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

The incidence of hop powdery mildew on leaves, caused by Podosphaera macularis, collected from 1,606 transects in 77 commercial hop yards in Oregon and Washington over 9 years was used to assess variability in heterogeneity of disease and the estimated binary power law parameters. Spatial analyses of data sets were conducted at the level of individual rows (row level) and multiple rows within a yard (yard level). The binary power law provided a good fit to all data sets, with R(2) values ranging from 0.933 to 0.993. At the row level, the intercept parameter ln(A(x)) was >0 for 8 years, but was not significantly greater than 0 in 2006. The parameter b was greater than 1 for all row-level data sets collected from 1999 to 2005, but was <1 in 2006 and not significantly different from 1 in 2007. Covariance analysis indicated the factor 'region' affected ln(A(x)) in 3 years, and b in 2 years. 'Cultivar' had an effect on ln(A(x)) in 3 years and b in year. At the yard level, ln(A(x)) was greater than 0 for 6 years, but in 2006 and 2007, ln(A(x)) was not significantly different from 0. The slope parameter b was greater than 1 in 6 years, but was not significantly different from 1 in 2006 and 2007. Differences in b among years were large enough to have practical implications for sample sizes and precision of fixed and sequential sampling. Although the binary power law parameter tended to be relatively stable, variability of the estimated parameters may have practical consequences for sampling precision and costs.     

Spatial distribution of purple seed stain of soybean caused by <Emphasis Type="Italic">Cercospora kikuchii</Emphasis> in fields

To investigate the frequency distribution of purple seed stain of soybean caused by Cercospora kikuchii in two experimental fields in 2004, we set up rows 75 cm apart and sowed two asymptomatic seeds at each of positions 20 cm apart in each row. We sowed purple-stained seeds infected with the pathogen as inocula at four points instead of asymptomatic seeds in each field. We assessed disease incidence in harvested seeds by counting the numbers of purple-stained and asymptomatic seeds. To determine the spatial distribution of the disease, we grouped the field points into analytical units of several sizes. Beta-binomial and binomial distributions described the distribution patterns of purple-stained seeds. The smallest value of α, a beta-binomial parameter, occurred with analytical units that contained three or nine points next to each other within a single row, suggesting that these units showed the most aggregated distribution of the disease, each of the patches of seeds infected with C. kikuchii could be defined approximately by the area covered by three or nine points (75 × 60 or 75 × 180 cm), and the disease tended to infect plants next to each other within rows.     

Relationships between disease incidence at two levels in a spatial hierarchy

ABSTRACT Relationships between disease incidence measured at two levels in a spatial hierarchy are derived. These relationships are based on the properties of the binomial distribution, the beta-binomial distribution, and an empirical power-law relationship that relates observed variance to theoretical binomial variance of disease incidence. Data sets for demonstrating and testing these relationships are based on observations of the incidence of grape downy mildew, citrus tristeza, and citrus scab. Disease incidence at the higher of the two scales is shown to be an asymptotic function of incidence at the lower scale, the degree of aggregation at that scale, and the size of the sampling unit. For a random pattern, the relationship between incidence measured at two spatial scales does not depend on any unknown parameters. In that case, an equation for estimating an approximate variance of disease incidence at the lower of the two scales from incidence measurements made at the higher scale is derived for use in the context of sampling. It is further shown that the effect of aggregation of incidence at the lower of the two scales is to reduce the rate of increase of disease incidence at the higher scale.     

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.     

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.     

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.     

小麦白粉病田间分布型的初步研究

Al-sohaily 等研究丝黑穗病菌的生理分化指出,玉米丝黑穗病菌与高粱丝黑穗病菌应为2个不同的“变种”,分别命名为:Sphacelotheca reiliana var.Zeae 和 S.rei-(?)iana var.reiliana。国内的初步研究结果表明,来自不同地区的玉米丝黑穗病菌不存在明显的致病力差异。为探明高梁丝黑穗病菌的地区间差异性,深入研究病菌生理分化,为抗病育种提供依据,进行了此项试验,简报如下。     

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.     

