Leaf Spot Disease of Broad Bean (vicia faba L.) Caused by Alternaria tenuissima— A New Disease in Japan

Farmers' fields were surveyed for a new disease on broad bean in different parts of Shimane Prefecture. The disease was found in all surveyed fields. The fungus frequently associated with diseased broad bean leaves having the characteristic leaf spot symptom was identified as Alternaria tenuissima, based on morphological characteristics. The initial lesion was brown, water soaked, circular to slightly irregular. Then the lesion enlarged and became concentric. Mature leaves had coalescing necrosis surrounded by yellowing. Older leaves of the plant were particularly affected. In a later stage of the disease, the leaves became blighted from the margin to the center and most of the diseased plants defoliated. In severely infected fields, circular to irregularly shaped lesions also appeared on stems and pods, and plants defoliated completely. All tested isolates were pathogenic to broad bean leaves. Different isolates of the fungus varied in pathogenicity on different broad bean cultivars. In a comparison of symptoms of the disease and morphological characteristics of the isolated fungus with other broad bean diseases, this disease represented a new, as yet undescribed disease of broad bean in Japan. Therefore, we propose the name "leaf spot of broad bean" and "Soramame hanten-by?" in Japanese. Received 12 April 2001/ Accepted in revised form 18 October 2001     

Hierarchical models for white mould in snap bean

Limitations on the acceptable proportion (incidence) of pods with white mould may lead to the rejection of entire fields of processing snap bean. The low tolerances (no more than 2% to 6% of pods with white mould) are difficult to estimate with sufficient precision in the field when time is limited. These constraints motivated this study of white mould across three spatial hierarchical levels: pods, plants and quadrats consisting of two adjacent plants within rows. Hierarchical relationships are required when designing formal rules for estimating the incidence of pods with white mould from units higher in the spatial hierarchy. Disease assessments were made on all pods from 38 within‐row transects of 40 plants each of the snap bean cultivar Hystyle. Using probability‐based principles, equations were derived and fitted to data on the incidence of white mould on pods (i_pod), plants (i_pad) and quadrats (i_q(2)), which led to a function directly linking i_pod to i_q(2). The variance of i_pod increased with i_q(2), but that may be of little consequence at the lower values of i_q(2) likely to be associated with i_pod values at processor‐set tolerances. For example, at i_q(2) = 0.1 there was a 92% probability that i_pod was less than 0.02. Assessing i_q(2) may be more efficient than directly estimating i_pod because i_q(2) was about an order of magnitude higher than i_pod. Results suggest it may be feasible to design sampling plans for estimating the proportion of pods with white mould from an assessment of the proportion of diseased quadrats.     

Analysis of the spatial distribution of rust-infected leek plants with the Black-White join-count statistic

Leek rust, caused byPuccinia allii Rudolphi, is an important disease of leek (Allium porrum L.) in the Netherlands. For the development of a practical sampling method for early detection of leek rust in commercial fields, information on the spatial distribution of the disease is necessary. In this study, the spatial distribution of diseased plants during three naturally occurring epidemics of leek rust was observed. The observations were analysed with the Black-White join-count statistic. The spatial distribution of rust-infected leek plants was different for each of the three epidemics, ranging from random to highly clustered. These results show, that in the development of a practical sampling method for detection of leek rust, it is necessary to take into consideration a possibly clustered distribution of diseased plants.     

