The influence of turning angles on the success of non-oriented animal searches

Dynamics, statistics, and task allocation of foraging ants

Ant foraging is one of the most fascinating examples of cooperative behavior observed in nature. It is well studied from an entomology viewpoint, but there is currently a lack of mathematical synthesis of this phenomenon. We address this by constructing an ant foraging model that incorporates simple behavioral rules within three task groups of the ant colony during foraging (foragers, transporters, and followers), pheromone trails, and memory effects. The motion of an ant is modeled as a discrete correlated random walk, with a characteristic zigzag path that is congruent with experimental data. We simulate the foraging cycle, which consists of ants searching for food, transporting food, and depositing chemical trails to recruit and orient more ants (en masse) to the food source. This allows us to gain insights into the basic mechanism of the cooperative interactions between ants and the dynamical division of labor within an ant colony during foraging to achieve optimal efficiency. We observe a disorder-order phase transition from the start to the end of a foraging process, signaling collective motion at the population level. Finally, we present a set of time delay ODEs that corroborates with numerical simulations.

Drosophila genotypes can be predicted from their exploration locomotive trajectories using supervised machine learning

This study employs supervised machine learning algorithms to test whether locomotive features during exploratory activity in open field arenas can serve as predictors for the genotype of fruit flies. Because of the nonlinearity in locomotive trajectories, traditional statistical methods that are used to compare exploratory activity between genotypes of fruit flies may not reveal all insights. 10-minute-long trajectories of four different genotypes of fruit flies in an open-field arena environment were captured. Turn angles and step size features extracted from the trajectories were used for training supervised learning models to predict the genotype of the fruit flies. Using the first five minute locomotive trajectories, an accuracy of 83% was achieved in differentiating wild-type flies from three other mutant genotypes. Using the final 5 min and the entire ten minute duration decreased the performance indicating that the most variations between the genotypes in their exploratory activity are exhibited in the first few minutes. Feature importance analysis revealed that turn angle is a better predictor than step size in predicting fruit fly genotype. Overall, this study demonstrates that features of trajectories can be used to predict the genotype of fruit flies through supervised machine learning methods.

Logging, linear features, and human infrastructure shape the spatial dynamics of wolf predation on an ungulate neonate

Humans are increasingly recognized as important players in predator-prey dynamics by modifying landscapes. This trend has been well-documented for large mammal communities in North American boreal forests: logging creates early seral forests that benefit ungulates such as white-tailed deer (Odocoileus virginianus), while the combination of infrastructure development and resource extraction practices generate linear features that allow predators such as wolves (Canis lupus) to travel and forage more efficiently throughout the landscape. Disturbances from recreational activities and residential development are other major sources of human activity in boreal ecosystems that may further alter wolf-ungulate dynamics. Here, we evaluate the influence that several major types of anthropogenic landscape modifications (timber harvest, linear features, and residential infrastructure) have on where and how wolves hunt ungulate neonates in a southern boreal forest ecosystem in Minnesota, USA. We demonstrate that each major anthropogenic disturbance significantly influences wolf predation of white-tailed deer fawns (n = 427 kill sites). In contrast with the "human shield hypothesis" that posits prey use human-modified areas as refuge, wolves killed fawns closer to residential buildings than expected based on spatial availability. Fawns were also killed within recently-logged areas more than expected. Concealment cover was higher at kill sites than random sites, suggesting wolves use senses other than vision, probably olfaction, to detect hidden fawns. Wolves showed strong selection for hunting along linear features, and kill sites were also closer to linear features than expected. We hypothesize that linear features facilitated wolf predation on fawns by allowing wolves to travel efficiently among high-quality prey patches (recently logged areas, near buildings), and also increase encounter rates with olfactory cues that allow them to detect hidden fawns. These findings provide novel insight into the strategies predators use to hunt ungulate neonates and the many ways human activity alters wolf-ungulate neonate predator-prey dynamics, which have remained elusive due to the challenges of locating sites where predators kill small prey. Our research has important management and conservation implications for wolf-ungulate systems subjected to anthropogenic pressures, particularly as the range of overlap between wolves and deer expands and appears to be altering food web dynamics in boreal ecosystems.

