Iwao's Patchiness Research Articles

감귤원에서 귤녹응애 공간분포 분석과 표본조사법 개발

온주밀감에서 귤녹응애, Aculops pelekassi의 분산지수와 분포양상, 표본조사시 적정 표본수에 대하여 조사하였다. 귤녹응애는 집중분포를 하고 있었으며, 분산지수는 Taylor's power law가 Iwao's patchiness regression보다 더 잘 설명하고 있었다. Taylor's power law의 상수를 이용하여 고정 정확도 수준에서 열매 표면 <TEX>$cm^2$</TEX>당 누적충수에 따라 조사를 중지할 수 있는 표본조사법을 만들었다. 경제적인 표본조사를 위하여 Kono-sugino의 경험적 이항모델을 개발하였으며, 이항모델을 이용하면 귤녹응애가 <TEX>$cm^2$</TEX>당 12마리 이상 발생한 열매 비율을 이용하여 평균밀도를 추정할 수 있었다 : <TEX>$ln(m)=4.61+1.23ln[-ln(1-p_{12})]$</TEX>. 최적의 tally threshold를 결정하기 위하여 추정평균에 대한 분산을 계산한 결과 tally threshold가 12일 때 추정평균의 분산이 적었으며, 발생과율 0.1~0.5의 범위에서 분산의 변동이 거의 없어 다른 tally threshold에 비해 높은 정확도로 평균을 추정할 수 있었다. 적정 표본수를 결정하기 위하여 계층표본조사법을 이용하여 분석한 결과 고정 정확도 0.25수준에서 감귤원당 적정 조사 나무수는 13주였으며, 나무당 조사 열매수는 5개, 열매당 2지점에서 <TEX>$cm^2$</TEX>당 귤녹응애수 조사가 바람직하였다(총 130표본). The dispersion indices, spatial pattern and sampling plan for pink citrus rust mite (PCRM), Aculops pelekassi, monitoring was investigated. Dispersion indices of PCRM indicated the aggregated spatial pattern. Taylor's power law provided better description of variance-mean relationship than Iwao's patchiness regression. Fixed-precision levels (D) of a sequential sampling plan were developed using by Taylor's power law parameters generated from PCRM on fruit sample (cumulated number of PCRM in <TEX>$cm^2$</TEX> of fruit). Based on Kono-Sugino's empirical binomial the mean density per <TEX>$cm^2$</TEX> could be estimated from fruit ratio with more than 12 rust mites per <TEX>$cm^2$</TEX>: <TEX>$ln(m)=4.61+1.23ln[-ln(1-p_{12})]$</TEX>. To determine the optimal tally threshold, the variance (var(lnm)) for mean (lnm) in Kono-Sugino equation was estimated. The lower and narrow ranged change of variance for esimated mean showed at a tally threshold of 12. To estimate PCRM mean density per <TEX>$cm^2$</TEX> at fixed precision level 0.25, the required sample number was 13 trees, 5 fruits per tree and 2 points per fruit (total 130 samples).

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.

Dispersion Models and Sampling of Cacao Mirid BugSahlbergella singularis(Hemiptera: Miridae) onTheobroma Cacaoin 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.

Seasonal dynamics, dispersion, sequential sampling plans and treatment thresholds for the citrus leafminer, Phyllocnistis citrella Stainton (Lepidoptera: Gracillariidae), in a mature lemon block in coastal New South Wales, Australia

Abstract Studies of citrus leafminer in a coastal orchard in NSW, Australia indicated that an increase in abundance to about one mine per flush was followed during the midseason flush by a rapid increase in population that was related to an increase in the percentage of leaves infested within flushes and the number of mines per leaf. The fits of frequency distributions and Iwao's patchiness regression indicated that populations were highly contagious initially, and as the exponent k of the negative binomial distribution increased with increasing population density, the distribution approached random. Concurrently, the coefficient of variation of mines per flush (which was strongly related to the proportion of un‐infested flushes) decreased to about unity as the proportion of un‐infested flushes reached zero and fell further as the number of mines per flush increased. Both numerative and binomial sequential sampling plans were developed using a decision threshold based on 1.2 mines per flush. The binomial sampling plan was based on a closely fitting model of the functional relationship between mean density and proportion of infested flushes. Functional relationships using the parameters determined from Iwao's patchiness regression and Taylor's power law were equally satisfactory, and one based on the negative binomial model also fitted well, but the Poisson model did not. The three best fitting models indicated that a decision threshold of 1.2 mines per flush was equivalent to 50% of flushes infested. From a practical point of view, the transition from 25% infestation of flushes through 50% is so rapid that it may be prudent to take action when the 25% level is reached; otherwise, the 50% may be passed before the crop is checked again. For valuable nursery stock should infestation be detected in spring, it may be advisable to apply prophylactic treatment as the midseason flush starts.