Spatial analysis and incidence–density relationships for downy mildew on hop

The spatial pattern of downy mildew (Pseudoperonospora humuli) on hop (Humulus lupulus) was characterized over 4 years to aid in deriving an appropriate incidence–density relationship. From 472 disease assessments (datasets), discrete distributions were fitted to the datasets to determine aggregation of disease density. Where distributions were able to be fitted, the Poisson distribution fitted 4% of the datasets and the negative binomial distribution fitted 87% of the datasets. Larger‐scale patterns of disease were assessed by autocorrelation and runs analysis; both indicated aggregation of diseased plants was less common than aggregation of disease within plants. Taylor’s power law indicated disease density was aggregated and related to mean disease density in all years. Disease incidence and density were linked by saturation‐type relationships based on the zero term of the negative binomial distribution or an empirical regression. Certain individual datasets were not described well by any incidence–density model, particularly when disease density was greater than about 0·8 diseased shoots per plant with the cultivar Cascade. When applied to 56 validation datasets, 88% of the variation in observed disease incidence was explained by the incidence–density models. Under conditions where sampling would be implemented for disease management, the requisite conditions appear to be in place for a binomial sampling plan for downy mildew.     

Spatiotemporal Description of Epidemics Caused by Phoma ligulicola in Tasmanian Pyrethrum Fields

ABSTRACT Spatial and temporal patterns of foliar disease caused by Phoma ligulicola were quantified in naturally occurring epidemics in Tasmanian pyrethrum fields. Disease assessments (defoliation incidence, defoliation severity, incidence of stems with ray blight, and incidence of flowers with ray blight) were performed four times each year in 2002 and 2003. Spatial analyses based on distribution fitting, runs analysis, and spatial analysis by distance indices (SADIE) demonstrated aggregation in fields approaching their first harvest for all assessment times between September and December. In second-year harvest fields, however, the incidence of stems with ray blight was random for the first and last samplings, but aggregated between these times. Spatiotemporal analyses were conducted between the same disease intensity measures at subsequent assessment times with the association function of SADIE. In first-year harvest fields, the presence of steep spatial gradients was suggested, most likely from dispersal of conidia from foci within the field. The importance of exogenous inoculum sources, such as wind-dispersed ascospores, was suggested by the absence of significant association between defoliation intensity (incidence and severity) and incidence of stems with ray blight in second-year harvest fields. The logistic model provided the best temporal fit to the increase in defoliation severity in each of six first-year harvest fields in 2003. The logistic model also provided the best fit for the incidence of stems with ray blight and the incidence of flowers with ray blight in four of six and three of six fields, respectively, whereas the Gompertz model provided the best fit in the remaining fields. Fungicides applied prior to mid-October (early spring) significantly reduced the area under disease progress curve (P < 0.001) for defoliation severity, the incidence of stems with ray blight, and the incidence of flowers with ray blight for epidemics at all field locations. This study provides information concerning the epidemiology of foliar disease and ray blight epidemics in pyrethrum and offers insight on how to best manage these diseases.     

Sampling for plant disease incidence

ABSTRACT Knowledge of the distribution of diseased plant units (such as leaves, plants, or roots) or of the relationship between the variance and mean incidence is essential to efficiently sample for diseased plant units. Cluster sampling, consisting of N sampling units of n individuals each, is needed to determine whether the binomial or beta-binomial distribution describes the data or to estimate parameters of the binary power law for disease incidence. The precision of estimated disease incidence can then be evaluated under a wide range of settings including the hierarchical sampling of groups of individuals, the various levels of spatial heterogeneity of disease, and the situation when all individuals are disease free. Precision, quantified with the standard error or the width of the confidence interval for incidence, is directly related to N and inversely related to the degree of heterogeneity (characterized by the intracluster correlation, rho). Based on direct estimates of rho (determined from the theta parameter of the beta-binomial distribution or from the observed variance) or a model predicting rho as a function of incidence (derived from the binary power law), one can calculate, before a sampling bout, the value of N needed to achieve a desired level of precision. The value of N can also be determined during a sampling bout using sequential sampling methods, either to estimate incidence with desired precision or to test a hypothesis about true disease incidence. In the latter case, the sequential probability ratio test is shown here to be useful for classifying incidence relative to a hypothesized threshold when the data follows the beta-binomial distribution with either a fixed rho or a rho that depends on incidence.     

