Logarithmic confidence estimation of a ratio of binomial proportions for dependent populations.

This article investigates the logarithmic interval estimation of a ratio of two binomial proportions in dependent samples. Previous studies suggest that the confidence intervals of the difference between two correlated proportions and their ratio typically do not possess closed-form solutions. Moreover, the computation process is complex and often based on a maximum likelihood estimator, which is a biased estimator of the ratio. We look at the data from two dependent samples and explore the general problem of estimating the ratio of two proportions. Each sample is obtained in the framework of direct binomial sampling. Our goal is to demonstrate that the normal approximation for the estimation of the ratio is reliable for the construction of a confidence interval. The main characteristics of confidence estimators will be investigated by a Monte Carlo simulation. We also provide recommendations for applying the asymptotic logarithmic interval. The estimations of the coverage probability, average width, standard deviation of interval width, and index H are presented as the criteria of our judgment. The simulation studies indicate that the proposed interval performs well based on the aforementioned criteria. Finally, the confidence intervals are illustrated with three real data examples.

Presence-Absence Sampling Plans for Stink Bugs (Hemiptera: Pentatomidae) in the Midwest Region of the United States.

Stink bugs represent an increasing risk to soybean production in the Midwest region of the United States. The current sampling protocol for stink bugs in this region is tailored for population density estimation and thus is more relevant to research purposes. A practical decision-making framework with more efficient sampling effort for management of herbivorous stink bugs is needed. Therefore, a binomial sequential sampling plan was developed for herbivorous stink bugs in the Midwest region. A total of 146 soybean fields were sampled across 11 states using sweep nets in 2016, 2017, and 2018. The binomial sequential sampling plans were developed using combinations of five tally thresholds at two proportion infested action thresholds to identify those that provided the best sampling outcomes. Final assessment of the operating characteristic curves for each plan indicated that a tally threshold of 3 stink bugs per 25 sweeps, and proportion infested action thresholds of 0.75 and 0.95 corresponding to the action thresholds of 5 and 10 stink bugs per 25 sweeps, provided the optimal balance between highest probability of correct decisions (≥ 99%) and lowest probability of incorrect decisions (≤ 1%). In addition, the average sample size for both plans (18 and 12 sets of 25 sweeps, respectively) was lower than that for the other proposed plans. The binomial sequential sampling plan can reduce the number of sample units required to achieve a management decision, which is important because it can potentially reduce risk/cost of management for stink bugs in soybean in this region.

Evaluation of Two-Leaf Sampling Units to Estimate Sugarcane Aphid (Hemiptera: Aphididae) Economic Thresholds in Commercial Grain Sorghum.

Sugarcane aphid Melanaphis sacchari Zehntner is a significant economic pest of grain sorghum in the United States. Effective monitoring and early detection are cornerstones for managing invasive pests. The recently developed binomial sequential sampling plan estimates sugarcane aphid economic thresholds (ETs) based on classification whether a 2-leaf sample unit has ≤ or ≥ 50 M. sacchari. In this study, we evaluated eight 2-leaf sampling units for potential use in the sequential sampling plan. From 2016 through 2017, whole plant counts of M. sacchari were recorded non-destructively in situ on sorghum plants from 140 fields located in five states. Plant canopies were stratified into three categories. Two leaves from each stratum were used to compare linear relationships between M. sacchari numbers per two-leaf sample unit and total M. sacchari density per plant. Analysis revealed that two randomly selected leaves from the middle stratum accounted more variation for estimating M. sacchari density when compared to two leaves from the other strata. Comparison of eight two-leaf sampling units within plant growth stages were variable in quantifying variation of M. sacchari densities. When growth stages were combined, the standard uppermost + lowermost leaf sample unit and a unit consisting of two randomly selected leaves from the middle stratum revealed little difference in their enumeration of variation in M. sacchari density. Because other sample units were either less predictive and/or more variable in estimating M. sacchari density, we suggest that the (L1+U1) sample unit remain the preferred method for appraising M. sacchari ETs.

Development of Binomial Sequential Sampling Plans for Sugarcane Aphid (Hemiptera: Aphididae) in Commercial Grain Sorghum.

