Spatial distribution of Tenuipalpus heveae Baker (Acari: Tenuipalpidae) on rubber tree plantations

The objective of this work was to study the spatial distribution of Tenuipalpus heveae Baker in rubber tree plantations. The experimental area was located in Marinópolis, State of S?o Paulo, and corresponded to a total of 1,000 plants (clone RRIM 600) divided in 100 plots of ten plants each. A total of 16 samplings were conducted, approximately once every 10 days, between December 2007 and June 2008. On each date, samples were taken from two plants per plot, each sample corresponding to the top 30 cm of a branch randomly taken from the median region of the canopy of each plant. The number of T. heveae was evaluated on three leaflets randomly taken from each sample, using a 20x power pocket magnifying glass. The number of mites was evaluated in two areas of 1 cm2 delimited on the lower surface of each leaflet, being one along the midrib and the other along a lateral vein. The calculated dispersion indexes were: variance/mean relationship (I), index of Morisita (I′), coefficient of Green (Cx) and k exponent of negative binomial distribution. Tenuipalpus heveae showed aggregate distribution. The negative binomial distribution model was the most appropriate to represent the spatial distribution of the mite in the rubber tree plantation.     

Spatial distribution of Oncometopiafacialis (Signoret) (Hemiptera: Cicadellidae) in citrus orchard

The spatial distribution of Oncometopia facialis (Signoret) was studied in sweet orange to elaborate sampling plans and decision-making procedure for the control of this sharpshooter in the field. The samplings were carried out fortnightly in a grid design disposition of 100 points (plants) in citrus orchard, with yellow sticky traps. The average number of O. facialis ranged from 0.35 to 1.17 insects/trap, with the I index varying from 0.89 to 1.82. The fit tests to negative binomial, Poisson distribution, I index and Morisita index indicated aggregated distribution of this insect. The b result of Taylor's power law was 1.6382 (t = 2.71; d.f. = 11; P < 0.05). Sampling plans were elaborated with a precision level of 10, 20 and 25% of error in the mean estimation.     

Probability distribution of Orthezia praelonga Douglas (Hemiptera: Sternorrhyncha: Ortheziidae) in citrus

The probability distribution of the orthezia scale, Orthezia praelonga Douglas, was studied in plots of commercial orange orchards (Citrus sinensis L., var. "Pêra Rio"), with 5, 9 and 15 years of age, during one year. The survey of presence or absence of the pest in the plants was carried through twenty samplings in the total area of each plot visually inspecting each plant. The dispersion indexes used were: variance/mean relationship (I), index of Morisita (Id), coefficient of Green (Cx) and k exponent of negative binomial distribution for each sampling. The negative binomial distribution was more representative of the frequency distribution data of this scale in citrus, since the variance was superior to the average in all samplings. The analysis of the aggregation index showed that the majority of the samplings presented aggregate distribution for the scales.     

Spatial Distribution of Adult <Emphasis Type="Italic">Anthonomus grandis</Emphasis> Boheman (Coleoptera: Curculionidae) and Damage to Cotton Flower Buds Due to Feeding and Oviposition

The cotton boll weevil Anthonomus grandis Boheman (Coleoptera: Curculionidae) is the main pest in cotton crop around the world, directly affecting cotton production. In order to establish a sequential sampling plan, it is crucial to understand the spatial distribution of the pest population and the damage it causes to the crop through the different developmental stages of cotton plants. Therefore, this study aimed to investigate the spatial distribution of adults in the cultivation area and their oviposition and feeding behavior throughout the development of the cotton plants. The experiment was conducted in Maracaju, Mato Grosso do Sul, Brazil, in the 2012/2013 and 2013/2014 growing seasons, in an area of 10,000 m², planted with the cotton cultivar FM 993. The experimental area was divided into 100 plots of 100 m² (10 × 10 m) each, and five plants per plot were sampled weekly throughout the crop cycle. The number of flower buds with feeding and oviposition punctures and of adult A. grandis was recorded throughout the crop cycle in five plants per plot. After determining the aggregation indices (variance/mean ratio, Morisita’s index, exponent k of the negative binomial distribution, and Green’s coefficient) and adjusting the frequencies observed in the field to the distribution of frequencies (Poisson, negative binomial, and positive binomial) using the chi-squared test, it was observed that flower buds with punctures derived from feeding, oviposition, and feeding + oviposition showed an aggregated distribution in the cultivation area until 85 days after emergence and a random distribution after this stage. The adults of A. grandis presented a random distribution in the cultivation area.     

