Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence

Turechek, William W.; Madden, L. V.; Gent, DH; Xu, Xiangming

doi:10.1094/phyto-04-11-0100

Cited by 13 publications

(12 citation statements)

References 45 publications

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“…Given that the BPL provides a good description of the heterogeneity of numerous empirical and theoretical data sets across spatiotemporal scales [as recently reviewed in Turechek et al . (), and previously in Madden & Hughes () and Madden et al . ()], two questions naturally arise: (i) what is the extent of the conditions under which the simple BPL relationship, or somewhat more complex ABPL, holds?…”

Section: Introductionsupporting

confidence: 66%

“…Given the generality of the BPL results across many plant diseases, several mechanisms based on environmental, biological, physical and demographic stochasticity are likely to be responsible for the BPL (Turechek et al ., ). Stochastic simulations based on a spatially explicit model of plant diseases have shown that the BPL (Eqn , with b > 1) arises naturally over a wide range of epidemiological conditions (Xu & Ridout, , ).…”

Section: Introductionmentioning

confidence: 97%

“…In the formulation of Eqn , the counts per sampling unit are divided by n before the observed variance ( V obs ) is estimated; Turechek et al . () discuss other formulations of the BPL. Logarithmic transformation of both sides of Eqn produces:

\ln false(V_{obs} false) = \ln false(italicκ false) + b \cdot \ln false(p \cdot (1 - p) false/ n false)

with a slope of b and an intercept of α = ln( κ ).…”

Section: Introductionmentioning

confidence: 99%

“…Eqn is also specifically referred to as the symmetrical BPL because the observed variance is assumed to be symmetrical around p = 0·5. The BPL has been found to be appropriate for describing dynamics of heterogeneity (overdispersion) in plant diseases (Madden et al ., ; Turechek et al ., ) and used for optimizing sampling schemes (Madden & Hughes, ; Kriss et al ., ).…”

Section: Introductionmentioning

confidence: 99%

“…Because of high correlation between κ and b in real and simulated data, the degree of overdispersion normally increases with increasing κ and b values (Xu & Ridout, , ; Turechek et al ., ). When b > 1, or when b = 1 and κ > 1, the beta‐binomial distribution (BBD) is generally appropriate for describing the discrete diseased data, where the BBD parameters are nonlinear functions of κ and b (Hughes & Madden, ; Madden & Hughes, ; Turechek et al ., ). The aggregation parameter ( θ ) of the BBD measures small‐scale spatial patterns (Madden et al ., ), because it reflects the average correlation of disease status of individual plants within sampling units.…”

Section: Introductionmentioning

confidence: 99%

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

Madden²

2013

Plant Pathology

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Taylor's power law (TPL), an empirical law relating the observed variance to mean density (or abundance), has found wide applicability for characterizing heterogeneity in many disciplines. However, when the density variable has an upper bound, the TPL does not hold and the binary power law (BPL) needs to be used instead. The BPL has been shown to describe the heterogeneity of numerous plant disease epidemic systems. In this study, a generic stochastic simulator was used to study the extent to which the BPL can satisfactorily describe incidence data. Results showed that the symmetrical BPL does hold whenever there is a positive correlation among neighbours on the probability of a plant becoming infected, or where disease development is not influenced by the neighbours. These results held for a wide range of neighbourhood sizes, strengths of neighbourhood influence, and size of the sampling quadrats. However, the symmetrical BPL did not hold when there is a negative influence among neighbours. The more general asymmetrical BPL (ABPL) fitted the data with positive or negative neighbourhood influence, but because a negative neighbourhood effect is generally unlikely for plant epidemics, the symmetrical BPL is preferred over the ABPL because of its parsimony. The magnitude of the estimated BPL parameters increased with increasing neighbourhood influence and sampling-quadrat size. However, except when the power parameter equals 1, inferring specific underlying mechanisms generating the data or comparing BPL estimates from different studies is difficult, because of the large effect of sampling on the BPL parameter estimates.

