The Random Walk of Trichostrongylus retortaeformis

Broadbent, Simon; Kendall, David G.

doi:10.2307/3001437

Cited by 84 publications

(43 citation statements)

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“…These functional forms are consistent with a diffusive form of one-dimensional dispersal in which there is a constant probability per unit time of settling (Broadbent and Kendall 1953;Neubert et al 1995). (See app.…”

mentioning

confidence: 61%

When Can Herbivores Slow or Reverse the Spread of an Invading Plant? A Test Case from Mount St. Helens

Fagan¹,

Lewis²,

Neubert³

et al. 2005

The American Naturalist

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Here we study the spatial dynamics of a coinvading consumer-resource pair. We present a theoretical treatment with extensive empirical data from a long-studied field system in which native herbivorous insects attack a population of lupine plants recolonizing a primary successional landscape created by the 1980 volcanic eruption of Mount St. Helens. Using detailed data on the life history and interaction strengths of the lupine and one of its herbivores, we develop a system of integrodifference equations to study plant-herbivore invasion dynamics. Our analyses yield several new insights into the spatial dynamics of coinvasions. In particular, we demonstrate that aspects of plant population growth and the intensity of herbivory under low-density conditions can determine whether the plant population spreads across a landscape or is prevented from doing so by the herbivore. In addition, we characterize the existence of threshold levels of spatial extent and/or temporal advantage for the plant that together define critical values of "invasion momentum," beyond which herbivores are unable to reverse a plant invasion. We conclude by discussing the implications of our findings for successional dynamics and the use of biological control agents to limit the spread of pest species.

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mentioning

confidence: 61%

When Can Herbivores Slow or Reverse the Spread of an Invading Plant? A Test Case from Mount St. Helens

Fagan¹,

Lewis²,

Neubert³

et al. 2005

The American Naturalist

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“…Similarly, the case A(n, 100, 1, 20) approximates the BoseEinstein distribution B(n, 20) = A(n, X, 1,20). This is just 20n/21(n+l), which varies exponentially with n. …”

Section: Results For the Photon-counting Distributionsmentioning

confidence: 99%

Multiply stochastic representations for K distributions and their Poisson transforms

Teich

Diament

1989

J. Opt. Soc. Am. A

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“…A simple model giving rise to K distributions is that dispersal is a two-dimensional diffusion process (random walk), but that the time during which dispersal occurs is also a random variable following a gamma distribution with parameter b (or a x2 distribution with 2b degrees of freedom). The case when b = 1, which corresponds to an exponential distribution for the dispersal time, has been considered by Broadbent and Kendall (1953) and by Pielou (1969). The first two moments about the origin of the K distribution with parameters h and b are E(r) = 2P(b+)P(l)/hf(b)…”

Section: Dispersal Of Young Birdsmentioning

confidence: 99%

Inbreeding in the great tit

Bulmer

1973

Heredity

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SUMMARYData are presented on the frequency of close inbreeding and on inbreeding depression in a Great Tit population in Wytham Wood near Oxford. A theoretical distribution is fitted to data on the dispersal of young birds, and a model is constructed to predict the amount of inbreeding expected in a large, uniform habitat in terms of the dispersal distribution and of the breeding structure of the population.

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The Random Walk of Trichostrongylus retortaeformis

Cited by 84 publications

References 0 publications

When Can Herbivores Slow or Reverse the Spread of an Invading Plant? A Test Case from Mount St. Helens

When Can Herbivores Slow or Reverse the Spread of an Invading Plant? A Test Case from Mount St. Helens

Multiply stochastic representations for K distributions and their Poisson transforms

Inbreeding in the great tit

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