Optimal Lévy-flight foraging in a finite landscape

Optimal foraging strategies for mutually avoiding competitors

Many animals are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy-tailed Lévy distribution. Previous studies have shown that, under sparse and random resource conditions, solitary non-destructive (with regenerating resources) foragers perform a maximally efficient search with Lévy exponent μ equal to 2, while for destructive foragers, efficiency decreases with μ monotonically and there is no optimal μ. However, in nature, there also exist situations where multiple foragers, displaying avoidance behavior, interact with each other competitively. To understand the effects of such competition, we develop a stochastic agent-based simulation that models competitive foraging among mutually avoiding individuals by incorporating an avoidance zone, or territory, of a certain size around each forager which is not accessible for foraging by other competitors. For non-destructive foraging, our results show that with increasing size of the territory and number of agents the optimal Lévy exponent is still approximately 2 while the overall efficiency of the search decreases. At low values of the Lévy exponent, however, increasing territory size actually increases efficiency. For destructive foraging, we show that certain kinds of avoidance can lead to qualitatively different behavior from solitary foraging, such as the existence of an optimal search with 1<μ<2. Finally, we show that the variance among the efficiencies of the agents increases with increasing Lévy exponent for both solitary and competing foragers, suggesting that reducing variance might be a selective pressure for foragers adopting lower values of μ. Taken together, our results suggest that, for multiple foragers, mutual avoidance and efficiency variance among individuals can lead to optimal Lévy searches with exponents different from those for solitary foragers.

Parallelization of Array Method with Hybrid Programming: OpenMP and MPI

For parallelization of applications with high processing times and large amounts of storage in High Performance Computing (HPC) systems, shared memory programming and distributed memory programming have been used; a parallel application is represented by Parallel Task Graphs (PTGs) using Directed Acyclic Graphs (DAGs). For the execution of PTGs in HPC systems, a scheduler is executed in two phases: scheduling and allocation; the execution of the scheduler is considered an NP-complete combinatorial problem and requires large amounts of storage and long processing times. Array Method (AM) is a scheduler to execute the task schedule in a set of clusters; this method was programmed sequentially, analyzed and tested using real and synthetic application workloads in previous work. Analyzing the proposed designs of this method in this research work, the parallelization of the method is extended using hybrid OpenMP and MPI programming in a server farm and using a set of geographically distributed clusters; at the same time, a novel method for searching free resources in clusters using Lévy random walks is proposed. Synthetic and real workloads have been experimented with to evaluate the performance of the new parallel schedule and compare it to the sequential schedule. The metrics of makespan, waiting time, quality of assignments and search for free resources were evaluated; the results obtained and described in the experiments section show a better performance with the new version of the parallel algorithm compared to the sequential version. By using the parallel approach with hybrid programming applied to the extraction of characteristics of the PTGs, applied to the search for geographically distributed resources with Lévy random walks and applied to the metaheuristic used, the results of the metrics are improved. The makespan is decreased even when the loads increase, the times of the tasks in the waiting queue are decreased, the quality of assignments in the clusters is improved by causing the tasks with their subtasks to be assigned in the same clusters or in cluster neighbors and, finally, the searches for free resources are executed in different geographically distributed clusters, not sequentially.

Foraging behaviour and patch size distribution jointly determine population dynamics in fragmented landscapes

Increased fragmentation caused by habitat loss represents a major threat to the persistence of animal populations. How fragmentation affects populations depends on the rate at which individuals move between spatially separated patches. Whereas negative effects of habitat loss on biodiversity are well known, the effects of fragmentation per se on population dynamics and ecosystem stability remain less well understood. Here, we use a spatially explicit predator-prey model to investigate how the interplay between fragmentation and optimal foraging behaviour affects predator-prey interactions and, subsequently, ecosystem stability. We study systems wherein prey occupies isolated patches and are consumed by predators that disperse following Lévy random walks. Our results show that the Lévy exponent and the degree of fragmentation jointly determine coexistence probabilities. In highly fragmented landscapes, Brownian and ballistic predators go extinct and only scale-free predators can coexist with prey. Furthermore, our results confirm that predation causes irreversible habitat loss in fragmented landscapes owing to overexploitation of smaller patches of prey. Moreover, we show that predator dispersal can reduce, but not prevent or minimize, the amount of lost habitat. Our results suggest that integrating optimal foraging theory into population and landscape ecology is crucial to assessing the impact of fragmentation on biodiversity and ecosystem stability.

