The “Lévy or Diffusion” Controversy: How Important Is the Movement Pattern in the Context of Trapping?

Ahmed, Danish A.; Petrovskii, Sergei; Tilles, Paulo F. C.

doi:10.3390/math6050077

Cited by 9 publications

(7 citation statements)

References 88 publications

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“…In the context of trapping, it was recently shown that almost identical trap counts are reproduced for inherently different movement models, such as BM with time dependent mobility rate and the LW, which suggests that the type of underlying movement pattern is not that important after all, unless placed under some ecological context, e.g. pest monitoring (Ahmed et al., ). Although controversy persists, our motivation for including LWs stems from the fact that such mechanistic processes have received much attention in the movement ecology literature (Reynolds, ).…”

Section: Discussionmentioning

confidence: 99%

“…In the literature, other more complicated processes have been documented, such as; intermittent stop‐start movement (Mashanova, Olive, & Jansen, ), behavioural intensive‐extensive changes (Knell & Codling, ), individual interactions (De Jager, Weissing, Herman, Nolet, & de Koppel, ), density or time dependent diffusion (Ahmed & Petrovskii, ; Ellis, Petrovskaya, & Petrovskii, ), Lévy walks (LW; Sims et al., ) or even a mixture or composition of the above (Auger‐Méthé, Derocher, Plank, & Codling, ). The issue is more perplexing, since movement patterns can be misidentified (Petrovskii, Mashanova, & Jansen, ) or even, in the context of trapping, almost identical trap counts can be reproduced for inherently different movement models (Ahmed, Petrovskii, & Tilles, ). Also, the conceptual case of BM is often revisited due to its relative simplicity and on occasion shown to be in excellent agreement with field data (Bearup et al., ).…”

Section: Introductionmentioning

confidence: 99%

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Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

Ahmed

Petrovskii

2019

Methods Ecol Evol

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The most reliable estimates of the population abundance of ground‐dwelling arthropods are obtained almost entirely through trap counts. Trap shape can be easily controlled by the researcher, commonly the same trap design is employed in all sites within a given study. Few researchers really try to compare abundances (numbers of collected individuals) between studies because these are heavily influenced by environmental conditions, e.g. temperature, habitat structure and food sources available, directly affecting insect movement activity. We propose that useful insights can be obtained from a theoretical‐based approach. We focus on the interplay between trap shape (circle, square, slot), the underlying movement behaviour and the subsequent effect on captures. We simulate trap counts within these different geometries whilst considering movement processes with clear distinct properties, such as Brownian motion (BM), the correlated random walk (CRW) and the Lévy walk (LW). (a) We find that slot shaped traps are far less efficient than circular or square traps assuming same perimeter length, with differences which can exceed more than two‐fold. Such impacts of trap geometry are only realized if insect mobility is sufficiently large, which is known to significantly vary depending on type of habitat. (b) If the movement pattern incorporates localized forward persistence then trap counts accumulate at a much slower rate, and this rate decreases further with higher persistency. (c) If the movement behaviour is of Lévy type, then fastest catch rates are recorded in the case of circular trap, and the slowest for the slot trap, indicating that trap counts can strongly depend on trap shape. Lévy walks exacerbate the impact of geometry while CRW make these differences more inconsequential. In this study we reveal trap efficiencies and how movement type can alter capture rates. Such information contributes towards improved trap count interpretations, as required in ecological studies which make use of trapping systems.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

Ahmed

Petrovskii

2019

Methods Ecol Evol

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“…The x min value, in this case, was set at the smallest non-zero value of the data rather than the value for x min calculated by power.law.fit function (Virkar and Clauset, 2014). Secondly, a power-law fitting only the tail of the data was considered as this is an indicative feature of Lévy walk behaviour (Edwards et al ., 2007; Sims et al ., 2007; Reynolds et al ., 2013; Ahmed et al ., 2018). The tail of the data was calculated by using the best fit x min value calculated by the power.law.fit() function.…”

Section: Methodsmentioning

confidence: 99%

Walking behaviour in the ground beetle,Poecilus cupreus: dispersal potential, intermittency and individual variation

Bailey

Benefer

Blackshaw

et al. 2020

Bull. Entomol. Res.

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Dispersal is a key ecological process affecting community dynamics and the maintenance of populations. There is increasing awareness of the need to understand individual dispersal potential to better inform population-level dispersal, allowing more accurate models of the spread of invasive and beneficial insects, aiding crop and pest management strategies. Here, fine-scale movements of Poecilus cupreus, an important agricultural carabid predator, were recorded using a locomotion compensator and key movement characteristics were quantified. Net displacement increased more rapidly than predicted by a simple correlated random walk model with near ballistic behaviour observed. Individuals displayed a latent ability to head on a constant bearing for protracted time periods, despite no clear evidence of a population level global orientation bias. Intermittent bouts of movement and non-movement were observed, with both the frequency and duration of bouts of movement varying at the inter- and intra-individual level. Variation in movement behaviour was observed at both the inter- and intra- individual level. Analysis suggests that individuals have the potential to rapidly disperse over a wider area than predicted by simple movement models parametrised at the population level. This highlights the importance of considering the role of individual variation when analysing movement and attempting to predict dispersal distances.

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“…Different types of movement behaviours can be characterized by the rate of asymptotic decay in the end tail of the step length distribution λ (l). If the end tail decays exponentially or faster (referred to as a 'thin' tail), then the variance of step lengths is finite, and therefore the movement process is scale-specific and diffusive (Kareiva and Shigesada, 1983;Codling et al, 2008;Ahmed et al, 2018). See for example, the case of the SRW with Rayleigh distributed step lengths in equation 5.…”

Section: The Correlated Lévy Walkmentioning

confidence: 99%

Mechanistic modelling of coronavirus infections and the impact of confined neighbourhoods on a short time scale

Ahmed

Ansari

Imran

et al. 2020

Preprint

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Background: To mitigate the spread of the COVID-19 coronavirus, some countries have adopted more stringent non-pharmaceutical interventions in contrast to those widely used (for e.g. the state of Kuwait). In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies such as the total confinement of highly populated areas has also been implemented.Methods: In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host may be infected if in close spatial proximity of the infectious host. Our focus is only on the short-time scale prior to the infectious period, so that no further transmission is assumed.Results: We find that the level of infection depends heavily on the population dynamics, and increases in the case of slow population diffusion, but remains stable for a high or superdiffusive population. Also, we find that the confinement of homogeneous or overcrowded sub-populations has minimal impact in the short term.Conclusion: Our results indicate that on a short time scale, confinement restrictions or complete lock down of whole residential areas may not be effective. Finally, we discuss the possible implications of our findings for total confinement in the context of the current situation in Kuwait.

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The “Lévy or Diffusion” Controversy: How Important Is the Movement Pattern in the Context of Trapping?

Cited by 9 publications

References 88 publications

Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

Walking behaviour in the ground beetle,Poecilus cupreus: dispersal potential, intermittency and individual variation

Mechanistic modelling of coronavirus infections and the impact of confined neighbourhoods on a short time scale

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