Use of SADIE statistics to study spatial dynamics of plant disease epidemics

Using a previously developed stochastic simulation model for plant disease epidemics, the relationship of the SADIE aggregation statistic I _a with initial epidemic conditions, spore dispersal distance, sampling quadrat size and other spatial statistics was investigated. Most variation in I _a was attributable to the initial spatial pattern of infected plants and sampling quadrat size. The importance of initial spatial pattern on SADIE clustering indices (for patches and gaps) was also demonstrated using a number of selected data sets. Correlation of I _a with clustering indices was close to 1·0. Epidemics arising from the regular and random initial patterns resulted in the smallest and greatest I _a values, respectively, at sampling times after disease spread had occurred. Furthermore, the variability in I _a between simulation runs also varied greatly with initial patterns, being lowest and greatest for the clumped and random initial patterns, respectively. I _a increased initially and then decreased with increasing incidence, especially for the clumped and random initial patterns. Overall, the effect of median spore dispersal distance on I _a was very small, especially for the random initial pattern. The correlation between I _a and intraclass correlation was generally small and varied greatly between initial patterns. However, there was a high positive correlation between I _a and a parameter describing the rate of decline of autocorrelation over spatial lags, indicating that I _a, clustering indices and autocorrelations measure some common properties of patterns.     

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.     

Spatiotemporal relationships between disease development and airborne inoculum in unmanaged and managed Botrytis leaf blight epidemics

Comparatively little quantitative information is available on both the spatial and temporal relationships that develop between airborne inoculum and disease intensity during the course of aerially spread epidemics. Botrytis leaf blight and Botrytis squamosa airborne inoculum were analyzed over space and time during 2 years (2002 and 2004) in a nonprotected experimental field, using a 6 x 8 lattice of quadrats of 10 x 10 m each. A similar experiment was conducted in 2004 and 2006 in a commercial field managed for Botrytis leaf blight using a 5 x 5 lattice of quadrats of 25 x 25 m each. Each quadrat was monitored weekly for lesion density (LD) and aerial conidium concentration (ACC). The adjustment of the Taylor's power law showed that heterogeneity in both LD and ACC generally increased with increasing mean. Unmanaged epidemics were characterized in either year, with aggregation indices derived from SADIE (Spatial Analysis by Distance Indices). For LD, the aggregation indices suggested a random pattern of disease early in the season, followed by an aggregated pattern in the second part of the epidemic. The index of aggregation for ACC in 2002 was significantly greater than 1 at only one date, while it was significantly greater than 1 at most sampling dates in 2004. In both years and for both variables, positive trends in partial autocorrelation were observed mainly for a spatial lag of 1. In 2002, the overall pattern of partial autocorrelations over sampling dates was similar for LD and ACC with no significant partial autocorrelation during the first part of the epidemic, followed by a period with significant positive autocorrelation, and again no autocorrelation on the last three sampling dates. In 2004, there was no significant positive autocorrelation for LD at most sampling dates while for ACC, there was a fluctuation between significant and non-significant positive correlation over sampling dates. There was a significant spatial correlation between ACC at given date (t(i)) and LD 1 week later (t(i + 1)) on most sampling dates in both 2002 and 2004 for the unmanaged and managed sites. It was concluded that LD and ACC were not aggregated in the early stage of epidemics, when both disease intensity and airborne conidia concentration were low. This was supported by the analysis of LD and ACC from a commercial field, where managed levels of disease were low, and where no aggregation of both variables was detected. It was further concluded that a reliable monitoring of airborne inoculum for management of Botrytis leaf blight is achievable in managed fields using few spore samplers per field.     

Spatial Pattern Analysis of Sharka Disease (Plum pox virus Strain M) in Peach Orchards of Southern France

ABSTRACT The spatial pattern of Sharka disease, caused by Plum pox virus (PPV) strain M, was investigated in 18 peach plots located in two areas of southern France. PPV infections were monitored visually for each individual tree during one to three consecutive years. Point pattern and correlation-type approaches were undertaken using the binary data directly or after parsing them in contiguous quadrats of 4, 9, and 16 trees. Ordinary runs generally revealed a low but variable proportion of rows with adjacent symptomatic trees. Aggregation of disease incidence was indicated by the theta parameter of the beta-binomial distribution and related indices in 15 of the 18 plots tested for at least one assessment date of each. When aggregation was detected, it was indicated at all quadrat sizes and tended to be a function of disease incidence, as shown by the binary form of Taylor's power law. Spatial analysis by distance indices (SADIE) showed a nonrandom arrangement of quadrats with infected trees in 14 plots. The detection of patch clusters enclosing quadrats with above-average density of symptomatic trees, ellipsoidal in shape and generally extending from 4 to 14 trees within rows and from 4 to 10 trees perpendicular to the rows, could be interpreted as local areas of influence of PPV spread. Spatial patterns at the plot scale were often characterized by the occurrence of several clusters of infected trees located up to 90 m apart in the direction of the rows. When several time assessments were available, increasing clustering over time was generally evidenced by stronger values of the clustering index and by increasing patch cluster size. The combination of the different approaches revealed a wide range of spatial patterns of PPV-M, from no aggregation to high aggregation of symptomatic trees at all spatial scales investigated. Such patterns suggested that aphid transmission to neighboring trees occurred frequently but was not systematic. The mechanism of primary virus introduction, the age and structure of the orchards when infected, and the diversity of vector species probably had a strong influence on the secondary spread of the disease. This study provides a more complete understanding of PPV-M patterns which could help to improve targeting of removal of PPV-infected trees for more effective disease control.     

