scholarly journals Scaling laws of ambush predator ‘waiting’ behaviour are tuned to a common ecology

2014 ◽  
Vol 281 (1782) ◽  
pp. 20132997 ◽  
Author(s):  
Victoria J. Wearmouth ◽  
Matthew J. McHugh ◽  
Nicolas E. Humphries ◽  
Aurore Naegelen ◽  
Mohammed Z. Ahmed ◽  
...  
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Group Formation ◽  
Waiting Times ◽  
Natural Environments ◽  
Scale Invariant ◽  
Foraging Mode ◽  
Predator Species ◽  
Magnitude Scaling ◽  
Species Specific

The decisions animals make about how long to wait between activities can determine the success of diverse behaviours such as foraging, group formation or risk avoidance. Remarkably, for diverse animal species, including humans, spontaneous patterns of waiting times show random ‘burstiness’ that appears scale-invariant across a broad set of scales. However, a general theory linking this phenomenon across the animal kingdom currently lacks an ecological basis. Here, we demonstrate from tracking the activities of 15 sympatric predator species (cephalopods, sharks, skates and teleosts) under natural and controlled conditions that bursty waiting times are an intrinsic spontaneous behaviour well approximated by heavy-tailed (power-law) models over data ranges up to four orders of magnitude. Scaling exponents quantifying ratios of frequent short to rare very long waits are species-specific, being determined by traits such as foraging mode (active versus ambush predation), body size and prey preference. A stochastic–deterministic decision model reproduced the empirical waiting time scaling and species-specific exponents, indicating that apparently complex scaling can emerge from simple decisions. Results indicate temporal power-law scaling is a behavioural ‘rule of thumb’ that is tuned to species’ ecological traits, implying a common pattern may have naturally evolved that optimizes move–wait decisions in less predictable natural environments.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Clustered continuous-time random walks: diffusion and relaxation consequences

2012 ◽  
Vol 468 (2142) ◽  
pp. 1615-1628 ◽  
Author(s):  
Karina Weron ◽  
Aleksander Stanislavsky ◽  
Agnieszka Jurlewicz ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Continuous Time ◽  
Waiting Times ◽  
Scaling Limit ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
The Novel ◽  
Fractional Diffusion Equations ◽  
Continuous Time Random Walks

We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.

KINETIC RESPONSE OF SURFACES DEFINED BY FINITE FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (04) ◽  
pp. 461-476 ◽  
Author(s):  
PRADEEP R. NAIR ◽  
MUHAMMAD A. ALAM
Keyword(s):  
Scaling Laws ◽  
Finite Size ◽  
Critical Dimension ◽  
The Novel ◽  
Scale Invariant ◽  
Fractal Surfaces ◽  
Dimension Formula ◽  
Diffusion Limited ◽  
Engineered Systems ◽  
Size Limits

Historically, fractal analysis has been remarkably successful in describing wide ranging kinetic processes on (idealized) scale invariant objects in terms of elegantly simple universal scaling laws. However, as nanostructured materials find increasing applications in energy storage, energy conversion, healthcare, etc., one must reexamine the premise of traditional fractal scaling laws as it only applies to physically unrealistic infinite systems, while all natural/engineered systems are necessarily finite. In this article, we address the consequences of the 'finite-size' problem in the context of time dependent diffusion towards fractal surfaces via the novel technique of Cantor-transforms to (i) illustrate how finiteness modifies its classical scaling exponents; (ii) establish that for finite systems, the diffusion-limited reaction is decelerated below a critical dimension [Formula: see text] and accelerated above it; and (iii) to identify the crossover size-limits beyond which a finite system can be considered (practically) infinite and redefine the very notion of 'finiteness' of fractals in terms of its kinetic response. Our results have broad implications regarding dynamics of systems defined by the same fractal dimension, but differentiated by degree of scaling iteration or morphogenesis, e.g. variation in lung capacity between a child and adult.

scholarly journals Evidence for a pervasive ‘idling-mode’ activity template in flying and pedestrian insects

2015 ◽  
Vol 2 (5) ◽  
pp. 150085 ◽  
Author(s):  
Andrew M. Reynolds ◽  
Hayley B. C. Jones ◽  
Jane K. Hill ◽  
Aislinn J. Pearson ◽  
Kenneth Wilson ◽  
...  
Keyword(s):  
Activity Patterns ◽  
Movement Ecology ◽  
Movement Patterns ◽  
Environmental Cues ◽  
Natural Environments ◽  
Scale Invariant ◽  
Scale Free ◽  
Flight Mills ◽  
Innate Behaviour ◽  
Multiple Species

Understanding the complex movement patterns of animals in natural environments is a key objective of ‘movement ecology’. Complexity results from behavioural responses to external stimuli but can also arise spontaneously in their absence. Drawing on theoretical arguments about decision-making circuitry, we predict that the spontaneous patterns will be scale-free and universal, being independent of taxon and mode of locomotion. To test this hypothesis, we examined the activity patterns of the European honeybee, and multiple species of noctuid moth, tethered to flight mills and exposed to minimal external cues. We also reanalysed pre-existing data for Drosophila flies walking in featureless environments. Across these species, we found evidence of common scale-invariant properties in their movement patterns; pause and movement durations were typically power law distributed over a range of scales and characterized by exponents close to 3/2. Our analyses are suggestive of the presence of a pervasive scale-invariant template for locomotion which, when acted on by environmental cues, produces the movements with characteristic scales observed in nature. Our results indicate that scale-finite complexity as embodied, for instance, in correlated random walk models, may be the result of environmental cues overriding innate behaviour, and that scale-free movements may be intrinsic and not limited to ‘blind’ foragers as previously thought.

