First Passage Time Analysis Research Articles

Landscape effects on scales of movement by white-tailed deer in an agricultural–forest matrix

Understanding how organisms respond to landscape heterogeneity is foundational to landscape ecology. We characterized seasonal scales of movement of white-tailed deer (Odocoileus viginianus) in an agricultural–forest matrix using first-passage time analysis (FPT) for 62 GPS-collared individuals. We investigated whether those scales were driven by demographic or landscape features. We found FPT for each individual across all seasons was typically dominated by a peak in variance of FPT/area at scales (radii) from 425 to 1,675 m. These peaks occurred at scales consistent with seasonal space use. We observed additional lower magnitude peaks at larger scales (3,000–6,000 m) and small scales (25–150 m). Peaks at larger scales were associated with seasonal migrations and dispersal events. Small scale peaks may represent resting or foraging behavior. Female movements were organized at smaller scales than males in the spring/summer season. Models relating landscape features to movement scales suggest that deer perceive and move within the landscape differently as the roles of dominant land-cover types shift seasonally. During winter, configuration (interspersion/juxtaposition) of land-cover types is more important to deer than during spring/summer and fall. During spring/summer and fall, movement behavior may be dictated by reproductive and harvest activities.

First-passage time analysis of a one-dimensional diffusion-reaction model: application to protein transport along DNA

BackgroundProteins search along the DNA for targets, such as transcription initiation sequences, according to one-dimensional diffusion, which is interrupted by micro- and macro-hopping events and intersegmental transfers that occur under close packing conditions.ResultsA one-dimensional diffusion-reaction model in the form of difference-differential equations is proposed to analyze the nonequilibrium protein sliding kinetics along a segment of bacterial DNA. A renormalization approach is used to derive an expression for the mean first-passage time to arrive at sites downstream of the origin from the occupation probabilities given by the individual transport equations. Monte Carlo simulations are employed to assess the validity of the proposed approach, and all results are interpreted within the context of bacterial transcription.ConclusionsMean first-passage times decrease with increasing reaction rates, indicating that, on average, surviving proteins more rapidly locate downstream targets than their reaction-free counterparts, but at the price of increasing rarity. Two qualitatively different screening regimes are identified according to whether the search process operates under “small” or “large” values for the dissociation rate of the protein-DNA complex. Lower bounds are placed on the overall search time for varying reactive conditions. Good agreement with experimental estimates requires the reaction rate reside near the transition between both screening regimes, suggesting that biology balances a need for rapid searches against maximum exploration during each round of the sliding phase.

In situ measures of foraging success and prey encounter reveal marine habitat‐dependent search strategies

Predators are thought to reduce travel speed and increase turning rate in areas where resources are relatively more abundant, a behavior termed "area-restricted search." However, evidence for this is rare, and few empirical data exist for large predators. Animals exhibiting foraging site fidelity could also be spatially aware of suitable feeding areas based on prior experience; changes in movement patterns might therefore arise from the anticipation of higher prey density. We tested the hypothesis that regions of area-restricted search were associated with a higher number of daily speed spikes (a proxy for potential prey encounter rate) and foraging success in southern elephant seals (Mirounga leonina), a species exhibiting both area-restricted searches and high interannual foraging site fidelity. We used onshore morphological measurements and diving data from archival tags deployed during winter foraging trips. Foraging success was inferred from in situ changes in relative lipid content derived from measured changes in buoyancy, and first-passage time analysis was used to identify area-restricted search behavior. Seals exhibited relatively direct southerly movement on average, with intensive search behavior predominantly located at the distal end of tracks. The probability of being in search mode was positively related to changes in relative lipid content; thus, intensively searched areas were associated with the highest foraging success. However, there was high foraging success during the outward transit even though seals moved through quickly without slowing down and increasing turning rate to exploit these areas. In addition, the probability of being in search mode was negatively related to the number of daily speed spikes. These results suggest that movement patterns represent a response to prior expectation of the location of predictable and profitable resources. Shelf habitat was 4-9 times more profitable than the other habitats, emphasizing the importance of the East Antarctic shelf for this and other predators in the region. We have provided rare empirical data with which to investigate the relationship between predator foraging strategy and prey encounter/ foraging success, underlining the importance of inferring the timing and spatial arrangement of successful food acquisition for interpreting foraging strategies correctly.

