Confidence Intervals for the Risk Ratio in Cohort Studies under Inverse Sampling

Three simple interval estimates for the risk ratio in inverse sampling are considered. The first two interval estimates are derived on the basis of Fieller's Theorem and the delta method with the logarithmic transformation, respectively. The third interval estimate is derived on the basis of an F-test statistic proposed by BENNETT (1981) for testing equal probabilities of a disease between two comparison groups when the disease is rare. To evaluate the performance of these three methods, a Monte Carlo simulation is used to compare the actual coverage probability with the nominal confidence level for each method and to estimate the expected length of the corresponding confidence interval in a variety of situations. On the basis of the results found in the simulation, we have concluded that the method with the logarithmic transformation is either equivalent to or better than the other two methods for all situations considered here.     

Antagonistic and synergistic interactions between aluminum and manganese on growth of Vigna unguiculata at low ionic strength

Concentrations of soluble aluminum (Al) and manganese (Mn) frequently reach phytotoxic levels in acid soils. While dose response relationships for these metals are well documented, the effects of combined exposure have received less attention. We have examined the effect of combinations of Al and Mn on growth and metal accumulation in Vigna unguiculata (L.) Walp. grown in solution culture under conditions of low ionic strength (conductivities typically < 100 µS cm⁻¹). The nature of interaction between these metals varied with the specific physiological response, the part of the plant investigated, and the relative amount of stress imposed. Analysis of growth data provided evidence for amelioration of metal toxicity (antagonistic effects), although this effect was dose dependent. Analysis of metal content data provided evidence for antagonistic and synergistic (exacerbation of toxicity) effects, again depending on dose. Analysis of foliar symptoms also provided evidence for antagonisms and synergisms, with the nature of the response dependent on the specific physiological response and specific plant part investigated. In contrast with previous reports, evidence for antagonistic, synergistic, and multiplicative effects on growth, metal uptake, and expression of foliar symptoms have been obtained under physiologically and environmentally relevant conditions. These results suggest a more detailed analysis of the potential for interactions between metals in the environment is required.     

Bayesian Estimation of the Distribution Function of the Poisson Model

This paper presents the Bayes estimators of the Poisson distribution function based on complete and truncated data under a natural conjugate prior. Laplace transform of the incomplete gamma function and the Gauss hypergeometric function have been employed in order to overcome the intractability of the integrals. Numerical examples from biosciences are given to illustrate the results. A Monte Carlo study has been carried out to compare Bayes estimators under complete data with the corresponding maximum liklihood estimators.     

Statistical treatment of VAM infection data

Summary The amount of vesicular-arbuscular mycorrhizal (VAM) infection, when expressed as length of infected roots, is commonly quite variable among replicate pots within an experimental treatment. In this paper we show that frequency distributions of VAM infection parameters are often non-normal in form and may follow the negative binomial, a distribution commonly associated with aggregated organisms in nature. The lack of normality means that statistical procedures should either be non-parametric or should include data transformations.     

Best Linear Unbiased Prediction (BLUP) for regional yield trials: a comparison to additive main effects and multiplicative interaction (AMMI) analysis

Multilocation trials are often used to analyse the adaptability of genotypes in different environments and to find for each environment the genotype that is best adapted; i.e. that is highest yielding in that environment. For this purpose, it is of interest to obtain a reliable estimate of the mean yield of a cultivar in a given environment. This article compares two different statistical estimation procedures for this task: the Additive Main Effects and Multiplicative Interaction (AMMI) analysis and Best Linear Unbiased Prediction (BLUP). A modification of a cross validation procedure commonly used with AMMI is suggested for trials that are laid out as a randomized complete block design. The use of these procedure is exemplified using five faba bean datasets from German registration trails. BLUP was found to outperform AMMI in four of five faba bean datasets.     

