Sampling Stop Lines Research Articles

Optimizing a fixed-precision sequential sampling plan for adult Acrotomopus atropunctellus (Boheman) (Coleoptera: Curculionidae), new pest on sugarcane

Sugarcane weevil borer, Acrotomopus atropunctellus (Boheman) (Coleoptera: Curculionidae) has been detected across all sugarcane planting areas in the Argentinian Northwest with increasing population densities. The monitoring for its occurrence and the population density usually is made by visual inspection and consequently demands much effort and time. The objectives of this study were 1) to describe the sampling distribution pattern of A. atropunctellus adults 2) to develop and validate a fixed-precision sequential sampling plan for density estimation, and 3) to find the optimum inspection time for each sampling unit. On-farm data collection was performed at sugarcane fields located in Ranchillos (Tucumán, Argentina) during 2011–2012 to 2013–2014 sugarcane growing seasons. Thirty sampling units consisting on one meter of sugarcane furrow were randomly selected at 1-wk intervals. Within each sampling unit, weevils were counted and recorded independently for five increasing examination time per sampling unit (ETSU) (2, 4, 6, 8 and 10 min). For each ETSU, the sampling distribution pattern was assessed by Taylor's power law (TPL). The average sample number (ASN) and sampling stop lines were calculated according to Green's sequential sampling model, based on TPL estimated parameters, for fixed precision levels, C = 0.1 and C = 0.25. The resampling for validation of sample plans (RVSP) program was used to evaluate the performance of the different sampling plans. Parameters a and b from TPL regressions did not vary significantly between different ETSUs. All estimates of b coefficients were significantly >1 which can indicate an aggregated sampling distribution pattern. For each precision level, Green's sequential plans predicted very similar ASN between ETSU. This was confirmed through the validation process, with the five sampling protocols providing very similar mean sample sizes and mean precision levels. Variability of these parameters from validation results did not vary significantly among the different ETSUs. The relative net precision was the only performance parameter that varied with the ETSU, with the shortest ETSU resulting in the most efficient sampling plan. We conclude that A. atropunctellus has an aggregated sampling distribution and that the fixed precision sequential sampling plan developed using Green's model and based on a two-minute inspection of the sampling unit is the most convenient choice for estimating its population density in sugarcane. Our analysis of the ETSU effect on the performance of sugarcane weevil sampling protocols could contribute to develop more efficient monitoring plans for other arthropods.

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.

Sequential Sampling Plan for <I>Cameraria ohridella</I> (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.

Evaluation of binomial sequential classification sampling plan for leafmine of Liriomyza trifolii (Diptera: Agromyzidae) in greenhouse tomatoes

Sequential binomial sampling plans for classifying the leafmine density of Liriomyza trifolii (Burgess) were developed and evaluated in tomato greenhouses in southern Korea during 2003 – 2004. Two action thresholds (m AT), three and seven leafmines per tomato leaf, were set by examining the relationship between the leafmine density and the decrease in the tomato yield. An empirical P T -m model, which is expressed as ln(−ln(1−P T )) = γ + δ ln(m), was used to examine the relationship between the proportion of the infested tomato leaves (P T ) with at least T (tally threshold) leafmines and the mean leafmine density (m). The empirical model showed an improvement in the fit up to T = 5, which then stabilised at T > 5. Wald's sequential probability ratio test was used to formulate the sequential sampling stop lines relative to m AT = 3 and 7 with T = 1, 2, 3, 4, and 5. The sampling plans were evaluated using the operating characteristic (OC) and the average sample number (ASN) functions. The robustness of the sampling plans improved with increasing T values but the improvements were negligible at T ≥ 3. Simulation analysis with the OC and ASN functions indicated that a binomial model with T = 3 was optimal and less than 70 samples were required to classify the number of leafmines relative to either m AT values. Resampling simulation of eight independent data sets with T = 3 showed that the performance of the sampling plans was superior to that expected from the established OC and ASN functions. The correct classification rate was at least 99% and the matching sample size was <57.