Spatiotemporal analysis of spread of infections by Verticillium dahliae pathotypes within a high tree density olive orchard in southern Spain

The development of Verticillium wilt epidemics in olive cv. Arbequina was studied from November 1999 to May 2003 in a drip-irrigated, nontillage orchard established in a soil without a history of the disease at Córdoba, southern Spain. Disease incidence measured at 1-month-intervals increased from 0.2 to 7.8% during this period. Verticillium dahliae infecting the trees was characterized as defoliating (D) or nondefoliating (ND) pathotypes by a specific, multiplex-polymerase chain reaction (PCR) assay. Of the symptomatic trees, 87.2 and 12.8% were infected by the D or ND pathotypes, respectively. Dynamics of disease incidence were described by a generalized logistic model with a multiple sigmoid pattern. In the fitted model, the infection rate was highest in the winter to spring period and decreased to minimum values in the summer to fall period. Binary data of disease incidence was analyzed for point pattern and spatial correlation, either directly or after parsing them in contiguous quadrats. Overall, ordinary runs analysis indicated a departure from randomness of disease within rows. The binomial index of dispersion, interclass correlation, and Taylor's power law for various quadrat sizes suggested aggregation of diseased trees within the quadrat sizes tested. Spatial analysis by distance indices showed a nonrandom arrangement of quadrats containing infected trees. Spatial pattern was characterized by the occurrence of several clusters of infected trees. Increasing clustering over time was generally suggested by stronger values of clustering index over time and by the increase in the size of patch clusters. Significant spatial association was found in the clustering of diseased trees over time across cropping seasons; however, clustering was significant only for infections by D V. dahliae, indicating that infections by the D pathotype were aggregated around initial infections. The number and size of clusters of D V. dahliae-infected trees increased over time. Microsatellite-primed PCR assays of a representative number of V. dahliae isolates from diseased trees indicated that the majority of infecting D isolates shared the fingerprinting profile with D V. dahliae isolated from soil of a naturally infested cotton field in close proximity to the orchard, suggesting that short distance dispersal of the pathogen from this soil to the olive orchard may have occurred.     

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.     

草坪害虫中喙丽金龟幼虫的空间分布与理论抽样数

本文采用扩散指标法和Iwao、Taylor回归法测定了上海辰山植物园内‘矮生百慕大’Cynodon dactylon×C.transvaalensis‘Tifdwarf’和日本结缕草Zoysia japonica上的中喙丽金龟Adoretus sinicus越冬幼虫的空间分布型。结果表明,中喙丽金龟幼虫在两种草坪草根部土壤中不同区域的密度相差较大(5~139头/m~2);幼虫在两种草坪草土壤中空间分布型均为聚集型的负二项分布,分布的基本成分为个体群。根据空间分布型的参数,确定了理论抽样数和Kuno序贯抽样方法。     

Spatial aggregation of pathotypes of barley powdery mildew

Aggregation in the distribution of pathotypes of Erysiphe graminis f.sp. hordei , the barley powdery mildew pathogen, was investigated in field plots of 'Golden Promise', 'Proctor' and 'Tyra'. 'Golden Promise' and 'Proctor' have no effective mildew resistance alleles, whereas 'Tyra' has Mla1 , which was only effective against a proportion of the mildew population. Isolates of mildew were sampled according to a grid sampling scheme and their virulence spectra ascertained in order to group them according to pathotype. The populations were very diverse, and evidence for aggregation (quantified using join counts) was found only in the 'Tyra' plots, at distances of up to 1m. This aggregation was reduced in a subsequent sample. The results are consistent with a model in which mildew epidemics are started by a large number of initial infections, which then form diffuse, overlapping aggregations of clones. These aggregations then become more diffuse, so that the amount of aggregation reduces with time. The greater amount of aggregation seen in the 'Tyra' plots might have been caused by there being less initial inoculum with virulence towards that cultivar.     

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.     