Intrinsic and environmental factors modulating autonomous robotic search under high uncertainty

Autonomous robotic search problems deal with different levels of uncertainty. When uncertainty is low, deterministic strategies employing available knowledge result in most effective searches. However, there are domains where uncertainty is always high since information about robot location, environment boundaries or precise reference points is unattainable, e.g., in cave, deep ocean, planetary exploration, or upon sensor or communications impairment. Furthermore, latency regarding when search targets move, appear or disappear add to uncertainty sources. Here we study intrinsic and environmental factors that affect low-informed robotic search based on diffusive Brownian, naive ballistic, and superdiffusive strategies (Lévy walks), and in particular, the effectiveness of their random exploration. Representative strategies were evaluated considering both intrinsic (motion drift, energy or memory limitations) and extrinsic factors (obstacles and search boundaries). Our results point towards minimum-knowledge based modulation approaches that can adjust distinct spatial and temporal aspects of random exploration to lead to effective autonomous search under uncertainty.

Hybrid foraging in patchy environments using spatial memory

Efficient random searches are essential to the survival of foragers searching for sparsely distributed targets. Lévy walks have been found to optimize the search over a wide range of constraints. When targets are distributed within patches, generating a spatial memory over the detected targets can be beneficial towards optimizing the search efficiency. Because foragers have limited memory, storing each target location separately is unrealistic. Instead, we propose incrementally learning a spatial distribution in favour of memorizing target locations. We demonstrate that an ensemble of Gaussian mixture models is a suitable candidate for such a spatial distribution. Using this, a hybrid foraging strategy is proposed, which interchanges random searches with informed movement. Informed movement results in displacements towards target locations, and is more likely to occur if the learned spatial distribution is correct. We show that, depending on the strength of the memory effects, foragers optimize search efficiencies by continuous revisitation of non-destructive targets. However, this negatively affects both the target and patch diversity, indicating that memory does not necessarily optimize multi-objective searches. Hence, the benefits of memory depend on the specific goals of the forager. Furthermore, through analysis of the distribution over walking distances of the forager, we show that memory changes the underlying walk characteristics. Specifically, the forager resorts to Brownian motion instead of Lévy walks, due to truncation of the long straight line displacements resulting from memory effects. This study provides a framework that opens up new avenues for investigating memory effects on foraging in sparse environments.

Employing Very High Frequency (VHF) Radio Telemetry to Recreate Monarch Butterfly Flight Paths

The overwintering population of eastern North American monarch butterflies (Danaus plexippus) has declined significantly. Loss of milkweed (Asclepias sp.), the monarch's obligate host plant in the Midwest United States, is considered to be a major cause of the decline. Restoring breeding habitat is an actionable step towards population recovery. Monarch butterflies are highly vagile; therefore, the spatial arrangement of milkweed in the landscape influences movement patterns, habitat utilization, and reproductive output. Empirical studies of female movement patterns within and between habitat patches in representative agricultural landscapes support recommendations for habitat restoration. To track monarch movement at distances beyond human visual range, we employed very high frequency radio telemetry with handheld antennae to collect movement bearings on a biologically relevant time scale. Attachment of 220-300 mg transmitters did not significantly affect behavior and flight capability. Thirteen radio-tagged monarchs were released in a restored prairie, and locations were estimated every minute for up to 39 min by simultaneous triangulation from four operators. Monarchs that left the prairie were tracked and relocated at distances up to 250 m. Assuming straight flights between locations, the majority of steps within the prairie were below 50 m. Steps associated with exiting the prairie exceeded 50 m with high directionality. Because butterflies do not fly in straight lines between stationary points, we also illustrate how occurrence models can use location data obtained through radio telemetry to estimate movement within a prairie and over multiple land cover types.

Resource distribution and internal factors interact to govern movement of a freshwater snail

Movement enables mobile organisms to respond to local environmental conditions and is driven by a combination of external and internal factors operating at multiple scales. Here, we explored how resource distribution interacted with the internal state of organisms to drive patterns of movement. Specifically, we tracked snail movements on experimental landscapes where resource (algal biofilm) distribution varied from 0 to 100% coverage and quantified how that movement changed over a 24 h period. Resource distribution strongly affected snail movement. Trajectories were tortuous (i.e. Brownian-like) within resource patches but straighter (i.e. Lévy) in resource-free (bare) patches. The average snail speed was slower in resource patches, where snails spent most of their time. Different patterns of movement between resource and bare patches explained movement at larger spatial scales; movement was ballistic-like Lévy in resource-free landscapes, Lévy in landscapes with intermediate resource coverage and approximated Brownian in landscapes covered in resources. Our temporal analysis revealed that movement patterns changed predictably for snails that satiated their hunger and then performed other behaviours. These changes in movement patterns through time were similar across all treatments that contained resources. Thus, external and internal factors interacted to shape the inherently flexible movement of these snails.

