Enumerative and binomial sampling plans for citrus mealybug (Homoptera: pseudococcidae) in citrus groves

The spatial distribution of the citrus mealybug, Planococcus citri (Risso) (Homoptera: Pseudococcidae), was studied in citrus groves in northeastern Spain. Constant precision sampling plans were designed for all developmental stages of citrus mealybug under the fruit calyx, for late stages on fruit, and for females on trunks and main branches; more than 66, 286, and 101 data sets, respectively, were collected from nine commercial fields during 1992-1998. Dispersion parameters were determined using Taylor's power law, giving aggregated spatial patterns for citrus mealybug populations in three locations of the tree sampled. A significant relationship between the number of insects per organ and the percentage of occupied organs was established using either Wilson and Room's binomial model or Kono and Sugino's empirical formula. Constant precision (E = 0.25) sampling plans (i.e., enumerative plans) for estimating mean densities were developed using Green's equation and the two binomial models. For making management decisions, enumerative counts may be less labor-intensive than binomial sampling. Therefore, we recommend enumerative sampling plans for the use in an integrated pest management program in citrus. Required sample sizes for the range of population densities near current management thresholds, in the three plant locations calyx, fruit, and trunk were 50, 110-330, and 30, respectively. Binomial sampling, especially the empirical model, required a higher sample size to achieve equivalent levels of precision.     

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.     

Effects of reducing sample size on density estimates of citrus rust mite (Acari: Eriophyidae) on citrus fruit: simulated sampling

The consequence of reducing sample size on the accuracy and precision of estimates of citrus rust mite, Phyllocoptruta oleivora (Ashmead), densities on oranges was investigated. The sample unit was a 1-cm2 surface area on fruit. Sampling plans consisting of 360, 300, 200, 160, 80, 48, 36, or 20 samples per 4 ha were evaluated through computer simulations by using real count data from 32 data sets of 600 sample units per 4 ha. The original and reduced sampling plans were hierarchical with different numbers of sample areas per 4 ha, trees per area, fruit per tree, and samples per fruit. Individual estimates (n=100 simulations per data set) using each plan were sometimes considerably below or above target densities. In an original set of count data with a mean of six mites per cm2, simulations of 36 samples per 4 ha produced individual estimates ranging from one to 16 mites per cm2, whereas 80 samples per 4 ha produced estimates ranging from two to 10 mites per cm2. The plans consisting of 36 or more samples were projected to provide precision levels of 0.25 (SEM/mean) or better at densities of five or more mites per cm2 based on log-data, a projection that needs to be verified under real-grove situations. Each plan consistently provided mite detection in these sampling simulations except those consisting of 20 or 36 samples, which sometimes failed to detect mites when the target density was less than five mites per cm2. The study provided insight into the probable precision, accuracy and detection thresholds for eight candidate sampling plans varying from relatively low to high resource input.     

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.     

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.     

Development of an optimal monitoring program in cotton: Emphasis on spidermites and<Emphasis Type="Italic">Heliothis</Emphasis> spp.

To develop a monitoring program requires that not only the spatial pattern of distribution of a species be known, but also the cost of sampling the area(s) within the host plants occupied by a species. As sample unit size (plant, branch, leaf, etc.) decreases, cost to sample each unit decreases, while the number of units required to estimate a population parameter with a given reliability increases. The concept of costreliability allows for available sampling procedures to be compared and the best one to be chosen. The paper discusses several ways in which monitoring costs have been reduced forTetranychus spp.,Heliothis spp. and predators without reducing the reliability of the estimate. These include the use of subsampling plans, binomial sampling and sequential sampling.     