Distribution of Phytophthora spp. in Field Soils Determined by Immunoassay

ABSTRACT Populations of Phytophthora spp. were determined by enzyme-linked immunosorbent assay (ELISA) in field soils used for pepper and soybean production in Ohio. Soybean fields were sampled extensively (64 fields, n = 6 samples per field over 2 years) and intensively (4 fields, n = 64 samples per field in 1 year) to assess heterogeneity of P. sojae populations. Four pepper fields (n = 64), three of which had a history of Phytophthora blight (caused by P. capsici), also were sampled intensively during a 6-month period. Mean (m), variance (v), and measures of aggregation (e.g., variance-to-mean ratio [v/m]) of immunoassay values, translated to Phytophthora antigen units (PAU), were related to the disease history in each of the pepper and soybean fields. Mean PAU values for fields in which Phytophthora root rot (soybean) or blight (pepper) had been moderate to severe were higher than in fields in which disease incidence had been low or not observed. A detection threshold value of 11.3 PAU was calculated with values for 64 samples from one pepper field, all of which tested negative for Phytophthora by bioassay and ELISA. Seven of the eight intensively sampled fields contained at least some detectable Phytophthora propagules, with the percentage of positive samples ranging from 1.6 to 73.4. Mean PAU values ranged from 1 to 84 (extensive soybean field sampling), 6 to 24 (intensive soybean field sampling), and 4 to 30 (intensive pepper field sampling); however, variances ranged from 0 to 7,774 (extensive sampling), 30 to 848 (intensive soybean field sampling), and 5 to 2,401 (intensive pepper field sampling). Heterogeneity of PAU was high in most individual soybean and pepper fields, with values of v/m greater than 1, and log(v) increasing with log(m), with a slope of about 2.0. Spatial autocorrelation coefficients were not significant, indicating there was no relationship of PAU values in neighboring sampling units (i.e., field locations) of the intensively sampled fields. Combined results for autocorrelations and v/m values indicate that Phytophthora was highly aggregated in these fields but that the scale of the aggregation (e.g., average focus size) was less than the size of the sampling units. Because of the observed variability, we calculated that sample sizes of 20 or more would be needed to estimate precisely the mean density of Phytophthora in most cases.     

华南部分地区束翅亚目(Odonata:Zygoptera)蜻蜓区系聚类分析

采用类平均法和最近相邻法对位于广东、海南、香港、台湾、澳门等地8个动物地理小区现有分布的蜻蜓目束翅亚目41属进行系统聚类分析。类平均法将澳门、内伶仃、珠江三角洲、黑石顶、尖峰岭、香港、台湾等7个小区依次逐类聚合后在最大距离处与8个小区中地处最北的南岭聚合;南岭类群与其它类群的距离最远;整体呈现基于纬度,即南北向的束翅亚目类群合并。最近相邻法将8个小区先分别聚合成岛屿型(澳门与内伶仃)、山地型(黑石顶和尖峰岭、南岭)、山地与平原混合型(香港和台湾、珠江三角洲),最终聚合成一大类;岛屿型与其它两型的距离最远,联系性最小;整体呈现基于海拔高度的聚合,即主要体现束翅亚目类群垂直分布的差异。     

Spatial Patterns of Viable Spore Deposition of Gibberella zeae in Wheat Fields

ABSTRACT An increased understanding of the epidemiology of Gibberella zeae will contribute to a rational and informed approach to the management of Fusarium head blight (FHB). An integral phase of the FHB cycle is the deposition of airborne spores, yet there is no information available on the spatial pattern of spore deposition of G. zeae above wheat canopies. We examined spatial patterns of viable spore deposition of G. zeae over rotational (lacking cereal debris) wheat fields in New York in 2002 and 2004. Viable, airborne spores (ascospores and macroconidia) of G. zeae were collected above wheat spikes on petri plates containing a selective medium and the resulting colonies were counted. Spores of G. zeae were collected over a total of 68 field environments (three wheat fields during 54 day and night sample periods over 2 years) from spike emergence to kernel milk stages of local wheat. Spatial patterns of spore deposition were visualized by contour plots of spore counts over entire fields. The spatial pattern of spore deposition was unique for each field environment during each day and night sample period. Spore deposition patterns during individual sample periods were classified by spatial analysis by distance indices (SADIE) statistics and Mantel tests. Both analyses indicated that the majority (93%) of the spore deposition events were random, with the remainder being aggregated. All of the aggregated patterns were observed during the night. Observed patterns of spore deposition were independent of the mean number of viable spores deposited during individual sample periods. The spatial pattern for cumulative spore deposition during anthesis in both years became aggregated over time. Contour maps of daily and cumulative spore deposition could be compared with contour maps of FHB incidence to gain insights into inoculum thresholds and the timing of effective inoculum for infection.     

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.     