Use of covariates in Taylor’s power law for sequential sampling in pest management

In pest management, the pest density within a group of plants needs to be estimated for taking timely actions, such as spraying pesticides or releasing natural enemies. Taylor's power law is widely used for identifying the aggregation patterns of the pests and designing a sequential sampling plan to estimate the pest mean density. The conventional estimates given by Taylor's power law do not consider potential density differences due to various covariates, but focus only on the relationship between the sample means and the variances. In this article, we develop a new sequential sampling stop line based on Taylor's power law by using quasi-likelihood with covariate effects. The simulation results show that the proposed estimators are better than the conventional estimators in terms of mean squared error. For validation and evaluation of the sampling stop line given by the proposed estimator, we use RVSP software in which actual observations are randomly and iteratively sampled until the total number of a pest reaches the stop line. We demonstrate both types of sequential sampling stop lines, those based on the conventional method and those based on the new method, for the population density of spider mites on glasshouse roses.

Development of a Sampling Plan in Winter Wheat that Estimates Cereal Aphid Parasitism Levels and Predicts Population Suppression

From 1998 to 2001, the relationship between the proportion of tillers with >0 mummified aphids (Ptm) and the proportion of cereal aphids parasitized (Pp) was estimated on 57 occasions in fields of hard red winter wheat located in central and western Oklahoma. Both original (57 fields) and validation data (34 fields; 2001–2002) revealed weak relationships between Ptm and Pp, however, when Ptm > 0.1, Pp always exceeded the recommended parasitism natural enemy threshold of 0.2. Based on the relationship between Ptm and Pp, upper (Ptm1) and lower (Ptm0) decision threshold proportions were set at 0.1 and 0.02, respectively. We monitored cereal aphid populations in 16–25 winter wheat fields over time, and based on the upper and lower decision threshold proportions (Ptm1 = 0.1, Ptm0 = 0.02), predicted whether aphid intensities (# per tiller) would increase above or be maintained below selected economic thresholds (3, 9, and 15 aphids per tiller). Results of this validation study revealed that aphid intensity exceeded an economic threshold in only one field when predicted to remain below Ptm > 0.1, but aphid intensity reached a maximum of only four aphids per tiller. The sampling plan developed during this study allowed us to quickly classify Ptm, and independent of initial cereal aphid intensities, very accurately predict suppression of populations by parasitoids. Sequential sampling stop lines based on sequential probability ratio tests for classifying proportions were calculated for Ptm1 = 0.1 and Ptm0 = 0.02. A minimum of 26 tiller samples are required to classify Ptm as above 0.1 or below 0.02. Based on the results of this study, we believe that simultaneous use of aphid and parasitoid sampling plans will be efficient and useful tools for consultants and producers in the southern plains and decrease the number of unnecessary insecticide applications.

Development of a sampling plan in winter wheat that estimates cereal aphid parasitism levels and predicts population suppression.

From 1998 to 2001, the relationship between the proportion of tillers with >0 mummified aphids (Ptm) and the proportion of cereal aphids parasitized (Pp) was estimated on 57 occasions in fields of hard red winter wheat located in central and western Oklahoma. Both original (57 fields) and validation data (34 fields; 2001-2002) revealed weak relationships between Ptm and Pp, however, when Ptm > 0.1, Pp always exceeded the recommended parasitism natural enemy threshold of 0.2. Based on the relationship between Ptm and Pp, upper (Ptm1) and lower (Ptm0) decision threshold proportions were set at 0.1 and 0.02, respectively. We monitored cereal aphid populations in 16-25 winter wheat fields over time, and based on the upper and lower decision threshold proportions (Ptm1 = 0.1, Ptm0 = 0.02), predicted whether aphid intensities (# per tiller) would increase above or be maintained below selected economic thresholds (3, 9, and 15 aphids per tiller). Results of this validation study revealed that aphid intensity exceeded an economic threshold in only one field when predicted to remain below Ptm > 0.1, but aphid intensity reached a maximum of only four aphids per tiller. The sampling plan developed during this study allowed us to quickly classify Ptm, and independent of initial cereal aphid intensities, very accurately predict suppression of populations by parasitoids. Sequential sampling stop lines based on sequential probability ratio tests for classifying proportions were calculated for Ptm1 = 0.1 and Ptm0 = 0.02. A minimum of 26 tiller samples are required to classify Ptm as above 0.1 or below 0.02. Based on the results of this study, we believe that simultaneous use of aphid and parasitoid sampling plans will be efficient and useful tools for consultants and producers in the southern plains and decrease the number of unnecessary insecticide applications.