Spatial pattern analysis of strawberry leaf blight in perennial production systems

ABSTRACT Spatial pattern of the incidence of strawberry leaf blight, caused by Phomopsis obscurans, was quantified in commercial strawberry fields in Ohio using statistics for heterogeneity and spatial correlation. For each strawberry planting, two transects were randomly chosen and the proportion of leaflets (out of 15) and leaves (out of five) with leaf blight symptoms was determined from N = 49 to 106 (typically 75) evenly spaced sampling units, thus establishing a natural spatial hierarchy to compare patterns of disease. The beta-binomial distribution fitted the data better than the binomial in 92 and 26% of the 121 data sets over 2 years at the leaflet and leaf levels, respectively, based on a likelihood ratio test. Heterogeneity in individual data sets was measured with the index of dispersion (variance ratio), C(alpha) test, a standard normal-based test statistic, and estimated theta parameter of the beta-binomial. Using these indices, overdispersion was detected in approximately 94 and 36% of the data sets at the leaflet and leaf levels, respectively. Estimates of the slope from the binary power law were significantly (P < 0.01) greater than 1 and estimates of the intercept were significantly greater than 0 (P < 0.01) at both the leaflet and leaf levels for both years, indicating that degree of heterogeneity was a function of incidence. A covariance analysis indicated that cultivar, time, and commercial farm location of sampling had little influence on the degree of heterogeneity. The measures of heterogeneity indicated that there was a positive correlation of disease status of leaflets (or leaves) within sampling units. Measures of spatial association in disease incidence among sampling units were determined based on autocorrelation coefficients, runs analysis, and a new class of tests known as spatial analysis by distance indices (SADIE). In general, from 9 to 22% of the data sets had a significant nonrandom spatial arrangement of disease incidence among sampling units, depending on which test was used. When significant associations existed, the magnitude of the association was small but was about the same for leaflets and leaves. Comparing test results, SADIE analysis was found to be a viable alternative to spatial autocorrelation analysis and has the advantage of being an extension of heterogeneity analysis rather than a separate approach. Collectively, results showed that incidence of Phomopsis leaf blight was primarily characterized by small, loosely aggregated clusters of diseased leaflets, typically confined within the borders of the sampling units.     

Crop damage caused by powdery mildew on hop and its relationship to late season management

Powdery mildew of hop (Podosphaera macularis) may cause economic loss due to reductions in cone yield and quality. Quantitative estimates of crop damage from powdery mildew remain poorly characterized, especially the effect of late season disease management on crop yield and quality. Field studies in Washington State evaluated cone yield, bittering acid content and quality factors when fungicide applications were ceased at different stages of cone development. The incidence of cones with powdery mildew was linearly correlated with yield of cones, bittering acids and accelerated cone maturation. In cultivar Galena, the cumulative effect of every 1% increase in cones powdery mildew incidence was to reduce alpha‐acid yield by 0·33%, which was due to direct effects on cone yield but also indirect effects mediated by dry matter. In the more susceptible cultivar Zeus, alpha‐acid yield was increased 20% by controlling powdery mildew through the transition of bloom to early cone development compared to ceasing fungicide applications at bloom: additional applications provided only modest improvements in alpha‐acid yield. In both cultivars, the impact of powdery mildew on aroma characteristics and bittering acid content were less substantial than cone yield. The damage caused by powdery mildew to cone colour and alpha‐acid yield, as well as the effectiveness of fungicide applications made to manage the disease, appears inseparably linked to dry matter content of cones at harvest. Realising achievable yield potential in these cultivars requires control of the disease through early stages of cone development and harvest before maturity exceeds c. 25% dry matter.     

Analysis of the association between the incidence of two spatially aggregated foliar diseases of strawberry

