Amoeboid movement as a correlated walk

Hall, Roger L.

doi:10.1007/bf00275081

Cited by 67 publications

(62 citation statements)

References 13 publications

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“…II͒. We note 2) . We are interested now in computing the difference between the exact expression for the entropy production ͑21͒ and the second-order approximation ͑22͒,…”

Section: B Diffusive Processmentioning

confidence: 86%

Irreversible thermodynamics of Poisson processes with reaction

Méndez

Fort

1999

Phys. Rev. E

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A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics. ͓S1063-651X͑99͒15511-9͔

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“…II͒. We note 2) . We are interested now in computing the difference between the exact expression for the entropy production ͑21͒ and the second-order approximation ͑22͒,…”

Section: B Diffusive Processmentioning

confidence: 86%

Irreversible thermodynamics of Poisson processes with reaction

Méndez

Fort

1999

Phys. Rev. E

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“…;n ,nR1, with independent turning angles following a distribution characterized by mean turning angle a, mean vector length r, mean cosine c and mean sine s. If we denote by DR the variable step length then the mean squared displacement of the movement is equal to (Kareiva & Shigesada 1983) MSDðX n Þ Z EðjX n K X 0 j 2 Þ Z nEðDR 2 Þ C 2EðDRÞ 2 nðcKr 2 ÞKc (Hall 1977) MSDðX n Þ ZEðjX n K X 0 j 2 Þ Z nEðDR 2 Þ C EðDRÞ 2 2c 1Kc nK 1Kc…”

Section: A1 Dispersal Rate In a Crw Modelmentioning

confidence: 99%

Anomalous diffusion of heterogeneous populations characterized by normal diffusion at the individual level

Hapca

Crawford

Young

2008

J. R. Soc. Interface.

141

159

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The characterization of the dispersal of populations of non-identical individuals is relevant to most ecological and epidemiological processes. In practice, the movement is quantified by observing relatively few individuals, and averaging to estimate the rate of dispersal of the population as a whole. Here, we show that this can lead to serious errors in the predicted movement of the population if the individuals disperse at different rates. We develop a stochastic model for the diffusion of heterogeneous populations, inspired by the movement of the parasitic nematode Phasmarhabditis hermaphrodita. Direct observations of this nematode in homogeneous and heterogeneous environments reveal a large variation in individual behaviour within the population as reflected initially in the speed of the movement. Further statistical analysis shows that the movement is characterized by temporal correlations and in a heterogeneously structured environment the correlations that occur are of shorter range compared with those in a homogeneous environment. Therefore, by using the first-order correlated random walk techniques, we derive an effective diffusion coefficient for each individual, and show that there is a significant variation in this parameter among the population that follows a gamma distribution. Based on these findings, we build a new dispersal model in which we maintain the classical assumption that individual movement can be described by normal diffusion, but due to the variability in individual dispersal rates, the diffusion coefficient is not constant at the population level and follows a continuous distribution. The conclusions and methodology presented are relevant to any heterogeneous population of individuals with widely different diffusion rates.

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“…In contrast, a correlated random walk changes direction in subsequent time-steps randomly, but with bounded range dependent on the previous direction of travel. Such an approach has been used to model butterfly (Kareiva and Shigesada, 1983) and amoeboid movement (Hall, 1977) as well as a number of other species of animal. Cain (1990) (1996a) our data show no crowns developing below 30 cm from the surface.…”

Section: Surveymentioning

confidence: 99%