Variance estimation for systematic designs in spatial surveys

Summary In spatial surveys for estimating the density of objects in a survey region, systematic designs will generally yield lower variance than random designs. However, estimating the systematic variance is well known to be a difficult problem. Existing methods tend to overestimate the variance, so although the variance is genuinely reduced, it is over‐reported, and the gain from the more efficient design is lost. The current approaches to estimating a systematic variance for spatial surveys are to approximate the systematic design by a random design, or approximate it by a stratified design. Previous work has shown that approximation by a random design can perform very poorly, while approximation by a stratified design is an improvement but can still be severely biased in some situations. We develop a new estimator based on modeling the encounter process over space. The new “striplet” estimator has negligible bias and excellent precision in a wide range of simulation scenarios, including strip‐sampling, distance‐sampling, and quadrat‐sampling surveys, and including populations that are highly trended or have strong aggregation of objects. We apply the new estimator to survey data for the spotted hyena (Crocuta crocuta) in the Serengeti National Park, Tanzania, and find that the reported coefficient of variation for estimated density is 20% using approximation by a random design, 17% using approximation by a stratified design, and 11% using the new striplet estimator. This large reduction in reported variance is verified by simulation.     

二次等距抽样

本文提出了一种二次等距抽样方法,并提出了总体平均值的一个估计量：拼配部分的比型估计与轮换部分的样本均值的加权平均。当样本量较大时,求出了估计量的方差及最优轮换比．并对特殊情形进行了讨论和数值比较．     

A Compartment Model of the Effect of Early-season Temperatures on Potential Size and Growth of 'Delicious' Apple Fruits

A compartmental growth model was developed to describe expansionof ‘Delicious’ apple fruit diameter and the effectof early-season temperatures on potential size at harvest. Themodel was based on the assumption that growth may be describedas a function of transfer between two conceptual compartments.Under this scheme, the first compartment represented all tissuecontributing to the setting of potential fruit size (determinedas the integral of its output) whereas the second compartmentrepresented all other fruit tissue whose growth actualized thatpotential. Expansion of both compartments was assumed to havea temperature response with an optimum, whereas an aging processwith an asymptotic temperature response controlled transferto the second compartment. Model parameters were estimated byfitting to data from controlled environment experiments in whichearly-season temperature conditions were varied. Predicted fruitgrowth curves showed close agreement with measured diameterdata. The results were consistent with a two-fold impact ofearly-season temperatures on apple fruit size: an immediate,direct effect on growth rate and an enduring effect, mediatedthrough fruit cell number or resource allocation to young fruit,reflecting the establishment of a potential that subsequentgrowth actualizes.Copyright 1999 Annals of Botany Company. Malus domesticaBorkh., apples, ‘Delicious’, fruit growth, models, temperature, potential size, cell division.     

Rate of Increase in Size and Dry Weight of Individual Pods of Field Grown Soya Bean Plants

The dry weight of the whole fruit, the pod wall and an enclosedseed of randomly harvested soya beans is estimated from theexternal dimensions of the attached pod. The relations betweendimensions and dry weight are independent of cultivar and growthcondition and can be used on pods from 1 cm in length untilthe seeds reach their maximum fresh weight. Dimensions of tagged pods of three cultivars of field grownsoya beans differing in time to reach maturity were measuredevery 2–3 days from initial pod elongation until maturation.Dry weights for each pod were estimated from the dimensions,and the dry weight accumulation with time was fitted to thelogistic function to find the growth rate that best characterizedthe data for each pod. The final weight, the specific growthrate and the maximum growth rate of the whole fruit, the podwall and a single seed were subjected to analysis of variance. The most significant difference between pods of these cultivarswas the specific growth rate of individual seeds, which decreasedwith increasing maturity group. There were no differences ingrowth of the pod wall. However, most of the variation was betweenindividual pods within a cultivar, where the rate of dry weightaccumulation of the whole fruit, governed largely by the seedgrowth rate times the number of seeds, was highly correlatedwith the earlier growth of the pod wall. This suggests thatthe growth of individual whole fruit was determined early inpod development and was slightly influenced by factors appliedduring the period of rapid seed growth. Glycine max (L.) Merrill, Soya bean, seed growth analysis, specific growth rate     

