as performance criteria for a comparative evaluation of the investigated algorithms. In particular, the present study investigates the exposure to air contaminants of persons moving in heterogeneously polluted urban areas by help of movement simulations. For that purpose we applied four different movement algorithms: Lévy-modulated correlated random walk (LMCRW), Potential field controlled walk (PTW), Reference point mobility model (RPM), and RPM with a pre-defined daily agenda of targets (RPMA). We find that none of the studied algorithm results in purely random trajectories. PTW and RPMA prove to be suitable for human mobility modelling, because they provide conditions for very individual-specific trajectories and exposure. Suggesting these models we demonstrate the plausibility of their results for exposure to air-borne benzene and the combined exposure to benzene and nonane. It appears however that inter-individual variation in the individual-specific short-term exposure diminishes with runtime and when long-term exposure is considered.

Random walk models in biology

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.

Animal navigation: general properties of directed walks

The ability to locomote is a defining characteristic of all animals. Yet, all but the most trivial forms of navigation are poorly understood. Here we report and discuss the analytical results of an in-depth study of a simple navigation problem. In principle, there are two strategies for navigating a straight course. One is to use an external directional reference and to continually reorient with reference to it. The other is to monitor body rotations from internal sensory information only. We showed previously that, at least for simple representations of locomotion, the first strategy will enable an animal or mobile agent to move arbitrarily far away from its starting point, but the second strategy will not do so, even after an infinite number of steps. This paper extends and generalizes the earlier results by demonstrating that these findings are true even when a very general model of locomotion is used. In this general model, error components within individual steps are not independent, and directional errors may be biased. In the absence of a compass, the expected path of a directed walk in general approximates a logarithmic spiral. Some examples are given to illustrate potential applications of the quantitative results derived here. Motivated by the analytical results developed in this work, a nomenclature for directed walks is proposed and discussed. Issues related to path integration in mammals and robots, and measuring the curvature of a noisy path are also addressed using directed walk theory.