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ARS Home » Southeast Area » Fort Pierce, Florida » U.S. Horticultural Research Laboratory » Subtropical Plant Pathology Research » Research » Publications at this Location » Publication #343467

Research Project: Mitigating High Consequence Domestic, Exotic, and Emerging Diseases of Fruits, Vegetables, and Ornamentals

Location: Subtropical Plant Pathology Research

Title: Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence

Author
item Madden, Larry - The Ohio State University
item Hughes, Gareth - Sruc-Scotland'S Rural College
item Bucker-moraes, Wanderson - The Ohio State University
item Xingming, Xu - East Malling Research
item Turechek, William

Submitted to: Phytopathology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 11/13/2017
Publication Date: 6/1/2018
Citation: Madden, L., Hughes, G., Bucker-Moraes, W., Xingming, X., Turechek, W. 2018. Twenty-five years of the binary power law for characterizing heterogeneity of disease incidence. Phytopathology. 108:656-680.

Interpretive Summary: Spatial pattern is an important epidemiological property of plant diseases. The binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence, as an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound. In this paper 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 over the last quarter century; 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.

Technical Abstract: Spatial pattern is an important epidemiological property of plant diseases. The spatial heterogeneity (or overdispersion) of disease incidence (i.e., number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit), can be quantified using a range of methods and is an especially important measure of small-scale pattern. The binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence, as an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound. 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. In this paper 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 over the last quarter century; 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. Ninety percent of estimated slope (b) values from field studies were between 1.05 and 1.49, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with epidemiological processes and holds whenever there is a positive correlation of disease status of individuals comprising sampling units.