The limits of the binary power law describing spatial variability for incidence data

Xu, Xiangming; Madden, L. V.

doi:10.1111/ppa.12172

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…They used binary form of Taylor"s power law to relate heterogeneity of disease incidence by taking the natural logarithm of observed and theoretical variance, power function transformed into a linear function (Equation 9). Xu and Madden (2014) described the limits of binary power law and according to them, performance of this parameter affected whenever there is a positive correlation among neighbors on the probability of a plant becoming infected, or where disease development is not influenced by the neighbors.…”

Section: Taylor's Power Lawmentioning

confidence: 99%

Spatial Patterns of Host-Pathogen Complex: A Geostatistical Insight

Mathur¹

2018

Int.J.Curr.Microbiol.App.Sci

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Section: Taylor's Power Lawmentioning

confidence: 99%

Spatial Patterns of Host-Pathogen Complex: A Geostatistical Insight

Mathur¹

2018

Int.J.Curr.Microbiol.App.Sci

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A Meta-Analytical Assessment of the Aggregation Parameter of the Binary Power Law for Characterizing Spatial Heterogeneity of Plant Disease Incidence

Madden¹,

Moraes

Hughes

et al. 2021

Phytopathology®

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The binary power law (BPL) is often used to characterize spatial heterogeneity of disease incidence. A hierarchical mixed model, coupled with multiple imputation to randomly generate any missing standard errors, was used to conduct a meta-analysis of >200 published values of the estimated aggregation (b) parameter of the BPL. Approximately 50% of estimated b values ranged from 1.1 to 1.3. Moderator-variable analysis showed that the number of individuals per sampling unit (n) had a strong positive effect on b, with a linear relation between estimated b and ln(n). Estimated expected value of b for the population of published regressions at a reference n of 15 was 1.22. The increase in the variance due to the imputations was only 0.03, and the efficiency exceeded 0.98. Results were confirmed with an alternative mixed model that considered a range of possible within-trial correlations of the estimated b values, and with a random-coefficient mixed model fitted to the subset of the data. Cropping system, dispersal mode, and pathogen type all had significant effects on b, with annuals having larger expected value than woody perennials, soilborne and rain-splashed dispersed pathogens having the largest expected values for dispersal mode, and bacteria and Oomycetes having the largest expected values for pathogen type. However, there was considerable variation within each of the levels of the moderators, and the differences of expected values from smallest to largest were small, less than or equal to 0.16. Results are discussed in relation to previously published findings from stochastic simulations.

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Twenty-Five Years of the Binary Power Law for Characterizing Heterogeneity of Disease Incidence

et al. 2018

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Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor's power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

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The limits of the binary power law describing spatial variability for incidence data

Cited by 3 publications

References 24 publications

Spatial Patterns of Host-Pathogen Complex: A Geostatistical Insight

Spatial Patterns of Host-Pathogen Complex: A Geostatistical Insight

A Meta-Analytical Assessment of the Aggregation Parameter of the Binary Power Law for Characterizing Spatial Heterogeneity of Plant Disease Incidence

Twenty-Five Years of the Binary Power Law for Characterizing Heterogeneity of Disease Incidence

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