Developing Optimum Sample Size and Multistage Sampling Plans for &lt;I&gt;Lobesia botrana&lt;/I&gt; (Lepidoptera: Tortricidae) Larval Infestation and Injury in Northern Greece

The purpose of this research was to quantify the spatial pattern and develop a sampling program for larvae of Lobesia botrana Denis and Schiffermüller (Lepidoptera: Tortricidae), an important vineyard pest in northern Greece. Taylor's power law and Iwao's patchiness regression were used to model the relationship between the mean and the variance of larval counts. Analysis of covariance was carried out, separately for infestation and injury, with combined second and third generation data, for vine and half-vine sample units. Common regression coefficients were estimated to permit use of the sampling plan over a wide range of conditions. Optimum sample sizes for infestation and injury, at three levels of precision, were developed. An investigation of a multistage sampling plan with a nested analysis of variance showed that if the goal of sampling is focusing on larval infestation, three grape clusters should be sampled in a half-vine; if the goal of sampling is focusing on injury, then two grape clusters per half-vine are recommended.

Abundance and spatial distribution of aphids and scales select for different life histories in their ladybird beetle predators

Abstract: Life history parameters tend to differ between aphidophagous and coccidophagous ladybird beetles. It seems that the nature of prey, in particular the abundance, number and size of the colonies and their spatial distribution, may have been selected for the evolution of the life histories in these two groups of coccinellids, leading the aphidophagous ladybird beetles to develop at a fast pace and the coccidophagous beetles at a slower pace. To study the abundance, number and size of the colonies and the spatial distribution of aphid and coccid species, 100 sampling plots regularly spaced along four parallel transects were surveyed in the summer of 2004. At each sampling plot, species abundance, and the number and size of colonies of aphid and coccid species were recorded. Iwao's patchiness regression was used to assess the spatial distribution of aphids and coccids. From this study, it was found that coccids are much rarer than aphids but formed more colonies. Whereas aphids display a stonger tendency to crowding, aphid colonies are randomly distributed in space while coccid groups are aggregated. So, it seems that the abundance and spatial distribution of prey distribution may be factors selecting for the evolution of different life histories among aphidophagous and coccidophagous ladybird beetles.

Sampling procedure for density estimation of bamboo galls induced by Aiolomorphus rhopaloides (Hymenoptera: Eurytomidae) in a bamboo stand

To establish a sampling procedure for estimating the density of bamboo galls induced by Aiolomorphus rhopaloides Walker (Hymenoptera: Eurytomidae) in a stand of bamboo Phyllostachys heterocycla (Carr. Mitf.) (Monocotyledoneae: Gramineae), 5–12 bamboo culms were cut at random in late March of each year during 1998–2001 just before gall-maker emergence. The number of galls on the branches of each bamboo culm was counted. The spatial patterns of the galls on the culms in the stand and on the branches within each culm were measured by Iwao's patchiness regression. Galls were distributed contagiously both on culms and on branches. Current bamboo culms that emerged the previous summer did not require sampling because no galls were observed on them. Except for this, there was no difference in gall density on young and old culms, suggesting that it is not necessary to distinguish them. There were few (<4%) galls above 6m height during the 4 years. There was no significant difference in gall density up to 4m and above 4m, suggesting that branches up to 4m can be sampled with confidence. Kuno's two-stage sampling method at different precision levels showed that the number of culms to be sampled varied with gall density. For example, at mean density m = 1.0 per branch when the number of sampled branches per culm is 10, a total of 24 culms is required to estimate gall number at a precision level of D = 0.2, where D is the ratio of standard error to mean.

