Signatures of active and passive optimized Lévy searching in jellyfish

Some of the strongest empirical support for Lévy search theory has come from telemetry data for the dive patterns of marine predators (sharks, bony fishes, sea turtles and penguins). The dive patterns of the unusually large jellyfish Rhizostoma octopus do, however, sit outside of current Lévy search theory which predicts that a single search strategy is optimal. When searching the water column, the movement patterns of these jellyfish change over time. Movement bouts can be approximated by a variety of Lévy and Brownian (exponential) walks. The adaptive value of this variation is not known. On some occasions movement pattern data are consistent with the jellyfish prospecting away from a preferred depth, not finding an improvement in conditions elsewhere and so returning to their original depth. This ‘bounce’ behaviour also sits outside of current Lévy walk search theory. Here, it is shown that the jellyfish movement patterns are consistent with their using optimized ‘fast simulated annealing’—a novel kind of Lévy walk search pattern—to locate the maximum prey concentration in the water column and/or to locate the strongest of many olfactory trails emanating from more distant prey. Fast simulated annealing is a powerful stochastic search algorithm for locating a global maximum that is hidden among many poorer local maxima in a large search space. This new finding shows that the notion of active optimized Lévy walk searching is not limited to the search for randomly and sparsely distributed resources, as previously thought, but can be extended to embrace other scenarios, including that of the jellyfish R. octopus. In the presence of convective currents, it could become energetically favourable to search the water column by riding the convective currents. Here, it is shown that these passive movements can be represented accurately by Lévy walks of the type occasionally seen in R. octopus. This result vividly illustrates that Lévy walks are not necessarily the result of selection pressures for advantageous searching behaviour but can instead arise freely and naturally from simple processes. It also shows that the family of Lévy walkers is vastly larger than previously thought and includes spores, pollens, seeds and minute wingless arthropods that on warm days disperse passively within the atmospheric boundary layer.     

Assessing Lévy walks as models of animal foraging

The hypothesis that the optimal search strategy is a Lévy walk (LW) or Lévy flight, originally suggested in 1995, has generated an explosion of interest and controversy. Long-standing empirical evidence supporting the LW hypothesis has been overturned, while new models and data are constantly being published. Statistical methods have been criticized and new methods put forward. In parallel with the empirical studies, theoretical search models have been developed. Some theories have been disproved while others remain. Here, we gather together the current state of the art on the role of LWs in optimal foraging theory. We examine the body of theory underpinning the subject. Then we present new results showing that deviations from the idealized one-dimensional search model greatly reduce or remove the advantage of LWs. The search strategy of an LW with exponent μ = 2 is therefore not as robust as is widely thought. We also review the available techniques, and their potential pitfalls, for analysing field data. It is becoming increasingly recognized that there is a wide range of mechanisms that can lead to the apparent observation of power-law patterns. The consequence of this is that the detection of such patterns in field data implies neither that the foragers in question are performing an LW, nor that they have evolved to do so. We conclude that LWs are neither a universal optimal search strategy, nor are they as widespread in nature as was once thought.     

Fitness-maximizing foragers can use information about patch quality to decide how to search for and within patches: optimal Lévy walk searching patterns from optimal foraging theory

Optimal foraging theory shows how fitness-maximizing foragers can use information about patch quality to decide how to search within patches. It is amply supported by empirical studies. Nonetheless, the theory largely ignores the fact that foragers may need to search for patches as well as for the targets within them. Here, using an exact but simple mathematical argument, it is shown how foragers can use information about patch quality to facilitate the execution of Lévy walk movement patterns with μ = 2 at inter-patch scales. These movement patterns are advantageous when searching for patches that are not depleted or rejected once visited but instead remain profitable. The analytical results are verified by the results of numerical simulations. The findings bring forth an innovative theoretical synthesis of searching for and within patches and, suggest that foragers'' memories may be adaptive under spatially heterogeneous reward schedules.     

Collective foraging in heterogeneous landscapes

Animals foraging alone are hypothesized to optimize the encounter rates with resources through Lévy walks. However, the issue of how the interactions between multiple foragers influence their search efficiency is still not completely understood. To address this, we consider a model to study the optimal strategy for a group of foragers searching for targets distributed heterogeneously. In our model, foragers move on a square lattice containing immobile but regenerative targets. At any instant, a forager is able to detect only those targets that happen to be in the same site. However, we allow the foragers to have information about the state of other foragers. A forager who has not detected any target walks towards the nearest location, where another forager has detected a target, with a probability exp(−αd), where d is the distance between the foragers and α is a parameter characterizing the propensity of the foragers to aggregate. The model reveals that neither overcrowding (α → 0) nor independent searching (α → ∞) is beneficial for the foragers. For a patchy distribution of targets, the efficiency is maximum for intermediate values of α. In addition, in the limit α → 0, the length of the walks can become scale-free.     

Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual''s trajectory through space is represented by a sequence of distinct, independent randomly oriented ‘moves’. It has long been recognized that the transformation of an animal''s continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.     

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.     

Mechanistic analysis of the search behaviour of Caenorhabditis elegans

A central question in movement research is how animals use information and movement to promote encounter success. Current random search theory identifies reorientation patterns as key to the compromise between optimizing encounters for both nearby and faraway targets, but how the balance between intrinsic motor programmes and previous environmental experience determines the occurrence of these reorientation behaviours remains unknown. We used high-resolution tracking and imaging data to describe the complete motor behaviour of Caenorhabditis elegans when placed in a novel environment (one in which food is absent). Movement in C. elegans is structured around different reorientation behaviours, and we measured how these contributed to changing search strategies as worms became familiar with their new environment. This behavioural transition shows that different reorientation behaviours are governed by two processes: (i) an environmentally informed ‘extrinsic’ strategy that is influenced by recent experience and that controls for area-restricted search behaviour, and (ii) a time-independent, ‘intrinsic’ strategy that reduces spatial oversampling and improves random encounter success. Our results show how movement strategies arise from a balance between intrinsic and extrinsic mechanisms, that search behaviour in C. elegans is initially determined by expectations developed from previous environmental experiences, and which reorientation behaviours are modified as information is acquired from new environments.     

Flagellar phenotypic plasticity in volvocalean algae correlates with Péclet number

Flagella-generated fluid stirring has been suggested to enhance nutrient uptake for sufficiently large micro-organisms, and to have played a role in evolutionary transitions to multicellularity. A corollary to this predicted size-dependent benefit is a propensity for phenotypic plasticity in the flow-generating mechanism to appear in large species under nutrient deprivation. We examined four species of volvocalean algae whose radii and flow speeds differ greatly, with Péclet numbers (Pe) separated by several orders of magnitude. Populations of unicellular Chlamydomonas reinhardtii and one- to eight-celled Gonium pectorale (Pe ∼ 0.1–1) and multicellular Volvox carteri and Volvox barberi (Pe ∼ 100) were grown in diluted and undiluted media. For C. reinhardtii and G. pectorale, decreasing the nutrient concentration resulted in smaller cells, but had no effect on flagellar length and propulsion force. In contrast, these conditions induced Volvox colonies to grow larger and increase their flagellar length, separating the somatic cells further. Detailed studies on V. carteri found that the opposing effects of increasing beating force and flagellar spacing balance, so the fluid speed across the colony surface remains unchanged between nutrient conditions. These results lend further support to the hypothesized link between the Péclet number, nutrient uptake and the evolution of biological complexity in the Volvocales.     

A novel video-tracking system to quantify the behaviour of nocturnal mosquitoes attacking human hosts in the field

Many vectors of malaria and other infections spend most of their adult life within human homes, the environment where they bloodfeed and rest, and where control has been most successful. Yet, knowledge of peri-domestic mosquito behaviour is limited, particularly how mosquitoes find and attack human hosts or how insecticides impact on behaviour. This is partly because technology for tracking mosquitoes in their natural habitats, traditional dwellings in disease-endemic countries, has never been available. We describe a sensing device that enables observation and recording of nocturnal mosquitoes attacking humans with or without a bed net, in the laboratory and in rural Africa. The device addresses requirements for sub-millimetre resolution over a 2.0 × 1.2 × 2.0 m volume while using minimum irradiance. Data processing strategies to extract individual mosquito trajectories and algorithms to describe behaviour during host/net interactions are introduced. Results from UK laboratory and Tanzanian field tests showed that Culex quinquefasciatus activity was higher and focused on the bed net roof when a human host was present, in colonized and wild populations. Both C. quinquefasciatus and Anopheles gambiae exhibited similar behavioural modes, with average flight velocities varying by less than 10%. The system offers considerable potential for investigations in vector biology and many other fields.     

Evolutionary optimality in stochastic search problems

‘Optimal’ behaviour in a biological system is not simply that which maximizes a mean, or temporally and spatially averaged, fitness function. Rather, population dynamics and demographic and environmental stochasticity are fundamental evolutionary ingredients. Here, we revisit the problem of optimal foraging, where some recent studies claim that organisms should forage according to Lévy walks. We show that, in an ecological scenario dominated by uncertainty and high mortality, Lévy walks can indeed be evolutionarily favourable. However, this conclusion is dependent on the definition of efficiency and the details of the simulations. We analyse measures of efficiency that incorporate population-level characteristics, such as variance, superdiffusivity and heavy tails, and compare the results with those generated by simple maximizing of the average encounter rate. These results have implications on stochastic search problems in general, and also on computational models of evolutionary optima.     

