scholarly journals Sampling for Plant Disease Incidence

1999 ◽  
Vol 89 (11) ◽  
pp. 1088-1103 ◽  
Author(s):  
L. V. Madden ◽  
G. Hughes
Keyword(s):  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Sequential Sampling ◽  
Cluster Sampling ◽  
Diseased Plant ◽  
Ratio Test ◽  
Wide Range ◽  
Sequential Probability ◽  
The Relationship

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, ρ). Based on direct estimates of ρ (determined from the θ parameter of the beta-binomial distribution or from the observed variance) or a model predicting ρ 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 ρ or a ρ that depends on incidence.

scholarly journals Spatial Heterogeneity of the Incidence of Powdery Mildew on Hop Cones

Plant Disease ◽  
2006 ◽  
Vol 90 (11) ◽  
pp. 1433-1440 ◽  
Author(s):  
David H. Gent ◽  
Walter F. Mahaffee ◽  
William W. Turechek
Keyword(s):  
Powdery Mildew ◽  
Spatial Heterogeneity ◽  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Disease Assessment ◽  
Cluster Sampling ◽  
Data Sets ◽  
Ratio Test ◽  
Frequency Distributions

The spatial heterogeneity of the incidence of hop cones with powdery mildew (Podosphaera macularis) was characterized from transect surveys of 41 commercial hop yards in Oregon and Washington from 2000 to 2005. The proportion of sampled cones with powdery mildew ( p) was recorded for each of 221 transects, where N = 60 sampling units of n = 25 cones assessed in each transect according to a cluster sampling strategy. Disease incidence ranged from 0 to 0.92 among all yards and dates. The binomial and beta-binomial frequency distributions were fit to the N sampling units in a transect using maximum likelihood. The estimation procedure converged for 74% of the data sets where p > 0, and a loglikelihood ratio test indicated that the beta-binomial distribution provided a better fit to the data than the binomial distribution for 46% of the data sets, indicating an aggregated pattern of disease. Similarly, the C(α) test indicated that 54% could be described by the beta-binomial distribution. The heterogeneity parameter of the beta-binomial distribution, θ, a measure of variation among sampling units, ranged from 0.01 to 0.20, with a mean of 0.037 and a median of 0.015. Estimates of the index of dispersion ranged from 0.79 to 7.78, with a mean of 1.81 and a median of 1.37, and were significantly greater than 1 for 54% of the data sets. The binary power law provided an excellent fit to the data, with slope and intercept parameters significantly greater than 1, which indicated that heterogeneity varied systematically with the incidence of infected cones. A covariance analysis indicated that the geographic location (region) of the yards and the type of hop cultivar had little effect on heterogeneity; however, the year of sampling significantly influenced the intercept and slope parameters of the binary power law. Significant spatial autocorrelation was detected in only 11% of the data sets, with estimates of first-order autocorrelation, r1, ranging from -0.30 to 0.70, with a mean of 0.06 and a median of 0.04; however, correlation was detected in only 20 and 16% of the data sets by median and ordinary runs analysis, respectively. Together, these analyses suggest that the incidence of powdery mildew on cones was slightly aggregated among plants, but patterns of aggregation larger than the sampling unit were rare (20% or less of data sets). Knowledge of the heterogeneity of diseased cones was used to construct fixed sampling curves to precisely estimate the incidence of powdery mildew on cones at varying disease intensities. Use of the sampling curves developed in this research should help to improve sampling methods for disease assessment and management decisions.

scholarly journals Spatial Pattern of Strawberry Powdery Mildew (Podosphaera aphanis) and Airborne Inoculum

Plant Disease ◽  
2014 ◽  
Vol 98 (1) ◽  
pp. 43-54 ◽  
Author(s):  
H. Van der Heyden ◽  
M. Lefebvre ◽  
L. Roberge ◽  
L. Brodeur ◽  
O. Carisse
Keyword(s):  
Powdery Mildew ◽  
Power Law ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Disease Incidence ◽  
Data Sets ◽  
Incidence Data ◽  
Airborne Inoculum ◽  
The Relationship