Distribution and Sampling of Prostephanus truncates (Coleoptera: Bostrichidae) and Sitophilus zeamais (Coleoptera: Curculionidae) in Maize Stores in Benin

The distribution among and within grain stores of 2 grain store pests, Prostephanus Truncatus (Horn) and Sitophilus zeamais Motschulsky were examined over time using different maize cultivars. Incidence in stores was variable between seasons for both species. The b coefficient of Taylor's power law did not differ among maize cultivars. Within-store distribution among cobs could be approximated by the negative binomial and an overall k parameter was estimated for both species. These data were used to develop sampling plans to estimate sample size needed to determine insect density for both pest species over different densities given a desired precision. Sequential sampling stop lines were calculated to determine pest status given action and no-action threshold densities. The possibility of applying the sampling plans as an integrated pest management tool is discussed.

Binomial Sequential Sampling Plans for Cereal Aphids (Homoptera: Aphididae) in Spring Wheat

Binomial sequential sampling plans usually are more efficient than sampling plans based on counting the number of insects per sample. Our objective was to develop robust binomial sequential sampling plans based on a range of action thresholds for 3 species of cereal aphids, Rhopalosiphum padi (L), Sitobion avenae (F.), and Schizaphis graminum (Rondani). Aphid population data were collected from 45 eastern North Dakota spring wheat fields during 1993-1995. The proportion of infested stems (P T ) with more than T (tally threshold) aphids was related to mean aphid density (m) with the empirical model ln[-ln(1 - P T )] = a + bln(m). The P T -m relationship fit the data well for T values of 0-4, with T = 3 having the best fit. Binomial sequential sampling plans were developed using a Monte-Carlo computer program based on the empirical model. Tally thresholds were evaluated with operating characteristic and average sample number functions. Increasing the tally threshold from 0 to 3 improved the accuracy of the sampling plans but also increased the average sample number required to make a decision. Sampling stop lines for binomial sequential sampling plans with tally thresholds of and 3 and action thresholds of 9 and 13 aphids per stem, and with a tally threshold of 3 and an action threshold of 17 aphids per stem, are provided for use in spring wheat. Sampling plans should be useful tools for spring wheat growers and crop consultants in the northern Great Plains and be applicable over a range of crop values and management costs.

Binomial sampling plans for estimating and classifying population density of adult Bemisia tabaci in cotton

AbstractWe used an empirical relationship to develop models for estimating and for classifying the population density of adult Bemisia tabaci (Gennadius) (Homoptera: Aleyrodidae) in cotton based on the proportion of infested leaves. We examined models based on tally thresholds (the minimum number of insects present before a leaf is considered infested) of 1, 2, 3, 4, 5, and 6 adults per fifth mainstem node leaf from the terminal. For the estimation of density, sampling precision (SE/mean) increased with higher tally thresholds (T); however, there was negligible improvement in precision with T ≥ 3 adults per leaf. Using T = 3 as few as 30 samples were necessary to achieve a precision of 0.25 over a wide range of population densities. To evaluate these binomial models for the classification of population density for pest management application, we used simulation analyses to determine operating characteristic curves (error probabilities), and to estimate average sample size and cost functions. Error probabilities and average sample sizes declined with higher values of T, but there was negligible decline in error probabilities using T ≥ 3 adults per leaf, and the overall cost of sampling was lowest for T = 3. Wald's sequential probability ratio test was used to formulate sequential sampling stop lines for classifying population density relative to two nominal action thresholds, 5 or 10 adults per leaf. Simulation analysis indicated that by using T = 3, fewer than 30 samples, on average, were needed to classify populations relative to either action threshold. However, simulated error probabilities consistently exceeded the nominal error probabilities used to initially formulate sequential sampling stop lines regardless of the tally threshold. Comparing binomial models using T = 1 or T = 3 to independent data from four field sites, the model for T = 1 was generally biased towards overprediction of mean density, but the T = 3 model was a robust and relatively unbiased predictor of mean density. The binomial sampling plans presented here should permit the rapid estimation of population density and enhance the efficiency of pest management programs based on the prescriptive suppression of B. tabaci in cotton.