Alternative radical pairs for cryptochrome-based magnetoreception

There is growing evidence that the remarkable ability of animals, in particular birds, to sense the direction of the Earth''s magnetic field relies on magnetically sensitive photochemical reactions of the protein cryptochrome. It is generally assumed that the magnetic field acts on the radical pair [FAD^•− TrpH^•+] formed by the transfer of an electron from a group of three tryptophan residues to the photo-excited flavin adenine dinucleotide cofactor within the protein. Here, we examine the suitability of an [FAD^•− Z^•] radical pair as a compass magnetoreceptor, where Z^• is a radical in which the electron spin has no hyperfine interactions with magnetic nuclei, such as hydrogen and nitrogen. Quantum spin dynamics simulations of the reactivity of [FAD^•− Z^•] show that it is two orders of magnitude more sensitive to the direction of the geomagnetic field than is [FAD^•− TrpH^•+] under the same conditions (50 µT magnetic field, 1 µs radical lifetime). The favourable magnetic properties of [FAD^•− Z^•] arise from the asymmetric distribution of hyperfine interactions among the two radicals and the near-optimal magnetic properties of the flavin radical. We close by discussing the identity of Z^• and possible routes for its formation as part of a spin-correlated radical pair with an FAD radical in cryptochrome.     

Synchrotron imaging reveals bone healing and remodelling strategies in extinct and extant vertebrates

Current understanding of bone healing and remodelling strategies in vertebrates has traditionally relied on morphological observations through the histological analysis of thin sections. However, chemical analysis may also be used in such interpretations, as different elements are known to be absorbed and used by bone for different physiological purposes such as growth and healing. These chemical signatures are beyond the detection limit of most laboratory-based analytical techniques (e.g. scanning electron microscopy). However, synchrotron rapid scanning–X-ray fluorescence (SRS–XRF) is an elemental mapping technique that uniquely combines high sensitivity (ppm), excellent sample resolution (20–100 µm) and the ability to scan large specimens (decimetre scale) approximately 3000 times faster than other mapping techniques. Here, we use SRS–XRF combined with microfocus elemental mapping (2–20 µm) to determine the distribution and concentration of trace elements within pathological and normal bone of both extant and extinct archosaurs (Cathartes aura and Allosaurus fragilis). Results reveal discrete chemical inventories within different bone tissue types and preservation modes. Chemical inventories also revealed detail of histological features not observable in thin section, including fine structures within the interface between pathological and normal bone as well as woven texture within pathological tissue.     

Leaf surface structures enable the endemic Namib desert grass Stipagrostis sabulicola to irrigate itself with fog water

The Namib grass Stipagrostis sabulicola relies, to a large degree, upon fog for its water supply and is able to guide collected water towards the plant base. This directed irrigation of the plant base allows an efficient and rapid uptake of the fog water by the shallow roots. In this contribution, the mechanisms for this directed water flow are analysed. Stipagrostis sabulicola has a highly irregular surface. Advancing contact angle is 98° ± 5° and the receding angle is 56° ± 9°, with a mean of both values of approximately 77°. The surface is thus not hydrophobic, shows a substantial contact angle hysteresis and therefore, allows the development of pinned drops of a substantial size. The key factor for the water conduction is the presence of grooves within the leaf surface that run parallel to the long axis of the plant. These grooves provide a guided downslide of drops that have exceeded the maximum size for attachment. It also leads to a minimum of inefficient drop scattering around the plant. The combination of these surface traits together with the tall and upright stature of S. sabulicola contributes to a highly efficient natural fog-collecting system that enables this species to thrive in a hyperarid environment.     

Through the eyes of a bird: modelling visually guided obstacle flight

Various flight navigation strategies for birds have been identified at the large spatial scales of migratory and homing behaviours. However, relatively little is known about close-range obstacle negotiation through cluttered environments. To examine obstacle flight guidance, we tracked pigeons (Columba livia) flying through an artificial forest of vertical poles. Interestingly, pigeons adjusted their flight path only approximately 1.5 m from the forest entry, suggesting a reactive mode of path planning. Combining flight trajectories with obstacle pole positions, we reconstructed the visual experience of the pigeons throughout obstacle flights. Assuming proportional–derivative control with a constant delay, we searched the relevant parameter space of steering gains and visuomotor delays that best explained the observed steering. We found that a pigeon''s steering resembles proportional control driven by the error angle between the flight direction and the desired opening, or gap, between obstacles. Using this pigeon steering controller, we simulated obstacle flights and showed that pigeons do not simply steer to the nearest opening in the direction of flight or destination. Pigeons bias their flight direction towards larger visual gaps when making fast steering decisions. The proposed behavioural modelling method converts the obstacle avoidance behaviour into a (piecewise) target-aiming behaviour, which is better defined and understood. This study demonstrates how such an approach decomposes open-loop free-flight behaviours into components that can be independently evaluated.     

