The effect of pyrethroid lambdacyhalothrin applications on the spatial distribution of phytophagous and predatory mites in apple orchards

The spatial distribution of three phytophagous mites,Panonychus ulmi (Koch),Tetranychus urticae Koch andAculus schlechtendali (Nalepa), and two predacious mites,Zetzellia mali (Ewing) andAmblyseius fallacis (Garman), and the effect of pyrethroid lambdacyhalothrin applications on mite spatial dispersion were investigated over a 3-year period in an apple orchard in Ontario. The index of dispersion and the slope of Taylor's power law were used to evaluate dispersion patterns of mites. Panonychus ulmi showed that between-tree spatial variation decreased with an increase of population densities, whereas between-leaf variation increased with population densities. With all other four species it appeared that between-tree variation is much greater than between-leaf variation at all field population density levels. The values ofb by Taylor's power law suggested that all five species of mites are aggregated, but that in generalP. ulmi andT. urticae (b=1.427–1.872) are more aggregated than their predators (b=1.254–1.393). Taylor's regression technique suggests that pyrethroid applications causedP. ulmi, T. urticae, Z. mali andA. fallacis to be less aggregated whileA. schlechtendali was more aggregated. The impact of changes in mite spatial distribution following pyrethroid applications on sampling plans is discussed.     

Colony expansion model for describing the spatial distribution of populations

Two equations have been used frequently to describe the relation between the sample variance (s ²) and sample mean (m) of the number of individuals per quadrat: Taylor's power law, s ² = am ^b , and Iwao's m ^*−m regression, s ² = cm + dm ², where a, b, c, and d are constants. We can obtain biological information such as colony size and the degree of aggregation of colonies from parameters c and d of Iwao's m ^*−m regression. However, we cannot obtain such biological information from parameters a and b of Taylor's power law because these parameters have not been described by simple functions. To mitigate such in-convenience, I propose a mechanistic model that produces Taylor's power law; this model is called the colony expansion model. This model has the following two assumptions: (1) a population consists of a fixed number of colonies that lie across several quadrats, and (2) the number of individuals per unit occupied area of colony becomes v times larger in an allometric manner when the occupied area of colony becomes h times larger (v≥ 1, h≥ 1). The parameter h indicates the dispersal rate of organisms. We then obtain Taylor's power law with b = {ln[E(h)] + ln[E(v ²)]}/{ln[E(h)] + ln[E(v)]}, where E indicates the expectation. We can use the inverse of the exponent, 1/b, as an index of dispersal of individuals because it increases with increasing E(h). This model also yields a relation, known as the Kono–Sugino relation, between the proportion of occupied quadrats and the mean density per quadrat: −ln(1 −p) = fm ^g , where p is the proportion of occupied quadrats, f is a constant, and g = ln[E(h)]/{ln[E(h)] + ln[E(v)]}. We can use g as an index of dispersal as it increases with increasing E(h). The problem at low densities where Taylor's power law is not applicable is also discussed. Received: January 27, 2000 / Accepted: June 20, 2000     

Spatial distribution and sequential sampling of adults ofGonocephalum macleayi andPterohelaeus darlingensis in different cropping regimes

Counts of adults of the false wirewormsGonocephalum macleayi (Blackburn) andPterohelaeus darlingensis Carter in pitfall traps in burnt, mulched and sorghum treatments conformed to Taylor's power law. Within a species there were no significant differences in distributions of counts of either sex in any habitat butG. macleayi were more aggregated thanP. darlingensis (Taylor'sb 1.35 and 1.26, respectively). Relationships to determine sample sizes for fixed levels of precision and fixed-precision-level stop lines for sequential sampling are developed for each species using Taylor's parameters for combined data over all habitats.     