Aerial photography used for spatial pattern analysis of late blight infection in irrigated potato circles

ABSTRACT Spatial and temporal dynamics of late blight were investigated from color, infrared aerial photographs of five commercial potato fields in the Columbia Basin during epidemics in 1993, 1995, and 1998. Aerial photographs were taken one to four times at 6- to 21-day intervals. Photographs were scanned and pixels, representing approximately 1 m(2) in the field, were used in the analysis. Late blight-infected plants were aggregated as indicated by runs analysis. Significant z-tests were computed for four directions during each sampling date in each of the five fields. Absolute z-values for runs analysis increased, indicating increasing aggregation in the four directions, as disease incidence increased in the early and midphases of the epidemics in each field. Variograms indicated the existence of autocorrelation among infected plants in four directions; the range of influence increased as disease incidence increased except at the highest levels of disease. Late blight was observed to spread in fields as foci. Late blight foci enlarged in size, produced distinct daughter foci, and coalesced. A field where initial inoculum likely originated from infected seed tubers exhibited less initial aggregation than the other fields, perhaps due to a different source of primary inoculum. Aerial photography coupled with spatial analyses of late blight-infected plants was an effective technique to quantitatively assess disease patterns in relatively large fields and was useful in quantifying an intensification of aggregation during the epidemic process on a large scale.     

A generalized linear modeling approach for characterizing disease incidence in a spatial hierarchy

ABSTRACT Several statistical models are introduced to quantify the effect of heterogeneity on disease incidence relationships in a three-scale spatial hierarchy: the sampling unit level (highest), the leaf scale (intermediate), and the leaflet scale (lowest). The models are an extension of the theory previously developed for a two-scale hierarchy and were tested using data collected from strawberry leaf blight epidemics. Disease incidence at the sampling-unit scale (proportion of sampling units with one or more diseased leaflets) increased as a saturation-type curve with increasing leaflet or leaf disease incidence (proportion of leaflets or leaves diseased) as predicted by the good fit of the beta-binomial distribution to the leaflet and leaf data. The relationship could be accurately described, without curve fitting, by several simple nonlinear models, in which the aggregation of disease was represented by a modified binomial function incorporating an effective sample size that was either constant or dependent on mean incidence. The relationship between incidence at the leaflet and leaf scales could be modeled based on the combined sampling-unit models for leaflets and leaves. By taking the complementary log-log (CLL) transformation of incidence, the equations could be expressed as generalized linear models, and curve fitting used to estimate the parameters. Generally, curve fitting gave slight to no improvement in the accuracy of the predictions of incidence. These models have broad applicability in sampling for disease incidence, and results can be used to interpret how diseased individuals at the lowest level in a hierarchy are arranged within sampling units.     

Measuring spatial aggregation in binary epidemics: correlative analysis and the advantage of fractal-based sampling

ABSTRACT The incomplete sampling of a binary epidemic is nothing more than the overlap of two spatial patterns: the pattern of diseased plants and the pattern of sampled points. Thus, the information on the spatial arrangement of diseased plants obtained from such a sampling explicitly depends on the geometric locations of the sampled points. A number of procedures for sampling disease incidence are examined. These include samples placed on a regular grid, spatially clustered samples, randomly selected samples, and samples specified by a nested fractal design. The performance of these various sampling schemes was examined using simulated binary epidemics with varying degrees of spatial aggregation over different length scales, generated using a Neyman-Scott cluster process. A modification of spatial correlation analysis specifically geared to binary epidemics is derived and shown to be equivalent to a X(2) test comparing the number of infected plant pairs to that expected from a spatially random epidemic. This analysis was applied to the data obtained using the various sampling schemes and the results are compared and contrasted. For the same number of sampling points, the fractal design is most efficient in the detection of contagion and provides spatial information over a larger range of distance scales than other sampling schemes. However, the regular grid sampling scheme consistently yielded an estimate of average disease incidence that had the smallest variance. Sampling patterns consisting of randomly selected points were intermediate in behavior between the two extremes.     