Sampling of Diaphorina citri (Homoptera: Psyllidae) on Orange Jessamine in Southern Florida

Dispersion indices and related statistics of Asian citrus psyllid, Diaphorina citri Kuwayama, on orange jessamine [Murraya paniculata (L.) Jack] shoots in southern Florida from 1998 to 1999 were determined with 235 data sets and used to develop sampling plans. Three regression models, Taylor's power law, Iwao's patchiness regression, and k = c +dm [k = m2 / (S2 - m)] (where k is the parameter for the negative binomial distribution) were used to analyze the data. Taylor's power law (a = 0.3407 0.03, b = 1.2971 0.03, r2 = 0.88) fit the data better than Iwao's model (a = -0.3217 0.12, = 1.6979 0.06, r2 = 0.76). Taylor's b and Iwao's were both significantly > 1, indicating that D. citri populations were aggregated. Iwao's a was significantly

Spatial Distribution of Thrips in Greenhouse Cucumber and Development of a Fixed-Precision Sampling Plan for Estimating Population Density

Dispersion patterns of phytophagous thrips (Thysanoptera: Thripidae) were determined for greenhouse cucumber, Cucumis sativus L., in Cheju-do, Korea, during 1995 and 1996. Thrips populations were sampled using leaf sample, yellow sticky trap and visual estimate concurrently on each sampling date. Frankliniella occidentalis (Pergande) was the most dominant thrips species, accounting 92% of all specimens collected from leaf samples and yellow sticky traps. Dispersion indices generated by Taylor's power law and Iwao's patchiness regression were compared. Generally, Taylor's power law provided better description of mean-variance relationship than did Iwao's patchiness regression with exception of the data from the sticky trap. Slopes and intercepts of Taylor's power law from leaf sample and visual estimate did not differ among thrips species and surveyed greenhouses. A fixed-precision-level of sequential sampling plan was developed using Taylor's power law parameters generated from total number of thrips in leaf sample and visual estimate. This sampling plan for visual estimate was tested with sequential resampling simulation using 4 independent data sets. Resampling simulation analysis demonstrated that actual D values were always less than desired D values of 0.20, 0.25 and 0.30.

Spatial Distribution of Chironomid Larvae (Diptera: Chironomidae) in Two Central Florida Lakes

Spatial distribution of larval Chironomidae was investigated in 2 lakes, Jessup and Monroe, in central Florida. Each lake was divided into 6 sections and benthic samples were seasonally collected from each section from October 1995 to February 1997. Among >30 species of chironomids collected, Glyptotendipes paripes (Edward) was predominant in Lake Jessup. In Lake Monroe, G. paripes and Tanypodinae were codominant, with Chironomus crassicaudatus Malloch being abundant only in the summer. Spatial distribution of dominant chironomid species was analyzed by fitting to the negative binomial distribution, Iwao's patchiness regression, and Taylor's power law. The negative binomial gave variable fits with the chi-square test and with the second moment statistic. Four out of 6 data sets of G. paripes in Lake Monroe fitted the negative binomial distribution based on a chi-square test, whereas in Lake Jessup no data set fitted to this analysis. In contrast, using the second moment statistic, more data sets (4 out of 6) in Lake Jessup fitted to the negative binomial than in Lake Monroe (1 out of 6). Fitness of the negative binomial was good for Tanypodinae in Lake Monroe. The Iwao's regression statistically fitted 8 out of 12 data sets of G. paripes ; however, the wide range of β values (3.12–15.96) suggested this method to be inappropriate for our data. All data sets of G. paripes statistically fitted Taylor's power law with aggregation index, b , ranging from 1.498 to 2.162. Homogeneity of Taylor's regression for G. paripes over sampling seasons was revealed in both lakes. Overall, Taylor's power law was a better descriptor for aggregated populations of chironomid larvae in these 2 lakes and provided a basis for developing sequential sampling plans.

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.