Unbiased estimation of greenhouse whitefly, Trialeurodes vaporariorum, mean density using yellow sticky trap in cherry tomato greenhouses

The spatial distribution of the count of adult greenhouse whiteflies, Trialeurodes vaporariorum (Westwood), on yellow sticky traps was analyzed using Taylor's power law and spatial autocorrelation statistics in the cherry tomato greenhouses from 1998–1999. Samples were collected weekly using a cylindrically shaped yellow sticky trap placed in a 5 by 8 grid covering 0.10–0.15 ha in each of five cherry tomato greenhouses. Taylor's (1961) power law indicated that counts of T. vaporariorum on traps were aggregated within greenhouses. Spatial autocorrelation analysis showed that trap catches were similar (positively autocorrelated) to a distance of 12.5 m, and then dissimilar (negatively autocorrelated) at >12.5 m. Autocorrelation-lag plots showed a globally significant spatial relation in 34 of 57 sample-weeks according to Bonferroni's approximation. The presence of this spatial relation was not related to the changes of mean density. Trap counts at the second lag distance (12.5–25 m) showed little spatial autocorrelation and tended to be the most spatially independent. A fixed-precision-level sequential sampling plan was developed using the parameters from Taylor's power law. The presence of spatial dependency in data sets degraded the sampling plan's precision relative to performance in data sets lacking significant spatial autocorrelation. Therefore, to obtain an unbiased mean density of T. vaporariorum per greenhouse, sticky traps should be placed at least >12.5 m apart to ensure that they are spatially independent.     

Sequential sampling for adult coccinellids in wheat

Adult aphidophagous coccinellids are important predators of cereal aphids in wheat in the Great Plains of the United States for which sampling methods are needed to facilitate improved management. An equation relating the mean number of adult coccinellids per m² in a wheat field to its variance was obtained using Taylor's power law. A sequential sampling procedure was developed to estimate the number of adult coccinellids per m² with constant average statistical precision (standard error/mean). The procedure was constructed by an equation relating the number of adult coccinellids per m² to the number of adult coccinellids per minute of counting incorporating into the Taylor's power law relationship. The procedure involves conducting a series of 1-min counts while walking through a field at a constant velocity of 10 m per minute. After each 1-min count sequential sampling stop-lines are consulted to determine if the specified level of precision has been achieved. Two methods, a statistical procedure and comparison with independent data, were used to assess the consistency with which the specified level of precision was achieved by the procedure. Results indicated that observed precision was close to that specified by the user over a wide range of adult coccinellid density.     

The spatial distribution of the wheat-bulb fly,Leptohylemyia coarctata (fall.) (Diptera: Anthomyiidae)

The spatial distribution of the eggs, larvae, pupae and adults of the wheat-bulb fly was investigated by fitting 42 sets of data comprising 1334 samples to the Poisson and negative binomial distributions, and by using the power law (S²=am^b). In general, the tests indicated that all stages were aggregated and fitted the negative binomial model.     

Binomial sequential sampling of adult Saccharicoccus sacchari on sugarcane

The 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 & 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.     

Populations ofSitobion avenae andAphidius ervi on spring wheat in the northwestern United States Spatial distribution and sequential sampling plans based on numerical and binomial counts

During a three-year field survey of the English grain aphid,Sitobion avenae (F.) (Homoptera: Aphididae) and the parasitoid,Aphidius ervi Haliday (Hymenoptera: Aphidiidae; represented by aphid mummies) on spring wheat, data sets were generated which consisted of 47 estimates of mean density (m aphids per tiller), variance (s ²), and the proportion of empty tillers (P ₀ forS. avenae and 22 estimates of the same statistics forA. ervi, respectively. Each estimate of the aphid and parasitoid populations was based on counts per individual tiller on each sampling occasion. Taylor's power law was found to fit the data sets better than Iwao'sm ^*−m regression model. Taylor's slope forS. avenae (1.3076) was significantly higher than that forA. ervi (1.1519), indicating thatS. avenae was more aggregated thanA. ervi. Based on temporal changes in spatial aggregation represented by an index, 1/k [wherek was estimated asm ²/(s²−m)],S. avenae was most aggregated at low densities during the early infestation period and tended to be less aggregated as density increased, whereasA. ervi was more likely to be randomly distributed. A commonk was detected for neitherS. avenae norA. ervi because the slopes from the linear regression ofk onm significantly exceeded 0. Sequential sampling plans, based on numerical (complete) and binomial (presence or absence) counts, for the aphid and parasitoid species were developed using Taylor's parameters and those estimated from the linear regression of ln(m) on ln[−ln[P ₀], respectively. Suggestions are made concerning the use of the sampling plans and the levels of precision that may be attained.     

