Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

A high resolution study of the chlorophyll and bacteriochlorophyll pigment distributions in a calcite/gypsum microbial mat

Application of a high resolution high performance liquid chromatography-mass spectrometry method to the study of a microbial mat system has permitted the identification of a greater number of pigments derived from green bacteria than reported in a previous study. Although the green bacteria found in the mat were identified as Chloroflexus-like, bacteriochlorophylls and bacteriophaeophytins c that can be attributed to Chloroflexaceae on the basis of literature reports account for less than 10% of the pigments derived from green bacteria in the mat. Analysis of the bacteriochlorophylls and bacteriophaeophytins c and d using atmospheric pressure chemical ionisation-liquid chromatography-tandem mass spectrometry reveals complex depth profiles, signalling inputs from a number of organisms. The pigment compositions provide evidence for green bacteria living in close proximity to the living cyanobacterial mat. Depth profiles of pigments derived from green, purple and cyanobacteria indicate that the remnants of mats present in the deeper part of the section contain a record dominated by signatures from anoxygenic photoautotrophs.

Development and application of a high resolution liquid chromatographic method for the analysis of complex pigment distributions

Ternary and binary gradient systems have been developed for the high-performance liquid chromatographic analysis of complex pigment distributions typical of natural samples. Improved chromatographic resolution reveals significantly more pigment components in extracts from a sediment (Priest Pot, Cumbria, UK), a microbial mat (les Salines de la Trinital, South Catalonia, Spain) and a culture (C. phaeobacteroides) including novel bacteriochlorophyll derivatives. The methods developed are directly suited to LC–MS analysis and the automated acquisition of MS/MS data for pigments.

Quantifying pursuit diving seabirds' associations with fine-scale physical features in a high tidal energy environment

The rapid increase in the number of tidal stream turbine arrays will create novel and unprecedented levels of anthropogenic activity within habitats characterized by horizontal current speeds exceeding 2 ms−1. However, the potential impacts on pursuit‐diving seabirds exploiting these tidal stream environments remain largely unknown. Identifying similarities between the fine‐scale physical features (100s of metres) suitable for array installations, and those associated with foraging pursuit‐diving seabirds, could identify which species are most vulnerable to either collisions with moving components, or displacement from these installations. A combination of vessel‐based observational surveys, Finite Volume Community Ocean Model outputs and hydroacoustic seabed surveys provided concurrent measures of foraging distributions and physical characteristics at a fine temporal (15 min) and spatial (500 m) resolution across a tidal stream environment suitable for array installations, during both breeding and non‐breeding seasons. These data sets were then used to test for associations between foraging pursuit‐diving seabirds (Atlantic puffins Fratercula arctica, black guillemots Cepphus grylle, common guillemots Uria aalge, European shags Phalacrocorax aristotelis) and physical features. These species were associated with areas of fast horizontal currents, slow horizontal currents, high turbulence, downward vertical currents and also hard–rough seabeds. The identity and strength of associations differed among species, and also within species between seasons, indicative of interspecific and intraspecific variations in habitat use. However, Atlantic puffins were associated particularly strongly with areas of fast horizontal currents during breeding seasons, and European shags with areas of rough–hard seabeds and downward vertical currents during non‐breeding seasons. Synthesis and applications. Atlantic puffins’ strong association with fast horizontal current speeds indicates that they are particularly likely to interact with installations during breeding seasons. Any post‐installation monitoring and mitigation measures should therefore focus on this species and season. The multi‐species associations with high turbulence and downward vertical currents, which often coincide with fast horizontal current speeds, also highlight useful pre‐installation mitigation measures via the omission of devices from these areas, reducing the overall likelihood of interactions. Environmental impact assessments (EIA) generally involve once‐a‐month surveys across 2‐year periods. However, the approaches used in this study show that more focussed surveys can greatly benefit management strategies aiming to reduce the likelihood of negative impacts by facilitating the development of targeted mitigation measures. It is therefore recommended that these approaches contribute towards EIA within development sites.

Molecular Distributions in the Inner Regions of Protostellar Disks

The distributions of molecules in the inner regions of a protostellar disk are presented. These were calculated using an uncoupled chemical/dynamical model, with a numerical integration of the vertical disk structure. A comparison between models with and without the effects of X-ray ionisation is made, and molecules are identified which are good tracers of the ionisation level in this part of the disk, notably CN and C_2H. In the region considered in this paper (r

What motion distributions yield global transparency and spatial segmentation?

We have examined the ability of observers to parse bimodal local-motion distributions into two global motion surfaces, either overlapping (yielding transparent motion) or spatially segregated (yielding a motion boundary). The stimuli were random dot kinematograms in which the direction of motion of each dot was drawn from one of two rectangular probability distributions. A wide range of direction distribution widths and separations was tested. The ability to discriminate the direction of motion of one of the two motion surfaces from the direction of a comparison stimulus was used as an objective test of the perception of two discrete surfaces. Performance for both transparent and spatially segregated motion was remarkably good, being only slightly inferior to that achieved with a single global motion surface. Performance was consistently better for segregated motion than for transparency. Whereas transparent motion was only perceived with direction distributions which were separated by a significant gap, segregated motion could be seen with abutting or even partially overlapping direction distributions. For transparency, the critical gap increased with the range of directions in the distribution. This result does not support models in which transparency depends on detection of a minimum size of gap defining a bimodal direction distribution. We suggest, instead, that the operations which detect bimodality are scaled (in the direction domain) with the overall range of distributions. This yields a flexible, adaptive system that determines whether a gap in the direction distribution serves as a segmentation cue or is smoothed as part of a unitary computation of global motion.

Strong parallel magnetic field effects on the hydrogen molecular ion

Equilibrium distances, binding energies and dissociation energies for the ground and low-lying states of the hydrogen molecular ion in a strong magnetic field parallel to the internuclear axis are calculated and refined, by using the two- dimensional pseudospectral method. High-precision results are presented for the binding energies over a wider field regime than already given in the literature (Kravchenko and Liberman 1997 Phys. Rev. A 55 2701). The present work removes a long- standing discrepancy for the R-eq value in the 1sigma(u) state at a field strength of 1.0 x 10(6) T. The dissociation energies of the antibonding 1pi(g) state induced by magnetic fields are determined accurately. We have also observed that the antibonding 1pi(g) potential energy curve develops a minimum if the field is sufficiently strong. Some unreliable results in the literature are pointed out and discussed. A way to efficiently treat vibrational processes and coupling between the nuclear and the electronic motions in magnetic fields is also suggested within a three-dimensional pseudospectral scheme.