Spatial distribution and sampling plans for Thrips palmi (Thysanoptera: Thripidae) infesting fall potato in Korea

The spatial distribution of adult and immature Thrips palmi Karny on fall potato, Solanum tuberosum L., on Cheju Island, Korea, was studied over a 2-yr period by visually inspecting potato leaves. The majority of thrips collected from the leaves were observed in the top one-third of the plant. The within-field spatial patterns of adults and immature thrips were aggregated. The slopes and intercepts of Taylor's power law did not differ among adults and immature thrips. A fixed-precision-level sampling plan was developed using the parameters from Taylor's power law and was tested with resampling simulations using eight independent data sets. Over a wide range of densities, the simulation demonstrated that actual sampling precision (d = SEM/mean) values at d = 0.25 averaged < 0.24 in all cases. A binomial sampling plan for estimating mean density was developed using an empirical model evaluated at tally thresholds (the minimum number of insects present before a leaf is considered infested) of one, three, five, and eight thrips per leaf. Increasing sampling size had little effect on the precision of the estimated mean regardless of tally threshold (T). However, increasing T had a dramatic effect on precision. The best tally threshold for estimating thrips density based on the applicable density ranges and the precision of the model was T = 5. A binomial sampling plan with a tally threshold of five and a fixed sample size of 30 leaves should be an effective replacement for enumerative counts when thrips average < 10 per leaf.     

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.     

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.     

Development and economic evaluation of spatial sampling plans for corn rootworm Diabrotica spp. (Col., Chrysomelidae) adults

Abstract  To develop spatial sampling plans for corn rootworm ( Diabrotica spp.) adults, their spatial distributions were characterized and economics of sampling plans were evaluated by comparing sampling costs between spatial and conventional (non-spatial) sampling plans. Semivariogram modelling and spatial by with distance indices showed that corn rootworm adults were significantly (P < 0.05) aggregated at peak population densities and any two samples were spatially correlated within approximately 45 m, with 39–90% of the variability explained by spatial dependence. Sampling costs for spatial sampling plans linearly increased as the sampling distance decreased and exponentially increased as the field size increased. Although sampling costs for non-spatial sampling plans were generally lower, spatial sampling plans could be more economical when the mean insect density became lower and the field size became smaller. This study demonstrated that spatial sampling plans could be optimized to minimize the sampling costs and maximize the spatial resolution.     

Distribution et échantillonnage des populations de Amblyseius manihoti Moraes (Acari, Phytoseiidae) sur manioc au Brésil

Distribution of Amblyseius manihoti (Acari, Phytoseiidae) on manioc and development of sampling plan
Sampling plans were developed for Amblyseius manihoti , a predator of the cassava green mite Mononychellus progresivus Doreste (Acari, Tetranychidae). Analysis of intra-plant distribution showed a more stable and constant distribution of A. manihoti on the leaves 9–12 (numbering starting from the first fully developed leaf), hence leaves belonging to this stratum were chosen as the sampling unit. Within this unit, A. manihoti displayed aggregated distributions between plants. The proposed binomial and the enumerative sampling procedures permitted reliable estimates of A. manihoti densities. For population monitoring, 100 sample units per field were sufficient to provide satisfactory estimates of densities.     

Dispersion statistics and a sampling plan for Helicoverpa (Lepidoptera: Noctuidae) on fresh-market tomatoes (Lycopersicon esculentum)

Abstract  Helicoverpa spp. is the primary pest in the Australian fresh-market tomato industry. We describe the spatial distribution of Helicoverpa spp. eggs on fresh-market tomato crops in the Goulburn Valley region of Victoria, and present a sequential sampling plan for monitoring population densities. The distribution of Helicoverpa spp. eggs was highly contagious, as indicated by a Taylor's b -value of 1.59. This high level of contagion meant that relatively large sample sizes would need to be collected to obtain an estimate of population density. High-precision sampling plans generally necessitated impractical sample sizes, and thus the plan we present is a relatively low-precision level plan (SE/mean = 0.3). Nonetheless, this level of precision is considered adequate for most agronomic scenarios. The plan was validated using a statistical re-sampling approach. The level of precision achieved was generally close to the nominal level. Likewise, the number of samples collected generally showed little departure from the theoretically calculated minimum sample size.     