Spatial dispersion patterns of larval Aedes cantans (Diptera: Culicidae) in temporary woodland pools

AbstractThe spatial dispersion patterns of larvae of the Palaearctic mosquito Aedes cantans (Meigen) were studied in two temporary woodland pools in England, between 1988 and 1990. Variance to mean ratios indicated that all larval instars were aggregated, but the degree of aggregation differed between ponds and between years, depending on the population density. The negative binomial model was found to fit the majority of the data, and the values for the parameter k varied between 0.05 and 0.96. Taylor's power law gave a good fit to the data with values of b, an index of aggregation, varying between 1.42 and 1.91. Iwao's patchiness regression yielded values for α between –1.63 and 6.92, and β from 1.49 to 3.25. These values indicate that the population is aggregated due to habitat heterogeneity, and younger instars may demonstrate a propensity to congregate with one another. A relationship between water temperature and mean number of larvae sampled at each transect point was observed in Pond One in 1989, suggesting that larvae aggregate where water temperatures are higher.

Spatial Distribution of the Red Sunflower Seed Weevil (Coleoptera: Curculionidae) on Sunflower

Knowledge of the distribution of counts of an insect is an essential element for development of a sequential sampling plan. The objectives of this study were to determine the spatial distribution of red sunflower seed weevil, Smicronyx fulvus Le-Conte, counts in sunflower, and to determine the effect of plant stage on the density. Taylor's power law, Iwao's patchiness regression, and the negative binomial probability model were used to analyze the data. All three indices ( b , β, and k ) indicated an aggregated distribution of the weevil. Taylor's power law provided a better description than Iwao's patchiness regression. The negative binomial distribution parameter k was not dependent with mean density, indicating the presence of a common k ( kc ). The estimates of kc ranged from 0.4587 to 0.5255. Plant growth stage had a significant effect on the density of the weevil. When most plants were in the bud stages, more weevils were always found in the blooming sunflower heads (>R5.0 stage). When plants were in the anthesis stage (R5.0–6.0), the adult weevils preferred plants of stage R5.4–6.0, which were suitable for oviposition.

Spatial Patterns of Anopheles freeborni and Culex tarsalis (Diptera: Culicidae) Larvae in California Rice Fields

Spatial patterns of Anopheles freeborni Aitken and Culex tarsalis Coquillett larvae were studied during summer by sampling with a standard mosquito dipper in 104 rice fields in northern California. Culex tarsalis larval abundance was highest initially, then decreased and remained low through late summer. An. freeborni larval abundance was low initially, increased steadily, and peaked in mid-August. The degree of aggregation for both species as measured using Taylor's power law and Iwao's Patchiness Regression was highest among the first instars and then decreased as the larvae aged. Seasonal peaks in the degree of aggregation were observed. Analysis of covariance showed that for Taylor's model both instar and time effects were statistically significant, with instar showing the largest effect. In comparison, all slopes resulting from Iwao's model were significantly different, indicating that this model was affected by specific combinations of instar, week, and location and, thus, was less useful in developing an area-wide sampling plan. Optimal sample size was estimated using two methods. One method calculated the number of dips needed to estimate population abundance at three fixed-precision levels. The second calculated the minimum number of dips needed to collect at least one larva. The latter requires a substantially smaller sample size and may provide an effective method for monitoring larval mosquito abundance for control purposes.

Spatial distribution of the flower bug,Orius similisand its interaction with the pink bollworm,Pectinophora gossypiellain cotton fields

Abstract The distribution of the flower bug, Orius similis Zheng, was examined on cotton plants from the time of bud appearance until the end of harvest. Taylor's power function (Taylor, 1961) and Iwao's patchiness regression (Iwao, 1968) both showed that the population was almost randomly distributed with a slight tendency to aggregation. The coefficients of the patchiness regression indicated that the distributions of flower bugs within the plot could be described by a negative binomial distribution. The spatial association between the flower bug and its prey, the pink bollworm Pectinophora gossypiella Saunders, was investigated using 2 x 2 contingency tables. A statistically significant positive association was found between the two species after the first and second generation peaks of the pink bollworm. By the third generation of pink bollworm, the population of flower bugs was low and there was no longer a statistically significant relationship between the two species. It therefore seems likely that the pink bollworm population in the plot was partly controlled by flower bugs during the first two generations.