Analysis of Molecular Diffusion by First-Passage Time Variance Identifies the Size of Confinement Zones

The diffusion of receptors within the two-dimensional environment of the plasma membrane is a complex process. Although certain components diffuse according to a random walk model (Brownian diffusion), an overwhelming body of work has found that membrane diffusion is nonideal (anomalous diffusion). One of the most powerful methods for studying membrane diffusion is single particle tracking (SPT), which records the trajectory of a label attached to a membrane component of interest. One of the outstanding problems in SPT is the analysis of data to identify the presence of heterogeneity. We have adapted a first-passage time (FPT) algorithm, originally developed for the interpretation of animal movement, for the analysis of SPT data. We discuss the general application of the FPT analysis to molecular diffusion, and use simulations to test the method against data containing known regions of confinement. We conclude that FPT can be used to identify the presence and size of confinement within trajectories of the receptor LFA-1, and these results are consistent with previous reports on the size of LFA-1 clusters. The analysis of trajectory data for cell surface receptors by FPT provides a robust method to determine the presence and size of confined regions of diffusion.

Legitimacy of the stochastic Michaelis–Menten approximation

Michaelis-Menten kinetics are commonly used to represent enzyme-catalysed reactions in biochemical models. The Michaelis-Menten approximation has been thoroughly studied in the context of traditional differential equation models. The presence of small concentrations in biochemical systems, however, encourages the conversion to a discrete stochastic representation. It is shown that the Michaelis-Menten approximation is applicable in discrete stochastic models and that the validity conditions are the same as in the deterministic regime. The authors then compare the Michaelis-Menten approximation to a procedure called the slow-scale stochastic simulation algorithm (ssSSA). The theory underlying the ssSSA implies a formula that seems in some cases to be different from the well-known Michaelis-Menten formula. Here those differences are examined, and some special cases of the stochastic formulas are confirmed using a first-passage time analysis. This exercise serves to place the conventional Michaelis-Menten formula in a broader rigorous theoretical framework.

Crystal nucleation and cluster-growth kinetics in a model glass under shear

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster-growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster-growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency.

Interfacial Properties of an Ionic Liquid by Molecular Dynamics

We studied the influence of a liquid-vapor interface on dynamic properties like reorientation and diffusion as well as the surface tension of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF(6)]) by molecular dynamics simulations. In the interfacial region, reorientation of a short molecular axis is slightly faster than that in the central layer, while that of the longer molecular axis is retarded. The molecular reorientation is well-described by a stretched exponential decay modeled by the Kohlrausch-Williams-Watts equation. Analysis of the average translational diffusion coefficient of molecules in a central layer shows consistency with the Vogel-Fulcher-Tamann equation in a temperature range from 300 to 380 K. A first-passage time analysis of the system at 380 K yields a more refined spatial characterization of translational diffusion perpendicular to the liquid-vapor interfaces. In the central region of the slab, the diffusion coefficient of cations is only marginally higher than that of anions, but close to an interface, this difference is much higher, up to 50%. Apparent activation energies for rotational and diffusional dynamics, respectively, were estimated assuming Arrhenius behavior. They indicate that reorientation of the long molecular axis depends on the diffusion ability, whereas for the reorientation of the short axis, no such correlation is observed. The results are in general agreement with the literature, with slightly overestimated absolute values. This applies as well for the surface tension, where, however, a dependence on the treatment of the electrostatics was found. Particle-mesh Ewald (PME) or reaction field (RF) and the treatment of bonds by constraints have an influence. If no bond constraints are applied, the results are consistent for both methods for the description of the electrostatics.

Spherical First Passage Time: A tool to investigate area-restricted search in three-dimensional movements

A better understanding of animal movements is of crucial importance for investigating numerous ecological issues. Developments in bio-logging technologies largely contributed to the observation and recording of animal displacements. Recently, several devices were developed to track animals in a three-dimensional space. However, given the larger number of variables, these advances generated new analytical problems and currently, few methods exist to analyse 3-D movements. In this study, we present a new technique, the Spherical First Passage Time (SFPT), to determine the scale of search behaviour in a volume. Building on the development of the First Passage Time (FPT) approach, SFPT measures the time required to cross a sphere along a 3-D path. We used simulations as they provide an opportunity to better understand processes involved in a system. Moreover, they offer the advantage of considerably increasing sample size in cases where empiric data remain scarce. However, in order to be more realistic, simulations were constrained within the physiological and behavioural features inherent to a diving animal, in this case beluga whales. First, we modelled three-dimensional movements as a correlated random walk for which the vertical and horizontal dimensions were considered simultaneously. One restricted search event was included in each simulation. Spatial scales obtained with the SFPT approach were compared to those obtained from the classical FPT analysis over the corresponding horizontal path. Results indicate a significant difference between the two approaches, suggesting that, in most cases, an approach in 2-D misrepresents spatial scale of search behaviour occurring in 3-D. Although we tested the SFPT with the example of a diving marine mammal, we argue that this method is applicable for all animals moving in a three-dimensional space.