Ants combine systematic meandering and correlated random walks when searching for unknown resources

Animal search movements are typically assumed to be mostly random walks, although non-random elements may be widespread. We tracked ants (Temnothorax rugatulus) in a large empty arena, resulting in almost 5 km of trajectories. We tested for meandering by comparing the turn autocorrelations for empirical ant tracks and simulated, realistic Correlated Random Walks. We found that 78% of ants show significant negative autocorrelation around 10 mm (3 body lengths). This means that turns in one direction are likely followed by turns in the opposite direction after this distance. This meandering likely makes the search more efficient, as it allows ants to avoid crossing their own paths while staying close to the nest, avoiding return-travel time. Combining systematic search with stochastic elements may make the strategy less vulnerable to directional inaccuracies. This study is the first to find evidence for efficient search by regular meandering in a freely searching animal.

Making Drawings Speak Through Mathematical Metrics

Figurative drawing is a skill that takes time to learn, and it evolves during different childhood phases that begin with scribbling and end with representational drawing. Between these phases, it is difficult to assess when and how children demonstrate intentions and representativeness in their drawings. The marks produced are increasingly goal-oriented and efficient as the child's skills progress from scribbles to figurative drawings. Pre-figurative activities provide an opportunity to focus on drawing processes. We applied fourteen metrics to two different datasets (N = 65 and N = 344) to better understand the intentional and representational processes behind drawing, and combined these metrics using principal component analysis (PCA) in different biologically significant dimensions. Three dimensions were identified: efficiency based on spatial metrics, diversity with color metrics, and temporal sequentiality. The metrics at play in each dimension are similar for both datasets, and PCA explains 77% of the variance in both datasets. Gender had no effect, but age influenced all three dimensions differently. These analyses for instance differentiate scribbles by children from those drawn by adults. The three dimensions highlighted by this study provide a better understanding of the emergence of intentions and representativeness in drawings. We discussed the perspectives of such findings in comparative psychology and evolutionary anthropology.

Movement ecology of vulnerable lowland tapirs between areas of varying human disturbance

BACKGROUND

Animal movement is a key ecological process that is tightly coupled to local environmental conditions. While agriculture, urbanisation, and transportation infrastructure are critical to human socio-economic improvement, these have spurred substantial changes in animal movement across the globe with potential impacts on fitness and survival. Notably, however, human disturbance can have differential effects across species, and responses to human activities are thus largely taxa and context specific. As human disturbance is only expected to worsen over the next decade it is critical to better understand how species respond to human disturbance in order to develop effective, case-specific conservation strategies.

METHODS

Here, we use an extensive telemetry dataset collected over 22 years to fill a critical knowledge gap in the movement ecology of lowland tapirs (Tapirus terrestris) across areas of varying human disturbance within three biomes in southern Brazil: the Pantanal, Cerrado, and Atlantic Forest.

RESULTS

From these data we found that the mean home range size across all monitored tapirs was 8.31 km² (95% CI 6.53-10.42), with no evidence that home range sizes differed between sexes nor age groups. Interestingly, although the Atlantic Forest, Cerrado, and Pantanal vary substantially in habitat composition, levels of human disturbance, and tapir population densities, we found that lowland tapir movement behaviour and space use were consistent across all three biomes. Human disturbance also had no detectable effect on lowland tapir movement. Lowland tapirs living in the most altered habitats we monitored exhibited movement behaviour that was comparable to that of tapirs living in a near pristine environment.

CONCLUSIONS

Contrary to our expectations, although we observed individual variability in lowland tapir space use and movement, human impacts on the landscape also had no measurable effect on their movement. Lowland tapir movement behaviour thus appears to exhibit very little phenotypic plasticity in response to human disturbance. Crucially, the lack of any detectable response to anthropogenic disturbance suggests that human modified habitats risk being ecological traps for tapirs and this information should be factored into conservation actions and species management aimed towards protecting lowland tapir populations.

