Enumerative and binomial sequential sampling plans for soybean aphid (Homoptera: Aphididae) in soybean

Since the discovery of the soybean aphid, Aphis glycines Matsumura, in midwestern U.S. soybean, Glycine max L., in 2000, the aphid has become a significant economic pest. Basic information about estimating population density within fields is unknown. Therefore, we developed two sampling plans to efficiently characterize A. glycines densities. Enumerative and binomial sequential plans were developed using 89 data sets collected from 10 commercial fields sampled during 2001-2003. Re-sampling software was used to validate the enumerative plan on whole plant counts, based on Taylor's power law parameters (a = 9.157 and b = 1.543). For research applications, the enumerative plan was modified to provide an actual precision level of 0.10 (SE/mean), which resulted in an average sample number of 310 individual plants. For integrated pest management (IPM) purposes, we developed an enumerative plan with an actual precision of 0.25, which resulted in an average sample number of 38 individual plants. For IPM applications, the binomial plan will likely be more practical. Binomial plans were developed using two tally thresholds at five action thresholds. Final analysis of the operating characteristic curve for each plan indicated that the tally threshold of > or = 40 aphids per plant, and an action threshold of 0.837 (84% of the plants infested) provided the most correct treat (4%) and no-treat (95%) decisions, with very low incorrect treat (0.5%) and no-treat (0.5%) decisions. A tally threshold of > or = 40 aphids per plant and action thresholds of 84% of plants infested is equivalent to a mean density of 250 aphids per plant, a recently recommended economic threshold. Using this threshold, the minimum required sample number for the binomial plan was 11 plants.     

Operating characteristics of full count and binomial sampling plans for green peach aphid (Hemiptera: Aphididae) in potato

Counts of green peach aphid, Myzus persicae (Sulzer) (Hemiptera: Aphididae), in potato, Solanum tuberosum L., fields were used to evaluate the performance of the sampling plan from a pest management company. The counts were further used to develop a binomial sampling method, and both full count and binomial plans were evaluated using operating characteristic curves. Taylor's power law provided a good fit of the data (r2 = 0.95), with the relationship between the variance (s2) and mean (m) as ln(s2) = 1.81(+/- 0.02) + 1.55(+/- 0.01) ln(m). A binomial sampling method was developed using the empirical model ln(m) = c + dln(-ln(1 - P(T))), to which the data fit well for tally numbers (T) of 0, 1, 3, 5, 7, and 10. Although T = 3 was considered the most reasonable given its operating characteristics and presumed ease of classification above or below critical densities (i.e., action thresholds) of one and 10 M. persicae per leaf, the full count method is shown to be superior. The mean number of sample sites per field visit by the pest management company was 42 +/- 19, with more than one-half (54%) of the field visits involving sampling 31-50 sample sites, which was acceptable in the context of operating characteristic curves for a critical density of 10 M. persicae per leaf. Based on operating characteristics, actual sample sizes used by the pest management company can be reduced by at least 50%, on average, for a critical density of 10 M. persicae per leaf. For a critical density of one M. persicae per leaf used to avert the spread of potato leaf roll virus, sample sizes from 50 to 100 were considered more suitable.     

Sequential sampling plan for Cameraria ohridella (Lepidoptera: Gracillariidae) on horse chestnut tree

A fixed precision sequential sampling plan for estimating the density of the horse chestnut, Aesculus hippocastanum L., leafminer Cameraria ohridella Deschka & Dimic (Lepidoptera: Gracillariidae) was developed. Data were collected from 2002 to 2004 in Turin, northwestern Italy, with the aim of developing a sampling strategy for estimating populations of C. ohridella mines. Taylor's power law was used as a regression model. Sampling parameters were estimated from 216 data sets, and an additional 110 independent data sets were used to validate the fixed precision sequential sampling plan with resampling software. Covariance analysis indicated that there were not significant differences in the coefficient of Taylor's power law between heights of the foliage, months, and years. Dispersion patterns of C. ohridella were determined to be aggregated. The parameters of the Taylor's power law were used to calculate minimum sample sizes and sampling stop lines for different precision levels. Considering a mean density value of five mines per leaf, an average sample number of only 49 leaves was necessary to achieve a desired precision level of 0.25. As the precision level was increased to 0.10, the average sample size increased to 303 leaves. The sequential sampling plan should provide an effective management of C. ohridella in the urban areas, minimizing sampling time and cost, and at the same should be an effective tool to reduce insecticide applications and prevent the esthetic damage.     