Sequential sampling for incidence of phomopsis leaf blight of strawberry

ABSTRACT Sequential sampling models for estimation and classification were developed for the incidence of strawberry leaflets infected by Phomopsis obscurans. Sampling protocols were based on a binary power law analysis of the spatial heterogeneity of Phomopsis leaf blight in commercial fields in Ohio. For sequential estimation, samples were collected until mean disease incidence could be estimated with a preselected coefficient of variation of the mean (C). For sequential classification, samples were collected until there was sufficient evidence to classify mean incidence as being below or above a threshold (p(t)) based on the sequential probability ratio test. Monte-Carlo simulations were used to determine the theoretical average sample number (ASN) and probability of classifying mean incidence as less than p(t) (operating characteristic) for any true value of incidence. Estimation and classification sampling models were both tested with bootstrap simulations of randomly selected data sets and validated by data sets from another year that were not utilized in developing the models. In general, achieved (or calculated) C after sequentially sampling for estimation was close to the preselected C of 0.2, and mean incidence was estimated with little bias. Achieving a C of 0.1 with less than 75 sampling units (the nominal value for many original data sets) was more problematical, especially with true incidence less than 0.2. ASN for classification was only 9 to 18 at disease incidence values near p(t), and approximately five or less at incidence values far from p(t). Correct classification decisions were made in over 88% of the validation data sets. Results indicated that it is possible to estimate Phomopsis leaf blight with high precision and with high correct classification probabilities.     

不同供氮水平对芸豆碳氮代谢平衡的影响

采用盆栽土壤基施0、15、30 kg·hm-2三个氮素水平试验,研究了芸豆荚果形成后不同氮素水平下叶片和荚果的碳、氮代谢主要酶活性以及抗氧化酶系活性的变化。结果表明,芸豆荚果形成后,随着土壤供氮水平的增加,荚果的磷酸烯醇式丙酮酸羧化酶活性、多酚氧化酶活性、超氧化物歧化酶和过氧化氢酶活性逐渐增强;叶片的蔗糖合成酶活性、蔗糖磷酸合成酶活性、硝酸还原酶和磷酸烯醇式丙酮酸羧化酶活性大于同一供氮水平荚果的活性;且荚果的总可溶性糖和可溶性蛋白含量高于叶片;叶片的磷酸烯醇式丙酮酸羧化酶的活性与荚果的蔗糖磷酸合成酶和硝酸还原酶活性呈显著相关性。由此可以得出,源器官是芸豆植株的代谢活跃中心,而库器官成为植株的生长中心,且后者的碳、氮代谢过程主要受前者的调控。     

Temporal Progression of Bean Common Bacterial Blight (Xanthomonas Campestris pv. phaseoli) in Sole and Intercropping Systems

The effects of four planting patterns of bean (Phaseolus vulgaris) (bean only, maize–bean (MB), sorghum–bean (SB), and maize–bean–sorghum (MBS)) and four cropping systems (sole cropping, row, mixed, and broadcast intercropping) on the temporal epidemics of bean common bacterial blight (CBB) caused by Xanthomonas campestris pv. phaseoli were studied. The experiments were conducted during two consecutive spring and summer seasons in 1999 and 2000 in replicated field experiments. The Gompertz model described disease progress curves better than the logistic model. Intercropping delayed epidemic onset, lowered disease incidence and severity, and reduced the disease progress rate. The type of cropping system and planting pattern affected CBB incidence and severity at initial, final and overall assessments and also affected the rate of disease development. Statistical significance of treatment interactions based on disease assessments was found for incidence in all four experiments and for severity in three experiments. A slower disease progress rate and lower incidence and severity occurred on beans planted with maize or sorghum in row, mixed and broadcast intercropping than on bean planted alone. Incidence was reduced 36% and severity 20% in intercropping compared to sole cropping. The built-in disease delay and the slowing of the disease progress rate could provide protection for beans from severe CBB epidemics in intercropped systems. Variation between years appeared to be related to relative humidity (RH).     