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.     

粘虫种群空间结构的探讨

研究昆虫种群的空间结构可分为下列三个层次,即田间集团分布,地理分布和猖獗区的分布。伊藤正春(1959)曾提出这三种空间结构层次与时间上的联系,即(1)世代内构成种群的个体在其栖息场所内的分布,称为Intra-generation range。(2)世代间种群的季节性生境转移所造成的水平分布及垂直分布,称为Generation range。(3)年代间种群猖獗的常发区或偶发区的地理分布,称为Inter-generation range。     

山西翅果油树群落优势种群分布格局研究

 应用扩散系数、聚集指数、平均拥挤度、聚块性指数、Green指数、聚集强度、Poisson分布和负二项分布的X2拟合检验等方法,研究了山西翅果油树群落优势种群的分布格局,并用相关分析比较了6个指数间的关系,结果表明：翅果油树分布格局呈随机型,其余22个优势种的分布格局皆为聚集型,这主要与物种本身的生态和生物学特性有关,以及与物种的竞争排斥作用有密切联系。在判定物种分布格局的8种方法中,以方差／均值比率、Poisson分布和负二项分布的X2拟合检验联合运用效果较好,不仅生态学意义明确,而且结果具有严格的统计学意义。     

应用反频次比较法研究浙江双栉蝠蛾幼虫空间分布格局

本文应用反频次比较法在福建邵武市11块毛竹Phyllostachys heterocycla cv. pubescens林样地上调查浙江双栉蝠蛾Bipectilus zhejiangensis幼虫的空间分布格局及该虫的发生与生态环境的关系。调查结果表明： 以每株毛竹笋为单位, 通过正频次比较法分析, 浙江双栉蝠蛾幼虫在总计抽样的550株竹笋上的分布符合负二项分布。以样地为单位, 经过反频次比较法分析11块样地上浙江双栉蝠蛾的分布类型, 结果为： 样地1, 2, 4, 5和8属于奈曼分布, 样地7, 9, 10和11属于负二项分布, 样地3和6属于奈曼分布或负二项分布。判别分析法判别函数能够100%正确分组, 依据F值大小, 6个环境指标的重要性从大到小依次为： 土壤有机质（X₅）、 林地卫生（X₆）、 坡位（X₃）、 坡向（X₄）、 竹林结构（X₂）、 立竹度（X₁）。由此得出： 无论是以每株毛竹笋为单位, 还是以每个样地为研究对象或单位, 都表明浙江双栉蝠蛾幼虫在空间分布上属于非均匀的聚集型分布。土壤腐殖质厚、 林地卫生差可使双栉蝠蛾幼虫密度增大, 立竹度、 竹林结构、 坡位和坡向单个指标对浙江双栉蝠蛾幼虫密度的影响不明显, 但综合作用明显; 反频次比较法比聚集度指标评价更为详细科学。     

Bacterial Density in Water Determined by Poisson or Negative Binomial Distributions

The question of how to characterize the bacterial density in a body of water when data are available as counts from a number of small-volume samples was examined for cases where either the Poisson or negative binomial probability distributions could be used to describe the bacteriological data. The suitability of the Poisson distribution when replicate analyses were performed under carefully controlled conditions and of the negative binomial distribution for samples collected from different locations and over time were illustrated by two examples. In cases where the negative binomial distribution was appropriate, a procedure was given for characterizing the variability by dividing the bacterial counts into homogeneous groups. The usefulness of this procedure was illustrated for the second example based on survey data for Lake Erie. A further illustration of the difference between results based on the Poisson and negative binomial distributions was given by calculating the probability of obtaining all samples sterile, assuming various bacterial densities and sample sizes.     