Spatial Distribution and Minimum Sample Size for Overwintering Larvae of the Rice Stem Borer Chilo suppressalis (Walker) in Paddy Fields

The rice stem borer, Chilo suppressalis (Walker), feeds almost exclusively in paddy fields in most regions of the world. The study of its spatial distribution is fundamental for designing correct control strategies, improving sampling procedures, and adopting precise agricultural techniques. Field experiments were conducted during 2011 and 2012 to estimate the spatial distribution pattern of the overwintering larvae. Data were analyzed using five distribution indices and two regression models (Taylor and Iwao). All of the indices and Taylor’s model indicated random spatial distribution pattern of the rice stem borer overwintering larvae. Iwao’s patchiness regression was inappropriate for our data as shown by the non-homogeneity of variance, whereas Taylor’s power law fitted the data well. The coefficients of Taylor’s power law for a combined 2 years of data were a?=??0.1118, b?=?0.9202?±?0.02, and r ²?=?96.81. Taylor’s power law parameters were used to compute minimum sample size needed to estimate populations at three fixed precision levels, 5, 10, and 25% at 0.05 probabilities. Results based on this equation parameters suggesting that minimum sample sizes needed for a precision level of 0.25 were 74 and 20 rice stubble for rice stem borer larvae when the average larvae is near 0.10 and 0.20 larvae per rice stubble, respectively.     

Sampling Rhyparida nitida Clark (Coleoptera: Chrysomelidae) and symptoms of their damage on sugarcane

Sampling statistics were determined for larvae, pupae and adults of the chrysomelid Rhyparida nitida associated with sugarcane in Australia and for symptoms of their damage. Iwao's patchiness regression was inappropriate for modelling the mean–variance relationships of the insect counts. Taylor's power law was used to model these data and relationships were developed for counts of small, medium and large larvae, all larvae combined, pupae and adults. The mean–variance relationships of counts of live shoots and shoots killed by larvae of R. nitida were modelled using Iwao's patchiness regression; Taylor's power law was not appropriate to either data set. Relationships to determine sample sizes for fixed levels of precision and fixed-precision-level stop lines for sequential sampling of the different stages and live and dead shoots were also developed. Neither the ln(x + 1) transformation nor the Healy and Taylor transformation consistently standardised the mean–variance relationships of insect counts and the appropriate transformation should be selected on a case-by-case basis. Counts of both live and dead shoots were adequately transformed by the Iwao and Kuno transformation.     

烟草潜叶蛾幼虫空间分布型及其应用研究

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

The effect of the presence of a forage legume on nitrogen and carbon levels in soils under Brachiaria pastures in the Atlantic forest region of the South of Bahia,Brazil