scholarly journals The importance of motivation, weapons, and foul odors in driving encounter competition in carnivores

2020 ◽  
Author(s):  
ML Allen ◽  
CC Wilmers ◽  
LM Elbroch ◽  
JM Golla ◽  
Heiko Wittmer
Keyword(s):  
Interference Competition ◽  
Current Theory ◽  
Lynx Rufus ◽  
Natural Environments ◽  
Ecological Communities ◽  
Competitive Advantages ◽  
Ecological Society ◽  
Strategic Behaviors ◽  
Species Specific ◽  
Occurrence Patterns

© 2016 by the Ecological Society of America. Encounter competition is interference competition in which animals directly contend for resources. Ecological theory predicts the trait that determines the resource holding potential (RHP), and hence the winner of encounter competition, is most often body size or mass. The difficulties of observing encounter competition in complex organisms in natural environments, however, has limited opportunities to test this theory across diverse species. We studied the outcome of encounter competition contests among mesocarnivores at deer carcasses in California to determine the most important variables for winning these contests. We found some support for current theory in that body mass is important in determining the winner of encounter competition, but we found that other factors including hunger and species-specific traits were also important. In particular, our top models were "strength and hunger" and "size and hunger," with models emphasizing the complexity of variables influencing outcomes of encounter competition. In addition, our wins above predicted (WAP) statistic suggests that an important aspect that determines the winner of encounter competition is species-specific advantages that increase their RHP, as bobcats (Lynx rufus) and spotted skunks (Spilogale gracilis) won more often than predicted based on mass. In complex organisms, such as mesocarnivores, species-specific adaptations, including strategic behaviors, aggressiveness, and weapons, contribute to competitive advantages and may allow certain species to take control or defend resources better than others. Our results help explain how interspecific competition shapes the occurrence patterns of species in ecological communities.

scholarly journals Non-trivial avalanches triggered by shear banding in compression of metallic glass foams

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200186
Author(s):  
H. Lin ◽  
C. lu ◽  
H. Y. Wang ◽  
L. H. Dai
Keyword(s):  
Metallic Glass ◽  
Scaling Laws ◽  
Waiting Times ◽  
Shear Banding ◽  
Shear Bands ◽  
Mean Field ◽  
Structural Disorder ◽  
Aftershock Sequence ◽  
Atomic Scale ◽  
Characteristic Time Scale

Ductile metallic glass foams (DMGFs) are a new type of structural material with a perfect combination of high strength and toughness. Owing to their disordered atomic-scale microstructures and randomly distributed macroscopic voids, the compressive deformation of DMGFs proceeds through multiple nanoscale shear bands accompanied by local fracture of cellular structures, which induces avalanche-like intermittences in stress–strain curves. In this paper, we present a statistical analysis, including distributions of avalanche size, energy dissipation, waiting times and aftershock sequence, on such a complex dynamic process, which is dominated by shear banding. After eliminating the influence of structural disorder, we demonstrate that, in contrast to the mean-field results of their brittle counterparts, scaling laws in DMGFs are characterized by different exponents. It is shown that the occurrence of non-trivial scaling behaviours is attributed to the localized plastic yielding, which effectively prevents the system from building up a long-range correlation. This accounts for the high structural stability and energy absorption performance of DMGFs. Furthermore, our results suggest that such shear banding dynamics introduce an additional characteristic time scale, which leads to a universal gamma distribution of waiting times.

scholarly journals Space–Time Duality for Fractional Diffusion

2009 ◽  
Vol 46 (4) ◽  
pp. 1100-1115 ◽  
Author(s):  
Boris Baeumer ◽  
Mark M. Meerschaert ◽  
Erkan Nane
Keyword(s):  
Contaminant Transport ◽  
Power Law ◽  
Fractional Derivatives ◽  
Waiting Times ◽  
Stable Process ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equations ◽  
Lévy Motion ◽  
Current Controversy ◽  
A Current

Zolotarev (1961) proved a duality result that relates stable densities with different indices. In this paper we show how Zolotarev's duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer-order derivatives. They govern scaling limits of random walk models, with power-law jumps leading to fractional derivatives in space, and power-law waiting times between the jumps leading to fractional derivatives in time. The limit process is a stable Lévy motion that models the jumps, subordinated to an inverse stable process that models the waiting times. Using duality, we relate the density of a spectrally negative stable process with index 1<α<2 to the density of the hitting time of a stable subordinator with index 1/α, and thereby unify some recent results in the literature. These results provide a concrete interpretation of Zolotarev's duality in terms of the fractional diffusion model. They also illuminate a current controversy in hydrology, regarding the appropriate use of space- and time-fractional derivatives to model contaminant transport in river flows.

scholarly journals Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Long Shi
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Power Law ◽  
Continuous Time ◽  
Continuum Limit ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Continuous Time Random Walk ◽  
Mean Square ◽  
The Mean

In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function M(t)=tρ(ρ>-1). In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form 〈x2(t)〉∝tH=t1/(1+ρ+1/α). The anomy exponent H varies from α to α/(1+α) when -1<ρ<0 and from α/(1+α) to 0 when ρ>0. The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.

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