ABSTRACT Association of the incidence of leaf blight (caused by Phomopsis obscurans) and leaf spot of strawberry (caused by Mycosphaerella fragariae) was assessed at multiple scales in perennial plantings at several commercial farms over 3 years (1996 to 1998). For each field, the presence or absence of each disease was recorded from n = 15 leaflets in each of N approximately 70 evenly spaced sampling units, and the proportion of leaflets with blight, spot, and total disease (blight or spot) was determined. Individual diseases and total disease incidence were all well described by the beta-binomial distribution but not by the binomial distribution, indicating overdispersion of disease. The Jaccard similarity index was used to measure disease co-occurrence at the leaflet, sampling-unit, and field scales. Standard errors of this index for the lower two scales were obtained using the jackknife (resampling) procedure, and data randomizations were used to determine the expected Jaccard index for an independent arrangement of the two diseases, conditioned on the incidence and spatial heterogeneity of the observed disease data. Results based on these statistics showed that only 4 of 52 data sets at the leaflet level and no data sets at the sampling-unit level had Jaccard index values significantly different from that expected under an independent rearrangement of the two diseases. Rank correlation and cross-correlation statistics were calculated to determine the degree of covariation in incidence between the two diseases. Additionally, covariation between diseases was tested using a new procedure in the Spatial Analysis by Distance IndicEs (SADIE) class of tests. Covariation was detected in 21% of the data sets using rank correlation methods and in 15% of the data sets using the SADIE-based approach. The discrepancy between these two methods may be due to the rank correlation procedure not taking into account the effects of spatial pattern of disease incidence. There was no relationship between mean disease incidence per field of spot and blight or between degree of heterogeneity of the two diseases (as measured by theta of the beta-binomial distribution), demonstrating lack of covariation at the field scale. Incidence of leaflets with either disease (total disease incidence) could be well predicted using a linear combination of the estimated probabilities of leaf blight and leaf spot incidence based on independence of the two diseases. Heterogeneity of total disease incidence, measured with the estimated theta parameter of the beta-binomial distribution, could also be well predicted using a linear combination of the weighted theta values for leaf blight and leaf spot, with weights proportional to incidence of the individual diseases.     

Effect of Grapevine Training Systems on Development of Powdery Mildew

The effects of two training systems and row spacing on development of powdery mildew caused by Uncinula necator on clusters of 'Chardonnay' and 'Cabernet Sauvignon' grapevines were examined. Disease development was monitored in blocks with two different row spacing (2 and 3 m) in vertical shoot positioned vines (VSP) and in free-positioned, topped vines (FC) with no foliage support wires. The FC vines were hedged to about one meter shoot length. No fungicides were applied and disease powdery mildew level was recorded four to seven days after appearance of the first disease symptoms. During five consecutive years (1994–1998), disease incidence was higher in the VSP system than the FC vines. The difference was high when disease level was low (30% of the clusters in VSP vines infected, compared to 5% in the FC vines) and decreased when disease pressure was high (79% in VSP compared to 46% in FC vines). In the 'Cabernet Sauvignon', in four of the years, disease incidence was higher in the narrow spacing of 2 m between the rows than that in the wider 3 m spacing. Microclimate (temperature, relative humidity and light intensity) was monitored in the cluster zone near the spurs of 'Chardonnay' vines during three weeks in the 1998 season. In VSP vines light intensity was lower then that in FC vines both four and one week before disease symptoms appeared (72% and 18% respectively). The differences in temperature and relative humidity were less than 1°C and 3%, respectively, and most likely did not affect disease development. The results suggested that high light intensity is the primary factor, which limits powdery mildew growth development on field-grown grapevines in the Golan region of Israel. The use of the FC system might be useful in reducing the need of fungicides.     

Spatiotemporal analysis of epiphytotics of downy mildew of oilseed poppy in tasmania, australia

Downy mildew, caused by Peronospora arborescens, has become the major disease affecting oilseed poppy (Papaver somniferum) since its first record in Tasmania in 1996. Two field trials conducted in 2000 and 2001 studied the progression and spatial distribution of downy mildew epiphytotics. The logistic and exponential models best described the progression of disease incidence and severity, respectively. Incidence and severity increased rapidly following canopy closure. In 2001, incidence increased from 0.16%, prior to canopy closure, to 100% at late flowering (40 days). Spatial analyses of epiphytotics were conducted by fitting the beta-binomial and binomial distributions, median runs analysis, and the spatial analysis by distance indices. All analyses demonstrated that the distribution of incidence and severity was strongly spatially aggregated from canopy closure until at least late flowering. These results suggest that secondary spread from a few primary infections is the major factor in epiphytotics.     