Biased Diffusive Search Triggered by ATP Binding During Kinesin's Stepping

In this paper, we present an asymmetry conformational potential with a reflecting boundary and an absorbing boundary, in which the diffusive search of the free head of kinesin motor can be biased toward its forward binding site. Under a wide range of condition, using first-passage time analysis we perform numerical simulation to the Langevin equation, and obtain the dependence of the dwell time for forward steps on the load force. And we calculate the expression for the dwell time by the Laplace transform method. Both numerical and analytical results show that the dwell times exponentially depend on the load force, which provide a simple physical explanation for experimental data. Our results suggest that ATP binding-conformation change in the neck linker plays an important role in unidirectional steps during kinesin's mechanochemical cycle.

Fine‐scale foraging behaviour of a medium‐ranging marine predator

1. Movement patterns of predators should allow them to detect and respond to prey patches at different spatial scales, particularly through the adoption of area-restricted search (ARS) behaviour. Here we use fine-scale movement and activity data combined with first-passage time (FPT) analysis to examine the foraging strategy of northern gannets Morus bassanus in the western North Sea, and to test the following hypotheses: (i) birds adopt a hierarchical foraging strategy characterized by nested ARS behaviour; (ii) the locations and characteristics of ARS zones are strongly influenced by physical oceanography; (iii) the initiation of ARS behaviour is triggered by the detection and pursuit of prey; (iv) ARS behaviour is strongly linked to increased foraging effort, particularly within nested ARS areas. 2. Birds on 13 of 15 foraging trips adopted ARS behaviour at a scale of 9.1 +/- 1.9 km, and birds on 10 of these 13 trips adopted a second, nested ARS scale of 1.5 +/- 0.8 km, supporting hypothesis 1 above. ARS zones were located 117 +/- 55 km from the colony and over half were within 5 km of a tidal mixing front ~50 km offshore, supporting hypothesis 2 above. 3. The initiation of ARS behaviour was usually followed after only a short time interval (typically ~5 min) by the commencement of diving. Gannets do not dive until after they have located prey, and so this pattern strongly suggests that ARS behaviour was triggered by prey detection, supporting hypothesis 3 above. However, ~33% of dives in mixed coastal water and 16% of dives in stratified water were not associated with any detectable ARS behaviour. Hence, while ARS behaviour resulted from the detection and pursuit of prey, encounters with prey species did not inevitably induce ARS behaviour. 4. Following the initiation of ARS behaviour, dive rates were almost four times higher within ARS zones than elsewhere and almost three times higher in zones with nested ARS behaviour than in those without, supporting hypothesis 4 above and suggesting that the foraging success of birds was linked to their ability to match the hierarchical distribution of prey.

Balancing with positive feedback: the case for discontinuous control

Experimental observations indicate that positive feedback plays an important role for maintaining human balance in the upright position. This observation is used to motivate an investigation of a simple switch-like controller for postural sway in which corrective movements are made only when the vertical displacement angle exceeds a certain threshold. This mechanism is shown to be consistent with the experimentally observed variations in the two-point correlation for human postural sway. Analysis of first-passage times for this model suggests that this control strategy may slow escape by taking advantage of two intrinsic properties of a stochastic unstable first-order delay differential equation: (i) time delay and (ii) the possibility that the dynamics can be 'temporarily confined' near the origin.

A multi-patch use of the habitat: testing the First-Passage Time analysis on roe deer Capreolus capreolus paths

A heterogeneous environment includes several levels of resource aggregation. Individuals do not respond to this heterogeneity in the same way and their responses depend on the scale at which they perceive it, and they develop different foraging tactics accordingly. The development of methods to analyse animal movements has enabled the study of foraging tactics at several scales. Nevertheless, applied to large vertebrates, these methods have generally been used at large scales, such as for migration trips or for the study of marine patches several kilometres large. In our study, we applied a recent method, the First-Passage Time analysis, based on a measure of the foraging effort along the path, to a much finer scale, i.e. <500 m. We used 30 daily paths of highly sedentary roe deer Capreolus capreolus females. We modified the initial method, developed by Fauchald & Tveraa (2003), to detect a multi-patch use of the habitat. First-Passage Time analysis results showed that most of the female roe deer exploited their home range as a patchy resource, ranging within 1–5 areas of intensive use in their home range. These areas were identified as the most attractive sites within the roe deer female home range. Moreover, this method allowed us to rank the attractive areas according to the time spent in each area. Coupled with habitat selection analysis to identify what makes these areas attractive, the First-Passage Time analysis should offer a suitable tool for landscape ecology and management.

