Spatial and temporal stability of the estimated parameters of the binary power law

Catching Spores: Linking Epidemiology, Pathogen Biology, and Physics to Ground-Based Airborne Inoculum Monitoring

Monitoring airborne inoculum is gaining interest as a potential means of giving growers an earlier warning of disease risk in a management unit or region. This information is sought by growers to aid in adapting to changes in the management tools at their disposal and the market-driven need to reduce the use of fungicides and cost of production. To effectively use inoculum monitoring as a decision aid, there is an increasing need to understand the physics of particle transport in managed and natural plant canopies to effectively deploy and use near-ground aerial inoculum data. This understanding, combined with the nuances of pathogen-specific biology and disease epidemiology, can serve as a guide to designing improved monitoring approaches. The complexity of any pathosystem and local environment are such that there is not a generalized approach to near-ground air sampler placement, but there is a conceptual framework to arrive at a "semi-optimal" solution based on available resources. This review is intended as a brief synopsis of the linkages among pathogen biology, disease epidemiology, and the physics of the aerial dispersion of pathogen inoculum and what to consider when deciding where to locate ground-based air samplers. We leverage prior work in developing airborne monitoring tools for hops, grapes, spinach, and turf, and research into the fluid mechanics governing particle transport in sparse canopies and urban and forest environments. We present simulation studies to demonstrate how particles move in the complex environments of agricultural fields and to illustrate the limited sampling area of common air samplers.

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.

The Ebb and Flow of Airborne Pathogens: Monitoring and Use in Disease Management Decisions

Perhaps the earliest form of monitoring the regional spread of plant disease was a group of growers gathering together at the market and discussing what they see in their crops. This type of reporting continues to this day through regional extension blogs, by crop consultants and more formal scouting of sentential plots in the IPM PIPE network (http://www.ipmpipe.org/). As our knowledge of plant disease epidemiology has increased, we have also increased our ability to detect and monitor the presence of pathogens and use this information to make management decisions in commercial production systems. The advent of phylogenetics, next-generation sequencing, and nucleic acid amplification technologies has allowed for development of sensitive and accurate assays for pathogen inoculum detection and quantification. The application of these tools is beginning to change how we manage diseases with airborne inoculum by allowing for the detection of pathogen movement instead of assuming it and by targeting management strategies to the early phases of the epidemic development when there is the greatest opportunity to reduce the rate of disease development. While there are numerous advantages to using data on inoculum presence to aid management decisions, there are limitations in what the data represent that are often unrecognized. In addition, our understanding of where and how to effectively monitor airborne inoculum is limited. There is a strong need to improve our knowledge of the mechanisms that influence inoculum dispersion across scales as particles move from leaf to leaf, and everything in between.

Association of Spring Pruning Practices with Severity of Powdery Mildew and Downy Mildew on Hop

Downy mildew (caused by Pseudoperonospora humuli) and powdery mildew (caused by Podosphaera macularis) are important diseases of hop in the Pacific Northwest United States, and cultural practices may affect the severity of both diseases. The association of spring pruning quality and timing with severity of downy mildew and powdery mildew was assessed through analysis of survey data collected from commercial hop yards in Oregon and Washington. Among 149 hop yards surveyed, the most common pruning method was chemical desiccation (48% of yards), mechanical pruning (23%), or a combination of these practices (15%). The quality of pruning was assessed using a three-category ordinal scale ("excellent", "moderate", or "poor") based on the amount of foliage remaining on plants following pruning. Excellent pruning quality was attained more often in yards pruned twice (74.6 to 82.1% of yards) versus once (33.8% of yards), independent of pruning method. Seasonal severity of downy mildew in Oregon increased approximately twofold with reduction in pruning quality from excellent to moderate to poor. Pruning quality was not significantly related to levels of powdery mildew on leaves or cones in Oregon. Under more severe disease pressure in Washington, however, seasonal severity of powdery mildew on leaves and the incidence of cones with powdery mildew were significantly greater in yards that had poor pruning compared with excellent pruning. Moreover, yards that had excellent pruning quality received, on average, 1.1 to 1.5 fewer fungicide applications per season for downy mildew or powdery mildew compared with yards that had moderate or poor pruning quality. This savings was associated with delayed initiation of the first application by 7.5 to 14.2 days in yards with excellent pruning quality. Replicated experiments in commercial yards in Oregon quantified the effect of delaying pruning timing 5 to 21 days compared with growers' standard practices on the diseases and yield. Downy mildew suppression by delayed pruning was dependent on cultivar and year of sampling, being significantly reduced fivefold only in 'Willamette' in 2007. Severity of powdery mildew and cone yield was similar between plots that received the delayed or standard pruning timing treatments. Collectively, these studies emphasize that early spring sanitation measures are associated with reduced primary inoculum and are critically important for managing both downy mildew and powdery mildew. A savings of at least one fungicide application per year appears achievable when spring pruning is conducted thoroughly and slightly delayed compared with growers' current practices.