高寒草甸生态系统优势鼠种高原鼢鼠(Myospalax baileyi)和高原鼠兔(Ochotona curzoniae)种群空间格局的研究

本文研究于1983年7—8月,1985年8—10月期间,在中国科学院高寒草甸生态系统定位站进行。应用概率分布的方法研究小哺乳动物的种群空间格局,取得了与实际观察相吻合的结果。这项工作将为定量描述哺乳动物种群数量的空间配置做出尝试。 主要结果为: 1.高原鼢鼠和高原鼠兔(以下简称鼢鼠,鼠兔)的空间格局适合负二项分布,截尾负二项分布。 2.鼢鼠在空间的聚集强度高于鼠兔。 3.鼢鼠在高寒草甸和灌丛中的聚块面积分别为0.75公顷和1公顷以上;鼠兔均为0.5公顷。 4.大雪后(低密度鼠兔种群),鼠兔的空间格局呈随机分布,鼢鼠的格局不变,聚集强度均有下降。 5.两种动物空间分布总体上呈正相关,低密度样本与此相同;高密度样本为负相关。     

科尔沁沙地草地植被恢复演替进程中群落优势种群空间分布格局研究

通过对处于流动沙地、半固定沙地和固定沙地等不同恢复演替阶段的群落的取样调查 ,研究了科尔沁沙地草地植被恢复进程中群落优势种群的空间分布格局及其动态变化。运用扩散系数、聚集指数、平均拥挤度、聚块性指数、Green指数、聚集强度、Poisson分布和负二项分布的 χ2 拟合检验等 7项指标 ,对群落优势种群的分布格局的研究结果基本一致 ,大多数物种的空间分布呈显著的聚集分布。在演替进程中种群格局强度的变化和群落总体聚集程度的变化与种群动态和群落结构的空间异质性相对应 ,较高的聚集程度是种群分布斑块化和群落结构的空间异质性的反映 ,随着演替进展 ,优势种的种群数量扩展 ,但种群分布的聚集强度下降 ,群落结构的空间异质性降低。在 7种测定分布格局的指标中 ,聚块性指数、Green指数和聚集强度是无量纲的指标 ,其大小不受种群大小的影响 ,其变化可以较好地指示格局强度本身的变化 ,并与种群动态和群落结构变化相联系     

Sampling for the sugarcane borer (Lepidoptera: Crambidae) on sugarcane in Louisiana.

A 3-yr study was conducted in 0.6- to 2.0-ha sugarcane fields throughout south Louisiana under varying sugarcane borer, Diatraea saccharalis (F.), density levels to determine the spatial dispersion of infestations and to develop a sequential sampling plan. Infestations of D. saccharalis were randomly dispersed. Infestation levels (percentage of stalks infested) ranged from 0.6 to 33.3%. Frequency distributions of the number of infested stalks indicated that the Poisson distribution best fit the data Tests of other distributions (negative binomial [aggregated], binomial [uniform], geometric, and hypergeometric) resulted in poorer fits. The sequential sampling plan devised, with lower and upper D. saccharalis infestation limits of 2 and 5% and 5 and 10%, required maximum average sample numbers of 7.1 and 5.5 (20-stalk samples), respectively, to make terminating management decisions. It is our assessment that implementation of these plans would decrease sampling effort by 50-60% when compared with sampling programs currently in use for D. saccharalis management decisions in Louisiana.     

