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.     

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.     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model, p=1−(1+m/k)^−k, and the empirical model, p=1−exp(−am^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

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.     

Random median sampling to enhance the precision of population estimates

We describe the characteristics of a sampling procedure called random median sampling that was proposed to enhance the precision of population estimates. In performing random median sampling, we first select a sampling item at random from the sampling area. We roughly compare the abundance of individuals in the selected item with that of the adjacent two items in order to identify the item that has median abundance, i.e., the item that has the second largest abundance among the three items. We count the number of individuals of the item having the median abundance. This procedure is repeated n times in the sampling area (i = 1, 2, ..., n). Let m _i be the ith median abundance. The estimates of the mean abundance per sampling item and the variance of estimates are given by Σm _i /n and Σ(m _i –Σm _i /n)²/n(n – 1), respectively. This method is a local application of the median ranked set sampling that was proposed by Muttlak (J Appl Stat Sci 6:245–255, 1997). Random median sampling is effective when the correlation coefficient between adjacent items is small. If the correlation coefficient is close to zero, random median sampling reduces the variance of estimates to 45 or 32% of that in simple random sampling when the distribution follows a normal distribution or a Laplace distribution, respectively. The sample size required to achieve a given precision of estimate decreases accordingly. The effectiveness of random median sampling, however, is small if the correlation coefficient is large. The condition in which random median sampling is superior to simple random sampling is also discussed.     

Spatial distribution of greenhouse whitefly (Trialeurodes vaporariorum Westwood) and a suggested sampling plan for estimating its density in greenhouses

Spatial distribution of the greenhouse whitefly population infesting tomato plants in greenhouses was analyzed. A leaf of tomato consists of 7 leaflets, each being used as a basic sampling unit. Distribution patterns between plants, between leaves and between leaflets were analyzed by the analysis of variance and the method. It was found that populations of all the developmental stages were composed of contagiously distributed colonies or individuals between leaves and between leaflets. On the other hand, they showed random distribution of colonies between plants. On leaflets, egg populations were distributed as colonies, each consisting of several eggs, while in larval and adult populations, individuals were distributed rather independently of each other. A three-stage sampling plan was developed to estimate the density at the assigned level of precision.     

Identifying population units that comply with capture-recapture assumptions in an open community of alpine grasshoppers

Population units which are homogeneous with respect to capture-recapture assumptions are identified by applying 11 contingency table tests to grasshopper data according to various site, species, growth stage and sex groupings. The results of 2337 contingency table analyses have permitted a definition of the biological, spatial and temporal characteristics of those groupings which were found to be homogeneous. The same analyses suggest that dispersal rates and dispersal patterns pose the greatest single difficulty in defining population homogeneity within an open community. The effects of failures in capture-recapture assumptions are discussed in relation toJolly's 1965 stochastic model. A more detailed presentation of the study is available from the author on request.     

The relationship between percentage of singletons and sampling effort: A new approach to reduce the bias of richness estimates

Estimate the richness of a community with accuracy despite differences in sampling effort is a key aspect to monitoring high diverse ecosystems. We compiled a worldwide multitaxa database, comprising 185 communities, in order to study the relationship between the percentage of species represented by one individual (singletons) and the intensity of sampling (number of individuals divided by the number of species sampled). The database was used to empirically adjust a correction factor to improve the performance of non-parametrical estimators under conditions of low sampling effort. The correction factor was tested on seven estimators (Chao1, Chao2, Jack1, Jack2, ACE, ICE and Bootstrap). The correction factor was able to reduce the bias of all estimators tested under conditions of undersampling, while converging to the original uncorrected values at higher intensities. Our findings led us to recommend the threshold of 20 individuals/species, or less than 21% of singletons, as a minimum sampling effort to produce reliable richness estimates of high diverse ecosystems using corrected non-parametric estimators. This threshold rise for 50 individuals/species if non-corrected estimators are used which implies in an economy of 60% of sampling effort if the correction factor is used.     