The relationship between strawberry powdery mildew and airborne conidium concentration (ACC) of Podosphaera aphanis was studied using data collected from 2006 to 2009 in 15 fields, and spatial pattern was described using 2 years of airborne inoculum and disease incidence data collected in fields planted with the June-bearing strawberry (Fragaria × ananassa) cultivar Jewel. Disease incidence, expressed as the proportion of diseased leaflets, and ACC were monitored in fields divided into 3 × 8 grids containing 24 100 m2 quadrats. Variance-to-mean ratio, index of dispersion, negative binomial distribution, Poisson distribution, and binomial and beta-binomial distributions were used to characterize the level of spatial heterogeneity. The relationship between percent leaf area diseased and daily ACC was linear, while the relationship between ACC and disease incidence followed an exponential growth curve. The V/M ratios were significantly greater than 1 for 100 and 96% of the sampling dates for ACC sampled at 0.35 m from the ground (ACC0.35m) and for ACC sampled at 1.0 m from the ground (ACC1.0m), respectively. For disease incidence, the index of dispersion D was significantly greater than 1 for 79% of the sampling dates. The negative binomial distribution fitted 86% of the data sets for both ACC1.0m and ACC0.35m. For disease incidence data, the beta-binomial distribution provided a good fit of 75% of the data sets. Taylor's power law indicated that, for ACC at both sampling heights, heterogeneity increased with increasing mean ACC, whereas the binary form of the power law suggested that heterogeneity was not dependent on the mean for disease incidence. When the spatial location of each sampling location was taken into account, Spatial Analysis by Distance Indices showed low aggregation indices for both ACCs and disease incidence, and weak association between ACC and disease incidence. Based on these analyses, it was found that the distribution of strawberry powdery mildew was weakly aggregated. Although a higher level of heterogeneity was observed for airborne inoculum, the heterogeneity was low with no distinct foci, suggesting that epidemics are induced by well-distributed inoculum. This low level of heterogeneity allows mean airborne inoculum concentration to be estimated using only one sampler per field with an overall accuracy of at least 0.841. The results obtained in this study could be used to develop a sampling scheme that will improve strawberry powdery mildew risk estimation.

scholarly journals Sequential Sampling for Estimation and Classification of the Incidence of Hop Powdery Mildew II: Cone Sampling

Plant Disease ◽  
2007 ◽  
Vol 91 (8) ◽  
pp. 1013-1020 ◽  
Author(s):  
David H. Gent ◽  
William W. Turechek ◽  
Walter F. Mahaffee
Keyword(s):  
Powdery Mildew ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Sequential Sampling ◽  
Model Construction ◽  
Data Sets ◽  
Data Set ◽  
Sampling Plans ◽  
Simulated Sampling

Sequential sampling models for estimation and classification of the incidence of powdery mildew (caused by Podosphaera macularis) on hop (Humulus lupulus) cones were developed using parameter estimates of the binary power law derived from the analysis of 221 transect data sets (model construction data set) collected from 41 hop yards sampled in Oregon and Washington from 2000 to 2005. Stop lines, models that determine when sufficient information has been collected to estimate mean disease incidence and stop sampling, for sequential estimation were validated by bootstrap simulation using a subset of 21 model construction data sets and simulated sampling of an additional 13 model construction data sets. Achieved coefficient of variation (C) approached the prespecified C as the estimated disease incidence, [Formula: see text], increased, although achieving a C of 0.1 was not possible for data sets in which [Formula: see text] < 0.03 with the number of sampling units evaluated in this study. The 95% confidence interval of the median difference between [Formula: see text] of each yard (achieved by sequential sampling) and the true p of the original data set included 0 for all 21 data sets evaluated at levels of C of 0.1 and 0.2. For sequential classification, operating characteristic (OC) and average sample number (ASN) curves of the sequential sampling plans obtained by bootstrap analysis and simulated sampling were similar to the OC and ASN values determined by Monte Carlo simulation. Correct decisions of whether disease incidence was above or below prespecified thresholds (pt) were made for 84.6 or 100% of the data sets during simulated sampling when stop lines were determined assuming a binomial or beta-binomial distribution of disease incidence, respectively. However, the higher proportion of correct decisions obtained by assuming a beta-binomial distribution of disease incidence required, on average, sampling 3.9 more plants per sampling round to classify disease incidence compared with the binomial distribution. Use of these sequential sampling plans may aid growers in deciding the order in which to harvest hop yards to minimize the risk of a condition called “cone early maturity” caused by late-season infection of cones by P. macularis. Also, sequential sampling could aid in research efforts, such as efficacy trials, where many hop cones are assessed to determine disease incidence.

