Multi-stage sampling for population estimation

Summary Multi-stage sampling is a convenient technique suited to the desnity estimation of biological populations living in habitats with complicated structures. This paper describes a general method of its application to population estimation in which the preliminary information on the spatial distribution pattern of the population under study can be incorporated as the parameters of the mean crowding-mean relationship. The formulae that are necessary to perform sequential or double sampling plans for its efficient application are derived. The procedure of application of the method is explained with a numerical example. This study was supported by science research fund from the Ministry of Education.     

On fixed precision level sequential sampling

Summary It is proposed that the sequential sampling design ofKuno (1969) for estimating populations with a fixed level of precision be modified by using σ²=am ^b for the variance-mean relationship for most field distributions of organisms. This function yields a straight line “stop line” rather than a curve. An example is calculated and used with field data.     

A new method of sequential sampling to obtain the population estimates with a fixed level of precision

A simple method of sequential sampling is developed which would make it automatically possible to secure, without excess sampling, a predetermined level of precision for a series of population estimates being required. It appears to have wide application to sampling field populations under various situations since it is simply based upon the relationship of variance to mean for which a comprehensive formula deduced for biological populations from the linearity in the regression of mean crowding on mean density could be adopted. Some problems that may arise in practical application of the method are also discussed.     

A new method of sequential sampling to classify populations relative to a critical density

A method of sequential sampling for grading population level in relation to a critical density is proposed. The method is based on the relationship and can be used without restrictions on the distribution patterns. The formulae for simple random sampling as well as for two-stage sampling are given.     

菜蚜二项式抽样设计及其精度分析

１９９０～１９９２年间对杭州市郊区青菜上桃蚜（Ｍｙｚｕｓｐｅｒｓｉｃａｅ）、萝卜蚜（Ｌｉｐａｐｈｉｓｅｒｙｓｉｍｉ）及其混合种群的田间近１００组调查数据,利用每样方（株）虫口不超过数阈值Ｔ（分别为０、１、５、１０、２０、３０、４０）头蚜虫的植株比例（ＰＴ）与种群密度（ｍ,头·株－１）的关系,通过拟合经验公式ｌｎ（ｍ）＝ａ＋ｂｌｎ［－ｌｎ（ＰＴ）］而设计的二项式抽样．通过对三者不同数阈值（Ｔ）的回归决定系数（ｒ２）、种群密度的回归估计方差（Ｖａｒ（ｍ））、抽样精度（以ｄ表示）和实际应用等的比较,结果表明当桃蚜种群处于较高密度即ｍ≥１０时,其理想的Ｔ值为３０;当萝卜蚜种群处于较高密度即ｍ≥５时,其理想的Ｔ值为１０;而它们的混合种群未得到其理想的Ｔ值．数阈值Ｔ为３０和１０可分别用于桃蚜和萝卜蚜的二项式抽样设计．而传统的二项式抽样即０～１抽样由于应用于小白菜上菜蚜的抽样设计时产生很大的误差,不宜采用．     

The statistical and biological implications of sampling units for mountain pine beetle populations in lodgepole pine

Summary Populations of the mountain pine beetle in lodgepole pine were measured using two sample sizes: a single gallery—this is the basic family unit constructed by the parent beetles; and a 6- by 6-inch square area—the bark was removed and the brood counted. Data from the 6- by 6-inch sample were recorded in three ways. Each measurement unit provided different biological information and required different statistical considerations. The single gallery sample provided the most representative data of the entire population, but required additional biological measurement of attack density. The 6- by 6-inch sample brood data taken on an attack density basis provided the most statistically reliable information and encompassed the pertinent biological information. Percent survival, as could be used in elementary life tables, was rather consistent in all measurement units, regardless of point in time of sampling.     

Validating the reference unit method of aboveground phytomass estimation on shrubs and herbs

The validity of the reference unit method for ocularly estimating aboveground phytomass non-destructively was assessed on two shrubby and two herbaceous species using three observers. A calibration equation was developed for each observer-plant species combination using measured dry masses of harvested plants. These equations were then used to estimate phytomass of additional individuals of the same species (validation group), which were also later harvested. Average relative errors of estimated individual plant masses in the validation group ranged from 17.1 to 47.3% among the observers. However, when phytomass estimates of the observers were averaged and the resulting means averaged for the validation groups, the relative error of estimate of the mean plant biomass dropped to between 0.2 and 8.0%. The reference unit method appears to be a valid way to estimate the mean phytomass of a group of plants, as is frequently required in community- or population-level studies.     

Use of the regression of mean crowding on mean density for estimating sample size and the transformation of data for the analysis of variance

An approximate method for estimating the sample size in simple random sampling and a systematic way of transformation of sample data are derived by using the parameters α and β of the regression of mean crowding on mean density in the spatial distribution per quadrat of animal populations (Iwao , 1968). If the values of α and β have been known for the species concerned, the sample size needed to attain a desired precision can be estimated by simply knowing the approximate level of mean density of the population to be sampled. Also, an appropriate variance stabilizing transformation of sample data can be obtained by the method given here without restrictions on the distribution pattern of the frequency counts.     

Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance

In numerous species, individual dispersal is restricted in space so that "continuous" populations evolve under isolation by distance. A method based on individual genotypes assuming a lattice population model was recently developed to estimate the product Dsigma2, where D is the population density and sigma2 is the average squared parent-offspring distance. We evaluated the influence on this method of both mutation rate and mutation model, with a particular reference to microsatellite markers, as well as that of the spatial scale of sampling. Moreover, we developed and tested a nonparametric bootstrap procedure allowing the construction of confidence intervals for the estimation of Dsigma2. These two objectives prompted us to develop a computer simulation algorithm based on the coalescent theory giving individual genotypes for a continuous population under isolation by distance. Our results show that the characteristics of mutational processes at microsatellite loci, namely the allele size homoplasy generated by stepwise mutations, constraints on allele size, and change of slippage rate with repeat number, have little influence on the estimation of Dsigma2. In contrast, a high genetic diversity (approximately 0.7-0.8), as is commonly observed for microsatellite markers, substantially increases the precision of the estimation. However, very high levels of genetic diversity (>0.85) were found to bias the estimation. We also show that statistics taking into account allele size differences give unreliable estimations (i.e., high variance of Dsigma2 estimation) even under a strict stepwise mutation model. Finally, although we show that this method is reasonably robust with respect to the sampling scale, sampling individuals at a local geographical scale gives more precise estimations of Dsigma2.     

Experimental design for optimal parameter estimation of an enzyme kinetic process based on the analysis of the Fisher information matrix

The investigation of enzyme kinetics is increasingly important, especially for finding active substances and understanding intracellular behaviors. Therefore, the determination of an enzyme's kinetic parameters is crucial. For this a systematic experimental design procedure is necessary to avoid wasting time and resources. The parameter estimation error of a Michaelis-Menten enzyme kinetic process is analysed analytically to reduce the search area as well as numerically to specify the optimum for parameter estimation. From analytical analysis of the Fisher information matrix the fact is obtained, that an enzyme feed will not improve the estimation process, but substrate feeding is favorable with small volume flow. Unconstrained and constrained process conditions are considered. If substrate fed-batch process design is used instead of pure batch experiments the improvements of the Cramer-Rao lower bound of the variance of parameter estimation error reduces to 82% for mu(max) and to 60% for K(m) of the batch values in average.     

A Markov chain Monte Carlo strategy for sampling from the joint posterior distribution of pedigrees and population parameters under a Fisher-Wright model with partial selfing

A simple population genetic model is presented for a hermaphrodite annual species, allowing both selfing and outcrossing. Those male gametes (pollen) responsible for outcrossing are assumed to disperse much further than seeds. Under this model, the pedigree of a sample from a single locality is loop-free. A novel Markov chain Monte Carlo strategy is presented for sampling from the joint posterior distribution of the pedigree of such a sample and the parameters of the population genetic model (including the selfing rate) given the genotypes of the sampled individuals at unlinked marker loci. The computational costs of this Markov chain Monte Carlo strategy scale well with the number of individuals in the sample, and the number of marker loci, but increase exponentially with the age (time since colonisation from the source population) of the local population. Consequently, this strategy is particularly suited to situations where the sample has been collected from a population which is the result of a recent colonisation process.     

Calibration of sampling techniques and determination of sample size for the estimation of egg and larval populations of Helicoverpa spp. (Lepidoptera: Noctuidae) on irrigated soybean

Abstract  Informed spray decisions require accurate assessments of the target pest's density. Currently, no advice is provided to farmers on the best method for sampling soybean for insect pests, although spray thresholds for Helicoverpa larvae are provided. This article describes the results of a trial designed to calibrate relative sampling techniques for Helicoverpa larvae; visual inspection of plants in situ in the field, beat cloth, sweep net and D-vac sampling were compared with an absolute measure of population density. The absolute measure was derived from the bagging and removal of whole plants in the field, followed by subsequent examination in the laboratory. Analysis of the distribution of Helicoverpa larvae collected by the different samples was then used to calculate the number of samples required to determine whether the economic threshold had been reached to different levels of certainty and accuracy. Significant relationships were detected between all the relative sampling techniques and the absolute, suggesting that all could be used to estimate field populations. However, due to the high variance and therefore increased sample sizes required, or the length of time taken to collect samples, only beat-cloth sampling appeared to offer a realistic method for farmers in the field. The results also suggest that the current best practice of sampling six locations per crop provides an adequate assessment of the field populations at the currently accepted threshold level of 6 larvae m⁻². However, if the economic spray was reduced, the number of samples required to determine an accurate population estimate would increase dramatically.     