Comments regarding the binary power law for heterogeneity of disease incidence

The binary power law (BPL) has been successfully used to characterize heterogeneity (overdispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial distribution over the range of incidence values, and the estimated scale (?) and slope (b) parameters provide information on the characteristics of aggregation. When b = 1, the interpretation is that the degree of aggregation remains constant over the range of incidence values observed; otherwise, aggregation is variable. In two articles published in this journal in 2009, Gosme and Lucas used their stochastic simulation model, Cascade, to show a multiphasic (split-line) relationship of the variances, with straight-line (linear) relationships on a log-log scale within each phase. In particular, they showed a strong break point in the lines at very low incidence, with b considerably >1 in the first line segment (corresponding to a range of incidence values usually not observed in the field), and b being ?1 in the next segment (corresponding to the range of incidence values usually observed). We evaluated their findings by utilizing a general spatially explicit stochastic simulator developed by Xu and Ridout in 1998, with a wide range of median dispersal distances for the contact distribution and number of plants in the sampling units (quadrats), and through an assessment of published BPL results. The simulation results showed that the split-line phenomenon can occur, with a break point at incidence values of ?0.01; however, the split is most obvious for short median dispersal distances and large quadrat sizes. However, values of b in the second phase were almost always >1, and only approached 1 with extremely short median dispersal distances and small quadrat sizes. An appraisal of published results showed no evidence of multiple phases (although the minimum incidence may generally be too high to observe the break), and estimates of b were almost always >1. Thus, it appears that the results from the Cascade simulation model represent a special epidemiological case, corresponding primarily to a roughly nearest-neighbor population-dynamic process. Implications of a multiphasic BPL property may be important and are discussed.

Characterization of the Spatiotemporal Attributes of Sclerotinia Flower Blight Epidemics in a Perennial Pyrethrum Pathosystem

Sclerotinia flower blight, caused by Sclerotinia sclerotiorum, causes substantial losses in Australian pyrethrum fields. The spatiotemporal characteristics of epidemics were characterized in five fields over 3 years. Log likelihood tests indicated that the β-binomial distribution fit better than the binomial distribution for 92% of the data sets. The index of dispersion, D, was significantly greater than 1 in 97% of the data sets. The estimated parameters of the slope and intercept terms of the binary power law were 1.631 (standard error [SE] = 0.059) and 0.678 (SE = 0.099), indicating a high degree of aggregation at the individual sampling unit scale. In 69% of the data sets, the magnitude of the first-order autocorrelation coefficient , was significantly greater than 0. In 11 of the 12 epidemics, the monomolecular model provided the best fit, indicative of monocyclic processes. A significant spatial association between apothecia and incidence of Sclerotinia flower blight within the lag of one sampling unit was also quantified. This study suggests that S. sclerotiorum apothecia emergence was closely synchronized with flower development, and epidemics were dominated by localized sources of ascosporic inoculums. This research provides the basis for improved management strategies for Sclerotinia flower blight in pyrethrum.