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

Spatiotemporal Dynamics of Stemphylium Leaf Blight and Potential Inoculum Sources in New York Onion Fields

Stemphylium leaf blight (SLB) caused by Stemphylium vesicarium is the dominant foliar disease affecting large-scale onion production in New York. The disease is managed by fungicides, but control failures are prevalent and are attributed to fungicide resistance. Little is known of the relative role of inoculum sources in initiation and spread of SLB epidemics. Plate testing of 28 commercially available organic onion seedlots from 2016 and 2017 did not detect S. vesicarium. This finding suggests that although S. vesicarium has been reported as seed-transmitted, this is unlikely to be a significant inoculum source in commercially available organic seed lots and even less so in fungicide-treated seed used to establish conventional fields. The spatial and spatiotemporal dynamics of SLB epidemics in six onion fields were evaluated along linear transects in 2017 and 2018. Average SLB incidence increased from 0 to 100% throughout the cropping seasons with an average final lesion length of 28.3 cm. Disease progress was typical of a polycyclic epidemic and the logistic model provided the best fit to 83.3% of the datasets. Spatial patterns were better described by the beta-binomial than binomial distribution in half of the datasets (50%) and random patterns were more frequently observed by the index of dispersion (59%). Geostatistical analyses also found a low frequency of datasets with aggregation (60%). Spatiotemporal analysis of epidemics detected that the aggregation was influenced by disease incidence. However, diseased units were not frequently associated with the previous time period according to the spatiotemporal association function of spatial analyses by distance indices. Variable spatial patterns suggested mixed inoculum sources dependent upon location, and likely an external inoculum source at the sampling scale used in this study. A small-plot replicated trial was also conducted in each of 2 years to quantify the effect of S. vesicarium-infested onion residue on SLB epidemics in a field isolated from other onion fields. SLB incidence was significantly reduced in plots without residue compared with those in which residue remained on the soil surface. Burial of infested residue also significantly reduced epidemic progress in 1 year. The effect of infested onion residue on SLB epidemics in the subsequent onion crop suggests rotation or residue management may have a substantial effect on epidemics. However, the presence of an inoculum source external to fields in onion production regions, as indicated by a lack of spatial aggregation, may reduce the efficacy of in-field management techniques.

Characterizing Heterogeneity and Determining Sample Sizes for Accurately Estimating Wheat Fusarium Head Blight Index in Research Plots

Because Fusarium head blight (FHB) intensity is usually highly variable within a plot, the number of spikes rated for FHB index (IND) quantification must be considered when designing experiments. In addition, quantification of sources of IND heterogeneity is crucial for defining sampling protocols. Field experiments were conducted to quantify the variability of IND ("field severity") at different spatial scales and to investigate the effects of sample size on estimated plot-level mean IND and its accuracy. A total of 216 7-row × 6-m-long plots of a moderately resistant and a susceptible cultivar were spray-inoculated with different Fusarium graminearum spore concentrations at anthesis to generate a range of IND levels. A one-stage cluster sampling approach was used to estimate IND, with an average of 32 spikes rated at each of 10 equally spaced points per plot. Plot-level mean IND ranged from 0.9 to 37.9%. Heterogeneity of IND, quantified by fitting unconditional hierarchical linear models, was higher among spikes within clusters than among clusters within plots or among plots. The projected relative error of mean IND increased as mean IND decreased, and as sample size decreased to <100 spikes per plot. Simple random samples were drawn with replacement 50,000 times from the original dataset for each plot and used to estimate the effects of sample sizes on mean IND. Samples of 100 or more spikes resulted in more precise estimates of mean IND than smaller samples. Poor sampling may result in inaccurate estimates of IND and poor interpretation of results.

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

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, ≤0.16. Results are discussed in relation to previously published findings from stochastic simulations.

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

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 the state of New York. Assessments of CLS incidence were performed in six leaves arbitrarily selected in 51 sampling locations along each of 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 Spatial Analysis by Distance Indices, or 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 <51 sampling units, and only observed on datasets with incidence >0.3. Reducing the level of precision, i.e., increasing C to 0.2, allowed the preselected C to be achieved with a lower number of sampling units and with an estimated incidence ([Formula: see text]) close to the true value of p. For classification, the goal was to classify the datasets above or below prespecified thresholds (p_t) used for CLS management. The average sample number, or ASN, was determined by Monte Carlo simulations, and was between 20 and 45 at disease incidence values close to p_t, and approximately 11 when far from p_t. Correct decisions occurred in >76% of the validation datasets. Results indicated these sequential sampling plans can be used to effectively assess CLS incidence in table beet fields.

Remote Sensing of Diseases

Detection, identification, and quantification of plant diseases by sensor techniques are expected to enable a more precise disease control, as sensors are sensitive, objective, and highly available for disease assessment. Recent progress in sensor technology and data processing is very promising; nevertheless, technical constraints and issues inherent to variability in host-pathogen interactions currently limit the use of sensors in various fields of application. The information from spectral [e.g., RGB (red, green, blue)], multispectral, and hyperspectral sensors that measure reflectance, fluorescence, and emission of radiation or from electronic noses that detect volatile organic compounds released from plants or pathogens, as well as the potential of sensors to characterize the health status of crops, is evaluated based on the recent literature. Phytopathological aspects of remote sensing of plant diseases across different scales and for various purposes are discussed, including spatial disease patterns, epidemic spread of pathogens, crop characteristics, and links to disease control. Future challenges in sensor use are identified.

Basic Features of the Analysis of Germination Data with Generalized Linear Mixed Models

Germination data are discrete and binomial. Although analysis of variance (ANOVA) has long been used for the statistical analysis of these data, generalized linear mixed models (GzLMMs) provide a more consistent theoretical framework. GzLMMs are suitable for final germination percentages (FGP) as well as longitudinal studies of germination time-courses. Germination indices (i.e., single-value parameters summarizing the results of a germination assay by combining the level and rapidity of germination) and other data with a Gaussian error distribution can be analyzed too. There are, however, different kinds of GzLMMs: Conditional (i.e., random effects are modeled as deviations from the general intercept with a specific covariance structure), marginal (i.e., random effects are modeled solely as a variance/covariance structure of the error terms), and quasi-marginal (some random effects are modeled as deviations from the intercept and some are modeled as a covariance structure of the error terms) models can be applied to the same data. It is shown that: (a) For germination data, conditional, marginal, and quasi-marginal GzLMMs tend to converge to a similar inference; (b) conditional models are the first choice for FGP; (c) marginal or quasi-marginal models are more suited for longitudinal studies, although conditional models lead to a congruent inference; (d) in general, common random factors are better dealt with as random intercepts, whereas serial correlation is easier to model in terms of the covariance structure of the error terms; (e) germination indices are not binomial and can be easier to analyze with a marginal model; (f) in boundary conditions (when some means approach 0% or 100%), conditional models with an integral approximation of true likelihood are more appropriate; in non-boundary conditions, (g) germination data can be fitted with default pseudo-likelihood estimation techniques, on the basis of the SAS-based code templates provided here; (h) GzLMMs are remarkably good for the analysis of germination data except if some means are 0% or 100%. In this case, alternative statistical approaches may be used, such as survival analysis or linear mixed models (LMMs) with transformed data, unless an ad hoc data adjustment in estimates of limit means is considered, either experimentally or computationally. This review is intended as a basic tutorial for the application of GzLMMs, and is, therefore, of interest primarily to researchers in the agricultural sciences.