Biogenically engineered nanoparticles inhibit Fusarium oxysporum causing soft‐rot of ginger

Soft‐rot of ginger (Zingiber officinale) is the most important disease usually caused by Fusarium oxysporum (F. oxysporum) leading to significant yield loss. In this study, chitosan, copper and sulphur nanoparticles synthesised from leaf extract of selected plants were screened against two isolates of F. oxysporum recovered from the infected rhizome of ginger and soil samples. Moreover, among these, sulphur nanoparticles showed maximum inhibition of F. oxysporum isolated from soil samples (ZOI = 12.33 mm) followed by copper (ZOI = >12 mm) and chitosan nanoparticles (ZOI = >9 mm). Similarly, in the case of F. oxysporum isolated from infected ginger, sulphur nanoparticles showed maximum inhibition (ZOI = 13.33) as compared to copper (ZOI = >11 mm) and chitosan nanoparticles (ZOI = >9 mm). Considering the high efficacy, sulphur nanoparticles were further evaluated in combination with commercial fungicides, viz., bavistin, ridomil gold, sunflex and streptocycline. The combination of sulphur nanoparticles with bavistin demonstrated maximum inhibition (ZOI = 45.16 mm, MIC −20 µg/ml), whereas the minimum inhibition was shown by its combination with ridomil gold (ZOI = 10.5 mm, MIC –40 µg/ml). Therefore, it can be concluded that the combination of sulphur nanoparticles with bavistin can be used for effective and eco‐friendly management of F. oxysporum causing soft‐rot of ginger.Inspec keywords: nanoparticles, biotechnology, microorganisms, toxicology, mass spectroscopic chemical analysis, antibacterial activity, plant diseasesOther keywords: fusarium oxysporum, sulphur nanoparticles, f. oxysporum, soil samples, bavistin demonstrated maximum inhibition, biogenically engineered nanoparticles, ginger soft‐rot, chitosan nanoparticles, ridomil gold     

Ambiguities in Powder Indexing: the Impact of a Quaternary Lattice Metric Singularity on the Characterization of Mawsonite and Chatkalite

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The minerals Mawsonite and Chatkalite are of especial interest as both are characterized by tetragonal unit cells that correspond to the second member of a quaternary lattice metric singularity. This singularity includes lattices that are Cubic I, Tetragonal P, Orthorhombic F, and Orthorhombic P. The Mawsonite and Chatkalite lattices are unique in that they are highly specialized. In each case: (1) the determinative c/a ratio is very near 1/√2, (2) the symmetrical scalars of the reduced form [a · a : b · b : c · c = 1:2:2] have greater specialization than required for the given reduced form type, (3) the tetragonal lattice has derivative lattices of higher symmetry, and (4) the powder pattern is highly compressed. Mawsonite and Chatkalite serve as exemplar-type compounds. Their tetragonal structure has important implications in structure determination using powder diffraction data. First, any cubic I lattice — established solely on the basis of indexing procedures — may actually be tetragonal or orthorhombic. Second, in establishing the lattice of an unknown, results from powder data indexing require routine confirmation by other techniques (e.g., single crystal, optical, etc.).     

Evidence of strategic periodicities in collective conflict dynamics

We analyse the timescales of conflict decision-making in a primate society. We present evidence for multiple, periodic timescales associated with social decision-making and behavioural patterns. We demonstrate the existence of periodicities that are not directly coupled to environmental cycles or known ultraridian mechanisms. Among specific biological and socially defined demographic classes, periodicities span timescales between hours and days. Our results indicate that these periodicities are not driven by exogenous or internal regularities but are instead driven by strategic responses to social interaction patterns. Analyses also reveal that a class of individuals, playing a critical functional role, policing, have a signature timescale of the order of 1 h. We propose a classification of behavioural timescales analogous to those of the nervous system, with high frequency, or α-scale, behaviour occurring on hour-long scales, through to multi-hour, or β-scale, behaviour, and, finally γ periodicities observed on a timescale of days.     

Approximate Solutions of the Nonlinear Schr?dinger Equation for Ground and Excited States of Bose-Einstein Condensates

I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N₀ limit of the vortex critical frequency for a > 0, by approximate solution of the time-independent nonlinear Schrödinger equation.