Approaches for sampling the twospotted spider mite (Acari: Tetranychidae) on clementines in Spain

Tetranychus urticae Koch (Acari: Tetranychidae) is an important pest of clementine mandarins, Citrus reticulata Blanco, in Spain. As a first step toward the development of an integrated crop management program for clementines, dispersion patterns of T. urticae females were determined for different types of leaves and fruit. The study was carried out between 2001 and 2003 in different commercial clementine orchards in the provinces of Castelló and Tarragona (northeastern Spain). We found that symptomatic leaves (those exhibiting typical chlorotic spots) harbored 57.1% of the total mite counts. Furthermore, these leaves were representative of mite dynamics on other leaf types. Therefore, symptomatic leaves were selected as a sampling unit. Dispersion patterns generated by Taylor's power law demonstrated the occurrence of aggregated patterns of spatial distribution (b > 1.21) on both leaves and fruit. Based on these results, the incidence (proportion of infested samples) and mean density relationship were developed. We found that optimal binomial sample sizes for estimating low populations of T. urticae on leaves (up to 0.2 female per leaf) were very large. Therefore, enumerative sampling would be more reliable within this range of T. urticae densities. However, binomial sampling was the only valid method for estimating mite density on fruit.     

Spatial pattern and sequential sampling of squash bug (Heteroptera: Coreidae) adults in watermelon

Spatial distribution patterns of adult squash bugs were determined in watermelon, Citrullus lanatus (Thunberg) Matsumura and Nakai, during 2001 and 2002. Results of analysis using Taylor's power law regression model indicated that squash bugs were aggregated in watermelon. Taylor's power law provided a good fit with r2 = 0.94. A fixed precision sequential sampling plan was developed for estimating adult squash bug density at fixed precision levels in watermelon. The plan was tested using a resampling simulation method on nine and 13 independent data sets ranging in density from 0.15 to 2.52 adult squash bugs per plant. Average estimated means obtained in 100 repeated simulation runs were within the 95% CI of the true means for all the data. Average estimated levels of precision were similar to the desired level of precision, particularly when the sampling plan was tested on data having an average mean density of 1.19 adult squash bugs per plant. Also, a sequential sampling for classifying adult squash bug density as below or above economic threshold was developed to assist in the decision-making process. The classification sampling plan is advantageous in that it requires smaller sample sizes to estimate the population status when the population density differs greatly from the action threshold. However, the plan may require excessively large sample sizes when the density is close to the threshold. Therefore, an integrated sequential sampling plan was developed using a combination of a fixed precision and classification sequential sampling plans. The integration of sampling plans can help reduce sampling requirements.     

棉花苗期棉蚜的二项式抽样设计及其精度分析(英文)

1991年4月—7月在河北省北京农业大学曲周试验站的棉花地进行苗期棉蚜（Aphisgossypii）的田间抽样调查,共收集到24组抽样数据。用泰勒幂法则对数据进行拟合,得到棉花苗期棉蚜为聚集分布。利用每样方（株）虫口不超过数阈值T（分别为0,1,2…9,10,15,20,30）头蚜虫的植株比例（PT）与种群密度（m,头／株）的关系,拟合经验关系式ln（m）=a十bln[-ln（PT）],通过对不同数阈值T的回归决定系数（r2）、种群的回归估计方差（Var（m））和抽样精度（用d估计）等进行综合分析,结果表明该蚜虫在数阈值T为15时,回归估计方差最小,回归决定系数和d值最大,因而T=15为该蚜虫的理想数阈值;而小的T值尤其是T为O时,由于产生太大的回归估计方差,很小的回归决定系数和d值即抽样的精度极低,因而不宜在实际中应用于棉蚜的二项式抽样设计。     

Sequential sampling plans for western flower thrips (Thysanoptera: Thripidae) on greenhouse cucumbers

The development of cost-effective and reliable sampling programs for the management of western flower thrips, Frankliniella occidentalis (Pergande), on greenhouse cucumbers is important for getting growers to adopt economic injury levels and economic thresholds. The objectives of this study were to develop two sequential sampling plans. A fixed-precision sequential sampling plan was designed for estimating F. occidentalis adult density at a fixed-precision level on cucumber flowers. Also, a sequential sampling plan for classifying thrips population levels as below or above economic thresholds was developed to assist in decision making for the timing of pesticide applications. Both sequential sampling plans were validated using a resampling simulation technique on nine independent data sets ranging in density from 1.25 to 12.95 adults per flower. With the fixed-precision sampling plan, average means obtained in 100 repeated simulation runs were within the 95% CI of the estimated mean for all data sets. Appropriate levels of precision for the different population densities were recommended based on the simulation results. With sequential sampling for classifying the population levels of thrips in terms of an economic threshold, it has the advantage of requiring smaller sample sizes to determine the population status when the population densities differ greatly from the critical density (i.e., economic threshold). However, this plan needs a great number of samples when population density is close to the critical density. In this case, use of a combination of both sampling plans is recommended.     