The Stability of Weed Seedling Population Models and Parameters in Eastern Nebraska Corn (Zea mays) and Soybean (Glycine max) Fields

Weed Science ◽  
1995 ◽  
Vol 43 (4) ◽  
pp. 604-611 ◽  
Author(s):  
Gregg A. Johnson ◽  
David A. Mortensen ◽  
Linda J. Young ◽  
Alex R. Martin
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Mean Value ◽  
Distribution Model ◽  
Ratio Test ◽  
Weed Species ◽  
Sampling Procedures ◽  
Grass Weed

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is akparameter.kis a nonspatial aggregation parameter related to the variance at a given mean value. Thekparameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of thekparameter across field sites was assessed using the likelihood ratio test There was no stable or commonkvalue across field sites and years for all weed species populations. The lack of stability inkacross field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Becausekis not stable across field sites,kmust be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

scholarly journals Effects of Initial Epidemic Conditions, Sporulation Rate, and Spore Dispersal Gradient on the Spatio-Temporal Dynamics of Plant Disease Epidemics

1998 ◽  
Vol 88 (10) ◽  
pp. 1000-1012 ◽  
Author(s):  
X.-M. Xu ◽  
M. S. Ridout
Keyword(s):  
Spatial Pattern ◽  
Power Law ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Disease Incidence ◽  
Disease Status ◽  
Spatio Temporal ◽  
Disease Epidemics ◽  
Sporulation Rate ◽  
The Relationship

A stochastic model that simulates the spread of disease over space and time was developed to study the effects of initial epidemic conditions (number of initial inocula and their spatial pattern), sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance μ (units of distance). The rate of temporal increase in disease incidence (βI, per day) was influenced jointly by μ and by the sporulation rate λ (spores per lesion per day). The relationship between βI and μ was nonlinear: the increase in βI with increasing μ was greatest when μ was small (i.e., when the dispersal gradient was steep). The rate of temporal increase in disease severity of diseased plants (βS) was affected mainly by λ: βS increased directly with increasing λ. Intraclass correlation (κt), the correlation of disease status of plants within quadrats, increased initially with disease incidence, reached a peak, and then declined as disease incidence approached 1.0. This relationship was well described by a power-law model that is consistent with the binary form of the variance power law. The amplitude of the model relating κt to disease incidence was affected mainly by μ: κt decreased with increasing μ. The shape of the curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. Generally, the relationship of spatial autocorrelation (ρt,k), the correlation of disease status of plants at various distances apart, to disease incidence and distance was well described by a four-parameter power-law model. ρt,k increased with disease incidence to a maximum and then declined at higher values of disease incidence, in agreement with a power-law relationship. The amplitude of ρt,k was determined mainly by initial conditions and by μ: ρt,k decreased with increasing μ and was lower for regular patterns of initial inocula. The shape of the ρt,k curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. At any level of disease incidence, autocorrelation declined exponentially with spatial lag; the degree of this decline was determined mainly by μ: it was steeper with decreasing μ.

