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].     

An input-output balance study for PCBs in humans

Polychlorinated biphenyl (PCB) input-output balance studies were performed on five male volunteers, aged between 24 and 30, for periods of 8-14 days in 1998. Dietary exposure was quantified by the duplicate meals method and varied between 220 and 460 ng of sigmaPCB (sum of 20 congeners) per day for each of the five individuals over the study period. Dietary intake was dominated by congeners 118, 138, 153 and 180. Average faecal outputs for the five volunteers were 50-290 ng of sigmaPCB (sum of 20 congeners) per day for each of the five individuals over the same period and was dominated by the same four congeners. Whilst the total PCB fluxes were therefore into the body (i.e., accumulation), important differences were noted for different individual congeners. PCBs 44, 47, 49, 52, 60, 66, 101, 105, 110, 118, 149, 151 and 183 all showed net absorption for all five volunteers. Some congeners showed a net absorption in some of the individuals but net excretion in others, as seen by other workers. These congeners (PCBs 138, 153, 180, 187 and 194) are all higher chlorinated congeners and lack meta-para-vicinal hydrogen atoms. There were differences in the net absorption/excretion between individuals, which appeared to be a function of body fat index (BFI). The volunteers with the lowest BFIs showed net excretion for the greatest number of congeners, whilst the individual with the highest BFI was a net absorber of all the congeners studied. The problems in determining and interpreting absorption efficiency values for use in quantitative exposure assessments are discussed. Various factors that influence net absorption of PCBs and other persistent organic pollutants are identified. These include compound properties (including susceptibility to metabolism), the individual's fat status and balance, exposure history and diet.     

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.