The impact of forest clearance, and its replacement by Brachiaria pastures, on soil carbon reserves has been studied at many sites in the Brazilian Amazonia, but to date there appear to be no reports of similar studies undertaken in the Atlantic forest region of Brazil. In this study performed in the extreme south of Bahia, the changes in C and N content of the soil were evaluated from the time of establishment of grass-only B. humidicola and mixed B. humidicola/Desmodium ovalifolium pastures through 9 years of grazing in comparison with the C and N contents of the adjacent secondary forest. The decline in the content of soil C derived from the forest (C3) vegetation and the accumulation of that derived from the Brachiaria (C4) were followed by determining the ¹³C natural abundance of the soil organic matter (SOM). The pastures were established in 1987, 10 years after deforestation, and it was estimated that until 1994 there was a loss in forest-derived C in the top 30 cm of soil of approximately 20% (9.1 Mg C ha^–1). After the establishment of the pastures, C derived from Brachiaria accumulated steadily such that at the final sampling (1997) it was estimated 13.9 Mg ha^–1 was derived from this source under the grass-only pasture (0–30 cm). Samples taken from all pastures and the forest in 1997 to a depth of 100 cm showed that below 40 cm depth there was no significant contribution of the Brachiaria-derived C and that total C reserves under the grass/legume and the grass-only pastures were slightly higher than under the forest (not significant at P=0.05). The more detailed sampling under the pastures showed that to a depth of 30 cm there was significantly (P<0.05) more C under the mixed pasture than the grass-only pasture. It was estimated that from the time of establishment the apparent rate of C accumulation (0–100 cm depth) under the grass/legume pastures (1.17 Mg ha^–1 yr^–1) was almost double that under the grass-only pastures (0.66 Mg ha^–1 yr^–1). The data indicated that newly incorporated SOM derived from the Brachiaria had a considerably higher C:N ratio than that present under the forest.     

Spatial patterns of the red palm weevil and applied entomopathogenic nematode Heterorhabditis bacteriophora

The distribution and abundance of red palm weevil (Rhynchophorus ferrugineus) within palm tree-infected stems at Ismaelia governorate, Egypt, were investigated. Taylor's power law was fit (P ≤ 0.01) to its larvae, pupae and/or adults. The slope value of this power law indicated the clumped distribution of these insect stages. Sample size optimisation needed to achieve a predetermined level of sampling error for the insect stages was calculated. Also, soil samples were taken after uniform application of entomopathogenic nematode Heterorhabditis bacteriophora strain EG₁ to the soil under citrus tree canopies at the rate of 10⁴ infective juveniles/400 cm² plots, and assayed for the nematode using the Galleria bait method. At the first and second sampling dates, the nematode displayed contagious distribution and attained mean insect mortality of 15.3 and 4, respectively. At the third date of sampling, the nematode showed random distribution according to chi-squared test and caused 1.8 mean insect mortality. Evaluation of H. bacteriophora EG₁ as a biocontrol measure for the weevil was discussed based on their investigated dispersion indices.     

The spatial and temporal distribution of the grain aphid Sitobion avenae in winter wheat

The spatial and temporal distribution of the grain aphid Sitobion avenae F. (Homoptera: Aphididae) was studied within a field of winter wheat during the summer of 1996. Sampling was done using four nested grids comprising 133 locations. Analysis by Taylor's power law gave results typical for insect populations. Analysis by SADIE (Spatial Analysis by Distance Indices) showed spatial pattern due to edge effects and sampling scale, and positive but mild spatial association, although spatial patterns were ephemeral. Reasons for these findings and the implications for integrated crop management are discussed.     

Developing optimum sample size and multistage sampling plans for Lobesia botrana (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.     

Accounting for Spatial Variability in the Design of Sampling Programmes for Chaoborus Larvae

We developed a model to estimate the number of net hauls (n)needed to quantify the mean abundance (m) of vertically migratingspecies of Chaoborus larvae (C. flavicans, C. punctipennis andC.trivittatus) in the entire pelagic zone of lakes at a specifiedlevel of precision (D = SE/m, where SE is the standard error).The model was n = 1.94m^–0.30D^–2. It was derivedby combining Taylor's power law with a model that estimatedsample size (i.e. number of net hauls) for a specified levelof precision. The model indicates that for a typical temperatelake Chaoborus population of 50 larvae m^–3, 15 net haulsare required to obtain a precision of 0.2. As the precisionof a single pelagic, vertical haul is only 0.77 at such typicalChaoborus densities, caution should be exercised in assessingthe role of Chaoborus in food webs using data based on the traditionalapproach to plankton sampling, i.e. one mid-lake station.     

Aggregation and the transformation of counts of Aphis fabae Scop, on beans

In several sets of counts of Aphis fabae colonies on bean stems, obtained with different sampling methods, variance was always proportional to the same power of the mean; s²=am^b where b= 1.72 and a differed by different sampling methods. The resulting standard transformation for A. fabae on beans, z=x^{0 2}, is marginally more effective than z= log (x+1).     