Potential-driven random walks on interconnected systems

Interconnected systems have to route information to function properly: At the lowest scale neural cells exchange electrochemical signals to communicate, while at larger scales animals and humans move between distinct spatial patches and machines exchange information via the Internet through communication protocols. Nontrivial patterns emerge from the analysis of information flows, which are not captured either by broadcasting, such as in random walks, or by geodesic routing, such as shortest paths. In fact, alternative models between those extreme protocols are still eluding us. Here we propose a class of stochastic processes, based on biased random walks, where agents are driven by a physical potential pervading the underlying network topology. By considering a generalized Coulomb dependence on the distance on destination(s), we show that it is possible to interpolate between random walk and geodesic routing in a simple and effective way. We demonstrate that it is not possible to find a one-size-fit-all solution to efficient navigation and that network heterogeneity or modularity has measurable effects. We illustrate how our framework can describe the movements of animals and humans, capturing with a stylized model some measurable features of the latter. From a methodological perspective, our potential-driven random walks open the doors to a broad spectrum of analytical tools, ranging from random-walk centralities to geometry induced by potential-driven network processes.

A recipe for an optimal power law tailed walk

Lévy-like movements, which are an asymptotic power law tailed distribution with an upper cutoff, are known to represent an optimal search strategy in an unknown environment. Organisms seem to show a Lévy walk when μ ≈ 2.0. In the present study, I investigate how such a walk can emerge as a result of the decision making process of a single walker. In my proposed algorithm, a walker avoids a certain direction; this may be related to the emergence of a Lévy walk. Instead of remembering all visited positions, the walker in my algorithm uses and remembers only the direction from which it has come. Moreover, the walker sometimes reconsiders and alters the directions it avoids if it experiences some directional inconsistencies in a series of recent directional moves, i.e., the walker moves in a different direction from the previous one. My results show that a walker can demonstrate power law tailed movements over a long period with an optimal μ.

Transient dynamics in a nonequilibrium superdiffusive reaction-diffusion process: Nonequilibrium random search as a case study

Transient regimes, often difficult to characterize, can be fundamental in establishing final steady states features of reaction-diffusion phenomena. This is particularly true in ecological problems. Here, through both numerical simulations and an analytic approximation, we analyze the transient of a nonequilibrium superdiffusive random search when the targets are created at a certain rate and annihilated upon encounters (a key dynamics, e.g., in biological foraging). The steady state is achieved when the number of targets stabilizes to a constant value. Our results unveil how key features of the steady state are closely associated to the particularities of the initial evolution. The searching efficiency variation in time is also obtained. It presents a rather surprising universal behavior at the asymptotic limit. These analyses shed some light into the general relevance of transients in reaction-diffusion systems.

The importance of including habitat-specific behaviour in models of butterfly movement

Dispersal is a key process affecting population persistence and major factors affecting dispersal rates are the amounts, connectedness and properties of habitats in landscapes. We present new data on the butterfly Maniola jurtina in flower-rich and flower-poor habitats that demonstrates how movement and behaviour differ between sexes and habitat types, and how this effects consequent dispersal rates. Females had higher flight speeds than males, but their total time in flight was four times less. The effect of habitat type was strong for both sexes, flight speeds were ~ 2.5 × and ~ 1.7 × faster on resource-poor habitats for males and females, respectively, and flights were approximately 50% longer. With few exceptions females oviposited in the mown grass habitat, likely because growing grass offers better food for emerging caterpillars, but they foraged in the resource-rich habitat. It seems that females faced a trade-off between ovipositing without foraging in the mown grass or foraging without ovipositing where flowers were abundant. We show that taking account of habitat-dependent differences in activity, here categorised as flight or non-flight, is crucial to obtaining good fits of an individual-based model to observed movement. An important implication of this finding is that incorporating habitat-specific activity budgets is likely necessary for predicting longer-term dispersal in heterogeneous habitats, as habitat-specific behaviour substantially influences the mean (> 30% difference) and kurtosis (1.4 × difference) of dispersal kernels. The presented IBMs provide a simple method to explicitly incorporate known activity and movement rates when predicting dispersal in changing and heterogeneous landscapes.