A stochastic model for the mutation-selection balance in an infinite asexual population with a genome of fixed size

A stochastic model is presented which describes the evolution of a genome of a haploid species in an infinite population. The genome is a finite set of elements. The elements are divided into different classes according to their effect on the fitness of the organism. Repeated mutations of the genome elements are permitted, in particular positive mutations are introduced. The distribution of the deleterious elements in the genome with respect to the impact on the fitness is given after the replication step. The steady state is fully described including the distribution and the fitness.     

A comparison of three sampling techniques to estimate the population size of caterpillars in trees

Three sampling techniques commonly used to estimate the population size of caterpillars and sawfly larvae in trees (branch samples, frass production, water basins), were compared with respect to sampling error and economic costs. At the level of tree populations (e.g. forests), on an arbitrary date, the mean caterpillar intensity per tree (expressed in numbers of larvae or their biomass per 100 shoots) was predicted from the mean frass production per tree (expressed in mg frass per m² forest floor per day). At the level of the single tree, the frass production on an arbitrary date was related to the population intensity, but, due to the large sampling error, did not provide an accurate prediction. Summing the frass produced over the whole season reduced this error and predicted the seasonal abundance of larvae in single trees, estimated as their maximum intensity or their density (numbers of larvae or their biomass per m² forest floor). The maximum population intensity was not related to the population density. The sampling techniques suffer from large errors unrelated to larval abundance. The main sources of error (i.e. weather or predation of the larvae) usually cause an underestimation of population size. Labour, the main cause of high costs, was low in the basin technique and high in the frass production technique. Possible ways of reducing errors and applications of the three techniques are discussed.     

The use of simultaneous sampling bottle and vertical net collections to describe the dynamics of a zooplankton population

Simultaneous collections of zooplankton were made at four stations in the Plover Clove Reservoir using Friedinger sampling bottles and vertical Nakai plankton net hauls. Comparison of the results obtained revealed certain obvious numerical and spatial anomalies, and it is suggested that these result from inherent characteristics of the two types of apparatus together with behavioural responses and physical attributes of the individual zooplankton species. Statistical correlation between these two methods was generally good in terms of the seasonal patterns of distribution of the population, but in terms of depth distribution and the relative abundance of the individual species of the population few significant correlations resulted. It is therefore suggested that unless merely seasonal trends are required, it is advisable to use more than one sampling apparatus to obtain valid data concerning the overall dynamics of such a zooplankton population.Department of Botany, University of Hong Kong     

A simulation study of population interaction between the greenhouse whitefly,Trialeurodes vaporariorum Westwood (Homoptera: Aleyrodidae) and the parasitoidEncarsia formosa Gahan (Hymenoptera: Aphelinidae) II. Simulation analysis of population dynamics and strategy of biological control

Simulation studies were performed to analyze factors affecting the population dynamics of the system with the greenhouse whitefly (Trialeurodes vaporariorumWestwood ) and the parasitoid Encarsia formosaGahan and to develop strategies for the introduction of E. formosa. The reduction of parasitization efficiency with an increase in parasitoid density promotes the stability of the system, which coincides with the prediction from current theory. The stability of the system is also shown to be promoted by the effect of host feeding. The population levels of the system are remarkably suppressed with an increase in searching efficiency and a decrease in host oviposition. The control effect of the parasitoids is enhanced when the number of parasitoids is divided among many introductions. An optimal time, an optimal density ratio of parasitoids to hosts and optimal densities of hosts and parasitoids exist in the introduction programme of parasitoids.     

A new triple-resonance experiment for the sequential assignment of backbone resonances in proteins

Summary A new protocol is described for obtaining intraresidual and sequential correlations between carbonyl carbons and amide ¹H and ¹⁵N resonances of amino acids. Frequency labeling of ¹³CO spins occurs during a period required for the ¹³C-¹⁵N polarization transfer, leading to an optimized transfer efficiency. In a four-dimensional version of the experiment, ¹³C chemical shifts are used to improve the dispersion of signals. The resonance frequencies of all backbone nuclei can be detected in a 3D variant in which cross peaks are split along two frequency axes. This pulse scheme is the equivalent of a five-dimensional experiment. The novel pulse sequences are applied to flavodoxin from Desulfovibrio vulgaris.