Sampling Adults of Eoscarta carnifex (Hemiptera: Cercopidae) and Their Associated Symptoms on Sugarcane

Sampling statistics were determined for adults of the froghopper Eoscarta carnifex (F.) and associated symptoms on sugarcane crops in northern Queensland, Australia. Samples using 10 consecutive stems per sampling unit minimized the variance: mean ratios for all sample sizes used to sample adults. The Taylor power law described the relationship between mean and variance of samples based on 10-stem sampling units better than did the lwao regression model or the negative binomial model. All 3 models indicated that adults were aggregated in distribution. Relationships to determine sample sizes for fixed levels of precision and fixed-precision-level stop lines for sequential sampling of adults were developed. There was a functional relationship between the variance and mean of untransformed froghopper counts, but this was eliminated by the Healy and Taylor transformation. Samples using 5 consecutive stems per sampling unit minimized the variance: mean ratios for all sample sizes used to sample symptoms. The Iwao patchiness regression was the only appropriate model for symptom data, and the slope indicated that damage is distributed uniformly between samples. Relationships to determine fixed-precision-level stop lines for sampling of symptom data were developed.

Binomial Sequential Classification Sampling Plans for Russian Wheat Aphid (Homoptera: Aphididae) Management: Robustness Varying with Tally Thresholds of Aphids in Sample Units

Binomial sequential classification sampling plans were developed for use in classifying populations of the Russian wheat aphid, Diuraphis noxia (Mordvilko), below or above a mean intervention-threshold density (>miT) for management decision making. Based on 4 yr of field data from summer and fall populations on wheat and barley in the northwestern United States, the proportion of tillers with no more than T (tally threshold) aphids (PT) was related to mean aphid density (m) with an empirical model in the form of In[-In(PT)] = a + b ln(m) and the negative binomial distribution. Three mean intervention threshold (mIT) values (one, five, and 10 aphids per tiller) with a series of T values were used to satisfy needs for control of aphid populations varying in density at different crop stages. The sampling plans were evaluated using operating characteristic and average sample number functions computed using the empirical PT − m model or the negative binomial distribution model. The robustness of the sampling plans improved with increasing T values. When using empty tillers (T = 0), the resulting sampling plans were not robust for all mIT values considered. Based on the operating characteristic and average sample number functions, the recommended T values for use are 2-4 for crops at stages before the end of booting given mIT = 1, 15-25 for crops at stages before heading given mIT = 5, and 20-40 for crops at stages after heading or flowering given mIT = 10. Sampling stop lines for each mIT and T are provided along with a discussion of their application to sampling aphid populations in the field.

Spatial Distribution of Preimaginal Bemisia tabaci (Homoptera: Aleyrodidae) in Cotton and Development of Fixed-Precision Sequential Sampling Plans

Studies were conducted to examine distributional patterns of Bemisia tabaci (Gennadius) eggs and nymphs on two cultivars of upland cotton, Gossypium hirsutum L., and one American Pima cotton, G. barbadense L., and to develop efficient sampling plans for estimating densities of immatures. On a per square centimeter basis, both eggs and nymphs were equally distributed among the four leaf sectors delineated by the major leaf veins. This pattern was independent of the nodal location of the leaf, cultivar, or sampling date. However, based on counts on 3.88-cm2 disks near the petiole of the leaf, both egg and nymphal were aggregated at the proximal end of each sector. The relationship between disk and whole leaf counts varied with nodal position and cultivar. The greatest number of eggs and nymphs were found on mainstem leaves from nodes 2–4 and 4–7 (mainstem terminal = node 1), respectively. This pattern changed slightly with time but was similar among the three cultivars. The lowest coefficients of variation were associated with leaf counts from nodes 4–5 and 5–6 for eggs and nymphs, respectively. Based on variance partitioning and sampling cost analysis, a single 3.88-cm2 disk from the base of the second sector of the fifth mainstern node leaf was determined to be the most efficient sample unit for estimating egg and nymphal densities. Sequential sampling stop lines were calculated for this sample unit using Green's (1970) method. Sample plan validation using Monte Carlo simulation indicated that actual levels of precision (SEM/mean) were poorer than those specified at low densities of immatures and better than specified at high densities. Further simulations indicated that stop lines for specified precisions of 0.20, 0.25, or 0.30 would maintain an average precision of 0.25 when egg or nymphal densities are 100 per leaf disk, respectively. These sampling plans allow efficient monitoring for pest management application and will aid the study of B. tabaci population dynamics in cotton.