Modelling and analysis of recruitment distributions

Recruitment data for 18 marine fish stocks are smoothed using 10 parametric families of probability distributions. Comparative fit of the 10 families is assessed by means of the maximized log-likelihood. Results indicate that the gamma distribution provides an overall good fit in the right-hand tail of the data, but that some adjustment to the gamma distribution is called for in the left-hand tail. Weight functions and weighted distributions are suggested as one means of achieving the needed adjustment.     

Flow Dynamics in Eccentrically Rotating Flasks Used for Dispersant Effectiveness Testing

The evaluation of dispersant effectiveness used for oil spills is commonly done using tests conducted in laboratory flasks. We used a Hot Wire Anemometer (HWA) to characterize mixing dynamics in the Swirling Flask (SF) and the Baffled Flask (BF), the latter is being considered by the EPA to replace the prior to test dispersant effectiveness in the laboratory. Five rotation speeds of the orbital shaker carrying the flasks were considered, Ω = 50, 100, 150, 175 and 200 rpm. The radial and azimuthal water speeds were measured for each Ω. It was found that the flow in the SF is, in general, two-dimensional changing from horizontal at low Ω to axi-symmetric at high Ω. The flow in the BF appeared to be three-dimensional at all rotation speeds. This indicates that the BF is more suitable for representing the (inherently) 3-D flow at sea. In the SF, the speeds and energy dissipation rates ɛ increased gradually as the rotation speed increased. Those in the BF increased sharply at rotation speeds greater than 150 rpm. At 200 rpm, the Kolmogorov scale (i.e., size of smallest eddies) was about 250 and 50 μm in the SF and BF, respectively. Noting that the observed droplet sizes of dispersed oils range from 50 to 400 μm (hence most of it is less than 250 μm), one concludes that the mixing in the SF (even at 200 rpm) is not representative of the vigorous mixing occurring at sea.     

Probability distributions and statistical inference for axial data

Observations on axes which lack information on the direction of propagation are referred to as axial data. Such data are often encountered in enviromental sciences, e.g. observations on propagations of cracks or on faults in mining walls. Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced. Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle. In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution. Certain properties of this distribution are established. Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing. Finally we illustrate our results by several real life axial data sets. Received: September 2004/ Revised: December 2004     

Tests for a biased sex ratio when the data are clustered

In behavioral ecology the overall sex ratio in a population of birds is often tested to see if it differs from a 50/50 ratio. In recent publications the binomial test or the ² test are carried out although the sexes of chicks within the same nest may not be independent. The lack of independence occurs since female birds can adjust the sex ratio in an adaptive way as demonstrated in recent studies. In order to take dependence into consideration the Wilcoxon signed rank test based on the within-brood differences between the proportions of sons and daughters was performed in a study investigating great tit hatchling sex ratios. We compare this test with a test based on an optimally weighted estimator recently proposed for medical studies with clustered binary data. According to our simulation results, this novel test is more powerful than the Wilcoxon signed rank test and should be used for the analysis of avian sex ratios. The methods are illustrated with real data from the great reed warbler.     

Multistate models for monitoring individual trees in permanent observation plots

This interdisciplinary research on forest ecosystems begins with some characteristics of ecosystems which are the basis for the derivation of statistical models for the development and vitality of trees. Several ecological problems which could be solved by longitudinal studies are mentioned. Statistical methods for the evaluation of the crowns of spruce trees (Picea abies Karst) in three permanent observation plots in Switzerland are described. In particular, the time-dependent proportional odds model and a transitional model are used. Through application of these multistate models the data give information on the dependence of an ordered categorical response variable on covariates characterizing the ecosystem. The response variable is observed through infrared aerial photographs. This monitoring system gives insight into the dynamic behaviour of the forest ecosystem. The need for more eco-systematically motivated statistical research using longitudinal studies is identified.     