Distribution of Polymorphus minutus among its intermediate hosts

Hirsch R. P. 1979. Distribution of Polymorphus minutus among its intermediate hosts. International journal for Parasitology10: 243–248. In 1971, Crofton investigated patterns of distribution of Polymorphus minutus in the intermediate host, Gammarus pulex. Among his conclusions were: (1) P. minutus populations occur in patterns similar to negative binomial distributions, and (2) parasite-induced host mortality results in patterns similar to truncated (high end) negative binomial distributions. Those conclusions, however, were not tested by statistical analyses. To test Crofton's observations, Chi-square goodness of fit tests were applied to data used by Crofton and an additional two stations sampled by Hynes & Nicholas in 1963. Analyses were expanded to include five theoretical distributions, four patterns of host mortality and various rates of host mortality. Truncated forms of negative binomial, positive binomial and Poisson distributions were also investigated where nontruncated distributions failed to fit observed distributions. It was found that negative binomial distributions most frequently describe patterns of P. minutus distribution with the exception of one population described by Poisson and another by positive binomial distributions. Crofton's assumption that truncated distributions result from parasite-induced host mortality seems unlikely in light of those analyses.     

Energy–water and seasonal variations in climate underlie the spatial distribution patterns of gymnosperm species richness in China

Studying the pattern of species richness is crucial in understanding the diversity and distribution of organisms in the earth. Climate and human influences are the major driving factors that directly influence the large‐scale distributions of plant species, including gymnosperms. Understanding how gymnosperms respond to climate, topography, and human‐induced changes is useful in predicting the impacts of global change. Here, we attempt to evaluate how climatic and human‐induced processes could affect the spatial richness patterns of gymnosperms in China. Initially, we divided a map of the country into grid cells of 50 × 50 km² spatial resolution and plotted the geographical coordinate distribution occurrence of 236 native gymnosperm taxa. The gymnosperm taxa were separated into three response variables: (a) all species, (b) endemic species, and (c) nonendemic species, based on their distribution. The species richness patterns of these response variables to four predictor sets were also evaluated: (a) energy–water, (b) climatic seasonality, (c) habitat heterogeneity, and (d) human influences. We performed generalized linear models (GLMs) and variation partitioning analyses to determine the effect of predictors on spatial richness patterns. The results showed that the distribution pattern of species richness was highest in the southwestern mountainous area and Taiwan in China. We found a significant relationship between the predictor variable set and species richness pattern. Further, our findings provide evidence that climatic seasonality is the most important factor in explaining distinct fractions of variations in the species richness patterns of all studied response variables. Moreover, it was found that energy–water was the best predictor set to determine the richness pattern of all species and endemic species, while habitat heterogeneity has a better influence on nonendemic species. Therefore, we conclude that with the current climate fluctuations as a result of climate change and increasing human activities, gymnosperms might face a high risk of extinction.     

Estimating density of a forest-dwelling bat: a predictive model for Rafinesque’s big-eared bat

Data on species distribution and abundance are the foundation of population ecology. However, due to difficulties in surveying bats, abundance estimates for tree-roosting microchiropterans are non-existent. Therefore, our objective was to develop methods for estimating colony abundance and density, taking as our model Rafinesque’s big-eared bat Corynorhinus rafinesquii, a species of conservation concern found in cypress-gum swamps of the southeastern United States. We searched 123 transects at eight study sites in the Coastal Plain of Georgia, USA to locate and characterize diurnal summer roosts of C. rafinesquii. We modeled the relationship between the number of bat colonies and landscape-scale habitat variables with zero-inflated negative binomial regression and used Akaike’s information criterion to select the most parsimonious models. We generated a predictive density map to identify areas of high colony density and to estimate overall abundance. Colony density was predicted by the duration of wetland flooding, wetland width, and study site. Application of the regression model to a GIS indicated there were 3,734 colonies containing 6,910 adult bats on the eight study sites. Predicted density ranged from 0.07 colonies/ha and 0.07 adult bats/ha in saturated wetlands to 0.47 colonies/ha and 1.18 adult bats/ha in semi-permanently flooded wetlands. This study is the first to estimate density and abundance of forest-dwelling microchiropterans over a large area. Such data can serve as a baseline for future work on population trends in C. rafinesquii. In addition, our approach could be replicated for other bat species with moderately cryptic roosts.     

Large scale maximum average power multiple inference on time-course count data with application to RNA-seq analysis

Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.