Assessment of scale‐dependent foraging behaviour in southern elephant seals incorporating the vertical dimension: a development of the First Passage Time method

1. Identifying the spatial scales at which top marine predators forage is important for understanding oceanic ecosystems. Several methods quantify how individuals concentrate their search effort along a given path. Among these, First-Passage Time (FPT) analysis is particularly useful to identify transitions in movement patterns (e.g. between searching and feeding). This method has mainly been applied to terrestrial animals or flying seabirds that have little or no vertical component to their foraging, so we examined the differences between classic FPT and a modification of this approach using the time spent at the bottom of a dive for characterizing the foraging activity of a diving predator: the southern elephant seal. 2. Satellite relayed data loggers were deployed on 20 individuals during three successive summers at the Kerguelen Islands, providing a total of 72 978 dives from eight juvenile males and nine adult females. 3. Spatial scales identified using the time spent at the bottom of a dive ( = 68.2 +/- 42.1 km) were smaller than those obtained by the classic FPT analysis ( = 104.7 +/- 67.3 km). Moreover, foraging areas identified using the new approach clearly overlapped areas where individuals increased their body condition, indicating that it accurately reflected the foraging activity of the seals. 4. These results suggest that incorporating the vertical dimension into FPT provides a different result to the surface path alone. Close to the Antarctic continent, within the pack-ice, sinuosity of the path could be explained by a high sea-ice concentration (restricting elephant seal movements), and was not necessarily related to foraging activity. 5. Our approach distinguished between actual foraging activity and changes in behaviour induced by the physical environment like sea ice, and could be applied to other diving predators. Inclusion of diving parameters appears to be essential to identify the spatial scale of foraging areas of diving animals.

A novel method for quantifying habitat selection and predicting habitat use

1 The study of habitat selection and habitat use are crucial for understanding the biological requirements of animals and the strategies they use to fulfil their needs. A variety of statistical techniques are available to quantify habitat selection, most of them based on the comparison of habitat attributes in sites used by the animals and in unused, but available, sites. Because of the difficulties in defining what is available from an animal's perspective for many species, statistical approaches such as first-passage time (FPT) analysis have been developed, which explore habitat-use intensities through the areas used by animals. 2 In this study, we expand on that approach by using FPT-derived data within the framework of mixed-effects Cox proportional hazards models (CPH models) to quantify habitat selection. By modelling FPTs, CPH models evaluate which habitat attributes best explain the ‘risk’ or ‘hazard’ of the animal leaving an area of a given radius. For quantitative interpretations, the coefficients of the CPH model can be used to calculate hazard ratios that estimate relative habitat preferences: the lower the hazard ratio (i.e. the lower the risk of leaving), the higher the preference. Accounting for individual variability in habitat use by means of a random-effect term added to CPH models provides inferences that more appropriately reflect the typical hierarchical structure of telemetric data on animal space use. 3 Synthesis and applications. In addition to providing inferences about habitat selection based on the estimated parameters, survival functions of fixed-effects CPH models can be used to construct spatial predictions, for instance maps of population-level space use. Such predictions can be particularly useful for applied purposes, for example as a basis for species conservation plans and reserve selection. The method is illustrated using two data sets from marine mammal species: ringed seals Phoca hispida and white whales Delphinapterus leucas, but it is broadly applicable to habitat selection and prediction studies of other highly mobile animals in marine or terrestrial systems.

