Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

Ahmed, Danish A.; Benhamou, Simon; Bonsall, Michael B.; Petrovskii, Sergei

doi:10.1016/j.jtbi.2021.110728

Cited by 14 publications

(4 citation statements)

References 67 publications

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“…Flies in the field cage experiments had to reorient after being replaced at the release point and yet, as a group, flies chose subsequent flight directions within 90˚left or right of the directly previous flight (Fig 3). Turning angle biases observed throughout this study may be examples what is known as 'persistence' or 'forward persistence' [82], the tendency observed in many animals towards forward movement [83][84][85]. Correlations between successive step orientations led to the development of the correlated random walk model (CRW) [82] and successive models such as biased random walk (BRW, consistent bias in a preferred direction or towards a target), and biased and correlated random walk (BCRW) [85].…”

Section: Plos Onementioning

confidence: 72%

Harmonic radar tracking of individual melon flies, Zeugodacus cucurbitae, in Hawaii: Determining movement parameters in cage and field settings

et al. 2022

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Tephritid fruit flies, such as the melon fly, Zeugodacus cucurbitae, are major horticultural pests worldwide and pose invasion risks due primarily to international trade. Determining movement parameters for fruit flies is critical to effective surveillance and control strategies, from setting quarantine boundaries after incursions to development of agent-based models for management. While mark-release-recapture, flight mills, and visual observations have been used to study tephritid movement, none of these techniques give a full picture of fruit fly movement in nature. Tracking tagged flies offers an alternative method which has the potential to observe individual fly movements in the field, mirroring studies conducted by ecologists on larger animals. In this study, harmonic radar (HR) tags were fabricated using superelastic nitinol wire which is light (tags weighed less than 1 mg), flexible, and does not tangle. Flight tests with wild melon flies showed no obvious adverse effects of HR tag attachment. Subsequent experiments successfully tracked HR tagged flies in large field cages, a papaya field, and open parkland. Unexpectedly, a majority of tagged flies showed strong flight directional biases with these biases varying between flies, similar to what has been observed in the migratory butterfly Pieris brassicae. In field cage experiments, 30 of the 36 flies observed (83%) showed directionally biased flights while similar biases were observed in roughly half the flies tracked in a papaya field. Turning angles from both cage and field experiments were non-random and indicate a strong bias toward continued “forward” movement. At least some of the observed direction bias can be explained by wind direction with a correlation observed between collective melon fly flight directions in field cage, papaya field, and open field experiments. However, individual mean flight directions coincided with the observed wind direction for only 9 out of the 25 flies in the cage experiment and half of the flies in the papaya field, suggesting wind is unlikely to be the only factor affecting flight direction. Individual flight distances (meters per flight) differed between the field cage, papaya field, and open field experiments with longer mean step-distances observed in the open field. Data on flight directionality and step-distances determined in this study might assist in the development of more effective control and better parametrize models of pest tephritid fruit fly movement.

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Section: Plos Onementioning

confidence: 72%

Harmonic radar tracking of individual melon flies, Zeugodacus cucurbitae, in Hawaii: Determining movement parameters in cage and field settings

et al. 2022

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“…In an isotropic environment, θ is uniformly distributed from −π to π, and ξ is half-sine distributed 1 2 sin(ξ ) with values drawn between 0 and π (e.g., see Ahmed et al (2020)). Thus in this case, the movement pattern is characterised by the distribution of step lengths λ (l).…”

Section: Movement In 3d Spacementioning

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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“…These are two basic ways to use Markov chain in mathematics. According to Chapman-Kolmogorov equation [6], 𝑟 𝑖𝑗 (𝑛) = ∑ 𝑟 𝑖𝑘 (𝑛 − 1)𝑝 𝑘𝑗 𝑚 𝑘=1…”

Section: Markov Chainmentioning

confidence: 99%

Theory of Markov chain and its application in several representative examples

Shao

2024

TNS

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Markov chains can be widely used in a range of applied disciplines such as finance, physics, meteorology, chemistry, statistics, etc., which is not limited to theoretical mathematics. Markov chains were created by the Russian mathematician Markov and can be used to calculate the probability of various state transitions to each other, compared to many calculations in traditional probability calculations, Markov chains can be used to calculate the probability of each state transition easily, quickly, and accurately. Thus, Markov chains can be used to predict the probability of future events and in statistics to simulate complex distributions. In real life, Markov chains can be used to predict some impending disasters, such as tsunamis, earthquakes, and even the spread of diseases. If these are successfully predicted, the loss of life and property caused by these disasters could be greatly reduced. Moreover, the calculation method of the transfer matrix of the Markov chain is very suitable for the computing characteristics of artificial intelligence, so the convenience of using the Markov chain will be greatly increased.

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Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

Cited by 14 publications

References 67 publications

Harmonic radar tracking of individual melon flies, Zeugodacus cucurbitae, in Hawaii: Determining movement parameters in cage and field settings

Harmonic radar tracking of individual melon flies, Zeugodacus cucurbitae, in Hawaii: Determining movement parameters in cage and field settings

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

Theory of Markov chain and its application in several representative examples

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