Comments regarding the binary power law for 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.

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.

Effect of Cultivar Resistance and Soil Management on Spatial-Temporal Development of Verticillium Wilt of Olive: A Long-Term Study

Verticillium wilt, caused by Verticillium dahliae, challenges olive cultivation and an Integrated Disease Management (IDM) approach is the best-suited tool to combat it. Since 1998, an IDM strategy in an orchard (called Granon, Spain) of the susceptible cv. Picual was conducted by increasing planting density with moderately resistant cv. Frantoio, chemical weed control, and replanting of dead olives with cv. Frantoio following soil solarization. The Verticillium wilt epidemic in Granon orchard was compared to the epidemic in a non-IDM orchard (called Ancla, Spain) with plowed soil and dead Picual olives replanted with the same cultivar. Field evaluations (2012-2013) showed an incidence and severity of the disease as Picual-Ancla > Picual-Granon > Frantoio-Granon. The spatiotemporal dynamics of the Verticillium epidemics from 1998 to 2010 were monitored with digital images using SIG. The annual tree mortalities were 5.6% for Picual olives in Ancla orchard, and 3.1 and 0.7% for Picual and Frantoio olives in Granon orchard, respectively. There was a negative relationship between the mortality of olive trees (%) by the pathogen and the height (m) above sea level. The annual mortality of cv. Picual olives was positively correlated with spring rainfalls. The Index of Dispersion and beta-binomial distribution showed aggregation of Verticillium-dead olives. In conclusion, this IDM strategy considerably reduced the disease in comparison with traditional agronomic practices.

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

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.

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

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.

Cluster: A New Application for Spatial Analysis of Pixelated Data for Epiphytotics

Spatial analysis of epiphytotics is essential to develop and test hypotheses about pathogen ecology, disease dynamics, and to optimize plant disease management strategies. Data collection for spatial analysis requires substantial investment in time to depict patterns in various frames and hierarchies. We developed a new approach for spatial analysis of pixelated data in digital imagery and incorporated the method in a stand-alone desktop application called Cluster. The user isolates target entities (clusters) by designating up to 24 pixel colors as nontargets and moves a threshold slider to visualize the targets. The app calculates the percent area occupied by targeted pixels, identifies the centroids of targeted clusters, and computes the relative compass angle of orientation for each cluster. Users can deselect anomalous clusters manually and/or automatically by specifying a size threshold value to exclude smaller targets from the analysis. Up to 1,000 stochastic simulations randomly place the centroids of each cluster in ranked order of size (largest to smallest) within each matrix while preserving their calculated angles of orientation for the long axes. A two-tailed probability t test compares the mean inter-cluster distances for the observed versus the values derived from randomly simulated maps. This is the basis for statistical testing of the null hypothesis that the clusters are randomly distributed within the frame of interest. These frames can assume any shape, from natural (e.g., leaf) to arbitrary (e.g., a rectangular or polygonal field). Cluster summarizes normalized attributes of clusters, including pixel number, axis length, axis width, compass orientation, and the length/width ratio, available to the user as a downloadable spreadsheet. Each simulated map may be saved as an image and inspected. Provided examples demonstrate the utility of Cluster to analyze patterns at various spatial scales in plant pathology and ecology and highlight the limitations, trade-offs, and considerations for the sensitivities of variables and the biological interpretations of results. The Cluster app is available as a free download for Apple computers at iTunes, with a link to a user guide website.

Analysis of the Spatial Pattern of Strawberry Angular Leaf Spot in California Nursery Production

In California, angular leaf spot (ALS) is a common disease in strawberry nursery production, and a major concern for nurseries wishing to export plants. As the spatial pattern of a disease can offer insight into pathogen source, mode of dissemination, and how current crop management practices affect epidemic development, an understanding of the spatial pattern of ALS would allow nursery growers to make informed decisions regarding disease management. Ninety-seven field assessments of disease incidence were performed at different nursery locations in 2014 and 2015 to quantify ALS spatial pattern under commercial conditions. Both point-pattern and geostatistical statistical procedures were used to analyze the data. The spatial pattern of ALS was characterized by a high degree of heterogeneity, as indicated by high median values of the beta-binomial distribution's theta parameter (0.643), and the index of dispersion, D (4.218). The binary power law provided a robust description of the data with estimated slope and intercept parameters significantly greater than 1 and 0, respectively (P < 0.001). Spatial analysis by distance indices (SADIE) detected significant nonrandom spatial arrangements for 64% of the data sets. Analysis of directional disease spread showed a strong spatial association between sampling units along the same planting row. This suggests that recurrent crop operations during the growing season play a significant role in ALS spread and should be taken into account to improve disease control.

Spatial and Temporal Analysis of Squash vein yellowing virus Infections in Watermelon

Squash vein yellowing virus (SqVYV) is a whitefly-transmitted ipomovirus infecting watermelon and other cucurbits that was recently introduced to Florida. Effects on watermelon are devastating, with total vine collapse, often near harvest, and fruit rendered unmarketable by brown, discolored flesh. The epidemiology of SqVYV was studied in a 1-ha field of 'Fiesta' watermelon over six growing seasons (I to VI) to characterize the spatial patterning of disease and temporal rate of disease progress, as well as its association with Cucurbit leaf crumple virus (CuLCrV) and Cucurbit yellow stunting disorder virus (CYSDV), two additional whitefly-transmitted viruses that often occur with SqVYV. The field was scouted at regular intervals for the length of the season for incidence of virus and number of whiteflies. Incidence of SqVYV reached 100% during seasons I, II, and V and 20% during season III. SqVYV did not occur during seasons IV and VI. SqVYV progressed in a characteristic logistic fashion in seasons I, II, and V but less so in season III. The rate of disease progress was similar for the three seasons with high disease incidence, with an average value of 0.18. A positive correlation between the area under the disease progress curve and whitefly-days was found, where both progress curves were calculated as a function of thermal time (degree days, base 0°C). SqVYV displayed significant but variable levels of aggregation, as indicated by its fit to the β-binomial distribution, the binary power law, and ordinary runs analysis. Association analysis indicated that the viruses were largely transmitted independently. Results of this study provide epidemiological information that will be useful in the development of management strategies for SqVYV-induced vine decline, and provide new information for CuLCrV and CYSDV.

Considerations of scale in the analysis of spatial pattern of plant disease epidemics

Scale is an important but somewhat neglected subject in plant pathology. Scale serves as an abstract concept, providing a framework for organizing observations and theoretical models, and plays a functional role in the organization of ecological communities and physical processes. Rich methodological resources are available to plant pathologists interested in considering either or both aspects of scale in their research. We summarize important concepts in both areas of the literature, particularly as they apply to the spatial pattern of plant disease, and highlight some new results that emphasize the importance of scaling on the emergence of different types of probability distribution in empirical observation. We also highlight the important links between heterogeneity and scale, which are of central importance in plant disease epidemiology and the analysis of spatial pattern. We consider statistical approaches that are available, where actual physical scale is known, and for more conceptual research on hierarchies, where scale plays a more abstract role, particularly for field-based research. For the latter, we highlight methods that plant pathologists could consider to account for the effect of scale in the design of field studies.