Two-dimensional active motion

The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

Enhancing oncolytic virotherapy: Observations from a Voronoi Cell-Based model

Oncolytic virotherapy is a promising cancer treatment using genetically modified viruses. Unfortunately, virus particles rapidly decay inside the body, significantly hindering their efficacy. In this article, treatment perturbations that could overcome obstacles to oncolytic virotherapy are investigated through the development of a Voronoi Cell-Based model (VCBM). The VCBM derived captures the interaction between an oncolytic virus and cancer cells in a 2-dimensional setting by using an agent-based model, where cell edges are designated by a Voronoi tessellation. Here, we investigate the sensitivity of treatment efficacy to the configuration of the treatment injections for different tumour shapes: circular, rectangular and irregular. The model predicts that multiple off-centre injections improve treatment efficacy irrespective of tumour shape. Additionally, we investigate delaying the infection of cancer cells by modifying viral particles with a substance such as alginate (a hydrogel polymer used in a range of cancer treatments). Simulations of the VCBM show that delaying the infection of cancer cells, and thus allowing more time for virus dissemination, can improve the efficacy of oncolytic virotherapy. The simulated treatment noticeably decreases the tumour size with no increase in toxicity. Improving oncolytic virotherapy in this way allows for a more effective treatment without changing its fundamental essence.

Adaptive switch to sexually dimorphic movements by partner-seeking termites

How should females and males move to search for partners whose exact location is unknown? Theory predicts that the answer depends on what they know about where targets can be found, raising the question of how actual animals update their mate search patterns to increase encounter probability when conditions change. Here, we show that termites adaptively alternate between sexually monomorphic and dimorphic movements during mate search. When the location of potential mates was completely unpredictable, both sexes moved in straight lines to explore widely. In contrast, when the stray partner was at least nearby, males moved while females paused. Data-based simulations confirmed that these movements increase the rate of successful encounters. The context-dependent switch of search modes is a key to enhance random encounters.

A mechanistic theory of personality-dependent movement behaviour based on dynamic energy budgets

Consistent between-individual differences in movement are widely recognised across taxa. In addition, foraging plasticity at the within-individual level suggests a behavioural dependency on the internal energy demand. Because behaviour co-varies with fast-slow life history (LH) strategies in an adaptive context, as theoretically predicted by the pace-of-life syndrome hypothesis, mass/energy fluxes should link behaviour and its plasticity with physiology at both between- and within-individual levels. However, a mechanistic framework driving these links in a fluctuating ecological context is lacking. Focusing on home range behaviour, we propose a novel behavioural-bioenergetics theoretical model to address such complexities at the individual level based on energy balance. We propose explicit mechanistic links between behaviour, physiology/metabolism and LH by merging two well-founded theories, the movement ecology paradigm and the dynamic energetic budget theory. Overall, our behavioural-bioenergetics model integrates the mechanisms explaining how (1) behavioural between- and within-individual variabilities connect with internal state variable dynamics, (2) physiology and behaviour are explicitly interconnected by mass/energy fluxes, and (3) different LHs may arise from both behavioural and physiological variabilities in a given ecological context. Our novel theoretical model reveals encouraging opportunities for empiricists and theoreticians to delve into the eco-evolutionary processes that favour or hinder the development of between-individual differences in behaviour and the evolution of personality-dependent movement syndromes.

The evolutionary origins of Lévy walk foraging

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ²). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

Effects of environmental factors and landscape features on movement patterns of Florida black bears

A greater understanding of how environmental factors and anthropogenic landscape features influence animal movements can inform management and potentially aid in mitigating human–wildlife conflicts. We investigated the movement patterns of 16 Florida black bears (Ursus americanus floridanus; 6 females, 10 males) in north-central Florida at multiple temporal scales using GPS data collected from 2011 to 2014. We calculated bi-hourly step-lengths and directional persistence, as well as daily and weekly observed displacements and expected displacements. We used those movement metrics as response variables in linear mixed models and tested for effects of sex, season, and landscape features. We found that step-lengths of males were generally longer than step-lengths of females, and both sexes had the shortest step-lengths during the daytime. Bears moved more slowly (shorter step-lengths) and exhibited less directed movement when near creeks, in forested wetlands, and in marsh habitats, possibly indicating foraging behavior. In urban areas, bears moved more quickly (longer step-lengths) and along more directed paths. The results were similar across all temporal scales. Major roads tended to act as a semipermeable barrier to bear movement. Males crossed major roads more frequently than females but both sexes crossed major roads much less frequently than minor roads. Our findings regarding the influence of landscape and habitat features on movement patterns of Florida black bears could be useful for planning effective wildlife corridors and understanding how future residential or commercial development and road expansions may affect animal movement.