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Section: Introductionsupporting

confidence: 66%

Section: Introductionmentioning

confidence: 97%

\ln false(V_{obs} false) = \ln false(italicκ false) + b \cdot \ln false(p \cdot (1 - p) false/ n false)

with a slope of b and an intercept of α = ln( κ ).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Madden²

2013

Plant Pathology

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Spatiotemporal Attributes and Crop Loss Associated with Tan Spot Epidemics in Baby Lima Bean in New York

et al. 2018

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Tan spot, caused by the pycnidial fungi Didymella americana and Boeremia exigua var. exigua, is a foliar disease affecting processing baby lima bean production in New York. Tan spot epidemics are prevalent, occur annually, and may result in substantial defoliation. The disease is controlled by the prophylactic application of fungicides to maximize green leaf area. Information on yield losses due to tan spot on baby lima bean yield and the benefits of fungicide applications is needed to justify investments in disease management. Four small-plot, replicated trials were conducted over 2 years in commercial baby lima bean fields to evaluate the efficacy of fungicides for tan spot control at Piffard and Leicester, NY. Applications of pyraclostrobin or boscalid significantly reduced tan spot incidence and severity compared with nontreated plots, and increased the number of leaves per stem. In 2016, the increase in green leaf area associated with fungicide application was also documented in canopy reflectance values at 830 nm. Despite the decrease in tan spot incidence and corresponding increase in crop health obtained from fungicides, this effect did not translate into significant increases in pod yield. This finding suggested that the relationship between green leaf area and yield is highly variable in baby lima bean. The spatial and spatiotemporal patterns of naturally occurring tan spot epidemics were also characterized in baby lima bean fields across western New York using disease incidence data collected in transects and grids. The spatial pattern of data collected in transects was analyzed using median runs analysis. Disease incidence data collected in two-dimensional grids were analyzed to quantify spatial pattern using spatial analysis by distance indices (SADIE). The association function of SADIE was used to quantify the spatiotemporal patterns of tan spot epidemics after crop emergence and at harvest. These findings suggested that tan spot is likely to initiate at relatively frequent, randomly positioned foci, and that subsequent, limited spread results in significant local aggregation. Hypotheses for inoculum sources and recommendations for tan spot control in baby lima bean fields in New York are discussed.

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Development of a Sequential Sampling Plan using Spatial Attributes of Cercospora Leaf Spot Epidemics of Table Beet in New York

et al. 2021

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Sampling strategies that effectively assess disease intensity in the field are important to underpin management decisions. To develop a sequential sampling plan for the incidence of Cercospora leaf spot (CLS), caused by Cercospora beticola, 31 table beet fields were assessed in New York. Assessments of CLS incidence were performed in six leaves arbitrarily selected in 51 sampling locations along each of the three to six linear transects per field. Spatial pattern analyses were performed, and results were used to develop sequential sampling estimation and classification models. CLS incidence (p) ranged from 0.13 to 0.92 with a median of 0.31, and beta-binomial distribution, which is reflective of aggregation, best described the spatial patterns observed. Aggregation was commonly detected (>95%) by methods using the point-process approach, runs analyses, and autocorrelation up to the fourth spatial lag. For SADIE, 45% of the datasets were classified as a random pattern. In the sequential sampling estimation and classification models, disease units are sampled until a prespecified target is achieved. For estimation, the goal was sampling CLS incidence with a preselected coefficient of variation (C). Achieving the C = 0.1 was challenging with less than 51 sampling units, and only observed on datasets with an incidence above 0.3. Reducing the level of precision, i.e. increasing C to 0.2, allowed the preselected C be achieved with a lower number of sampling units and with an estimated incidence (p̂) close to the true value of p. For classification, the goal was to classify the datasets above or below prespecified thresholds (pt) used for CLS management. The average sample number (ASN) was determined by Monte Carlo simulations, and was between 20 and 45 at disease incidence values close to pt, and approximately 11 when far from pt. Correct decisions occurred in over 76% of the validation datasets. Results indicated these sequential sampling plans can be used to effectively assess CLS incidence in table beet fields.

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Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence

Cited by 13 publications

References 45 publications

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

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

Spatiotemporal Attributes and Crop Loss Associated with Tan Spot Epidemics in Baby Lima Bean in New York

Development of a Sequential Sampling Plan using Spatial Attributes of Cercospora Leaf Spot Epidemics of Table Beet in New York

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