Potato aphid, Macrosiphum euphorbiae (Thomas), in tomatoes: plant canopy distribution and binomial sampling on processing tomatoes in California

A binomial sampling method for the potato aphid, Macrosiphum euphorbiae (Thomas), on processing tomato plants, Lycopersicon esculentum (Mill), is proposed. Relationships between mean number of M. euphorbiae per leaf and proportion of leaves infested [P(I)] with M. euphorbiae for both upper and interior leaves of the processing tomato varieties 'Alta' and 'Halley' are presented. A split-plot design was used with variety, position in the plant canopy, and block as the factors examined through linear regression and analysis of variance (ANOVA). Results supported the hypotheses that M. euphorbiae densities on upper canopy leaves are predictive of densities on inner canopy leaves and that proportion of M. euphorbiae infested leaves are predictive of mean densities per leaf. Mean M. euphorbiae density was greater on 'Alta' than 'Halley' tomato plants, supporting the assumption that 'Alta' is the more susceptible variety. Taylor's Power Law coefficients, a and b, were similar for proportion of M. euphorbiae-infested upper and inner leaves of both 'Alta' and 'Halley'. Taylor's b coefficients ranged from 1.57 to 1.74, indicating a highly clumped distribution for M. euphorbiae.     

BINOMIAL COUNT ANALYSIS BASED ON THE SPATIAL DISTRIBUTION AND POPULATION DENSITY ESTIMATION OF COTTON APHIDS1)

Abstract  Based on field population sampling of Aphis gossypii on cotton seedlings in Quzhou Experiment Station of China Agricultural University in Hebei Province in 1991, we obtained a data set consisting of 24 estimates of mean aphid density ( m , number of aphids per plant), variance (s²) and the proportion of plants (P_T) with no more than T aphids (T=0, 1, 2,…, 8, 10, 15, 20, respectively and defined as tally threshold). Taylor's power law fitted the data well (r²= 0. 958). The resulting slope (1. 515) was significantly greater than 1, indicating that the spatial distribution of this aphid was in aggregated pattern. An empirical relationship between m and Pr was developed for each T value using the parameters from the linear regression In( m )= a +bln[- ln( P_T )}]. The importance of the T values in reduction of sampling errors and their application to binomial sampling plans are discussed. Small T values, particularly aphid-free plant (T = 0, conventional binomial sample), could lead to spurious estimates of m from P_T . A value of T from 10 to 15 was recommended to develop binomial sampling plans for the aphids on cotton seedlings because of the relatively small sampling errors.     

Within-plant distribution of twospotted spider mite, Tetranychus urticae Koch (Acari: Tetranychidae), on ivy geranium: development of a presence-absence sampling plan

The twospotted spider mite, Tetranychus urticae Koch, is an important pest of ivy geranium and other ornamental plants. As a part of our long-term goal to develop an integrated crop management program for ivy geraniums, the focus of this study was to produce a reliable sampling method for T. urticae on this bedding plant. Within-plant mite distribution data from a greenhouse experiment were used to identify the young-fully-opened leaf as the sampling unit. We found that 53% of the mites on a plant are on the young-fully-opened leaves. On average 22, 37, and 41% of the leaves belonged to the young, young-fully-opened, and old leaf categories, respectively. We then developed a presence-absence sampling method for T. urticae in ivy geranium using generic Taylor's coefficients for this pest. We found the optimal binomial sample sizes for estimating populations of T. urticae at densities of between 0 and 3 mites/leaf to be quite large; therefore, we recommend the use of numerical sampling within this range of T. urticae densities. We also suggest that population estimates of T. urticae on ivy geranium be done based on mite density/unit area of greenhouse space, both for conventional greenhouse pest management, and for determining how many phytoseid predators to release when using biological control.     

