Model Analysis of Spatial Patterns in Mountain Pine Beetle Outbreaks

Logan, Jesse A.; White, Peter; Bentz, Barbara; Powell, James A.

doi:10.1006/tpbi.1997.1350

Cited by 109 publications

(91 citation statements)

References 35 publications

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“…Modelling the role of chemotaxis in pathological processes is a large field: Luca et al [61] considered whether the chemotactic aggregation of microglia may provide a mechanistic basis for senile plaques during progression of Alzheimer's disease, while chemotaxis has been incorporated into the modelling of a number of distinct stages of tumour growth, including the migration of invasive cancer cells [88], tumour-induced angiogenesis (see the reviews [16,63]) and macrophage invasion into tumours [79]. Finally, we should not neglect the modelling of taxis in the context of spatial ecological processes, including "prey-taxis" [43,58], herd grazing [31] and the spatial dynamics of mountain pine beetle attacks [60].…”

Section: Derivation and Applications Of Chemotaxis Modelsmentioning

confidence: 99%

A user’s guide to PDE models for chemotaxis

2008

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Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399-415, 1970; 30:225-234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display "auto-aggregation", has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller-Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work.

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Section: Derivation and Applications Of Chemotaxis Modelsmentioning

confidence: 99%

A user’s guide to PDE models for chemotaxis

2008

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“…They found that even small changes in needle resin concentration may have a significant impact on population growth. Resin capacity of trees was also found to serve as a simple descriptor of tree resistance in a mathematical model of chemical ecology and spatial interaction between D. ponderosae and its hosts (Logan et al, 1998).…”

Section: Insectsmentioning

confidence: 99%

“…With regard to insect herbivory on phloem rather than on foliage, the Westwide Pine Beetle Model (Smith et al, 2005;Ager et al, 2007: FVS) represents a processoriented approach in which the beetle occupation level necessary to kill one square foot of basal area is used as a proxy for the physiological effects of phloem feeding. More detailed processbased models explicitly take into account the nesting population density per tree as well as tree defence and recovery (Logan et al, 1998). In addition, carbon balance approaches were applied to model physiological effects of phloem feeding (Dungan et al, 2007).…”

Section: Impactmentioning

confidence: 99%

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Modelling natural disturbances in forest ecosystems: a review

Seidl

Fernandes

Fonseca

et al. 2011

Ecological Modelling

357

219

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“…The 30 ha and 60 ha thresholds were developed based on spatial simulations of beetle populations and empirical mark-recapture studies. Logan et al (1998) demonstrate that when the source areas of beetles occur in high density (1 source cluster per 15 to 80 hectares, depending on population size), spatial patterns of attacked trees replicate the clustering pattern seen in incipient and epidemic infestations (Logan et al, 1998). Several experimental studies show that after release, 75 to 95% of the beetles recaptured are within a 30 ha area (300 m radius), and 90 to 95% are recaptured within a 60 ha area (between 400 to 500 m radius), although the percent recaptured depends on the experimental design Turchin and Thoeny, 1993;Byers, 1999).…”

Section: Beetle Pressure Using Density-based Modelmentioning

confidence: 99%

Calculating the Risk of Mountain Pine Beetle Attack: a Comparison of Distance- and Density-Based Estimates of Beetle Pressure

Wulder

2006

J ENV INFORM

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ABSTRACT. An established model for risk rating of Pinus contorta stands for potential mortality caused by mountain pine beetle (Dendroctonus ponderosae) combines information on stand susceptibility and beetle pressure. Susceptibility is determined using attributes in the forest inventory data, while beetle pressure is calculated based on the size and distance to existing infestation locations (distance-based model). An alternate model for calculating beetle pressure is presented in this paper, which uses Voronoi polygons to incorporate size and distance, while emphasizing the density of existing infestation locations (density-based model), in combination with empirical knowledge of beetle dispersal and forest inventory data. Survey data of existing beetle damage were collected using a helicopter mounted global positioning system (GPS) at a study site in central British Columbia, Canada in 1999, 2000, and 2001. These data facilitated the estimation of beetle pressure, and the comparison of risk ratings to actual attack locations. Using the distance-based model, 18 and 27% of areas identified as having a risk rating of greater than 50 in 1999 and 2000 were actually found to be attacked by beetles in surveys conducted in 2000 and 2001. Conversely, 39 and 49% of areas identified as having risk greater than 50 in 1999 and 2000 with the density-based model were attacked in 2000 and 2001. The results suggest that the density-based model of beetle pressure produced risk ratings that had a greater correspondence with actual infestation occurrence than risk ratings generated from the distance-based model. Using data that is typically collected to monitor beetle populations, novel methods of spatial processing may be applied in a transparent manner, generating results that incorporate knowledge of mountain pine beetle dynamics under certain population conditions, into calculations of the risk of mountain pine beetle attack.

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Model Analysis of Spatial Patterns in Mountain Pine Beetle Outbreaks

Cited by 109 publications

References 35 publications

A user’s guide to PDE models for chemotaxis

A user’s guide to PDE models for chemotaxis

Modelling natural disturbances in forest ecosystems: a review

Calculating the Risk of Mountain Pine Beetle Attack: a Comparison of Distance- and Density-Based Estimates of Beetle Pressure

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Model Analysis of Spatial Patterns in Mountain Pine Beetle Outbreaks

Cited by 109 publications

References 35 publications

A user’s guide to PDE models for chemotaxis

A user’s guide to PDE models for chemotaxis

Modelling natural disturbances in forest ecosystems: a review

﻿Calculating the Risk of Mountain Pine Beetle Attack: a Comparison of Distance- and Density-Based Estimates of Beetle Pressure

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Product

Resources

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Calculating the Risk of Mountain Pine Beetle Attack: a Comparison of Distance- and Density-Based Estimates of Beetle Pressure