A 3D Coverage Algorithm Based on Complex Surfaces for UAVs in Wireless Multimedia Sensor Networks

Following the development of wireless multimedia sensor networks (WMSN), the coverage of the sensors in the network constitutes one of the key technologies that have a significant influence on the monitoring ability, quality of service, and network lifetime. The application environment of WMSN is always a complex surface, such as a hilly surface, that would likely cause monitoring shadowing problems. In this study, a new coverage-enhancing algorithm is presented to achieve an optimal coverage ratio of WMSN based on three-dimensional (3D) complex surfaces. By aiming at the complex surface, the use of a 3D sensing model, including a sensor monitoring model and a surface map calculation algorithm, is proposed to calculate the WMSN coverage information in an accurate manner. The coverage base map allowed the efficient estimation of the degree of monitoring occlusion efficiently and improved the system’s accuracy. To meet the requests of complex 3D surface monitoring tasks for multiple sensors, we propose a modified cuckoo search algorithm that considers the features of the WMSN coverage problem and combines the survival of the fittest, dynamic discovery probability, and the self-adaptation strategy of rotation. The evaluation outcomes demonstrate that the proposed algorithm can describe the 3D covering field but also improve both the coverage quality and efficiency of the WMSN on a complex surface.

Long-term exposure to higher temperature increases the thermal sensitivity of grazer metabolism and movement

Ecological studies of global warming impacts have many constraints. Organisms are often exposed to higher temperatures for short periods of time, probably underestimating their ability to acclimate or adapt relative to slower but real rates of warming. Many studies also focus on a limited number of traits and miss the multifaceted effects that warming may have on organisms, from physiology to behaviour. Organisms exhibit different movement traits, some of which are primarily driven by metabolic processes and others by decision-making, which should influence the extent to which temperature affects them. We collected snails from streams that have been differentially heated by geothermal activity for decades to determine how long-term exposure to different temperatures affected their metabolism and movement. Additionally, we collected snails from a cold stream (5°C) and measured their metabolism and movement at higher temperatures (short-term exposure). We used respirometry to measure metabolic rates and automated in situ image-based tracking to quantify several movement traits from 5 to 21°C. Long-term exposure to higher temperatures resulted in a greater thermal sensitivity of metabolic rate compared to snails exposed for short durations, highlighting the need for caution when conducting acute temperature exposures in global warming research. Average speed, which is largely driven by metabolism, also increased more with temperature for long-term exposure compared to short-term exposure. Movement traits we interpret as more decision-based, such as time spent moving and trajectory shape, were less affected by temperature. Step length increased and step angle decreased at higher temperatures for both long- and short-term exposure, resulting in overall straighter trajectories. The power-law exponent of the step length distributions and fractal dimension of trajectories were independent of temperature, however, suggesting that snails retained the same movement strategy. The observed changes in snail movement at higher temperatures should lead to higher encounter rates and more efficient searching, providing a behavioural mechanism for stronger plant-herbivore interactions in warmer environments. Our research is among the first to show that temperature has contrasting effects on different movement traits, which may be determined by the metabolic contribution to those behaviours.

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.

System-wide organization of actin cytoskeleton determines organelle transport in hypocotyl plant cells

The actin cytoskeleton is an essential intracellular filamentous structure that underpins cellular transport and cytoplasmic streaming in plant cells. However, the system-level properties of actin-based cellular trafficking remain tenuous, largely due to the inability to quantify key features of the actin cytoskeleton. Here, we developed an automated image-based, network-driven framework to accurately segment and quantify actin cytoskeletal structures and Golgi transport. We show that the actin cytoskeleton in both growing and elongated hypocotyl cells has structural properties facilitating efficient transport. Our findings suggest that the erratic movement of Golgi is a stable cellular phenomenon that might optimize distribution efficiency of cell material. Moreover, we demonstrate that Golgi transport in hypocotyl cells can be accurately predicted from the actin network topology alone. Thus, our framework provides quantitative evidence for system-wide coordination of cellular transport in plant cells and can be readily applied to investigate cytoskeletal organization and transport in other organisms.