MEASUREMENT ERROR CAUSES SCALE-DEPENDENT THRESHOLD EROSION OF BIOLOGICAL SIGNALS IN ANIMAL MOVEMENT DATA

Recent advances in telemetry technology have created a wealth of tracking data available for many animal species moving over spatial scales from tens of meters to tens of thousands of kilometers. Increasingly, such data sets are being used for quantitative movement analyses aimed at extracting fundamental biological signals such as optimal searching behavior and scale-dependent foraging decisions. We show here that the location error inherent in various tracking technologies reduces the ability to detect patterns of behavior within movements. Our analyses endeavored to set out a series of initial ground rules for ecologists to help ensure that sampling noise is not misinterpreted as a real biological signal. We simulated animal movement tracks using specialized random walks known as Lévy flights at three spatial scales of investigation: 100-km, 10-km, and 1-km maximum daily step lengths. The locations generated in the simulations were then blurred using known error distributions associated with commonly applied tracking methods: the Global Positioning System (GPS), Argos polar-orbiting satellites, and light-level geolocation. Deviations from the idealized Lévy flight pattern were assessed for each track after incrementing levels of location error were applied at each spatial scale, with additional assessments of the effect of error on scale-dependent movement patterns measured using fractal mean dimension and first-passage time (FPT) analyses. The accuracy of parameter estimation (Lévy mu, fractal mean D, and variance in FPT) declined precipitously at threshold errors relative to each spatial scale. At 100-km maximum daily step lengths, error standard deviations of > or = 10 km seriously eroded the biological patterns evident in the simulated tracks, with analogous thresholds at the 10-km and 1-km scales (error SD > or = 1.3 km and 0.07 km, respectively). Temporal subsampling of the simulated tracks maintained some elements of the biological signals depending on error level and spatial scale. Failure to account for large errors relative to the scale of movement can produce substantial biases in the interpretation of movement patterns. This study provides researchers with a framework for understanding the limitations of their data and identifies how temporal subsampling can help to reduce the influence of spatial error on their conclusions.

At‐sea distribution and scale‐dependent foraging behaviour of petrels and albatrosses: a comparative study

1. In order to study and predict population distribution, it is crucial to identify and understand factors affecting individual movement decisions at different scales. Movements of foraging animals should be adjusted to the hierarchical spatial distribution of resources in the environment and this scale-dependent response to environmental heterogeneity should differ according to the forager's characteristics and exploited habitats. 2. Using First-Passage Time analysis, we studied scales of search effort and habitat used by individuals of seven sympatric Indian Ocean Procellariiform species fitted with satellite transmitters. We characterized their search effort distribution and examined whether species differ in scale-dependent adjustments of their movements according to the marine environment exploited. 3. All species and almost all individuals (91% of 122 individuals) exhibited an Area-Restricted Search (ARS) during foraging. At a regional scale (1000s km), foraging ranges showed a large spatial overlap between species. At a smaller scale (100s km, at which an increase in search effort occurred), a segregation in environmental characteristics of ARS zones (where search effort is high) was found between species. 4. Spatial scales at which individuals increased their search effort differed between species and also between exploited habitats, indicating a similar movement adjustment for predators foraging in the same habitat. ARS zones of the two populations of wandering albatross Diomedea exulans (Crozet and Kerguelen) were similar in their adjustments (i.e. same ARS scale) as well as in their environmental characteristics. These two populations showed a weak spatial overlap in their foraging distribution, with males foraging in more southerly waters than females in both populations. 5. This study demonstrates that predators of several species adjust their foraging behaviour to the heterogeneous environment and these scale-dependent movement adjustments depend on both forager and environment characteristics.

Foraging destinations and marine habitat use of short-tailed albatrosses: A multi-scale approach using first-passage time analysis

Abstract We used satellite telemetry, remotely sensed data (bathymetry, chlorophyll a (chl a), sea-surface temperature (SST), wind speed) and first-passage time (FPT) analysis to determine the distribution, movement patterns, and habitat associations of short-tailed albatrosses (Phoebastria albatrus) during the non-breeding season, 2002 and 2003. Satellite transmitters were deployed on birds immediately prior to their departure from a breeding colony at Torishima, Japan ( n = 11 ), or at-sea in the Aleutian Islands ( n = 3 ). Tracking durations ranged from 51 to 138 days for a total of 6709 locations after filtering (131 – 808 per bird). FPT (time required to transit a circle of given radius) revealed the location and spatial scale of area-restricted search (ARS) patterns along flight paths. On average, ARS occurred within 70 km radii. Consequently, the fit of the habitat use models increased at spatial scales beyond a 40 km FPT radius ( R 2 = 0.31 ) and stabilized for scales of 70 km and larger (R2=0.40– 0.51). At all scales, wind speed, depth or depth gradient, and chl a or chl a gradient had a significant effect on FPT (i.e., residence time). FPT increased within regions of higher gradients of depth and chl a. In contrast, FPT decreased within regions of greater depth and wind speed, with a significant interaction of wind speed and depth at some scales. Sea-surface temperature or its interactions were only significant at large spatial scales (⩾160 km FPT radius). Albatrosses engaged in ARS activities primarily over the shelf break and slope, including Kuroshio and Oyashio regions off the western subarctic gyre. Occasionally, birds transited the northern boundary of the Kuroshio Extension while in-route to the Aleutian Islands and Bering Sea, but overall spent little time in the western gyre. In the Aleutian Islands, ARS occurred within straits, particularly along the central and western part of the archipelago. In the Bering Sea, ARS occurred along the northern continental shelf break, the Kamchatka Current region, and east of the Commander Islands. Non-breeding short-tailed albatross concentrate foraging in oceanic areas characterized by gradients in topography and water column productivity. This study provides an understanding of the foraging ecology for a highly migratory, imperiled seabird, and confirms the importance of shelf break and slope regions as hot spots for a variety of top marine predators in the North Pacific.