Distribution of Trialeurodes vaporariorum and Bemisia tabaci (Homoptera: Aleyrodidae) on Some Greenhouse-grown Ornamental Plants

The within-plant and between-plant distributions of all stages of both greenhouse whitefly (GHWF), Trialeurodes vaporariorum (Westwood) on poinsettia, chrysanthemum and gerbera daisy, and sweetpotato whitefly (SPWF), Bemisia tabaci (Gennadius) on poinsettia, were examined using Taylor's power law (s2 = amb) and Iwao's patchiness () methods. We found that all developmental stages of the two whitefly species on all plants examined were aggregated within and between plants. The vertical distribution of whitefly stages is stratified among leaves within the plant with respect to leaf age rather than relative height of the leaves on the plants. Most of the adults, eggs and the first-instar nymphs occurred on young leaves. The second- and third-instar nymphs occurred on middle-aged leaves, and most of the pupae and empty pupal cases occurred on middle-aged and older leaves. Comparison of whitefly counts from the different combinations of top, middle, and bottom leaves with the whole-plant counts on poinsettia was correlated and these leaves can be sampled as an indication of population levels within a greenhouse population.

Sampling Methods for Prodiplosis longifila (Diptera: Cecidomyiidae) in Limes

Dispersion patterns of eggs, larvae, and adults of Prodiplosis longifila Gagne were determined for lime orchards in Dade County, Florida, during 1987 and 1989. Dispersion indices generated by Taylor's power law and Iwao's patchiness regression were compared. Taylor's power law provided a better description of variance-mean relationships for eggs, larvae, and adults than did Iwao's patchiness regression. All insect stages exhibited aggregated patterns of spatial distribution ( b > 1.4). Sample size requirements for fixed levels of precision were determined for eggs and larvae using estimated variance–mean relationships obtained from Taylor's power law regressions. Color sticky traps placed on the tree canopy provided a more efficient method of sampling P. longifila populations than ground emergence traps and collection of larval samples.

Vertical distribution, spatial dispersion and sequential sampling plan for fruit damage byHelicoverpa armigera(Hübner) (Lepidoptera: Noctuidae) on tomato crop in Burkina Faso

Abstract When tomato plants were vertically divided into three parts, damage by Helicoverpa armigera (Hubner) was regularly distributed in the dry season but significantly less damage was found at the top of the plant during the rainy season. The spatial distribution of damage in fields was studied by using Iwao's patchiness regression technique. Fruit damage was highly aggregated with a stabilization of this pattern with increased injury level. A sequential sampling plan, using 3% fruit damage per plant as an economic threshold, was prepared to evaluate damage prior to insecticide treatment. A maximum of 21 plants was needed when the damage level was at or near the economic threshold with this sampling plan.

Distribution patterns of and sampling plans for Tetranychus urticae Koch (Acarina: Tetranychidae) on roses

I sampled Tetranychus urticae Koch (Acarina: Tetranychidae) regularly from four rose gardens in Kyoto and Nara Prefectures in 1988–1990. When mite density was low, T. urticae showed an uneven vertical distribution, being more abundant in the lower third and absent from the upper third of the plants. Mite density was less variable within than between plants, suggesting that a sampling plan which includes more leaves from different plants rather than from different levels of a plant is favourable. Spatial distribution of T. urticae was nonrandom and followed the negative binomial distribution. In addition, both the Taylor's power law and the Iwao's patchiness regression described the distribution well. An empty-sample method for estimating mite density from the proportion of empty sampling units was developed. Sampling plans for determining the sample size required to reach a predetermined precision level, based on this method and by directly counting the mites, were designed. The counting method was more accurate than the empty-sample method. However, when the time factor was taken into account, the latter was more favourable, because it was faster than the former at a density range of 1.5–300 mites leaf−1, which was most commonly encountered in the field.

Binomial sequential sampling of adult Saccharicoccus sacchari on sugarcane

AbstractThe between‐stalk dispersion characteristics of adults of the pink sugarcane mealybug Saccharicoccus sacchari (Cockerell) were determined in southern Queensland. Iwao's patchiness regression was inappropriate to describe the relationship between mean and variance. Taylor's power law indicated that adults were aggregated, especially at the beginning and end of the ratoon growth period. Binomial data were modelled by the Nachman model; the model of Grout and two models of Wilson &amp; Room were inappropriate to describe the relationship between proportion of stalks infested and mean numbers of adults per stalk. Relationships to determine sample sizes for fixed levels of precision and binomial fixed‐precision‐level stop lines are developed for different sampling times using Taylor's power law and Nachman's equation.