Distribution of foundress group size in Ropalidia fasciata and R. plebeiana (Hymenoptera: Vespidae): an analysis using zero-truncated distribution models

Distribution patterns of the number of foundresses per newly established nest (foundress group size, FGS) of two primitively eusocial, independent-founding wasps, Ropalidia fasciata and R. plebeiana, were studied using zero-truncated distribution models. The distribution pattern of the FGS of R. fasciata is significantly different from a zero-truncated Poisson distribution but fits the zero-truncated negative binomial distribution well, indicating a strongly contagious distribution. R. plebeiana sometimes establishes new colonies by reusing old nests. In this case, distributions are strongly contagious. Competition among foundresses may be one reason for the contagious distribution of FGS in R. fasciata and in cases of old-nest reuse by R. plebeiana, but further studies, especially on the behaviour of foundresses in relation to FGS, are necessary. Electronic Publication     

Operational considerations for augmentation of Trichogramma exiguum (Hymenoptera: Trichogrammatidae) for suppression of Rhyacionia frustrana (Lepidoptera: Tortricidae) in Pinus taeda plantations

Studies were performed to assess the operational feasibility of Trichogramma exiguum Pinto & Platner (Hymenoptera: Trichogrammatidae) augmentation for suppression of the Nantucket pine tip moth, Rhyacionia frustrana (Comstock) (Lepidoptera: Tortricidae), in commercial loblolly pine, Pinus taeda L., plantations. Single inundative releases containing two cohorts of encapsulated T. exiguum at a potential rate of 224,200 +/- 27,600 females per ha per cohort were made into two 4-ha plots during the second R. frustrana generation in 2000. Augmentation failed to increase parasitism rates above those occurring naturally; yet, 10% fewer shoots were attacked by R. frustrana, but not below acceptable levels. Quality control data suggest that low emergence levels and intense predation by ants upon developing T. exiguum lowered actual release rates to 13,000 +/- 900 females per ha per cohort. The effect of capsule distribution and microclimate on the discovery of capsules by predators (indicated by some E. kuehniella egg removal), parasitoid predation (percentage of eggs removed or destroyed), and subsequent parasitoid emergence was investigated. Uniformly distributed capsules experienced significantly higher predation levels than clustered capsules, and capsules exposed to field conditions for 5 d experienced higher predation than those exposed for 3 d, independently of distribution. Discovery of capsules by predators was unaffected by distribution or exposure period. Microhabitat significantly impacted average maximum daily temperature, the number of consecutive hours per day at or above 35 degrees C, and parasitoid emergence percentages. Parasitoid emergence declined significantly in response to increasing number of consecutive hours per day above 35 degrees C. Microclimate did not impact capsule discovery by predators or predation levels. Augmentation of T. exiguum for suppression of R. frustrana damage may not be practical within P. taeda plantations.     

湘西油茶树群落中蛇足石杉种群的水平分布格局

采用方差,均值法、负二项参数K、Cassie指数、丛生指数、平均拥挤度、聚块性指数、Green指数、泊松分布、负二项分布及奈曼分布的X2理论拟合,研究了湘西油茶树群落中蛇足石杉种群的分布格局,结果表明湘西油茶树群落中蛇足石衫种群的分布格局类型呈集群分布,且符合n=1的奈曼分布,此格局的形成主要与其繁殖的生物学特性、特定的环境条件及共生真菌等因素密切相关．     

后河自然保护区水丝梨群落优势种群结构与格局

应用立木大小级对后河自然保护区水丝梨群落中水丝梨和曼青冈两优势种群径级结构进行了对比分析,同时采用方差／均值比的t检验法、Morisita指数Iq的F检验法、丛生指数I、负二项式指数k、平均拥挤系数m^*和聚块性指数m^*／m判定并检验了两优势种群的分布格局,并按径级分样地进行了格局类型及强度的比较．结果表明,水丝梨种群Ⅳ级占绝对优势,分别达到79．4％(Q1)和87．4％(Q2),I、Ⅱ级极少甚至缺乏,更新困难,为衰退成熟型;曼青冈种群在两样地中均为I级>Ⅱ级>Ⅲ级>Ⅳ级>V级,为增长型．群落中两优势种群均呈集群分布;但按径级结构分析两优势种群的分布格局有所区别：随径级的增大,水丝梨种群由随机分布到集聚程度逐渐增强的集群分布,而曼青冈种群的集聚程度逐渐下降直至随机分布。     