Dispersion models and sampling of cacao mirid bug Sahlbergella singularis (Hemiptera: Miridae) on Theobroma Cacao in southern Cameroon

The spatio-temporal distribution of Sahlbergella singularis Haglung, a major pest of cacao trees (Theobroma cacao) (Malvaceae), was studied for 2 yr in traditional cacao forest gardens in the humid forest area of southern Cameroon. The first objective was to analyze the dispersion of this insect on cacao trees. The second objective was to develop sampling plans based on fixed levels of precision for estimating S. singularis populations. The following models were used to analyze the data: Taylor's power law, Iwao's patchiness regression, the Nachman model, and the negative binomial distribution. Our results document that Taylor's power law was a better fit for the data than the Iwao and Nachman models. Taylor's b and Iwao's β were both significantly >1, indicating that S. singularis aggregated on specific trees. This result was further supported by the calculated common k of 1.75444. Iwao's α was significantly <0, indicating that the basic distribution component of S. singularis was the individual insect. Comparison of negative binomial (NBD) and Nachman models indicated that the NBD model was appropriate for studying S. singularis distribution. Optimal sample sizes for fixed precision levels of 0.10, 0.15, and 0.25 were estimated with Taylor's regression coefficients. Required sample sizes increased dramatically with increasing levels of precision. This is the first study on S. singularis dispersion in cacao plantations. Sampling plans, presented here, should be a tool for research on population dynamics and pest management decisions of mirid bugs on cacao.     

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.     

Sampling considerations for garden symphylans (Order: Cephalostigmata) in western Oregon

Sampling recommendations were developed for a potato bait sampling method used to estimate garden symphylan (Scutigerella immaculata Newport) densities in western Oregon. Sample size requirements were developed using Taylor's power law to describe the relationship between sample means and variances. Developed sampling recommendations performed well at sample sizes of 30 and greater, when validated by resampling a cohort of 40 independent data sets. Sample size requirements for the bait sampling method were 1.5 times greater than the requirements for the soil sampling method over densities from 1 to 20 S. immaculata per sample unit. As S. immaculata densities increased from April to May, sample size requirements decreased by 36% for fixed precision levels. For sampling in April, decreasing the damage threshold from 20, to 10 and five S. immaculata per sample unit, required a 1.6 and 2.5 times greater sample size requirement, respectively, for a fixed precision level (c) appropriate for pest management (c = 0.25). The bait sampling method provides an efficient reliable alternative to the standard soil sampling method used to monitor garden symphylan populations.     

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.     

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.     

Implications of changes in arthropod distribution following chemical application

The influence of pesticide application on the within-field distribution of arthropods was investigated for Tetranychus urticae, the twospotted spider mite, on strawberries. Analyses of dispersions based onGreen's coefficient,Iwao's regression of mean crowding on the mean, andTaylor's power law all indicated that mite populations were highly aggregated initially. As densities increased, more of the avialable niches were filled, leading to a less clumped dispersion. However, pesticide applications causing greater than 99.9% mortality acted in a nearly density independant fashion and, although the originating populations were similar in number, did not produce dispersions equivalent to the initial migrants. As a result, ignoring these changes by developing sampling plans based on dispersion indices which generated a single slope for an entire data set, led to statistical errors that invalidated the sampling programs. In order to accurately reflect the field biology of the spidermites, sampling plans for pre and post-treatment populations were substantially different. The impact of such changes in dispersion were graphically demonstrated using both sequential and binomial sampling techniques. Both methods showed that fewer samples were necessary to estimate densities at a given precision level for post-treatment populations. Also, these techniques indicated that post-treatment populations had similar, but significantly different, dispersions. The implications of changes in pre and post-treatment dispersions, as well as problems associated with inconsistant dispersions following pesticide use, are discussed.