桑蓟马在桑树中空间分布的研究

桑蓟马Pseudodendrothrips mori是桑树的一种主要害虫。它的寄生直接影响供桑叶的质量和产量。我们通过泰勒幂法则和Morisita的散度指标对桑树蓟马在植株和桑园内的空间分布进行检验,结果显示:P.mori种群在植株内和桑园里的分布都存在局部化。桑树中蓟马的分布在树内显示出幼虫蓟马位于低层(从上面叶子起5-10层),但成虫更喜欢上层(从上面叶子起1-5层)。同一植株叶子的不同方向上蓟马密度没有出现明显变化。桑园内蓟马主要分布在桑园东部、南部和北部的植株上,中部,西部植株上的蓟马密度较低。P.mori的成虫和幼虫在叶子上的分布呈现明显聚集化。     

Binomial sampling to estimate rust mite (Acari: Eriophyidae) densities on orange fruit

Binomial sampling based on the proportion of samples infested was investigated for estimating mean densities of citrus rust mite, Phyllocoptruta oleivora (Ashmead), and Aculops pelekassi (Keifer) (Acari: Eriophyidae), on oranges, Citrus sinensis (L.) Osbeck. Data for the investigation were obtained by counting the number of motile mites within 600 sample units (each unit a 1-cm2 surface area per fruit) across a 4-ha block of trees (32 blocks total): five areas per 4 ha, five trees per area, 12 fruit per tree, and two samples per fruit. A significant (r2 = 0.89), linear relationship was found between ln(-ln(1 -Po)) and ln(mean), where P0 is the proportion of samples with more than zero mites. The fitted binomial parameters adequately described a validation data set from a sampling plan consisting of 192 samples. Projections indicated the fitted parameters would apply to sampling plans with as few as 48 samples, but reducing sample size resulted in an increase of bootstrap estimates falling outside expected confidence limits. Although mite count data fit the binomial model, confidence limits for mean arithmetic predictions increased dramatically as proportion of samples infested increased. Binomial sampling using a tally threshold of 0 therefore has less value when proportions of samples infested are large. Increasing the tally threshold to two mites marginally improved estimates at larger densities. Overall, binomial sampling for a general estimate of mite densities seemed to be a viable alternative to absolute counts of mites per sample for a grower using a low management threshold such as two or three mites per sample.     

Assessing abundance and distribution of an invasive thrips Frankliniella schultzei (Thysanoptera: Thripidae) in south Florida

Within-plant and within-field distribution of larvae and adults of an invasive thrips species, Frankliniella schultzei (Trybom) on cucumber, Cucumis sativus L. was studied in 2008 and 2009 in Homestead, Florida. The majority of thrips were found inhabiting flowers of cucumber plants and little or none was found on the other parts of the plant. Thrips were aggregated in the field, as indicated by the two regression models, Taylor's power and Iwao's patchiness regression. Iwao's patchiness regression provided a better fit than Taylor's power law. The distribution was clumped during the initial stages of infestation at the edges of the field and became random thereafter. However, with increase in population density, thrips again formed aggregates in the field. Based on the average pest density per flower in a ～0.25-ha field, minimum sample size (number of flowers) required at the recommended precision level (0.25) was 51. The number of samples required at two levels of predetermined pest density was also calculated, which would help growers in collecting optimum number of samples required to determine the correct threshold level of pest in fields. Results from seasonal abundance indicated that density of thrips peaked during the fifth week of sampling with an average of 25 and 34 adults per ten flowers during autumn 2008 and 2009, respectively. Results from these studies will help growers and extension personnel in understanding the abundance and distribution of F. schultzei in the field, which are important components required in developing a sound management program.     

烟草潜叶蛾幼虫空间分布型及其应用研究

本文就烟草潜叶蛾幼虫空间分布型及其垂直分布规律进行了探讨,结果表明：烟草潜叶蛾幼虫在田间呈聚集分布,聚集强度不因种群密度的改变而改变,幼虫主要聚集分布在烟草下部第一段（4片叶）上;降集或随机分布在第二段上;随机分布在第三段上,此外,应用虫株率进行田间种群密度的估计,其中Wilson模型和Gerrard模型所配理论曲线的预测值与实测值显著适合,但Gerrard模型的抽样估计误差较Wilson模型的小,最后本文用Taylor式中的参数a,b确定理论抽样数及序贯抽样,其模型分别为。     

Enumerative and binomial sequential sampling plans for the multicolored Asian lady beetle (Coleoptera: Coccinellidae) in wine grapes