Evaluation of enantioselective gas chromatography for the determination of minute deviations from racemic composition of alpha-amino acids with emphasis on tyrosine: accuracy and precision of the method

Whereas the determination of high enantiomeric fractions (EF) of chiral compounds is very well established, the accurate determination of small deviations from racemic compositions has not yet received much attention despite its relevance to studies dealing with the origin of homochirality, where only small initial enantiomeric bias is expected. Racemic samples of representative alpha-amino acids were derivatized as N-(O,S)-trifluoroacetyl/ethylesters and analyzed by enantioselective gas chromatography (GC) on fused silica capillaries coated with the chiral stationary phases (CSPs) Chirasil-D-Val, Chirasil-L-Val, and Lipodex E with GC/FID and GC/MS detection. The validation (accuracy and precision) of the determination of the enantiomeric fraction EF of the D-enantiomer in racemic or near-racemic compositions for 10 DL-alpha-amino acids obtained from commercial sources has been carried out. Emphasis is given to DL-tyrosine, the enantiomers of which have recently been claimed to show different crystallization properties. Values of EF obtained from GC measurements using CSPs were compared with those from CE using chiral mobile phase additives. While the precision of the GC method is generally better than 0.08% for all DL-alpha-amino acids studied, accuracy (trueness) of determination of amino acids with polar side chains is poorer than expected from the precision as a result of systematic errors. The accuracy determined relied on measurements on two oppositely configurated CSPs.     

Application of a statistical design to the optimization of parameters and culture medium for alpha-amylase production by Aspergillus oryzae CBS 819.72 grown on gruel (wheat grinding by-product)

The production optimization of alpha-amylase (E.C.3.2.1.1) from Aspergillus oryzae CBS 819.72 fungus, using a by-product of wheat grinding (gruel) as sole carbon source, was performed with statistical methodology based on three experimental designs. The optimisation of temperature, agitation and inoculum size was attempted using a Box-Behnken design under the response surface methodology. The screening of nineteen nutrients for their influence on alpha-amylase production was achieved using a Plackett-Burman design. KH(2)PO(4), urea, glycerol, (NH(4))(2)SO(4), CoCl(2), casein hydrolysate, soybean meal hydrolysate, MgSO(4) were selected based on their positive influence on enzyme formation. The optimized nutrients concentration was obtained using a Taguchi experimental design and the analysis of the data predicts a theoretical increase in the alpha-amylase expression of 73.2% (from 40.1 to 151.1 U/ml). These conditions were validated experimentally and revealed an enhanced alpha-amylase yield of 72.7%.     

Evaluation of alkaline pretreatment temperature on a multi-product basis for the co-production of glucose and hemicellulose based films from lignocellulosic biomass

Cotton stalks were subjected to alkaline pretreatment for the co-production of glucose and hemicellulose based films with a multi-product approach. Three pretreatment temperatures (25, 60 and 90 °C) were evaluated for their effects both on the glucose yield and on the properties of hemicellulose based films. Compared to untreated cotton stalks, the glucose yields were enhanced 3.9, 4.1 and 4.2 times for pretreatments conducted at 25, 60 and 90 °C, respectively. The pretreatment temperature of 90 °C was detrimental in terms of film formation. Tensile energy to break values of the films obtained after pretreatments conducted at 25, 60 and 90 °C were 1.1, 0.8, and 0.4 MJ/m³, respectively. The hemicellulosic part of the process, which considers the production of hemicellulose based films, should govern the pretreatment temperature since it was more responsive to the changes in the pretreatment temperature compared to the cellulosic part that accounts for glucose production.     

Gene flow and population structure of the endemic Azorean bat (<Emphasis Type=Italic>Nyctalus azoreum</Emphasis>) based on microsatellites: implications for conservation

The Azorean bat (Nyctalus azoreum) is endemic to the Azores archipelago and is listed as endangered due to its reduced and fragmented distribution range. We assessed genetic diversity at eight microsatellite loci in 280 individuals from 14 locations throughout six islands. Overall, we found that the Azorean bat populations are not genetically impoverished. Indeed, the number of alleles per locus ranged from 8 to 10 and the observed heterozygosity ranged from 0.77 in Terceira to 0.83 in Faial. The highest genetic diversity and level of private alleles was observed in S. Miguel, the largest island, and the closest to the mainland. Private alleles occurred at all islands except in Graciosa. Global and pairwise F _ST among islands were all statistically significant, suggesting restricted gene flow. These results, together with those of factorial correspondence analysis, Bayesian clustering method, and individual assignment tests, corroborate the conclusions of a previous mtDNA based study, providing strong support for the existence of two major subpopulations: one includes all islands of the Central Group and the other corresponds to S. Miguel. Gene flow between them is very limited, suggesting that management plans should avoid translocations between these subpopulations. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.