田间小豆绿豆象卵空间分布型初探

采用5点取样法对北京地区夏播小豆田进行了调查,发现绿豆象在小豆鼓粒初期已将卵产到豆荚上,9月上、中旬为产卵高峰期,并逐渐发育成幼虫侵入豆粒中。绿豆象卵在小豆荚上的空间分布型为聚集分布,其聚集原因是由环境因素引起。9月10-15日是控制北京地区夏播小豆田间绿豆象产卵及卵发育的较好时机。     

Control of Aphis fabae on broad beans (Vicia faba) by the systemic action of gamma-bhc,thionazin and aldicarb

The in-row application of aldicarb granules at 2 lb active ingredient (a.i.)/acre (2·24 kg/ha) at sowing gave complete control of Aphis fabae Scop. on broad beans (Vicia faba L. cv. Seville) up to 7 days before harvest and resulted in a three-fold increase in yield compared with a similar thionazin treatment. Bean plants grown from seeds which were soaked in a gamma-BHC solution at 20 ppm for 24 h prior to planting were protected from this aphid for most of the growing season almost as effectively as with the thionazin treatment. A thin-layer chromatography method was developed for the determination in plants and soil of aldicarb and its two major toxic metabolites, the sulphoxide and sulphone. Gas-liquid chromatography was used to monitor the declining levels of gamma-BHC and thionazin, and simultaneous bioassays were made with Aphis fabae on excised leaf discs from the crop. Analysis of the bean seeds and pods at harvest 90 days after sowing indicated no detectable gamma-BHC, less than 0·01 ppm of thionazin and approximately 0·09 ppm total residue of aldicarb sulphone and sulphoxide. Approximately 22% and 13% of the applied aldicarb, in the form of sulphone and sulphoxide but not the parent compound, remained in the top 6 in (152 mm) of soil at the end of 2 and 4 months respectively. Toxicity studies with Aphis fabae, Acyrthosiphon pisum Harris, and Megoura viciae Buck showed an increasing sensitivity in that order to gamma-BHC at 1 ppm in bean plants. Acute toxicity investigations with feeding Aphis fabae indicated an increasing sensitivity in the order of gamma-BHC < aldicarb sulphone < aldicarb sulphoxide < thionazin < aldicarb. Despite the high acute toxicity of thionazin to Aphis fabae it gave low protection against aphids, possibly owing to its relatively short persistence in both plants and soil when compared with aldicarb.     

Sampling for the incidence of aphid-transmitted viruses in snap bean

ABSTRACT Data collected in 2002 and 2003 on Alfalfa mosaic virus and Cucumber mosaic virus incidences of infection in commercial snap bean fields in New York State were used to develop relationships between disease incidence (p(low)) and sample size while accounting for the inherent spatial aggregation of infected plants observed with these two viruses. For a plan consisting of 300 sampled plants (N = 60 quadrats, n = 5 plants per quadrat), estimating p(low) from the incidence of positive groups (p(high); testing of N = 60 grouped samples) provides the same precision in p(low) as testing 200 plants individually, up to about p(low) = 0.2. Above that, the confidence interval width for p(low) obtained via group testing becomes markedly larger than the width obtained by testing individual plants. Our results suggest using group testing until p(high) is in the range [0.35, 0.59], which corresponds to p(low) in [0.1, 0.2]. Results indicate that group testing can be more economical than the testing of individual plants without loss of precision, at lower incidences of infection. The approach presented provides a general framework for sampling and the estimation of incidence of other aphid-transmitted viruses in snap bean.     