The assessment of partial resistance to powdery mildew disease in hops

Progeny comprising 1643 hop seedlings from crosses between eight partially resistant parents were screened under glasshouse conditions for resistance to a single pathotype of Sphaerotheca humuli. Results indicated polygenic inheritance of resistance. Genotypes representative of seedlings with 'light', 'moderate' and 'severe' infection from each family were transplanted to a hop garden where a natural epidemic of an introduced pathotype of powdery mildew developed. There was a significant positive association between amounts of disease on seedlings and on leaves of adult male plants, but no corresponding agreement between amounts of disease on female plants. A weak positive association was found between infection of seedlings in the glasshouse and subsequent cone infection in the field. Estimates of infection on leaves of adult plants and on cones were very closely associated. Partial resistance to powdery mildew was not associated with any deleterious agronomic or brewing quality characters.     

PCR detection of Pseudoperonospora humuli in air samples from hop yards

Downy mildew of hop, caused by Pseudoperonospora humuli , is an important disease in most regions of hop production and is managed largely with regular fungicide applications. A PCR assay specific to P . humuli and the related organism P .  cubensis was developed and used to monitor airborne inoculum in hop yards to initiate fungicide applications. The PCR amplified as little as 1 fg of genomic DNA of P . humuli , and yielded an amplicon in 70% of reactions when DNA was extracted from single sporangia. In the presence of 25 mg of soil, an amplicon was amplified in 90% of reactions when DNA was extracted from 10 or more sporangia. During nine location-years of validation, PCR detection of the pathogen in air samples occurred no later than 8 days after the appearance of trace levels of disease signs and/or detection of airborne spores in a volumetric spore sampler. Inoculum was detected on average 4·5 days before (range −8 to 14 days) the first appearance of basal spikes in six commercial yards, or 1·3 days after (range −5 to 1 days) sporangia were detected in a volumetric spore sampler in experimental plots. In commercial yards, use of PCR to initiate the first fungicide application led to enhanced disease control or a reduction in fungicide use in four of six yards compared to growers' standard practices. These results indicate that the efficiency and efficacy of hop downy mildew management can be improved when control measures are timed according to first detection of inoculum.     

Spatial heterogeneity,incidence-incidence and incidence-lesion density relationship of apple scab (<Emphasis Type="Italic">Venturia inaequalis</Emphasis>) in managed orchards

The spatial pattern of apple scab was characterized using 10 years of disease incidence and lesion density data collected in managed orchards located in Quebec, Canada. Distributional analyses indicated that scab incidence was better characterized by the beta-binomial than the binomial distribution in 53 and 65% of the data sets at the leaf and shoot scales, respectively. Median values of the beta-binomial parameter θ, a measure of small-scale aggregation, were near 0 (0.003 and 0.028) at both sampling scales, indicating that disease incidence was close to being randomly distributed (low degree of aggregation). For lesion density, the negative binomial distribution fitted the data better than the Poisson distribution in 86% of the data sets at the leaf scale. The median value of the index of dispersion k was 0.068, indicating that aggregation was present. For all apple scab measurements, the power law models provided a good fit to the data. The estimated slope and intercept parameters were significantly greater than 1 and 0, respectively, suggesting that spatial heterogeneity changed systematically with disease incidence. Results of a covariance analysis showed that spatial heterogeneity of scab incidence at both scales and lesion density was not dependent upon shoot type but that spatial heterogeneity of scab incidence and lesion density at the leaf scale was influenced by the sampling period. A hierarchical analysis showed that scab incidence at the tree scale increased as a saturation-type curve with respect to incidence at the leaf or shoot scales. A similar relationship was observed for incidences at the shoot and leaf scales. An effective sample size model based on the binary power law parameters (Madden and Hughes, Phytopathology 89:770–781, 1999) gave the best fit to the leaf and shoot data, respectively. The incidence-lesion density relationship at both scales was well described by a complementary log-log (CLL) and log transformation model ( R_adj² = 0.97 and R_adj² = 0.94 ) \left( {R_{{adj}}^2 = 0.97\,and\,R_{{adj}}^2 = 0.94} \right) , however, the models tended to underestimate lesion density. The information of the spatial relations of apple scab within and between hierarchical scales acquired from this study can be used in developing and evaluating practical disease management strategies and to improve apple scab assessments for fungicide or cultivar susceptibility trials.     