Estimation of sample zooplankton abundance from Folsom splitter sub-samples

Procedures are described for estimating the abundance of eachzooplanklon species in a sample after counting at least twosub-samples from a Folsom splitter. A multinomiai model is assumedfor the splitting process. The method may be summarized as follows:two sub-samples, balanced with respect to the left — rightsplits, are counted. The counts for each species are testedfor homogeneity using a x² test. If the counts are homogeneous,an estimator is given which permits the estimation of the numberof animals in the sample, and the variance of this estimate.If the subsample counts are heterogeneous, it is assumed thatclumping has occurred. A procedure is described in which additionalsub-samples are counted to locate the clump, and estimatorsof abundance (and variance estimators) are derived. If the splitterbias is <5%, bias of the abundance estimator is negligiblecompared to the binomial sampling error. Comparisons of speciesabundance between plankton samples is made more rigorous usingthe estimates of mean abundance, and the variance of this mean,provided by the methods described here. ^*Present address: Dunoon Road, Dorroughby, NSW 2480, Australia.     

Effects of Density and Extinction Coefficient on Size Variability in Plant Populations

The effects of density and extinction coefficient on size variability,as measured by the coefficient of variation of plant weightin even-aged monocultures, were investigated theoretically usinga diffusion model of growth and size distribution and a canopyphotosynthesis model over the range of densities at which self-thinning(size-dependent mortality) does not occur. Size inequality (thecoefficient of variation of plant weight) increases with increasingdensity or leaf area index at each growth stage. Plants witherect leaves are prone to lower size inequality than plantswith horizontal leaves. These results agree well with existingobservations on even-aged plant monocultures and suggest thatcompetition between plants is mainly one-sided (competitionfor light). One sided competition affects size variability througha G(t, x) function (mean growth of plants of size x at timet per unit time). Two-sided competition (including competitionfor nutrients) affects size variability through a D(t, x) function(variance of growth of plants of size x at time t per unit time).In this case, size inequality decreases with increasing density.The importance of studying size variability is emphasized. Helianthus annus L., size variability, size inequality, coefficient of variation, competition, density effect, extinction coefficient, diffusion model, canopy photosynthesis model     

On pooling across strata when frequency matching has been followed in a cohort study

In a study designed to assess the relationship between a dichotomous exposure and the eventual occurrence of a dichotomous outcome, frequency matching has been proposed as a way to balance the exposure cohorts with respect to the sampling distribution of potential confounding factors. This paper discusses the pooled estimator for the log relative risk, and provides an estimator for its variance which takes into account the dependency in the pooled outcomes induced by frequency matching. The pooled estimator has asymptotic relative efficiency less than but close to 1, relative to the usual, inverse variance weighted, stratified estimator. Simulations suggest, however, that the pooled estimator is likely to outperform the stratified estimator when samples are of moderate size. This estimator carries the added advantage that it consistently estimates a meaningful population parameter under heterogeneity of the relative risk across strata.     

Spatial Analysis of the Canopy of Kiwifruit Vines as it Relates to the Physical, Chemical and Postharvest Attributes of the Fruit

The position of individual fruit on kiwifruit vines (Actinidiadeliciosa var. deliciosa) grown on a horizontal trellis (pergola)and on a T-bar trellis was determined using a theodolite. Thephysical, chemical, and postharvest attributes of the fruitwere related to their position on the vine during development. Fruit from the pergola vines were more numerous, of lesser weight,with lower concentrations of most mineral nutrients, but greaterconcentrations of soluble solids, and similar flesh firmnessafter 12 weeks of storage at 0 °C, than fruit from the T-barvines. The position on the vine accounted for most of the variationin the attributes of the fruit. Differences between fruit ona single lateral accounted for 43-56% of the variation. Variationbetween vines was relatively small (< 4% of the total variance). The heavier fruit were located at the apical ends of the laterals,while greater concentrations of soluble solids were associatedwith fruit located closer to the cordon. The larger fruit fromthe pergola vines developed from the early opening flowers.A similar relationship existed initially for the T-bar vines,but a reduction in growth of fruit from the early opening flowers8 weeks after anthesis resulted in a more even distributionof fruit size at harvest. The strongest relationship between mineral composition and postharvestattributes of the fruit was with soluble solids concentration(29-46% of the variance). The relationship with flesh firmnesswas weak (r = -0·14 to -0·32). Individual elementscould not be considered in isolation but rather in groups ofelements. Nitrogen was grouped strongly with phosphorus, sulphur,potassium, and copper, while calcium was linked with a secondgroup which included manganese and zinc. These two groups werenegatively related to one another. The greatest proportion of fruit with superior characteristicswas located in the denser parts of the canopy. Fruit with lessdesirable attributes were from the extremities of the canopywhere the leaf area index was low.Copyright 1994, 1999 AcademicPress Actinidia deliciosa, kiwifruit, fruit position, fruit quality, within-vine variation     