拟面积多波长数据线性双组合解析萘,1—萘酚和2—萘酚同步荧光光谱的研究

本文研究了Δλ（λｅｍ－λｅｘ）为１３０ｎｍ和ＰＨ１２．０条件下，萘、１－萘粉和２－萘酚混合物的同步荧光光谱，获三者同步荧光峰信息，且萘被完全分辨，另外，提出用拟面积多波长线性双组合计算解析重叠的１－萘酚和２－萘酚同步荧光光谱，解析结果的精密度、组份间浓度比范围均较多波长线性回归、双峰增配平和一阶导数解析混合物同步荧光光谱结果为优。     

Linear regression with Type I interval- and left-censored response data

Laboratory analyses in a variety of contexts may result in left- and interval-censored measurements. We develop and evaluate a maximum likelihood approach to linear regression analysis in this setting and compare this approach to commonly used simple substitution methods. We explore via simulation the impact on bias and power of censoring fraction and sample size in a range of settings. The maximum likelihood approach represents only a moderate increase in power, but we show that the bias in substitution estimates may be substantial.     

Soil Lead and Children’s Blood Lead Levels in Syracuse, NY, USA

A geo-referenced data set of 12 228 first-time blood lead screening values for Syracuse, NY, children was established for the 4-year period 1992–1996. Soil lead values were measured in a 600 m by 600 m tessellation grid covering the city. The two data sets were merged for evaluation of relationships between them. Strong seasonal variation in blood lead levels suggests the importance of contaminated soils as an exposure source. When the data were aggregated at a large geographic scale (3 km²), a logarithmic model showed an R² of > 0.65 for the regression of geometric mean blood lead on median soil lead values. Results showed a striking similarity to those obtained by Mielke et al. (1999) for a study in New Orleans, LA, USA.     

Bayesian analysis under ordered functions of parameters

Ordered parameter problems arise in a wide variety of real world situations and are dealt with extensively in the literature. Traditional frequentist methods for dealing with these problems are rather complicated theoretically, especially when sample sizes are small. Bayesian methods are not widely used because high dimensional numerical integration is often required. However, Markov chain Monte Carlo methods provide alternatives to such numerical integration and also deal with ordered parameter problems in a straightforward manner. Little is known about the situation where functions of parameters are ordered. Such problems may seem to be of little practical concern initially, but one can readily see their importance in situations where ordering is placed on the means and variances of several normal or Gamma populations. For the Gamma distribution we will present real examples where we will analyze monthly precipitation data from San Francisco, California and Oakland Mills, Iowa. For the San Francisco data we will simultaneously order both monthly precipitation means and variances. For the Iowa data we will place ordering on seasonal average while still estimating monthly means. Our results show that we would obtain sharper, more accurate inference when order restrictions are employed.     

河流营养物参照状态的建立方法研究进展

建立营养物参照状态是河流水污染控制的关键问题之一。系统论述了参照状态的各种内涵,重点分析了国外建立河流营养物参照状态的各种方法及优缺点,并分析了其在中国的适用性。最后,提出了河流营养物参照状态的进一步研究的重点。参照状态根据允许人类活动影响的程度可有多种含义:最小干扰状态、历史状态、最少干扰状态和最佳可达成状态。其中,最少干扰状态和最佳可达成状态在现实管理中具有一定程度的可操作性。参照河流百分比法是建立营养物参照状态的首选方法,但中国水环境污染形势严峻,参照点变得越来越少。当参照点不存在时,一般河流百分比法是参照河流百分比法的替代方法,然而一般河流百分比法和参照河流百分比法的匹配性关系并不完全保持一致。由于栖息地退化等因素对生物完整性的影响程度可能比营养物浓度更大,生物响应法在实际应用中是非常困难的。流域模型法虽然有众多优点,但是数据要求较高,并且常用流域模型的机理与中国有较大差距,在中国应用的结果具有较大的不确定性。综合考虑中国水环境污染现状和数据要求,以多元线性回归模型为代表的简易模型方法在中国应有最大的适用性。然而,环境因素与营养物质间的关系往往都是非线性的,今后应着重研究建立河流营养物参照状态的多元非线性回归模型方法。此外,还应加强季风河流营养物参照状态的季节性差异与年际差异研究,并在全国层面上根据自然因素划分适当规模的生态区,分区确定各生态区的河流营养物参照状态。