Scale‐dependent habitat use in a long‐ranging central place predator

1 It is predicted that the movements of foraging animals are adjusted to the hierarchical spatial distribution of resources in the environment, and that decisions to modify movement in response to heterogeneous resource distribution are scale-dependent. Thus, controlling for spatial scales of interaction with environment is critical for a better understanding of habitat selection, which is likely to follow scale-dependent processes. 2 Here we study the scales of interactions and habitat selection in a long-ranging marine predator foraging from a central place, the yellow-nosed albatross. We use first-passage time analysis to identify the scales of interaction with environmental variables and compositional analysis to study habitat selection. 3 Of 26 birds, 22 adopted an area restricted search (ARS) at a scale of 130 ± 85 km, and 11 of these 22 birds adopted a second, nested ARS scale at 34 ± 20 km. Habitat use differed according to the spatial scale considered. At the oceanic basin macro-scale, birds foraged in pelagic, subtropical waters. Birds commuted to the ARS zones after a c. 1500-km trip to reach predictable turbulence zones from Agulhas return current, where primary productivity was enhanced at large scale. At a smaller, meso-scale, birds increased their search effort according to sea surface height anomalies (SSHa) and chlorophyll-a concentrations (Chl-a), indicating association with productive cyclonic eddies. 4 Among birds, differences in search pattern were noted: 11 birds concentrated their search effort directly at a small scale of 77 ± 22 km, avoiding anticyclonic eddies. The 11 other birds showed two scales of ARS pattern: (i) first at 180 ± 90 km with a preference for high Chl-a concentrations but unrelated to SSHa; and (ii) secondly at a nested scale at 34 ± 20 km related exclusively to SSHa where prey patches were expected to be distributed at this scale. This second group of birds appeared to be less efficient, spending more time at sea for the same mass gain than the first group. 5 Our study is the first to demonstrate scale-dependent adjustments, with interindividual variability, in relation to environmental features for predators with a central-place constraint.

Power law diffusion coefficient and anomalous diffusion: Analysis of solutions and first passage time

We investigate one-dimensional equations for the diffusion with a nonconstant diffusion coefficient inside the second derivative and between the derivatives. In particular, we employ the diffusion coefficient D(x) proportional to /x/(-theta)(theta in R) and a quartic potential. These diffusion equations present a rich variety of behaviors associated with different regimes. Results of two approaches are analyzed and compared. We also investigate the mean first passage time of these systems. We show that the system with the coefficient D(x) between the derivatives can produce different behaviors for the mean first passage time in comparison with those obtained by the system with the coefficient inside the derivatives.

Exact computation of the mean velocity, molecular diffusivity, and dispersivity of a particle moving on a periodic lattice

A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice among an array of immobile, impenetrable obstacles. The results of this Taylor–Aris dispersion-based theory are exact, at least in an asymptotic sense, and furnish an analytical alternative to conventional numerical lattice Monte Carlo simulation techniques. Results obtained for an obstacle-free lattice are employed to establish generic relationships between the transition probabilities, lattice size, and jump time. As an example, the dispersivity is computed for a solute moving through an isotropic array of obstacles under the influence of a finite external field. The calculation scheme is also shown to agree with existing zero-field results, the latter obtained elsewhere either by first-passage time analysis or use of the Nernst–Einstein equation in the zero-field limit. The generality of this scheme permits the study of more complex lattice structures, in particular trapping geometries.