负二项分布与昆虫种群空间格局分析的研究现状

对农业有害生物及其天敌种群密度的正确估计是实施IPM(有害生物综合治理)方案的先决条件,因此,抽样方法一直被列为昆虫学,生态学和植物保护科学中最重要的基本     

Oviposition pattern of phytophagous insects: on the importance of host population heterogeneity

Frequency distributions of insect immatures per host are often fitted to contagious distributions, such as the negative binomial, to deduce oviposition pattern. However, different mechanisms can be involved for each theoretical distribution and additional biological information is needed to correctly interpret the fits. We chose the chestnut weevil Curculio elephas, a pest of the European chestnut Castanea sativa, as a model to illustrate the difficulties of inferring oviposition pattern from fits to theoretical distributions and from the variance/mean ratio. From field studies over 13–16 years, we show that 20 out of the 31 yearly distributions available fit a negative binomial and 25 a zero-inflated Poisson (ZIP). No distribution fits a Poisson distribution. The ZIP distribution assumes heterogeneity within the fruit population. There are two categories of host: the first comprises chestnuts unsuitable for weevil oviposition or in excess relative to the number of weevil females, and the second comprises suitable fruits in which oviposition behavior is random. Our results confirm this host heterogeneity. According to the ZIP distribution, the first category of hosts includes on average 74% of the chestnuts. A negative binomial distribution may be generated by either true or false contagion. We show that neither interference between weevil females, nor spatial variation in the infestation rate exist. Consequently, the observed distributions of immatures are not the result of false contagion. Nevertheless, we cannot totally exlude true contagion of immatures. In this paper we discuss the difficulty of testing true contagion in natural conditions. These results show that we cannot systematically conclude in favour of contagion when fitting a distribution such as the negative binomial or when a variance/mean ratio is higher than unity. Received: 22 September 1997 / Accepted: 15 December 1997     

Use of Geostatistics to Determine the Spatial Distribution and Infestation Rate of Leaf-Cutting Ant Nests (Hymenoptera: Formicidae) in Eucalyptus Plantations

One of the fundamental steps in pest sampling is the assessment of the population distribution in the field. Several studies have investigated the distribution and appropriate sampling methods for leaf-cutting ants; however, more reliable methods are still required, such as those that use geostatistics. The objective of this study was to determine the spatial distribution and infestation rate of leaf-cutting ant nests in eucalyptus plantations by using geostatistics. The study was carried out in 2008 in two eucalyptus stands in Paraopeba, Minas Gerais, Brazil. All of the nests in the studied area were located and used for the generation of GIS maps, and the spatial pattern of distribution was determined considering the number and size of nests. Each analysis and map was made using the R statistics program and the geoR package. The nest spatial distribution in a savanna area of Minas Gerais was clustered to a certain extent. The models generated allowed the production of kriging maps of areas infested with leaf-cutting ants, where chemical intervention would be necessary, reducing the control costs, impact on humans, and the environment.     

Efficient Simulation of Multivariate Binomial and Poisson Distributions

Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the multivariate Poisson distribution are combined to obtain an algorithm for the quick implementation of its multivariate dependence structure. Simulation of the multivariate Poisson distribution then becomes feasible by first generating and then convoluting independent univariate Poisson variates with appropriate expectations. The latter can be computed via linear recursion formulae. Similar means for simulation are also considered for the binomial setting. In this scenario it turns out, however, that exact computation of the probability function is even easier to perform; therefore corresponding linear recursion formulae for the point probabilities of multivariate binomial distributions are presented, which only require information about the index parameter and the (simultaneous) success probabilities, that is the multivariate dependence structure among the binomial marginals.