Multiple Mating and Reproductive Success of Male and Female Apple Maggot Flies, Rhagoletis pomonella (Diptera: Tephritidae)

Mature male and female apple maggot flies mated frequently on a field-caged host tree during a 14-day study. Each sex averaged one mating per day (mean of 1.0 ± 0.1), but some females mated up to eight times per day and some males up to six times per day. Reproductive success was estimated based both on observed numbers of matings in the field cage and on previous work relating fecundity and fertility to female mating status. Male and female flies did not differ in mean or variance in reproductive success, indicating that this is a polygamous mating system consisting of both polygyny and polyandry. We discuss the significance of this with regard to the framework of insect mating control and frequency proposed by others. We also discuss behaviors (such as movements, agonistic encounters, occurrences on fruit, and ovipositions) that do and do not show correlations with mating success in apple maggot flies.     

A Jackknife Variance Estimator for Unistage Stratified Samples with Unequal Probabilities

Existing jackknife variance estimators used with sample surveyscan seriously overestimate the true variance under unistagestratified sampling without replacement with unequal probabilities.A novel jackknife variance estimator is proposed which is asnumerically simple as existing jackknife variance estimators.Under certain regularity conditions, the proposed variance estimatoris consistent under stratified sampling without replacementwith unequal probabilities. The high entropy regularity conditionnecessary for consistency is shown to hold for the Rao–Sampforddesign. An empirical study of three unequal probability samplingdesigns supports our findings.     

Seasonal and cultivar-associated variation in oviposition preference of Oriental fruit moth (Lepidoptera: Tortricidae) adults and feeding behavior of neonate larvae in apples

The Oriental fruit moth, Grapholita molesta (Busck) (Lepidoptera: Tortricidae) has become a pest of tree fruits since its introduction to the United States in the early twentieth century. Oriental fruit moth has historically been a major pest problem in peach production, and outbreaks in commercial apple (Malus spp.) orchards in the eastern United States were rare until the late 1990s. Recent outbreaks in Mid-Atlantic apple orchards have lead researchers to investigate host-associated effects on oriental fruit moth biology, behavior, and population dynamics. Studies were designed to assess cultivar level effects in apples on oviposition and larval feeding behavior of oriental fruit moth. In a mixed cultivar apple orchard, total oriental fruit moth oviposition and oviposition site preferences varied between cultivars. These preferences also varied over time, when sampling was repeated at various times of the growing season. Although most adult female oriental fruit moth preferentially oviposited in the calyx and stem areas of apple fruit, noticeable numbers of eggs also were laid on the sides of fruit, contradicting some previous reports. Oriental fruit moth females exhibited a strong ovipositional preference for fruit that were previously damaged by oriental fruit moth or codling moth, Cydia ponmonella (L.). The majority of newly hatched oriental fruit moth larvae were observed to spend <24 h on the surface of apple fruit before entry, and this behavior was observed on several apple cultivars. Neonate larvae exhibited a preference for entering fruit at either the stem or calyx ends, regardless of their initial site of placement. Our findings underscore the importance of adequate spray coverage and accurate timing of insecticide applications targeting oriental fruit moth.     

基于高光谱的苹果果期冠层光谱特征及其果量估测

苹果冠层光谱特征是苹果树遥感生理监测和生产管理的重要依据。对栖霞市苹果果期的冠层反射光谱进行实测,结合数码照相技术探明了苹果果期的反射光谱特性和敏感波段,并通过敏感波段与果树比指标建立回归模型,实现了对苹果冠层果量(果树比)的无损估测。结果表明:苹果树果期冠层光谱曲线总体表现为对蓝光和红光的吸收及对绿光的反射,在近红外750—1300nm之间表现为强烈的反射,且在1650nm和2200nm附近呈现两个反射峰。选择435、670、730、940、1140nm和1480nm等6个波段为苹果果期的敏感波段。利用这些波段分别构建了差值、比值及归一化植被指数,筛选了最佳光谱参数,进而构建了果量(果树比)估测模型,经筛选验证确定苹果果量的最佳估测模型为:y=0.0086[NDVI(940,730)]2-1.0934NDVI(940,730)+0.3209。模型为苹果果期果量的精确估测提供了比较快捷的方法途径。     