scholarly journals Flexible and consistent quantile estimation for intensity–duration–frequency curves

2021 ◽  
Vol 25 (12) ◽  
pp. 6479-6494
Author(s):  
Felix S. Fauer ◽  
Jana Ulrich ◽  
Oscar E. Jurado ◽  
Henning W. Rust
Keyword(s):  
Power Law ◽  
Skill Score ◽  
Observation Time ◽  
Performance Model ◽  
Wide Range ◽  
Intensity Duration Frequency ◽  
The Individual ◽  
The Relationship ◽  
Flexible Model

Abstract. Assessing the relationship between the intensity, duration, and frequency (IDF) of extreme precipitation is required for the design of water management systems. However, when modeling sub-daily precipitation extremes, there are commonly only short observation time series available. This problem can be overcome by applying the duration-dependent formulation of the generalized extreme value (GEV) distribution which fits an IDF model with a range of durations simultaneously. The originally proposed duration-dependent GEV model exhibits a power-law-like behavior of the quantiles and takes care of a deviation from this scaling relation (curvature) for sub-hourly durations (Koutsoyiannis et al., 1998). We suggest that a more flexible model might be required to model a wide range of durations (1 min to 5 d). Therefore, we extend the model with the following two features: (i) different slopes for different quantiles (multiscaling) and (ii) the deviation from the power law for large durations (flattening), which is newly introduced in this study. Based on the quantile skill score, we investigate the performance of the resulting flexible model with respect to the benefit of the individual features (curvature, multiscaling, and flattening) with simulated and empirical data. We provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features leads to improvements for stations in a case study area in the Wupper catchment (Germany). Our results show that allowing curvature or multiscaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening on average leads to an improvement for medium durations between 1 h and 1 d, without affecting other duration regimes. Overall, the new parametric form offers a flexible and enhanced performance model for consistently describing IDF relations over a wide range of durations, which has not been done before as most existing studies focus on durations longer than 1 h or day and do not address the deviation from the power law for very long durations (2–5 d).

The SPRT Sign Chart for Process Dispersion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dadasaheb G. Godase ◽  
Shashibhushan B. Mahadik
Keyword(s):  
Control Chart ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Probability Ratio ◽  
Wide Range ◽  
Sequential Probability ◽  
Process Dispersion ◽  
Test Control

Abstract A nonparametric sequential probability ratio test control chart to monitor the process dispersion based on the sequential sign statistic is proposed. The statistical performance of this chart is evaluated by comparing it with that of the charts for dispersion based on sign statistic in the existing literature. It is found that the proposed chart outperforms all these charts uniformly in detecting a shift of any size over a wide range. An implementation of the chart is illustrated through an example.

scholarly journals Spatial Distribution and Development of Sequential Sampling Plans for Diaphorina citri Kuwayama (Hemiptera: Liviidae)

Agronomy ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1434
Author(s):  
Gabriel Díaz-Padilla ◽  
J. Isabel López-Arroyo ◽  
Rafael A. Guajardo-Panes ◽  
Ignacio Sánchez-Cohen
Keyword(s):  
Spatial Distribution ◽  
Sequential Sampling ◽  
Field Evaluation ◽  
Production Costs ◽  
Ratio Test ◽  
Operational Characteristic ◽  
Diaphorina Citri ◽  
Sample Number ◽  
Sampling Plans ◽  
Sequential Probability