Relationships between incidence and severity of fusarium head blight on winter wheat in ohio

ABSTRACT To determine the relationship between incidence (I; proportion of diseased spikes) and severity (S; mean proportion of diseased spikelets per spike) for Fusarium head blight of wheat and to determine if severity could be predicted reliably from incidence data, disease assessments were made visually at multiple sample sites in artificially and naturally inoculated research and production fields between 1999 and 2002. Ten distinct data sets were collected. Mean disease intensity ranged from 0.023 to 0.975 for incidence and from 0.0003 to 0.808 for severity. A model based on complementary log-log transformation of incidence and severity performed well for all data sets, based on calculated coefficients of determination and random residual plots. The I-S relationship was consistent among years and locations, with similar slopes for all data sets. For 7 of the 10 data sets and for the pooled data from all locations and years, the estimated slope from the fit of the model ranged from 1.03 to 1.26. Time of disease assessment affected the relationship between incidence and severity; however, the estimated slopes from each assessment time were also close to 1. Based on the width of the 95% prediction interval, severity was estimated more precisely at lower incidence values than at higher values. The number of sampling units and the index of dispersion of disease incidence had only minor effects on the precision with which S was predicted from I. The estimation of mean S from I would substantially reduce the time required to assess Fusarium head blight in field surveys and treatment comparisons, and the observed relationship between I and S could be used to identify genotypes with some types of disease resistance.     

An effective sample size for predicting plant disease incidence in a spatial hierarchy

ABSTRACT For aggregated or heterogeneous disease incidence, one can predict the proportion of sampling units diseased at a higher scale (e.g., plants) based on the proportion of diseased individuals and heterogeneity of diseased individuals at a lower scale (e.g., leaves) using a function derived from the beta-binomial distribution. Here, a simple approximation for the beta-binomial-based function is derived. This approximation has a functional form based on the binomial distribution, but with the number of individuals per sampling unit (n) replaced by a parameter (v) that has similar interpretation as, but is not the same as, the effective sample size (n(deff) ) often used in survey sampling. The value of v is inversely related to the degree of heterogeneity of disease and generally is intermediate between n(deff) and n in magnitude. The choice of v was determined iteratively by finding a parameter value that allowed the zero term (probability that a sampling unit is disease free) of the binomial distribution to equal the zero term of the beta-binomial. The approximation function was successfully tested on observations of Eutypa dieback of grapes collected over several years and with simulated data. Unlike the beta-binomial-based function, the approximation can be rearranged to predict incidence at the lower scale from observed incidence data at the higher scale, making group sampling for heterogeneous data a more practical proposition.     

Monitoring the occurrence of tomato bacterial spot and range of the causal agent Xanthomonas perforans in Iran

A 2‐year comprehensive field survey was conducted across major tomato‐growing areas of Iran. Two hundred and thirty‐four tomato fields and six tomato‐producing greenhouses were surveyed for the potential presence of bacterial spot disease. Five hundred and ninety‐six tomato samples with and without symptoms were analysed. While Xanthomonas spp. were found in association with tomato plants both with and without symptoms from five surveyed counties, the bacterial spot disease was observed only in plants from three of them. Only strains isolated from plants with symptoms induced disease symptoms on tomato, while those isolated from symptomless plants caused symptoms only on cabbage and common bean. None of the isolates caused disease symptoms on pepper and eggplant. Phylogenetic analysis showed that X. perforans is the causal agent of tomato bacterial spot in Iran, although X. campestris and X. axonopodis were also associated with symptomless tomato plants. All X. perforans isolates in this study were sensitive to streptomycin, copper sulphate and copper oxychloride at concentrations of 50 mg L^?1, 200 mg L^?1 and 0.8 g L^?1, respectively. Unlike the type strain of X. perforans, isolates in this study did not produce bacteriocin against other Xanthomonas spp., nor were they detected using the usual species‐specific primer pair Bs‐XpF/Bs‐XpR. This suggests an atypical nature of X. perforans strains in Iran, which leads to the hypothesis that X. perforans strains in Iran may have a separate origin to those causing disease epidemics elsewhere. The aggregated dispersal pattern of the diseased tomato fields signifies the seedborne introduction of the pathogen into the country.     