Environmental,Spatial and Structural Components in the Composition of Mountain Forest in the Bavarian Alps

A combined systematic and stratified sampling design was conducted in mountain forests of the Bavarian Alps to find the principal dimensions of compositional variation of vegetation and their environmental drivers. In 1,505 plots species composition, forest types and soil profiles were recorded. Data from 14 climate stations were included. As we hypothesized that the tree layer is more influenced by management than the understorey and that the former modifies the habitat of the latter, the two matrices were analysed separately and the species composition of the tree layer was used as a structural predictor variable for the understorey. We applied constrained ordination to reveal the main gradients in floristic composition and variance partitioning to examine the portions of climatic, edaphic, spatial and structural components. Ellenberg indicator values and a generalized linear model were used to test whether a significant spatial gradient exists from east to west, the main spatial extent of the investigation area. Forest types were used as an overlay to assess the underlying environmental factors. It turned out that explained variance of the tree layer was considerably lower than in the understorey. Tree layer composition was more influenced by climatic variables than by soil. In the understorey, edaphic and climatic variables contributed almost equally to explained variance, but the tree layer had an additional explanatory power. No continentality gradient could be detected within the investigation area. Plant communities were well separated along gradients of acidity, moisture, nutrients and climate, which broadly confirms the known gradients for montane and subalpine zonal forests in the region. The study provides a quantitative synthesis of the knowledge on a diverse set of community types, which has so far been subject to disparate and sectorial treatment in the Bavarian Alps.     

Intraspecific variation in fruit size and shape in Corema album (Ericaceae) along a latitudinal gradient: from fruits to populations

Plant trait variation can be the result of environmental variability, developmental instability, and plasticity, although it can also arise from previous selective pressures on fruit traits themselves or directly on their variation. We aimed to quantify fruit size and shape variability at within‐plant, among‐plant, among‐population, and among‐year levels. For 2 years, we measured fruit size and shape along the geographical range of Corema album, aiming to determine whether (1) the population level among‐plant variation is lower than within‐plant and among‐population variation and (2) the ratio of within‐plant to among‐plant variation follows a latitudinal pattern. Levels of fruit variation were in accordance with the reported mean levels for reproductive organs. Most variance concentrated on within‐ and among‐individual levels for size, showing higher values for among‐individual variation in fruit shape. Although fruit size retained important variation among populations, this source of variance was negligible for fruit shape. This difference could arise from contrasting mechanical or developmental constraints. Despite the marked climatic differences along the latitudinal range of the species, latitude did not affect the ratio of within‐ to among‐plant variation. We show that an analysis of the often‐disregarded sources of intraspecific variation can produce unexpected results that deserve further investigation.     

Quantitative Analysis of Relationships between Inflorescence Size, Bearing-axis Size and Fruit-Set --An Apple Tree Case Study

Inflorescence size was investigated in a range of apple treecultivars. Each inflorescence size was quantified by the numberof foliage leaves and flowers. A first analysis was carriedout usingdependence stereogramsand standardized non-parametriccorrelation coefficients, based on Kendall 's     

Indolyl-3-acetic Acid and Ethylene Levels in Ripening Apple Fruits

Indolyl-3-acetic acid (IAA) levels in apple (Malus domesticaBorkh.) fruits were determined fluorimetrically after formationof 2-methylindolo--pyrone in purified extracts. The propertiesof the fluorescent products in apple samples were identicalwith those of authentic IAA. The assays were performed on samplesof cortex with or without peel from the varieties James Grieveand Worcester Pearmain during the last 50—70 d of theirdevelopment on the tree. At the same time the ethylene concentrationin the core cavity of the fruits was measured as a guide tothe progress of ripening. IAA concentration showed a 3—4-foldincrease prior to the rapid rise in ethylene concentration butfell to about its original level as this rise occurred. IAAwas also measured in the seeds of James Grieve apples, whereit rose to a peak concentration and declined before the peakobserved in the fleshy tissue of the fruit. IAA in the seedsincreased markedly after 15 d storage of the fruit harvested136 d after full bloom.     