Escape rate and diffusion of a Stochastically Driven particle

The dynamical properties of a tracer repeatedly colliding with heat bath particles can be described within a Langevin framework provided that the tracer is more massive than the bath particles, and that the collisions are frequent. Here we consider the escape of a particle from a potential well, and the diffusion coefficient in a periodic potential, without making these assumptions. We have thus investigated the dynamical properties of a Stochastically Driven particle that moves under the influence of the confining potential in between successive collisions with the heat bath. In the overdamped limit, both the escape rate and the diffusion coefficient coincide with those of a Langevin particle. Conversely, in the underdamped limit the two dynamics have a different temperature dependence. In particular, at low temperature the Stochastically Driven particle has a smaller escape rate, but a larger diffusion coefficient.

Diffusion of active chiral particles

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v[over ̂] at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

The Spatial Dynamics of Predators and the Benefits and Costs of Sharing Information

Predators of all kinds, be they lions hunting in the Serengeti or fishermen searching for their catch, display various collective strategies. A common strategy is to share information about the location of prey. However, depending on the spatial characteristics and mobility of predators and prey, information sharing can either improve or hinder individual success. Here, our goal is to investigate the interacting effects of space and information sharing on predation efficiency, represented by the expected rate at which prey are found and consumed. We derive a feeding functional response that accounts for both spatio-temporal heterogeneity and communication, and validate this mathematical analysis with a computational agent-based model. This agent-based model has an explicit yet minimal representation of space, as well as information sharing about the location of prey. The analytical model simplifies predator behavior into a few discrete states and one essential trade-off, between the individual benefit of acquiring information and the cost of creating spatial and temporal correlation between predators. Despite the absence of an explicit spatial dimension in these equations, they quantitatively predict the predator consumption rates measured in the agent-based simulations across the explored parameter space. Together, the mathematical analysis and agent-based simulations identify the conditions for when there is a benefit to sharing information, and also when there is a cost.

When should we work together and when should we work alone? This question is central to our efforts to understand social and ecological systems alike, from lions hunting in the Serengeti to fishermen searching for their catch. Here, we develop a mathematical modeling framework to identify the essential spatial factors controlling the benefits and costs of sharing information. Our approach marries computation with mathematical analysis, and our results highlight that it is only under certain spatial conditions that information sharing is a useful cooperative strategy. Notably, we find conditions for which fully collective and fully individual search are both attractive.

Efficient search of multiple types of targets

Random searches often take place in fragmented landscapes. Also, in many instances like animal foraging, significant benefits to the searcher arise from visits to a large diversity of patches with a well-balanced distribution of targets found. Up to date, such aspects have been widely ignored in the usual single-objective analysis of search efficiency, in which one seeks to maximize just the number of targets found per distance traversed. Here we address the problem of determining the best strategies for the random search when these multiple-objective factors play a key role in the process. We consider a figure of merit (efficiency function), which properly "scores" the mentioned tasks. By considering random walk searchers with a power-law asymptotic Lévy distribution of step lengths, p(ℓ)∼ℓ(-μ), with 1<μ≤3, we show that the standard optimal strategy with μ(opt)≈2 no longer holds universally. Instead, optimal searches with enhanced superdiffusivity emerge, including values as low as μ(opt)≈1.3 (i.e., tending to the ballistic limit). For the general theory of random search optimization, our findings emphasize the necessity to correctly characterize the multitude of aims in any concrete metric to compare among possible candidates to efficient strategies. In the context of animal foraging, our results might explain some empirical data pointing to stronger superdiffusion (μ<2) in the search behavior of different animal species, conceivably associated to multiple goals to be achieved in fragmented landscapes.

Inferring Lévy walks from curved trajectories: A rescaling method

An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D).

