A Bayesian approach to meta-analysis of plant pathology studies.

Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework. Bayesian meta-analysis can readily include information not easily incorporated in classical methods, and allow for a full evaluation of competing models. Given the power and flexibility of Bayesian methods, we expect them to become widely adopted for meta-analysis of plant pathology studies.

Explaining loss caused by tomato spotted wilt virus on tobacco with boreal winter weather: a Bayesian approach.

In North Carolina, Tomato spotted wilt virus (TSWV) has regularly been reported since 1997, with incidence being the highest in 2002. At the end of each season, a questionnaire is sent to the county agents to report disease losses. TSWV reported losses in 1993 to 2007 from 58 counties were available. A county-year combination was considered a case and, in total, 494 cases were analyzed. The winter months' temperature and precipitation significantly explained the reported TSWV loss (R(2) = 0.82). Specifically, the monthly average air temperature for December to February had a positive association with TSWV loss (P < 0.0001) whereas the total precipitation for the same months had a negative effect (P < 0.0001). Bayesian hierarchical models were implemented to include spatial and nonspatial random effects to investigate if there were significant spatial correlations or unexplained variability, respectively, and, thus, other significant variables that were ignored in the model development. The spatial random effects were not significant but the nonspatial random effects were significant in 36 cases. The importance of spring weather to dispersal of thrips and TSWV has been previously identified. Winter weather also may be a good indicator of potential available TSWV inoculum for the upcoming season.

Effects of Fluctuating Soil Temperature and Water Potential on Sclerotia Germination and Apothecial Production of Sclerotinia sclerotiorum.

The effects of fluctuating soil temperature and water potential on sclerotial germination and apothecial production by Sclerotinia sclerotiorum were investigated in growth chamber experiments. In the temperature experiments, temperature fluctuations of 4, 8, 12, and 16°C around a median of 20°C, and a constant of 20°C, were tested. Daily temperature fluctuations of 8°C resulted in highest levels of sclerotial germination and apothecial production. The earliest appearance of apothecia occurred in the 8°C fluctuation treatment, 24 days after the start of the experiment. Sclerotia in the 12°C fluctuation treatment germinated last; its first sclerotium germinated 44 days after experiment initiation. For the soil water potential experiments, constant saturation (approximately -0.001 MPa) and three levels of soil water potential fluctuation from saturation-"low" (-0.03 to -0.04 MPa), "medium" (-0.06 to -0.07 MPa), and "high" (-0.09 to -0.1 MPa)-were tested. Constant saturation yielded the highest number of germinated sclerotia and apothecia. All soil water potential fluctuations were detrimental to sclerotial germination and apothecial production, with sclerotial germination under fluctuating moisture conditions less than a tenth of that occurring under constant saturation. The first sclerotium in the constant saturation treatment germinated in 35 days; however, 76 days were required in the high soil water potential fluctuation treatment.

Effects of latent infection, temperature, precipitation, and irrigation on panicle and shoot blight of pistachio in california.

ABSTRACT Panicle and shoot blight, caused by a Fusicoccum sp., is an economically important disease of pistachio in California. Between 1999 and 2001, the disease severity was monitored throughout the growing season in 10 pistachio orchards, irrigated with drip, microsprinklers, low-angled (12 degrees ) sprinklers, or flood. The effect of temperature, precipitation pattern, irrigation system, and incidence of Fusicoccum sp. latent infection on panicle and shoot blight severity was quantified with a generalized linear model for repeated measures. The number of continuous rainy days in April and May and the cumulative daily mean temperatures from June to early September had a significant positive effect on panicle and shoot blight of pistachio leaves and fruit. Drip irrigation significantly decreased disease risk. Other factors, such as the number of discontinuous rainy days in April and May, the cumulative deviation from the 30-year average temperature during the dry days of April and May, the incidence of latent infection (only on leaves), and irrigation with microsprinklers or lowangled (12 degrees ) sprinklers were weak explanatory variables of panicle and shoot blight severity. Knowledge of panicle and shoot blight risk may contribute significantly to decisions regarding the appropriate application of fungicides, especially in years or fields of low risk.

Bayesian analysis in plant pathology.

ABSTRACT Bayesian methods are currently much discussed and applied in several disciplines from molecular biology to engineering. Bayesian inference is the process of fitting a probability model to a set of data and summarizing the results via probability distributions on the parameters of the model and unobserved quantities such as predictions for new observations. In this paper, after a short introduction of Bayesian inference, we present the basic features of Bayesian methodology using examples from sequencing genomic fragments and analyzing microarray gene-expressing levels, reconstructing disease maps, and designing experiments.