Annual weed distributions can be mapped with kriging

The authenticity of weed distribution maps prepared by the geostatistical estimation method, kriging, was investigated. We concentrated on the total number of weed plants and the dominant weed genus Veronica spp. in a 2.1-ha field of winter wheat. Different sampling distances were evaluated. Our analyses showed that kriging weed densities based on seedling counts collected in, 0.25.m² circles in a sampling grid of approximately 10 m × 10 m gave good agreement with actual observations. Reducing the sampling grid to 20 m × 30 m gave poor agreement. New sampling methods combined with positioning devices and injection sprayers are discussed with reference to site-specific weed management.     

锈色粒肩天牛卵空间分布型及抽样技术初步研究

通过对洛阳市区8个区段的国槐抽样调查,应用组内单因素方差分析、8种聚集度指标检测和7种回归分析,对该虫虫卵进行了垂直分布和空间分布分析研究。结果表明,该虫虫卵在单株上的垂直分布无显著差异;其空间分布为聚集分布,并利用聚集均数λ分析了聚集原因,利用个体群大小指标L分析了个体群形成原因。在此基础上,建立了该虫虫卵的理论抽样数公式n=(1/D)²(9.565 4/m+0.287 7)和序贯抽样决策限模式T′o(n),T″0(n)=14n±13.795 1n。     

桃蛀螟幼虫在板栗上的空间分布型研究

通过对不同板栗园桃蛀螟Dichocrocis punctiferalis Guenee幼虫的调查,用昆虫分布型的4种常用理论公式分别进行配合适度的χ2检验,再用6种空间分布型聚集度指标、Taylor幂法则及Iwao回归法对桃蛀螟幼虫的空间分布型进行测定。结果表明:桃蛀螟幼虫种群在板栗园中全部呈聚集分布,而且均符合负二项分布,其聚集原因是由该虫习性与环境因素共同造成的。此外,还利用了分布型参数确定了桃蛀螟幼虫的理论抽样数。     

Farm Scale Evaluations of herbicide-tolerant crops: assessment of within-field variation and sampling methodology for arable weeds

The Farm Scale Evaluations (FSEs) of genetically modified herbicide‐tolerant crops (GMHT) compared the effects of conventional and GMHT crop management regimes on weed densities. Weeds were sampled in quadrats at 5 distances along 12 transects systematically arranged within experimental half‐field treatment units. Weed densities declined with increasing distance from field margins. Random variation within transects was about 80% of the total within‐half‐field variation, i.e. relatively large variation at a small scale. The spatial autocorrelation between counts on the same transect declined as the distance between quadrats increased. Sampling schemes with fewer distances along transects required more transects but fewer quadrats to achieve similar precision as the 5‐distance scheme; on average 32 quadrats were sufficient. The frequency of detection of treatment effects (5% level) was little affected by using six or even three transects (30 and 15 quadrats respectively). However, the use of the 12 transects greatly improved the detection of treatment effects at 1% and 0.1% levels. The effectiveness of the reduced schemes for detecting differences between treatments (5% level) with as few as three transects compared with 12, reflects, in part, the relatively large treatment effects (e.g. 1.5‐fold or greater), which emerged for many of the sampling occasions. The FSEs provide an unusually extensive data set. Both the data and the methodology developed for their design and analysis are valuable for the planning of future weed sampling schemes.     

枣树缩果病空间分布格局和抽样技术研究

应用聚集指标法和Taylor幂指数及Iwaom*-m回归分析法测定了枣缩果病病株的空间分布型。结果表明:枣缩果病病株田间分布趋于聚集分布,其聚集原因主要是由风雨气候因素、病菌本身生物学特性和刺吸式昆虫吸食传毒扩散共同引起的。运用Iwaom*-m回归中的两个参数α、β值,建立了理论抽样数模型:N1.96=3.842/D(1.463/m+0.083),N1.64=2.69/D(1.463/m+0.083);序贯抽样模型:T0(n)=5n±6.0053n,确定了不同精度下的理论抽样数及序贯抽样数,提高了调查抽样的效率,可为枣缩果病林间抽样调查及防治提供依据。     

番茄地烟粉虱空间格局参数特征及其应用

2006年通过对春季番茄烟粉虱不同发生密度地块调查,取得了11组样本资料,应用聚集度指标法I、wao法和Taylor法等对其空间分布型进行测定检验,结果表明烟粉虱成虫在番茄上呈聚集分布,其聚集度是随着种群密度升高而增加。其聚集原因经Blackith种群聚集均数测定,当m<2.9638时,其聚集是由于某些环境如气候、栽培条件、植株生育状况等所引起的;当m≥2.9638时,其聚集是由害虫本身的聚集行为与环境条件综合影响所致。比较几种抽样方式以五点式为最佳,并提出了最佳理论抽样数和最佳序贯抽样模型:N=1.962/D2[1.007 9/m+0.0633],Tn=1.0079/[D20-0.0633/n]。