Mathematical Bases for 2D Insect Trap Counts Modelling

Ahmed, Danish A.; Bailey, Joseph D.; Petrovskii, Sergei; Bonsall, Michael B.

doi:10.1007/978-3-030-69951-2_6

Cited by 2 publications

(4 citation statements)

References 52 publications

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“…where E [v] is the mean speed and L = nE[l] is the total path length (Benhamou, 2004(Benhamou, , 2006Codling et al, 2008, see also Ahmed et al, 2021).…”

Section: Asymptotic Msd As Followsmentioning

confidence: 99%

“…The sinuosity index S measures the tortuosity in an individual's movement path, and can be related to the diffusion coefficient as

S goodbreak= \sqrt{\frac{E [v]}{D}} goodbreak= 2 \sqrt{\frac{L}{MS {normalD}^{*}}},

where E [ v ] is the mean speed and L = nE [ l ] is the total path length (Benhamou, 2004, 2006; Codling et al, 2008, see also Ahmed et al, 2021).…”

Section: Modelling Movement and Trapping Of Ground‐dwelling Arthropodsmentioning

confidence: 99%

“…However, in the case of circular traps, if the mean step length is less than the trap diameter (i.e. E [ l ] < 2 r ), then the probability of undetected trap passes is very low, and thus the impact on trap counts is negligible (see figure 6.4 in Ahmed et al, 2021).…”

Section: Modelling Movement and Trapping Of Ground‐dwelling Arthropodsmentioning

confidence: 99%

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Simulating capture efficiency of pitfall traps based on sampling strategy and the movement of ground‐dwelling arthropods

Ahmed,

Beidas,

Petrovskii

et al. 2023

Methods Ecol Evol

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Pitfall traps are frequently used to capture ground‐dwelling arthropods, particularly beetles, ants and spiders. The capture efficiency of a pitfall trapping system strongly depends on the number and opening size of traps, how traps are distributed over the sampling area (spatial arrangement) and the movement characteristics of arthropods. We use numerical simulations for a single species to analyse the trap count patterns that emerge from these variables. Arthropod movement of individuals is modelled as correlated random walks, with multiple traps placed over an area, and catches are simulated as individual interaction with traps. We consider four different types of spatial arrangements of traps across a homogeneous landscape: grid (i.e. rectangular array), transect, nested‐cross and randomised. We contextualise our results by considering the locomotion of Pterostichus melanarius, a highly active carabid beetle often serving as a biocontrol agent for the suppression of pest insects and weeds. By simulating the trapping of randomly moving ground‐dwelling arthropods, we show that there is an optimal inter‐trap separation distance (trap spacing) that maximises captures, that can be expressed using exact formulae in terms of trap opening sizes, sampling area and trap number. Moreover, for the grid and nested‐cross arrangements, larger trap spacing to maximise spatial coverage over the whole sampling area is suboptimal. Also, we find that over a large sampling area, there is a hierarchical order for spatial arrangements in relation to capture efficiency: grid, randomised, transect, followed by the nested‐cross. However, over smaller sampling areas, this order is changed as the rate at which trap counts accumulate with trap number varies across arrangements—eventually saturating at different levels. In terms of movement effects, capture efficiency is maximised over a narrow diffusive range and does not depend strongly on the type of spatial arrangement—indicating an approximate optimal mode of arthropod activity, i.e. rate of spread. Our approach simultaneously considers several important experimental design aspects of pitfall trapping providing a basis to optimise and adapt sampling protocols to other types of traps to better reflect their various purposes, such as monitoring, conservation or pest management.

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“…where E [v] is the mean speed and L = nE[l] is the total path length (Benhamou, 2004(Benhamou, , 2006Codling et al, 2008, see also Ahmed et al, 2021).…”

Section: Asymptotic Msd As Followsmentioning

confidence: 99%

“…The sinuosity index S measures the tortuosity in an individual's movement path, and can be related to the diffusion coefficient as

S goodbreak= \sqrt{\frac{E [v]}{D}} goodbreak= 2 \sqrt{\frac{L}{MS {normalD}^{*}}},

where E [ v ] is the mean speed and L = nE [ l ] is the total path length (Benhamou, 2004, 2006; Codling et al, 2008, see also Ahmed et al, 2021).…”

Section: Modelling Movement and Trapping Of Ground‐dwelling Arthropodsmentioning

confidence: 99%

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Simulating capture efficiency of pitfall traps based on sampling strategy and the movement of ground‐dwelling arthropods

Ahmed,

Beidas,

Petrovskii

et al. 2023

Methods Ecol Evol

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“…A direct consequence is that the mean-squared displacement (MSD) is defined (i.e., the expected value of the squared beeline distance between an individuals' initial and final positions), which is a key metric to analyse movement paths and can be expressed as an exact formula in terms of the number of steps in the walk and the mean-squared step length (Kareiva and Shigesada, 1983). Therefore, any two scale-specific RWs that are parametrised differently can be related by assuming equal MSD (Ahmed et al, 2021b). A specific example of a movement process that has a thin-tailed dispersal kernel is Brownian motion.…”

Section: Introductionmentioning

confidence: 99%

Equivalence between short- and long-distance dispersal in individual animal movement

Ahmed,

Petrovskii

et al. 2024

Preprint

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Random walks (RW) provide a useful modelling framework for the movement of animals at an individual level. If the RW is uncorrelated and unbiased such that the direction of movement is completely random, the dispersal is characterised by the statistical properties of the probability distribution of step lengths, or the dispersal kernel. Whether an individual exhibits short-or long-distance dispersal can be distinguished by the rate of asymptotic decay in the end-tail of the distribution of step-lengths. If the decay is exponential or faster, referred to as a thin-tail, then the step length variance is finite -as occurs in Brownian motion. On the other hand, inverse power-law step length distributions have a heavy end-tail with slower decay, resulting in an infinite step length variance, which is the hallmark of a Lévy walk. Although different approaches to relate these different dispersal mechanisms have been used, they are ad hoc and sub-optimal. We provide a more robust method by ensuring that the survival probability, that is the probability of occurrence of steps longer than a fixed characteristic step length is the same for both distributions. Moreover, we derive an optimal value for the survival probability by minimising the L2-distance between the dispersal kernels. By computing the optimal probability for movement paths with commonly used thin- and heavy-tailed step length distributions, we form equivalence between short-and long-distance dispersal of animals in different spatial dimensions. We also demonstrate how our findings can be applied to ecological scenarios, to more accurately relate dispersal mechanisms within a modelling framework for spatio-temporal population dynamics.

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Mathematical Bases for 2D Insect Trap Counts Modelling

Cited by 2 publications

References 52 publications

Simulating capture efficiency of pitfall traps based on sampling strategy and the movement of ground‐dwelling arthropods

Simulating capture efficiency of pitfall traps based on sampling strategy and the movement of ground‐dwelling arthropods

Equivalence between short- and long-distance dispersal in individual animal movement

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