Vector control in huanglongbing management has been conducted on a calendar basis resulting in high production costs. We addressed this issue and proposed a sequential sampling plan to support decision making for intervention against Diaphorina citri Kuwayama, which is involved in the transmission of the bacteria Candidatus Liberibacter asiaticus, associated with such lethal disease. We analyzed 3,264,660 records from samples gathered from the Mexican trapping program for the monitoring of D. citri; it included weekly inspection of 86,004 yellow sticky traps distributed in the country. Spatial distribution of the insect, estimation of a common k (kc), and sequential sampling plans based on Sequential Probability Ratio Test (SPRT) were determined. Taylor’s power law coefficients were ≥1 indicating aggregation in the spatial distribution of the insect. Common k ranged from 0.0183 to 0.2253 and varied independently of geographic zone or citrus species. We obtained 18 sequential sampling plans, one for each state. In the Average Sample Number (ASN) function, the minimal number of samples to make a decision ranged from 17 to 65. In the Operational Characteristic (OC) function, probabilities for a correct intervention at the threshold of 0.2 D. citri adults/trap in most cases were above 80%. In a field evaluation, the application of sampling plans yielded savings obtained by reduction in the number of interventions for insect control.

The Use of Wald’s Sequential Probability Ratio Test (SPRT) in Cocoa Pod Borer Management

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Albert Ling Sheng Chang
Keyword(s):  
Sample Size ◽  
Pest Management ◽  
Control Measure ◽  
Sequential Sampling ◽  
Sequential Probability Ratio Test ◽  
Effective Control ◽  
Ratio Test ◽  
Probability Ratio ◽  
Pod Borer ◽  
Sequential Probability

Sequential sampling plan (SSP) has been widely used in many engineering and quality control study. The advantage of using the SSP is the sample size is not fixed in advance, but is determined in part by the results of the sampling process. The application of the SSP is not limited to the industry, it also being used in pest management. This is because the SSP are generally more cost effective than plans based on a fixed sample size. Wald's Sequential Probability Ratio Test (SPRT) is one of the most common sequential sampling plans in insect pest management. It has been used to determine pest status at one time which could be used, through time, to monitor the status of the population and to take action when the pest density exceeded the Economic Threshold Level (ETL). Cocoa pod borer or CPB (Conopomorpha cramerella (Snell)) is a pest of concern to the cocoa growers in South-East Asia that has become one of the major factors that dampened the interest expressed in cocoa cultivation because of the heavy losses of cocoa pods due to the pest if effective control measure is not employed. The chemical control appeared to be one of the effective control measure used by the growers to control the CPB. Current practice used by the growers in applying the chemical is biweekly spraying which could see the increasing cost of chemical and labor used. The study was conducted to develop the Wald’s SPRT to monitor the CPB infestation level relative to the ETL based on counting the CPB eggs found on the pods aged 1 month before ripen or pod length 131 mm to 150 mm. The performance of the Wald’s SPRT was validated using independent data sets collected from Cocoa Research and Development Center (CRDC) Madai.

Accuracy of sequential sampling plans based on Wald's sequential probability ratio test

1983 ◽  
Vol 13 (6) ◽  
pp. 1197-1203 ◽  
Author(s):  
Gary W. Fowler
Keyword(s):  
Monte Carlo ◽  
Sequential Sampling ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Type I ◽  
Sample Number ◽  
Sampling Plans ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Relative Errors

Monte Carlo operating characteristic (OC) and average sample number (ASN) functions were compared with Wald's OC and ASN equations for sequential sampling plans based on Wald's sequential probability ratio test (SPRT) using the binomial, negative binomial, normal, and Poisson distributions. This comparison showed that the errors inherent in Wald's equations as a result of "overshooting" the decision boundaries of the SPRT can be large. Relative errors increased for the OC and ASN equations as the difference between the null (θ0)) and alternative (θ1) test parameter values increased. Relative errors also increased for the ASN equation as the probabilities of type I (α) and type II (β) errors increased. For discrete distributions, the relative errors also increased as θ0 increased with θ1/θ0 fixed. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN. For the values of θ0, θ1, α, and β used in many sequential sampling plans in forestry, Wald's equations may not be adequate. For those cases where the errors in Wald's equations are important compared with the other errors associated with the sampling plan, two alternative Monte Carlo OC and ASN functions are proposed.

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