Analysing disease incidence data from designed experiments by generalized linear mixed models

As a result of aggregation or clustering of sampling units, disease incidence data from designed experiments frequently show overdispersion relative to the binomial distribution. This paper discusses generalized linear mixed models (GLMM) suitable for analysing overdispersed disease incidence data. The methods are exemplified using data from a randomized complete block experiment on the incidence of downy mildew ( Plasmopara viticola ) of grape ( Vitis lambrusca ). Hints are given regarding implementation of the methods using the %GLIMMIX macro for the SAS system.     

Forecasting the national incidence of sugar-beet powdery mildew from weather data in Britain

In a national survey of the incidence of powdery mildew (Erysiphe betae) in sugar beet in Britain, between 1980 and 1989, in which between 335 and 717 fields were inspected at the end of August each year, the average crop area infected ranged from 2% in 1986 to 68% in 1989. The effect of various climatic factors that might be expected to influence powdery mildew development over this period was examined, using meteorological records from Broom's Barn Experimental Station, Using simple linear regression analyses, a significant association was found between disease incidence and both air temperature and rainfall incidence in the period April-August, However, air temperature and frost incidence in some winter months were also closely associated with the incidence of powdery mildew in the following crop.
Combinations of these variables were examined in stepwise multiple-regression analyses, The model of best fit, incorporating winter frost incidence with summer temperature and rainfall incidence, accounted for 95% of the variation. Model validation procedures demonstrated the superiority of this model over those involving single variables. Nevertheless, for forecasting purposes, the best correlation was found between the crop area infected at the end of August each year and the number of days with a ground frost in the preceding February and March. This single climatic variable accounted for 82% of the variation and its potential use to forecast powdery mildew incidence in the national sugar-beet crop is discussed.     

入侵移栽稻田的福寿螺卵块空间分布型及其抽样技术

福寿螺Pomacea canaliculata Lamarck是重要外来入侵有害生物,严重危害水稻苗期至分蘖期的秧苗植株.为明确福寿螺在水稻田的空间分布,以1、4丛水稻为取样单位(样方)调查了14块移栽稻、每块田300个样方的福寿螺卵块密度,并利用聚集度指标法、Taylor幂法则和Iwao的M-m回归法进行分析.结果表明,移栽稻田中的福寿螺卵块主要呈聚集分布,部分田块呈随机或均匀分布.根据福寿螺卵块的分布型,通过计算抽样时间和抽样准确率的关系、不同样方和误差条件下的理论抽样数,确定以准确估计田间卵块密度为目标的最佳抽样方法,以横(行)向平行线跳跃法间隔30～45行调查1行,共调查6行90个4丛水稻样方,即两人以常规速度按上述方法取样18min以上,可达85%以上的取样准确率.     

Sporenverteilung des Echten Mehltaus im Hopfen ausgehend von Infektionsherden und Abhängigkeit vom Vegetationsstadium

In order to assess the potential of infection of hop powdery mildew it is important to know the spore dissemination coming from different sources. Overwintering via cleitothecia is not provable in experiments. So wild hops, not correctly cleared cultural hops and non-cultivation hops are potential carriers of powdery mildew which is overwintering via mycel. In 2007 we found a source which has infected an area of about 30?ha cultural hops. By the observation of infections in these hop gardens we found that half of the amount of conidia is in a distance of 9,55?m away from the source. In a smaller dimension we counted the amount of conidia around one single plant in a commercial hop garden by a special spore trap. In the single plant the amount of spores is lower than outside, while it is decreasing in a higher distance from the single plant. Analysing the micro spore dissemination in a single plant there was a big diversity of the amount of spores because of the complex architecture of the hop plants. Further studies showed that the susceptibility of hop is much higher in May than later in the year. Thus, statistically a lower amount of conidia is needed for one complete infection. However, a lower amount of conidia can easily be transported for long distances by wind. As a result a source of powdery mildew in a long distance from the cultural hops is a serious danger for the commercial hop gardens early in the year. Later each source of conidia looses its influence nearly completely.