Survival in patchy landscapes: the interplay between dispersal, habitat loss and fragmentation

Habitat loss and fragmentation are important factors determining animal population dynamics and spatial distribution. Such landscape changes can lead to the deleterious impact of a significant drop in the number of species, caused by critically reduced survival rates for organisms. In order to obtain a deeper understanding of the threeway interplay between habitat loss, fragmentation and survival rates, we propose here a spatially explicit multi-scaled movement model of individuals that search for habitat. By considering basic ecological processes, such as predation, starvation (outside the habitat area), and competition, together with dispersal movement as a link among habitat areas, we show that a higher survival rate is achieved in instances with a lower number of patches of larger areas. Our results demonstrate how movement may counterbalance the effects of habitat loss and fragmentation in altered landscapes. In particular, they have important implications for conservation planning and ecosystem management, including the design of specific features of conservation areas in order to enhance landscape connectivity and population viability.

Tortuosity entropy: a measure of spatial complexity of behavioral changes in animal movement

The goal of animal movement analysis is to understand how organisms explore and exploit complex and varying environments. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviours to highly random behaviours. It has been a common method to assess movement efficiency and foraging strategies by means of quantifying and analyzing movement trajectories. Here we introduce a tortuosity entropy (TorEn), a simple measure for quantifying the behavioral change in animal movement data. In our approach, the differences between pairwise successive track points are transformed into symbolic sequences, then we map these symbols into a group of pattern vectors and calculate the information entropy of pattern vectors. We test the algorithm on both simulated trajectories and real trajectories to show that it can accurately identify not only the mixed segments in simulated data, but also the different phases in real movement data. Tortuosity entropy can be easily applied to arbitrary real-world data, whether deterministic or stochastic, stationary or non-stationary. It could be a promising tool to reveal behavioral mechanism in movement data.

Normal and tumoral melanocytes exhibit q-Gaussian random search patterns

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.

Unveiling a mechanism for species decline in fragmented habitats: fragmentation induced reduction in encounter rates

Several studies have reported that fragmentation (e.g. of anthropogenic origin) of habitats often leads to a decrease in the number of species in the region. An important mechanism causing this adverse ecological impact is the change in the encounter rates (i.e. the rates at which individuals meet other organisms of the same or different species). Yet, how fragmentation can change encounter rates is poorly understood. To gain insight into the problem, here we ask how landscape fragmentation affects encounter rates when all other relevant variables remain fixed. We present strong numerical evidence that fragmentation decreases search efficiencies thus encounter rates. What is surprising is that it falls even when the global average densities of interacting organisms are held constant. In other words, fragmentation per se can reduce encounter rates. As encounter rates are fundamental for biological interactions, it can explain part of the observed diminishing in animal biodiversity. Neglecting this effect may underestimate the negative outcomes of fragmentation. Partial deforestation and roads that cut through forests, for instance, might be responsible for far greater damage than thought. Preservation policies should take into account this previously overlooked scientific fact.

Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models

BACKGROUND

In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion.

RESULTS

Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk.

CONCLUSION

We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the "move" package for R.

Spatial foraging in free ranging bearded sakis: traveling salesmen or Lévy Walkers?

According to optimal foraging theory and most current models of primate socioecology, primate foraging involves a series of decisions concerning when is the most optimal time to leave a food patch, how to travel to the next patch in an efficient manner, and how to minimize the time and distance traveled to all patches throughout the course of the day. In this study, I assess how bearded sakis solve these challenges by presenting data on their patch use, distance minimization, and by comparing their movements with non-deterministic foraging patterns. The study group, composed of 38 ± 15 individuals, fed significantly longer in higher quality patches (quality defined by patch size and productivity) and in those that contained ripe fruit pulp. However, group size was not a significant predictor of patch occupancy. Bearded sakis traveled relatively directly between food patches, sometimes over distances > 300 m. In addition, they chose the optimal daily path among all patches visited on 9 of 17 occasions, and on average traveled only 21% more than the least distance route. Bearded saki step lengths were consistent with a Brownian rather than a Lévy Walk pattern while waiting times were consistent with a Lévy pattern. However, the distribution of their turning angles indicated a high degree of directional persistence between patches. These results suggest that bearded sakis exploit food patches that are randomly distributed spatially but heterogenous in patch quality. They appear to encode the locations of high quality food patches and minimize travel between them, despite opportunistically feeding from more abundant and randomly distributed, lower quality patches en route.