Yield Loss in Apple Caused by Monilinia fructigena (Aderh. & Ruhl.) Honey, and Spatio-temporal Dynamics of Disease Development

Monilinia fructigena (Aderh. & Ruhl.) Honey causes considerable yield losses in pome fruit culture. During a field study in the Netherlands in 1997 and 1998, the increase in disease incidence in time was assessed and final pre- and post-harvest losses were recorded in the susceptible apple cultivars James Grieve and Cox's Orange Pippin. Each individual tree was considered as a unique quadrat, and the spatial distribution of diseased fruits among fruit trees at every assessment date was characterised by a dispersion index, Lloyd's index of patchiness (LIP). Spatial autocorrelation was applied to detect potential clustering of trees with diseased fruits within rows. In cv. James Grieve, the rate of increase of disease incidence was constant up to harvest time, whereas in cv. Cox's Orange Pippin disease incidence increased markedly 3 weeks before harvest time, which coincided with the harvest of cv. James Grieve in neighbouring rows. Pre-harvest disease incidence was 4.2–4.3% in cv. James Grieve in both years, in cv. Cox's Orange Pippin this was 4.4% in 1997 and 2.7% in 1998. Post-harvest yield losses amounted on average 1.5–2.0% for both cultivars, no significant differences were found between the cultivars (t-test, P=0.05). Both in 1997 and 1998, clustering of diseased fruits among fruit trees was detected; LIP values were significantly higher than 1 (P=0.05 in 1997, P=0.01 in 1998). Clustering of trees with diseased fruits was detected in 1998, when significant (P=0.05) positive correlation coefficients occurred for 2nd, 3rd and 4th lag-order distances in cv. James Grieve, and a significant (P=0.05) positive first-order correlation in cv. Cox's Orange Pippin. Wounding agents, such as insects and birds, may play an important role in the underlying disease dynamics, and crop losses may be minimised by control of these agents.     

Spatial pattern analysis of hop powdery mildew in the pacific northwest: implications for sampling

ABSTRACT The spatial pattern of hop powdery mildew was characterized using 3 years of disease incidence data collected in commercial hop yards in the Pacific Northwest. Yards were selected randomly from yards with a history of powdery mildew, and two to five rows were selected for sampling within each yard. The proportion of symptomatic leaves out of 10 was determined from each of N sampling units in a row. The binomial and the beta-binomial frequency distributions were fit to the N sampling units observed in each row and to SigmaN sampling units observed in each yard. Distributional analyses indicated that disease incidence was better characterized by the beta-binomial than the binomial distribution in 25 and 47% of the data sets at the row and yard scales, respectively, according to a log-likelihood ratio test. Median values of the beta-binomial parameter theta, a measure of small-scale aggregation, were near 0 at both sampling scales, indicating that disease incidence was close to being randomly distributed. The variability in disease incidence among rows sampled in the same yard generally increased with mean incidence at the yard scale. Spatial autocorrelation analysis, used to measure large-scale patterns of aggregation, indicated that disease incidence was not correlated between sampling units over several lag distances. Results of a covariance analysis showed that heterogeneity of disease incidence was not dependent upon cultivar, region, or time of year when sampling was conducted. A hierarchical analysis showed that disease incidence at the sampling unit scale (proportion of sampling units with one or more diseased leaves) increased as a saturation-type curve with respect to incidence at the leaf level and could be described by a binomial function modified to account for the effects of heterogeneity through an effective sample size. Use of these models permits sampling at the sampling unit scale while allowing inferences to be made at the leaf scale. Taken together, hop powdery mildew was nearly randomly distributed with no discernable foci, suggesting epidemics are initiated from a well-distributed or readily dispersible overwintering population. Implications for sampling are discussed.