To develop a practical integrated pest management (IPM) system for the multicolored Asian lady beetle, Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae), in wine grapes, we assessed the spatial distribution of H. axyridis and developed eight sampling plans to estimate adult density or infestation level in grape clusters. We used 49 data sets collected from commercial vineyards in 2004 and 2005, in Minnesota and Wisconsin. Enumerative plans were developed using two precision levels (0.10 and 0.25); the six binomial plans reflected six unique action thresholds (3, 7, 12, 18, 22, and 31% of cluster samples infested with at least one H. axyridis). The spatial distribution of H. axyridis in wine grapes was aggregated, independent of cultivar and year, but it was more randomly distributed as mean density declined. The average sample number (ASN) for each sampling plan was determined using resampling software. For research purposes, an enumerative plan with a precision level of 0.10 (SE/X) resulted in a mean ASN of 546 clusters. For IPM applications, the enumerative plan with a precision level of 0.25 resulted in a mean ASN of 180 clusters. In contrast, the binomial plans resulted in much lower ASNs and provided high probabilities of arriving at correct "treat or no-treat" decisions, making these plans more efficient for IPM applications. For a tally threshold of one adult per cluster, the operating characteristic curves for the six action thresholds provided binomial sequential sampling plans with mean ASNs of only 19-26 clusters, and probabilities of making correct decisions between 83 and 96%. The benefits of the binomial sampling plans are discussed within the context of improving IPM programs for wine grapes.     

Spatial dependence, dispersion, and sequential sampling of Anaphothrips obscurus (Thysanoptera: Thripidae) in timothy

The spatial distribution and dispersion of Anaphothrips obscurus (Müller) (Thysanoptera: Thripidae) was examined with the goal of establishing a sequential sampling plan for this pest in timothy, Phleum pratense L. (Poaceae). Approximately 16 different California timothy fields were sampled twice yearly from 2006 to 2008 using direct observation and the beat cup method. For direct observation, the number of thrips on each leaf of the plant was counted. For the beat cup method, tillers were tapped into a cup and dislodged thrips were counted. Samples were separated by ≈3 m in 2006 and 2007 and exactly 3 m in 2008. Spatial autocorrelation of intrafield population distribution was tested for significance in 2008 using Moran's I, but autocorrelation was not detected. The population dispersion was assessed by Taylor's power law and was determined to be aggregated and density-dependent. Intraplant population dispersion and distribution for each year were also evaluated for adults, larvae, and total thrips. All lifestages were highly spatially dependent and more thrips were found near the top of the plant than the bottom. Direct observation proved to be a more accurate and precise method than the beat cup method, especially when thrips abundances were greater than one. However, the number of samples required to provide an accurate level of precision was unrealistic for both methods. A sequential sampling plan was evaluated, but was not practical for the beat cup method because few thrips were found using this method. Because there was no spatial autocorrelation at sampling distances of 3 m, samples can be taken at intervals at 3 m to obtain spatially independent population abundance estimates.     

Cascading tripartite binomial classification plans to monitor European red mite (Acari,Tetranychidae) through a season; development and evaluation of a new methodology for pest monitoring

A monitoring protocol that schedules future sample bouts based on the outcome of density classification and expected population growth has been developed and applied to monitoring European red mite (Panonychus ulmi Koch) through a growing season. The monitoring protocol is based on concatenating through time tripartite sequential classification sampling plans that use binomial counts in lieu of complete enumeration. Binomial counts are scored positive when the number of organisms (mites) on a sample unit (leaves) exceeds a tally number. At each sample occasion the monitoring procedure leads to one of three possible decisions; intervene when the density is high, sample at the next sample occasion (after one week) when the density is intermediate, and sample at the second next sample occasion (after two weeks) when the density is low. Evaluation of the monitoring protocol under field conditions showed that the protocol with constituent tally 0 binomial count sampling plans was quite successful in timing intervention at the moment when population densities were about to exceed an established threshold that dictated intervention. The performance of this monitoring protocol and another protocol in which constituent sampling plans used binomial counts with a tally number of 4 were compared using simulation. Sampling plans that used a tally number of 4 were more precise than plans that used a tally number of 0. However, the overall performance of the monitoring protocol based on tally 0 sampling plans did not greatly differ from the monitoring protocol based on tally 4 sampling plans. Simulated performance of the tally 0 protocol was corroborated by field evaluation. The monitoring protocol based on tripartite classification required 30 to 45 percent fewer sample bouts than a protocol based on conventional sequential classification at weekly intervals. The monitoring protocol based on tripartite classification was also better able to schedule intervention when needed compared to a protocol based on conventional classification at two week intervals. Using the tally 0 protocol and current thresholds forP. ulmi, cumulative mite density was kept below 300 mite-days per leaf, which is well below levels regarded damaging. A tally 0 protocol with raised thresholds, developed on the basis of this finding, gave the best simulated performance of all protocols evaluated.