Detecting Lévy walks without turn designation

Many organisms have been reported to have movement patterns that are well approximated as Lévy walks. This is typically because distributions of straight line distances between consecutive significant turns in movement paths have heavy power law tails. This diagnostic tool has been called into question because there is currently no standard, unambiguous way to identify significant turns. Even if such a way could be found, statistical analyses based on significant turns cannot account for actual movements made between turns and as a consequence cannot distinguish between true Lévy walks and other fractal random walks such as Lévy modulated correlated random walks where organisms randomly meander rather than move in straight lines between consecutive reorientation events. Here, I show that structure functions (i.e. moments of net displacements made across fixed time intervals) can distinguish between different kinds of Lévy walks and between Lévy walks and random walks with a few scales such as composite correlated random walks and correlated random walks. Distinguishing between these processes will lead to a better understanding of how and why animals perform Lévy walks and help bridge the apparent divide between correlated random walks and Lévy walks. Structure functions do not require turn identification and instead take account of entire movement paths. Using this diagnostic tool, I bolster previous claims that honeybees use a movement strategy that can be approximated by Lévy walks when searching for their hive. I also show how structure functions can be used to establish the extent of self-similar behaviour in meandering Lévy walks.     

Are Lévy flight patterns derived from the Weber–Fechner law in distance estimation?

Honeybees (Apis mellifera) are regularly faced with the task of navigating back to their hives from remote food sources. They have evolved several methods to do this, including compass-directed “vector” flights and the use of landmarks. If these hive-centered mechanisms are disrupted, bees revert to searching for the hive, using an optimal Lévy flight searching strategy. The same strategy is adopted when a food source at a known location ceases to be available. Here, we show that the programming for this Lévy strategy does not need to be very sophisticated or clever on the bee’s part, as Lévy flight patterns can be derived from the Weber–Fechner law in a bee’s odometer. Odometry errors of a different kind occur in desert ants (Cataglyphis spp., Melophorus bagoti). The searching behaviors of these ants are very similar in overall structure to that of honeybees but do not display any Lévy flight characteristics. We suggest that errors in the estimation of distance can be implicitly involved in shaping the structure of systematic search behavior and should not be regarded as merely deficiencies in the odometer.     

Reproductive interference via interspecific pairing in an amphipod species complex

Many species experience reproductive interference defined as interspecific mating interactions that reduce the fitness of individuals in at least one of the species. We examined reproductive interference among three cryptic amphipod species that co-occur in the vegetated zone of lakes. Because these animals form precopulatory pairs and males commonly have indiscriminant mating behavior, we predicted that (1) there would be interspecific pairing, (2) interspecific pairing would be more common when conspecifics were rare, and (3) interspecific pairing would be more common in species combinations where males are larger than females. Using color phenotypes to distinguish species, a novel discovery reported here, we conducted experiments to evaluate patterns of interspecific pairing. In a no-choice experiment (i.e., amphipods had access to mates of only one species), we observed a low rate (5 %) of interspecific pairing and 80 % of these cases involved males that were larger than females. In a second experiment where individuals had access to conspecific mates at varying relative abundance, only 0.04 % of the pairs observed were between heterospecifics, suggesting that the interspecific pairing observed in the no-choice experiment was an artifact of not having access to conspecific mates. Our results suggest that at least one sex has sufficient species-recognition abilities to circumvent the formation of interspecific pairs; therefore, reproductive interference may be minimal in these species.     