Evaluation of trap deployment patterns for behavioural control of apple maggot flies (Dipt., Tephritidae)

Abstract: We evaluated three different deployment patterns of sticky red sphere traps, baited with a five-component blend of synthetic attractive fruit odour and placed on perimeter apple trees bordering adjacent habitat (front-row trees), for control of apple maggot flies, Rhagoletis pomonella (Walsh), in small plots of apple trees (about 30 × 30 m) in Massachusetts commercial apple orchards. Degree of fly penetration from front-row to interior apple trees was assessed for R. pomonella of wild origin and for marked adults released in habitats adjacent to front-row trees. Traps placed 10  and 5 m apart on front-row trees or grouped on a single central front-row tree performed as well as grower-applied insecticide sprays in preventing penetration of plots by wild and released flies and in preventing fruit injury . This was equally true for plots whose front-row trees consisted of cultivars comparatively susceptible to apple maggot as for plots whose front-row trees were comprised of comparatively tolerant cultivars. It was also true for each seasonal period during which sampling for treatment performance occurred.     

Scaling of the variance and the quantification of resource monopolization

Behavioral and evolutionary ecologists often attempt to quantifymonopolization of mates or food items using indices such asthe variance, the coefficient of variation (CV), the coefficientof dispersion (CD), or the opportunity for selection (I). Becauseof the tendency for the variance to increase with the mean andbecause of the relationship between variance and the numberof competitors, such indices are of limited value for comparisonsbetween systems that differ in the mean number of resourcesper competitor or in the number of competitors. Here we examinean alternative index of relative monopolization, Q in whichthe observed variance in resource distribution is expressedas a fraction of the maximum possible variance (assuming discreteresource items) for a given resource abundance, both correctedby an estimate of the variance expected under a random distributionof resources. Q = 1 when the variance in resource distributionis maximum, and Q = 0 when resources are randomly distributed.We demonstrate analytically that (1) on average, Q is independentof mean resource abundance for overdispersed systems and, (2)Q can be used to compare systems with different numbers of competitorsas long as the total number of resource units is not largerthan the number that can be monopolized by a single individual.We illustrate the advantages of this method using data fromstudies on feeding competition in fish and on mating competitionin crickets.     

Estimating Genetic Variability with Restriction Endonucleases

The estimation of the amount of sequence variation in samples of homologous DNA segments is considered. The data are assumed to have been obtained by restriction endonuclease digestion of the segments, from which the numbers and frequencies of the cleavage sites in the sample are determined. An estimator, p, of the proportion of sites that are polymorphic in the sample is derived without assuming any particular population genetic model for the evolution of the population. The estimator is very close to the EWENS, SPIELMAN and HARRIS (1981) estimator that was derived with the symmetric WRIGHT-FISHER neutral mode. ENGELS (1981) has also recently proposed an estimator of the same quantity, and he arrived at his estimator without assuming a particular population genetic model. The sampling variance of p and ENGELS' estimator are derived. It is found that the sampling variance of p is lower than the sampling variance of ENGELS' estimator. Also, the sampling variance of theta, an estimate of theta (=4Nu) is obtained for the symmetric WRIGHT-FISHER neutral model with free recombination and with no recombination.     

Response of female oriental fruit moth to volatiles from apple and peach trees at three phenological stages

The attractiveness of peach ( Prunus persica L. Batsch) and apple ( Malus domestica L. Borkh.) (both Rosaceae) tissue to gravid female oriental fruit moth, Grapholita (=  Cydia ) molesta (Busck) (Lepidoptera: Tortricidae), was assessed at three distinct stages throughout the growing season using a dual-choice bioassay. Plant material offered to the female moths consisted of a plant shoot in early spring, before fruit became available. Later, it consisted of a leaf-bearing twig and a fruit, either alone or in combination. The level of attraction of the female moths to the various plant tissues varied substantially over time and according to the plant species. Before fruit became available, female moths were significantly attracted to peach as well as to apple shoots. During the early fruit growth stage, moths were attracted to a leaf-bearing twig originating from a peach tree, but not to that from an apple tree. In peach, it was the vegetative tissue that accounted for the attraction, whereas in apple, it was the reproductive tissue (a developing fruit). During the late fruit growth stage, both peach fruit and apple fruit were highly attractive, whereas a twig with leaves from either an apple or a peach tree was neither attractive nor repellent to the female moths. This changing female olfactory response to volatiles emitted by vegetative tissue and fruits from the two host plant species with progressing season is discussed with respect to the biology and the dispersal of this moth species.