Individual-to-resource landscape interaction strength can explain different collective feeding behaviours

Taking in sufficient quantities of nutrients is vital for all living beings and in doing so, individuals interact with the local resource environment. Here, we focus explicitly on the interactions between feeding individuals and the resource landscape. In particular, we are interested in the emergent movement dynamics resulting from these interactions. We present an individual-based simulation model for the movement of populations in a resource landscape that allows us to vary the strength of the interactions mentioned above. The key assumption and novelty of our model is that individuals can cause the release of additional nutrients, as well as consuming them. Our model produces clear predictions. For example, we expect more tortuous individual movement paths and higher levels of aggregation in populations occupying homogeneous environments where individual movement makes more nutrients available. We also show how observed movement dynamics could change when local nutrient sources are depleted or when the population density increases. Our predictions are testable and qualitatively reproduce the different feeding behaviours observed in filter-feeding ducks, for example. We suggest that considering two-way interactions between feeding individuals and resource landscapes could help to explain fine-scale movement dynamics.

Exploration-exploitation trade-off features a saltatory search behaviour

Searching experiments conducted in different virtual environments over a gender-balanced group of people revealed a gender irrelevant scale-free spread of searching activity on large spatio-temporal scales. We have suggested and solved analytically a simple statistical model of the coherent-noise type describing the exploration-exploitation trade-off in humans ('should I stay' or 'should I go'). The model exhibits a variety of saltatory behaviours, ranging from Lévy flights occurring under uncertainty to Brownian walks performed by a treasure hunter confident of the eventual success.

Emergence of an optimal search strategy from a simple random walk

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.

Foraging parameters influencing the detection and interpretation of area-restricted search behaviour in marine predators: a case study with the masked booby

Identification of Area-restricted search (ARS) behaviour is used to better understand foraging movements and strategies of marine predators. Track-based descriptive analyses are commonly used to detect ARS behaviour, but they may be biased by factors such as foraging trip duration or non-foraging behaviours (i.e. resting on the water). Using first-passage time analysis we tested if (I) daylight resting at the sea surface positions falsely increase the detection of ARS behaviour and (II) short foraging trips are less likely to include ARS behaviour in Masked Boobies Sula dactylatra. We further analysed whether ARS behaviour may be used as a proxy to identify important feeding areas. Depth-acceleration and GPS-loggers were simultaneously deployed on chick-rearing adults to obtain (1) location data every 4 minutes and (2) detailed foraging activity such as diving rates, time spent sitting on the water surface and in flight. In 82% of 50 foraging trips, birds adopted ARS behaviour. In 19.3% of 57 detected ARS zones, birds spent more than 70% of total ARS duration resting on the water, suggesting that these ARS zones were falsely detected. Based on generalized linear mixed models, the probability of detecting false ARS zones was 80%. False ARS zones mostly occurred during short trips in close proximity to the colony, with low or no diving activity. This demonstrates the need to account for resting on the water surface positions in marine animals when determining ARS behaviour based on foraging locations. Dive rates were positively correlated with trip duration and the probability of ARS behaviour increased with increasing number of dives, suggesting that the adoption of ARS behaviour in Masked Boobies is linked to enhanced foraging activity. We conclude that ARS behaviour may be used as a proxy to identify important feeding areas in this species.

Modeling novelty habituation during exploratory activity in Drosophila

Habituation is a common form of non-associative learning in which the organism gradually decreases its response to repeated stimuli. The decrease in exploratory activity of many animal species during exposure to a novel open field arena is a widely studied habituation paradigm. However, a theoretical framework to quantify how the novelty of the arena is learned during habituation is currently missing. Drosophila melanogaster display a high mean absolute activity and a high probability for directional persistence when first introduced to a novel arena. Both measures decrease during habituation to the arena. Here, we propose a phenomenological model of habituation for Drosophila exploration based on two principles: Drosophila form a spatial representation of the arena edge as a set of connected local patches, and repeated exposure to these patches is essential for the habituation of the novelty. The level of exposure depends on the number of visitations and is quantified by a variable referred to as "coverage". This model was tested by comparing predictions against the experimentally measured behavior of wild type Drosophila. The novelty habituation of wild type Canton-S depends on coverage and is specifically independent of the arena radius. Our model describes the time dependent locomotor activity, ΔD, of Canton-S using an experimentally established stochastic process Pn(ΔD), which depends on the coverage. The quantitative measures of exploration and habituation were further applied to three mutant genotypes. Consistent with a requirement for vision in novelty habituation, blind no receptor potential A(7) mutants display a failure in the decay of probability for directional persistence and mean absolute activity. The rutabaga(2080) habituation mutant also shows defects in these measures. The kurtz(1) non-visual arrestin mutant demonstrates a rapid decay in these measures, implying reduced motivation. The model and the habituation measures offer a powerful framework for understanding mechanisms associated with open field habituation.