Enhanced dechlorination of chlorobenzene by microwave-induced zero-valent iron: particle effects and activation energy

Organic compounds such as chlorobenzene cannot be effectively decomposed with currently available biological and chemical treatment methods. Preliminary studies show that nano-scale zero-valent iron particles irradiated by microwave is effective in decomposing chemically refractive organic compounds such as chlorobenzene. In this study, microwave is applied to enhance chlorobenzene removal using micron-scale iron particles and nano-scale zero-valent iron particles suspended in the chlorobenzene solution as the dielectric media. The results show that better chlorobenzene removal can be achieved when the chlorobenzene solution is irradiated with 250 W microwave for 150 s than without microwave irradiation. The microwave radiation increases iron reaction rate and surface activity, thus enhancing the chlorobenzene removal. The microwave-induced iron particles cause the chlorobenzene activation energy to drop 34.0% for micron-scale iron and 16.1% for nano-scale zero-valent iron. They can remove 13.6 times more chlorobenzene for micro iron, and 3.6 times more chlorobenzene for nano iron. We have demonstrated that the microwave-induced nano-scale iron particles are effective in treating toxic organic substances as demonstrated in this laboratory study.     

Lévy flight patterns are predicted to be an emergent property of a bumblebees’ foraging strategy

Bumblebees forage uninterrupted for long periods of time because they are not distracted by sex or territorial defense and have few predators. This has led to a long running debate about whether bumblebees forage optimally. This debate has been enriched by the possibility that bumblebees foraging within clover patches have flight patterns that can be approximated by Lévy flights. Such flight patterns optimise the success of random searches. Bumblebees foraging within a flower patch tend to approach the nearest flower but then often depart without landing or probing it if it has been visited previously; unvisited flowers are not rejected in this manner. Here, this foraging behaviour has been replicated in numerical simulations. Lévy flight patterns are found to be an inconsequential emergent property of a bumblebees’ foraging behaviour. Lévy flights are predicted to emerge when bees reject at least 99% of previously visited flowers. A foraging bumblebee can certainly empty a clover flower head of nectar in one visit, but lower rates of rejection are observed for many other flowers. These findings suggest that Lévy flight patterns in foraging bumblebees are rare and specific to a few flower species and that if they exist, then they are not part of an innate, evolved optimal searching strategy.     

Modelling of concentrations along a moving observer in an inhomogeneous plume. Biological application: model of odour-mediated insect flights

We develop a stochastic model for the time-evolution of scalar concentrations and temporal gradients in concentration experienced by observers moving within inhomogeneous plumes that are dispersing within turbulent flows. In this model, scalar concentrations and their gradients evolve jointly as a Markovian process. Underlying the model formulation is a natural generalisation of Thomson’s well mixed condition [Thomson DJ (1987) J Fluid Mech 180:529–556]. As a consequence model outputs are necessarily compatible with statistical properties of scalars observed in experiment that are used here as model input. We then use the model to examine how insects aloft within the atmospheric boundary-layer can locate odour sources by modulating their flight patterns in response to odour cues. Mechanisms underlying odour-mediated flights have been studied extensively at laboratory-scale but an understanding of these flights over landscape scales is still lacking. Insect flights are simulated by combining the stochastic model with a simple model of insect olfactory response. These simulations show the strong influence of wind speed on the distributions of the times taken by insects to locate the source. In accordance with experimental observations [Baker TC, Vickers NJ (1997) In: Insect pheromone research: new directions, pp 248–264; Mafra-Neto A, Cardé RT (1994) Nature 369:142–144], flight patterns are predicted to become straighter and shorter, and source location is predicted to become more likely as the mean wind speed increases. The most probable arrival time to the source decreases with the mean wind speed. It is shown that scale-free movement patterns arising from olfactory-driven foraging stem directly from the power-law distribution of concentration excursion times above/below a threshold level and are robust with respect to variations in Reynolds number. Flight lengths are well represented by a power law distribution in agreement with the observed patterns of foraging bumblebees [Heinrich B (1979) Oecologia 40(3):235–245].     