Understanding the spatiotemporal pattern of grazing cattle movement

Understanding the drivers of animal movement is significant for ecology and biology. Yet researchers have so far been unable to fully understand these drivers, largely due to low data resolution. In this study, we analyse a high-frequency movement dataset for a group of grazing cattle and investigate their spatiotemporal patterns using a simple two-state 'stop-and-move' mobility model. We find that the dispersal kernel in the moving state is best described by a mixture exponential distribution, indicating the hierarchical nature of the movement. On the other hand, the waiting time appears to be scale-invariant below a certain cut-off and is best described by a truncated power-law distribution, suggesting that the non-moving state is governed by time-varying dynamics. We explore possible explanations for the observed phenomena, covering factors that can play a role in the generation of mobility patterns, such as the context of grazing environment, the intrinsic decision-making mechanism or the energy status of different activities. In particular, we propose a new hypothesis that the underlying movement pattern can be attributed to the most probable observable energy status under the maximum entropy configuration. These results are not only valuable for modelling cattle movement but also provide new insights for understanding the underlying biological basis of grazing behaviour.

Computational Methods for Tracking, Quantitative Assessment, and Visualization of C. elegans Locomotory Behavior

The nematode Caenorhabditis elegans provides a unique opportunity to interrogate the neural basis of behavior at single neuron resolution. In C. elegans, neural circuits that control behaviors can be formulated based on its complete neural connection map, and easily assessed by applying advanced genetic tools that allow for modulation in the activity of specific neurons. Importantly, C. elegans exhibits several elaborate behaviors that can be empirically quantified and analyzed, thus providing a means to assess the contribution of specific neural circuits to behavioral output. Particularly, locomotory behavior can be recorded and analyzed with computational and mathematical tools. Here, we describe a robust single worm-tracking system, which is based on the open-source Python programming language, and an analysis system, which implements path-related algorithms. Our tracking system was designed to accommodate worms that explore a large area with frequent turns and reversals at high speeds. As a proof of principle, we used our tracker to record the movements of wild-type animals that were freshly removed from abundant bacterial food, and determined how wild-type animals change locomotory behavior over a long period of time. Consistent with previous findings, we observed that wild-type animals show a transition from area-restricted local search to global search over time. Intriguingly, we found that wild-type animals initially exhibit short, random movements interrupted by infrequent long trajectories. This movement pattern often coincides with local/global search behavior, and visually resembles Lévy flight search, a search behavior conserved across species. Our mathematical analysis showed that while most of the animals exhibited Brownian walks, approximately 20% of the animals exhibited Lévy flights, indicating that C. elegans can use Lévy flights for efficient food search. In summary, our tracker and analysis software will help analyze the neural basis of the alteration and transition of C. elegans locomotory behavior in a food-deprived condition.

Optimal first-arrival times in Lévy flights with resetting

We consider the diffusive motion of a particle performing a random walk with Lévy distributed jump lengths and subject to a resetting mechanism, bringing the walker to an initial position at uniformly distributed times. In the limit of an infinite number of steps and for long times, the process converges to superdiffusive motion with replenishment. We derive a formula for the mean first arrival time (MFAT) to a predefined target position reached by a meandering particle and we analyze the efficiency of the proposed searching strategy by investigating criteria for an optimal (a shortest possible) MFAT.

Extending Lévy search theory from one to higher dimensions: Lévy walking favours the blind

A diverse range of organisms, including T cells, E. coli, honeybees, sharks, turtles, bony fish, jellyfish, wandering albatrosses and even human hunter-gatherers have movement patterns that can be approximated by Lévy walks (LW; sometimes called Lévy flights in the biological and ecological literature). These observations lend support to the 'Lévy flight foraging hypothesis' which asserts that natural selection should have led to adaptations for Lévy flight foraging, because Lévy flights can optimize search efficiencies. The hypothesis stems from a rigorous theory of one-dimensional searching and from simulation data for two-dimensional searching. The potential effectiveness of three-dimensional Lévy searches has not been examined but is central to a proper understanding of marine predators and T cells which have provided the most compelling empirical evidence for LW. Here I extend Lévy search theory from one to three dimensions. The new theory predicts that three-dimensional Lévy searching can be advantageous but only when targets are large compared with the perceptual range of the searchers, i.e. only when foragers are effectively blind and need to come into contact with a target to establish its presence. This may explain why effective blindness is a common factor among three-dimensional Lévy walkers.