Constructing a stochastic model of bumblebee flights from experimental data

The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and energy constraints. As the number of factors is large, it is very hard to build comprehensive movement models. Even when movement patterns in simple environments are analysed, the organisms can display very complex behaviours. While for largely undirected motion or long observation times the dynamics can sometimes be described by isotropic random walks, usually the directional persistence due to a preference to move forward has to be accounted for, e.g., by a correlated random walk. In this paper we generalise these descriptions to a model in terms of stochastic differential equations of Langevin type, which we use to analyse experimental search flight data of foraging bumblebees. Using parameter estimates we discuss the differences and similarities to correlated random walks. From simulations we generate artificial bumblebee trajectories which we use as a validation by comparing the generated ones to the experimental data.

Females roam while males patrol: divergence in breeding season movements of pack-ice polar bears (Ursus maritimus)

Intraspecific differences in movement behaviour reflect different tactics used by individuals or sexes to favour strategies that maximize fitness. We report movement data collected from n = 23 adult male polar bears with novel ear-attached transmitters in two separate pack ice subpopulations over five breeding seasons. We compared movements with n = 26 concurrently tagged adult females, and analysed velocities, movement tortuosity, range sizes and habitat selection with respect to sex, reproductive status and body mass. There were no differences in 4-day displacements or sea ice habitat selection for sex or population. By contrast, adult females in all years and both populations had significantly more linear movements and significantly larger breeding range sizes than males. We hypothesized that differences were related to encounter rates, and used observed movement metrics to parametrize a simulation model of male-male and male-female encounter. The simulation showed that the more tortuous movement of males leads to significantly longer times to male-male encounter, while having little impact on male-female encounter. By contrast, linear movements of females are consistent with a prioritized search for sparsely distributed prey. These results suggest a possible mechanism for explaining the smaller breeding range sizes of some solitary male carnivores compared to females.

On higher ground: how well can dynamic body acceleration determine speed in variable terrain?

Introduction

Animal travel speed is an ecologically significant parameter, with implications for the study of energetics and animal behaviour. It is also necessary for the calculation of animal paths by dead-reckoning. Dead-reckoning uses heading and speed to calculate an animal’s path through its environment on a fine scale. It is often used in aquatic environments, where transmission telemetry is difficult. However, its adoption for tracking terrestrial animals is limited by our ability to measure speed accurately on a fine scale. Recently, tri-axial accelerometers have shown promise for estimating speed, but their accuracy appears affected by changes in substrate and surface gradients. The purpose of the present study was to evaluate four metrics of acceleration; Overall dynamic body acceleration (ODBA), vectorial dynamic body acceleration (VDBA), acceleration peak frequency and acceleration peak amplitude, as proxies for speed over hard, soft and inclined surfaces, using humans as a model species.

Results

A general linear model (GLM) showed a significant difference in the relationships between the metrics and speed depending on substrate or surface gradient. When the data from all surface types were considered together, VeDBA had the highest coefficient of determination.

Conclusions

All of the metrics showed some variation in their relationship with speed according to the surface type. This indicates that changes in the substrate or surface gradient during locomotion by animals would produce errors in speed estimates, and also in dead-reckoned tracks if they were calculated from speeds based entirely on a priori calibrations. However, we describe a method by which the relationship between acceleration metrics and speed can be corrected ad hoc, until tracks accord with periodic ground truthed positions, obtained via a secondary means (e.g. VHF or GPS telemetry). In this way, dead-reckoning provides a means to obtain fine scale movement data for terrestrial animals, without the need for additional data on substrate or gradient.