Logistic regression modeling of prevalence of soybean sclerotinia stem rot in the north-central region of the United States.

ABSTRACT Regional prevalence of soybean Sclerotinia stem rot (SSR), caused by Sclerotinia sclerotiorum, was modeled using tillage practices, soil texture, and weather variables (monthly air temperature and monthly precipitation from April to August) as inputs. Logistic regression was used to estimate the probability of stem rot prevalence with historical disease data from four states of the north-central region of the United States. Potential differences in disease prevalence between states in the region were addressed using regional indicator variables. Two models were developed: model I used spring (April) weather conditions and model II used summer (July and August) weather conditions as input variables. Both models had high explanatory power (78.5 and 77.8% for models I and II, respectively). To investigate the explanatory power of the models, each of the four states was divided into small geographic areas, and disease prevalence in each area was estimated using both models. The R(2) value of the regression analysis between observed and estimated SSR prevalence was 0.65 and 0.71 for models I and II, respectively. The same input variables were tested for their significance to explain the within-field SSR incidence by using Poisson regression analysis. Although all input variables were significant, only a small amount of variation of SSR incidence was explained, because R(2) of the regression analysis between observed and estimated SSR incidence was 0.065. Incorporation of available site-specific information (i.e., fungicide seed treatment, weed cultivation, and manure and fertilizer applications in a field) improved slightly the explained amount of SSR incidence (R(2) = 0.076). Predicted values of field incidence generally were overestimated in both models compared with the observed incidence. Our results suggest that preseason prediction of regional prevalence would be feasible. However, prediction of field incidence would not, and a different site-specific approach should be followed.

Bayesian logistic regression of soybean sclerotinia stem rot prevalence in the u.s. North-central region: accounting for uncertainty in parameter estimation.

ABSTRACT Bayesian ideas have recently gained considerable ground in several scientific fields mainly due to the rapid progress in computing resources. Nevertheless, in plant epidemiology, Bayesian methodology is not yet commonly discussed or applied. Results of a logistic regression analysis of a 4-year data set collected between 1995 and 1998 on soybean Sclerotinia stem rot (SSR) prevalence in the north-central region of the United States were reexamined with Bayesian methodology. The objective of this study was to use Bayesian methodology to explore the level of uncertainty associated with the parameter estimates derived from the logistic regression analysis of SSR prevalence. Our results suggest that the 4-year data set used in the logistic regression analysis of SSR prevalence in the north-central region of the United States may not be informative enough to produce reliable estimates of the effect of some explanatory variables on SSR prevalence. Such confident estimations are necessary for deriving robust conclusions and high quality predictions.

Impact of Management Practices on Prevalence of Soybean Sclerotinia Stem Rot in the North-Central United States and on Farmers' Decisions Under Uncertainty.

Regional prevalence of soybean Sclerotinia stem rot (SSR), caused by Sclerotinia sclerotiorum, was modeled using management practices (tillage, herbicide, manure and fertilizer application, and seed treatment with fungicide) and summer weather variables (mean monthly air temperature and precipitation for the months of June, July, August, and September) as inputs. Logistic regression analysis was used to estimate the probability of stem rot prevalence with disease data from four states in the north-central region of the United States (Illinois, Iowa, Minnesota, and Ohio). Goodness-of-fit criteria indicated that the resulting model explained well the observed frequency of occurrence. The relationship of management practices and weather variables with soybean yield was examined using multiple linear regression (R 2 = 0.27). Variables significant to SSR prevalence, including average air temperature during July and August, precipitation during July, tillage, seed treatment, liquid manure, fertilizer, and herbicide applications, were also associated with high attainable yield. The results suggested that SSR occurrence in the north-central region of the United States was associated with environments of high potential yield. Farmers' decisions about SSR management, when the effect of management practices on disease prevalence and expected attainable yield was taken into account, were examined. Bayesian decision procedures were used to combine information from our model (prediction) with farmers' subjective estimation of SSR incidence (personal estimate, based on farmers' previous experience with SSR incidence). MAXIMIN and MAXIMAX criteria were used to incorporate farmers' site-specific past experience with SSR incidence, and optimum actions were derived using the criterion of profit maximization. Our results suggest that management practices should be applied to increase attainable yield despite their association with high disease risk.