Projecting Cumulative Benefits of Multiple River Restoration Projects: An Example from the Sacramento-San Joaquin River System in California

Despite increasingly large investments, the potential ecological effects of river restoration programs are still small compared to the degree of human alterations to physical and ecological function. Thus, it is rarely possible to “restore” pre-disturbance conditions; rather restoration programs (even large, well-funded ones) will nearly always involve multiple small projects, each of which can make some modest change to selected ecosystem processes and habitats. At present, such projects are typically selected based on their attributes as individual projects (e.g., consistency with programmatic goals of the funders, scientific soundness, and acceptance by local communities), and ease of implementation. Projects are rarely prioritized (at least explicitly) based on how they will cumulatively affect ecosystem function over coming decades. Such projections require an understanding of the form of the restoration response curve, or at least that we assume some plausible relations and estimate cumulative effects based thereon. Drawing on our experience with the CALFED Bay-Delta Ecosystem Restoration Program in California, we consider potential cumulative system-wide benefits of a restoration activity extensively implemented in the region: isolating/filling abandoned floodplain gravel pits captured by rivers to reduce predation of outmigrating juvenile salmon by exotic warmwater species inhabiting the pits. We present a simple spreadsheet model to show how different assumptions about gravel pit bathymetry and predator behavior would affect the cumulative benefits of multiple pit-filling and isolation projects, and how these insights could help managers prioritize which pits to fill.     

Coupling GIS and mulitvariate approaches to reference site selection for wadeable stream monitoring

Geographic Information System (GIS) was used to identify potential reference sites for wadeable stream monitoring, and multivariate analyses were applied to test whether invertebrate communities reflected a priori spatial and stream type classifications. We identified potential reference sites in segments with unmodified vegetation cover adjacent to the stream and in >85% of the upstream catchment. We then used various landcover, amenity and environmental impact databases to eliminate sites that had potential anthropogenic influences upstream and that fell into a range of access classes. Each site identified by this process was coded by four dominant stream classes and seven zones, and 119 candidate sites were randomly selected for follow-up assessment. This process yielded 16 sites conforming to reference site criteria using a conditional-probabilistic design, and these were augmented by an additional 14 existing or special interest reference sites. Non-metric multidimensional scaling (NMS) analysis of percent abundance invertebrate data indicated significant differences in community composition among some of the zones and stream classes identified a priori providing qualified support for this framework in reference site selection. NMS analysis of a range standardised condition and diversity metrics derived from the invertebrate data indicated a core set of 26 closely related sites, and four outliers that were considered atypical of reference site conditions and subsequently dropped from the network. Use of GIS linked to stream typology, available spatial databases and aerial photography greatly enhanced the objectivity and efficiency of reference site selection. The multi-metric ordination approach reduced variability among stream types and bias associated with non-random site selection, and provided an effective way to identify representative reference sites.     

A hedonic model of public market transactions for open space protection

A hedonic price function is estimated that illustrates how the price per acre of open space paid by public buyers such as counties or land trusts, is influenced by local demand and supply factors. The empirical regression model is illustrated using 133 public transactions (73% are purchases and 27% are easements) of open space in the Front Range of Colorado. The mean price per acre was $13 635. If a property provides access to water bodies, this feature increases the price per acre by $937, while adjacency of the parcel to existing park or open space adds $11 039 an acre. A 1% increase in county population results in a 0.27% increase in price per acre. Easements cost $6783 less than purchases, a sizeable cost saving. The prediction capability of the hedonic price equation may be an alternative to traditional real estate appraisal techniques when agencies must determine fair market values of prospective open space parcels that vary in attributes from existing ones.     

Concentrations of dioxin-like PCB congeners in unweathered Aroclors by HRGC/HRMS using EPA Method 1668A

We have determined the congener compositions of nine commercial Aroclor products of polychlorinated biphenyls (PCBs) to the sub-part-per-million level using high-resolution gas chromatography combined with high-resolution mass spectrometry according to US Environmental Protection Agency (EPA) Method 1668A. These Aroclor composition data should allow improved characterization and risk assessment of PCB contamination at hazardous waste sites, particularly for dioxin-like PCB congeners. By combining the data on the concentrations of each dioxin-like congener with its World Health Organization toxicity equivalency factor, we have established dioxin toxic equivalent concentrations for each pure Aroclor product.