The sugarcane aphid (Melanaphis sacchari Zehntner) is a significant economic pest of grain sorghum (Sorghum bicolor (L.) Moench) in the Southern United States. Current nominal and research-based economic thresholds are based on estimates of mean aphids per leaf. Because enumerating aphids per leaf is potentially time consuming, binomial sequential sampling plans for M. sacchari were developed that allow users to quickly classify the economic status of field populations and determine when an economic threshold has been exceeded. During 2016 and 2017, counts of M. sacchari were recorded from 281 sampling events in 140 sorghum fields located in six states (Oklahoma, Kansas, Texas, Arkansas, Louisiana, Mississippi) . Regression analysis was used to describe the relationships between the mean M. sacchari density per two-leaf sample and proportion of plants infested with one or more aphids. Tally thresholds of T50 and T100 aphids per two-leaf sample were selected based on goodness of fit and practicality. Stop lines for both tally thresholds were developed for selected economic thresholds using Wald's sequential probability ratio test. Model validations using an additional 48 fields demonstrated that reliable classification decisions could be made with an average of 11 samples regardless of location. This sampling system, when adopted, can allow users to easily and rapidly determine when M. sacchari infestations need to be treated.

Spatial Dependence and Sampling of Phytoseiid Populations on Hass Avocados in Southern California.

Research on phytoseiid mites has been critical for developing an effective biocontrol strategy for suppressing Oligonchus perseae Tuttle, Baker, and Abatiello (Acari: Tetranychidae) in California avocado orchards. However, basic understanding of the spatial ecology of natural populations of phytoseiids in relation to O. perseae infestations and the validation of research-based strategies for assessing densities of these predators has been limited. To address these shortcomings, cross-sectional and longitudinal observations consisting of >3,000 phytoseiids and 500,000 O. perseae counted on 11,341 leaves were collected across 10 avocado orchards during a 10-yr period. Subsets of these data were analyzed statistically to characterize the spatial distribution of phytoseiids in avocado orchards and to evaluate the merits of developing binomial and enumerative sampling strategies for these predators. Spatial correlation of phytoseiids between trees was detected at one site, and a strong association of phytoseiids with elevated O. perseae densities was detected at four sites. Sampling simulations revealed that enumeration-based sampling performed better than binomial sampling for estimating phytoseiid densities. The ecological implications of these findings and potential for developing a custom sampling plan to estimate densities of phytoseiids inhabiting sampled trees in avocado orchards in California are discussed.

Comparison and Field Validation of Binomial Sampling Plans for Oligonychus perseae (Acari: Tetranychidae) on Hass Avocado in Southern California.

Oligonychus perseae Tuttle, Baker, & Abatiello is a foliar pest of 'Hass' avocados [Persea americana Miller (Lauraceae)]. The recommended action threshold is 50-100 motile mites per leaf, but this count range and other ecological factors associated with O. perseae infestations limit the application of enumerative sampling plans in the field. Consequently, a comprehensive modeling approach was implemented to compare the practical application of various binomial sampling models for decision-making of O. perseae in California. An initial set of sequential binomial sampling models were developed using three mean-proportion modeling techniques (i.e., Taylor's power law, maximum likelihood, and an empirical model) in combination with two-leaf infestation tally thresholds of either one or two mites. Model performance was evaluated using a robust mite count database consisting of >20,000 Hass avocado leaves infested with varying densities of O. perseae and collected from multiple locations. Operating characteristic and average sample number results for sequential binomial models were used as the basis to develop and validate a standardized fixed-size binomial sampling model with guidelines on sample tree and leaf selection within blocks of avocado trees. This final validated model requires a leaf sampling cost of 30 leaves and takes into account the spatial dynamics of O. perseae to make reliable mite density classifications for a 50-mite action threshold. Recommendations for implementing this fixed-size binomial sampling plan to assess densities of O. perseae in commercial California avocado orchards are discussed.

Spatial distribution and sequential sampling plans for Tuta absoluta (Lepidoptera: Gelechiidae) in greenhouse tomato crops.

BACKGROUND: The within- and between-plant distribution of the tomato leafminer, Tuta absoluta (Meyrick), was investigated in order to define action thresholds based on leaf infestation and to propose enumerative and binomial sequential sampling plans for pest management applications in protected crops. RESULTS: The pest spatial distribution was aggregated between plants, and median leaves were the most suitable sample to evaluate the pest density. Action thresholds of 36 and 48%, 43 and 56% and 60 and 73% infested leaves, corresponding to economic thresholds of 1 and 3% damaged fruits, were defined for tomato cultivars with big, medium and small fruits respectively. Green's method was a more suitable enumerative sampling plan as it required a lower sampling effort. Binomial sampling plans needed lower average sample sizes than enumerative plans to make a treatment decision, with probabilities of error of <0.10. CONCLUSIONS: The enumerative sampling plan required 87 or 343 leaves to estimate the population density in extensive or intensive ecological studies respectively. Binomial plans would be more practical and efficient for control purposes, needing average sample sizes of 17, 20 and 14 leaves to take a pest management decision in order to avoid fruit damage higher than 1% in cultivars with big, medium and small fruits respectively.