Continuous soil carbon storage of old permanent pastures in Amazonia

Amazonian forests continuously accumulate carbon (C) in biomass and in soil, representing a carbon sink of 0.42–0.65 GtC yr^?1. In recent decades, more than 15% of Amazonian forests have been converted into pastures, resulting in net C emissions (~200 tC ha^?1) due to biomass burning and litter mineralization in the first years after deforestation. However, little is known about the capacity of tropical pastures to restore a C sink. Our study shows in French Amazonia that the C storage observed in native forest can be partly restored in old (≥24 year) tropical pastures managed with a low stocking rate (±1 LSU ha^?1) and without the use of fire since their establishment. A unique combination of a large chronosequence study and eddy covariance measurements showed that pastures stored between ?1.27 ± 0.37 and ?5.31 ± 2.08 tC ha^?1 yr^?1 while the nearby native forest stored ?3.31 ± 0.44 tC ha^?1 yr^?1. This carbon is mainly sequestered in the humus of deep soil layers (20–100 cm), whereas no C storage was observed in the 0‐ to 20‐cm layer. C storage in C4 tropical pasture is associated with the installation and development of C3 species, which increase either the input of N to the ecosystem or the C:N ratio of soil organic matter. Efforts to curb deforestation remain an obvious priority to preserve forest C stocks and biodiversity. However, our results show that if sustainable management is applied in tropical pastures coming from deforestation (avoiding fires and overgrazing, using a grazing rotation plan and a mixture of C3 and C4 species), they can ensure a continuous C storage, thereby adding to the current C sink of Amazonian forests.     

Sequential sampling protocols for Spodoptera frugiperda (Lepidoptera: Noctuidae), on Zea mays fields: influence of sampling unit size

Spodoptera frugiperda (J.E. Smith) is a major pest in maize fields in Argentina. However, a sampling method that accounts for spatial pattern and allows reliable pest density estimations is still lacking. This paper addresses the issue of how sampling unit size can influence the characterization of S. frugiperda spatial pattern and the performance of sampling plans. An intensive sampling programme for S. frugiperda larvae was carried out in maize fields from October until March in four growing seasons. On each sampling date, 12 to 20 sampling units were taken at random. Each unit consisted of 1, 2, 4, 6, 8, 10 or 12 consecutive plants along a row. The linearized version of the Taylor's power law (TPL) was fitted to mean and variance estimated for each sampling date and data set through least squares regression. In general, b values from TPL were significantly >1 (P<0.05), indicating an aggregated sampling distribution. Regression slopes (b) ranged from 1.28 to 1.48 in small larvae and from 1.06 to 1.24 in large larvae, indicating stronger clumping in the former. TPL parameters were used to develop constant precision sampling plans. The efficiency of these plans in terms of expected total cost (searching and handling sampling units) was very sensitive to the size of the sampling units with small larvae but not with large larvae. The influence of sampling unit size and spatial pattern on TPL parameters and sampling costs is discussed.     

柳厚壁叶蜂幼虫空间格局及抽样技术

应用Taylor的幂法则、Iwao m^*-m回归分析法及6个聚集指标,对柳厚壁叶蜂幼虫空间分布型进行了研究,并进行了影响因素分析.结果表明,该幼虫在柳树的枝条和叶片两个空间阶元都属于聚集分布,分布的基本成分是个体群,其聚集性随密度的增大而增加.在枝条上,聚集的原因是由柳厚壁叶蜂成虫集中产卵的习性与枝条上叶片空间位点共同影响所致;在叶片上,当m＜2.37时,其聚集原因与春季柳树新叶空间位置有关,当m＞2.37时,虫瘿聚集除与春季新叶空间位置有关外,还与柳厚壁叶蜂成虫羽化和在叶片上集中产卵的习性有关.运用Iwao m^*-m回归中的两个参数α和β值,确定了在不同精度下的理论抽样数及序贯抽样数.