Plano de amostragem para Dichopelmus notus (Eriophyidae) na cultura da erva-mate / Sampling plan for Dichopelmus notus (Eriophyidae) on mate-tea orchard

O objetivo deste trabalho foi avaliar a amostragem presença-ausência para Dichopelmus notus Keifer (Eriophyidae) na cultura da erva-mate. O trabalho foi realizado em plantação comercial, em Cascavel, PR, entre abril de 1999 e julho de 2000. Procederam-se a coletas quinzenais de 240 folhas em diferentes partes de 10 plantas. A contagem dos ácaros nas folhas foi realizada, em laboratório, com auxílio de microscópio estereoscópico. Foi determinado o padrão de agregação com o modelo da potência de Taylor, e também a proporção de folhas infestadas e o número de amostras requeridas foram estimados por análise de regressão. D. notus apresentou distribuição agregada. A proporção de folhas infestadas estimadas pelo modelo matemático mostrou ser um parâmetro confiável para se estimar a densidade populacional do ácaro, sendo que o número de amostras requeridas foi pequeno, o que viabiliza a aplicação prática do método.

The objective of this research was to evaluate presence-absence sampling plan for Dichopelmus notus Keifer (Eriophyidae) on mate-tea orchard. This study was conducted in Cascavel, State of Paraná, Brazil, from April 1999 to July 2000, in a mate-tea tree commercial plantation. Biweekly sampling of 240 leaves in different parts of 10 plants was conducted, and the number of mites was registered. The aggregation pattern was determined using the Taylor’s power law model. The proportion of the infested leaves and the number of required samples were estimated by regression analysis. D. notus presented aggregated distribution. The estimated proportion of infested leaves showed to be reliable in order to estimate the population density of mites. The number of sample unities required to estimate infestation density was low, which makes practical application of this sampling method to be feasible.

Plano de amostragem presença-ausência para Oligonychus yothersi (McGregor) (Acari: Tetranychidae) na cultura da erva-mate / Presence-absence sampling plan for Oligonychus yothersi (McGregor) (Acari: Tetranychidae) on mate-tea orchard

O ataque de ácaros na cultura da erva-mate tem freqüentemente provocado perdas pela queda precoce das folhas. Assim, há necessidade de se monitorar a população desses artrópodes e adotar estratégias de manejo. O objetivo deste trabalho foi avaliar a confiabilidade da amostragem presença-ausência para Oligonychus yothersi (McGregor) na erva-mate. O trabalho foi realizado em um erval comercial, em Cascavel, PR, de abril de 1999 a julho de 2000. Coletas quinzenais de 240 folhas foram feitas em diferentes partes de 10 plantas escolhidas ao acaso. A contagem dos ácaros nas folhas foi realizada em laboratório com auxílio de microscópio estereoscópico. Foi determinado o padrão de agregação através dos coeficientes a e b da lei da potência de Taylor; a proporção de folhas infestadas e o número de amostras requeridas foram estimados através de modelo matemático. O. yothersi apresentou distribuição agregada. A proporção de folhas infestadas calculada pelo modelo matemático mostrou ser um parâmetro confiável para estimar a densidade populacional do ácaro. O número de amostras requeridas foi pequeno, viabilizando a aplicação prática do método de amostragem presença-ausência para O. yothersi na cultura da erva-mate.

Mite infestations to the culture of mate-tea frequently causes losses by the premature fall of the leaves. So, it is necessary to monitor the population of these arthropods, and to adopt management strategies for their control. The objective of this research was to evaluate the trustworthiness of presence-absence sampling for Oligonychus yothersi (McGregor) on mate-tea orchard. This study was conducted in Cascavel, Paraná State, from April 2001 to July 2000, in a mate-tea tree commercial plantation. Biweekly sampling of 240 leaves were collected in different parts of 10 plants, and the number of mites was counted. The aggregation pattern was determined through the coefficients a and b of Taylor's power law. The proportion of infested leaves and the number of required samples were estimated through mathematical model. The mite O. yothersi presented aggregate distribution. The proportion of infested leaves calculated by means of mathematical model showed to be a trustworthy parameter to estimate the population density of the mite. The number of required samples was small, making feasible the practical application of the presence-absence sampling method for O. yothersi in the culture of mate-tea.