Putting background information about relative risks into conjugate prior distributions

In Bayesian and empirical Bayes analyses of epidemiologic data, the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector. This article describes problems in translating background information about relative risks into conjugate priors and a solution. Traditionally, conjugate priors have been specified through flattening constants, an approach that leads to conflicts with the true prior covariance structure for the log relative risks. One can, however, derive a conjugate prior consistent with that structure by using a data-augmentation approximation to the true log relative-risk prior, although a rescaling step is needed to ensure the accuracy of the approximation. These points are illustrated with a logistic regression analysis of neonatal-death risk.     

On small-sample confidence intervals for parameters in discrete distributions

The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio.     

Modeling the vertical foliage distribution of an individual <Emphasis Type="Italic">Castanopsis cuspidata</Emphasis> (Thunb.) Schottky,a dominant broad-leaved tree in Japanese warm-temperate forest

The vertical foliage distribution of Castanopsis cuspidata (Thunb.) Schottky was examined in trees of various sizes to clarify its variation in relation to tree size and the light environment in a stand. As indices of these parameters, we analyzed crown social position (CSP: percent of stand height) and specific leaf area (SLA). The vertical foliage distribution of trees was expressed by a Weibull function. The variation in the vertical foliage distribution of C. cuspidata could be categorized into three types using crown social position and light environment. In the first type, leaves were concentrated to the top 20% of the tree; such trees are canopy trees that can receive full sunlight. The second type had a large relative crown depth and an asymmetric distribution with the maximum foliage located near the top of the tree; such trees are suppressed trees whose crowns do not receive sufficient light. The third type had a large relative crown depth and a symmetric distribution; such trees occur in high light environments, although their crowns are in the understory layer. The differences in the vertical foliage distribution are related to the strategies used to capture light. Multiple regression analysis showed that CSP and SLA at the top layer of the tree explained successive changes in the vertical foliage distribution. These results will contribute to scaling-up the vertical foliage distribution to the community level in pure stands of C. cuspidata using an individual-based model.     

Resource pulses,species interactions,and diversity maintenance in arid and semi-arid environments

Arid environments are characterized by limited and variable rainfall that supplies resources in pulses. Resource pulsing is a special form of environmental variation, and the general theory of coexistence in variable environments suggests specific mechanisms by which rainfall variability might contribute to the maintenance of high species diversity in arid ecosystems. In this review, we discuss physiological, morphological, and life-history traits that facilitate plant survival and growth in strongly water-limited variable environments, outlining how species differences in these traits may promote diversity. Our analysis emphasizes that the variability of pulsed environments does not reduce the importance of species interactions in structuring communities, but instead provides axes of ecological differentiation between species that facilitate their coexistence. Pulses of rainfall also influence higher trophic levels and entire food webs. Better understanding of how rainfall affects the diversity, species composition, and dynamics of arid environments can contribute to solving environmental problems stemming from land use and global climate change.     

Information gain for genetic parameter estimation with incorporation of marker data

Genetic marker data has been increasingly incorporated into segregation analysis, as combined segregation and linkage analysis has been performed more frequently. In this article, we study the extent of information gains with incorporation of marker data in segregation analysis, a topic that has not been investigated rigorously. Specifically, the current study is to investigate the influence of marker data on genetic model parameter estimation. A variance matrix criterion (as the inverse of the Fisher information matrix) and a relative entropy criterion (a measure of flatness of expected log-likelihood surface) are used to quantify the information gains. Our results indicate that substantial information gain can be achieved with the incorporation of marker data. The amount of variance reduction increases as the heterozygosity of the linked marker increases and as the trait gets closer to the linked marker(s). Incorporation of marker data in larger pedigrees also yields greater information gains based on both criteria. The effect of pedigree structure is also studied.     

Comparative Molecular Evolution of Primary (<Emphasis Type="BoldItalic">Buchnera</Emphasis>) and Secondary Symbionts of Aphids Based on Two Protein-Coding Genes

A+T content, phylogenetic relationships, codon usage, evolutionary rates, and ratio of synonymous versus non-synonymous substitutions have been studied in partial sequences of the atpD and aroQ/pheA genes of primary (Buchnera) and secondary symbionts of aphids and a set of selected non-symbiotic bacteria, belonging to the five subdivisions of the Proteobacteria. Compared to the homologous genes of the last group, both genes belonging to Buchnera behave in a similar way, showing a higher A+T content, forming a monophyletic group, a loss in codon bias, especially in third base position, an evolutionary acceleration and an increase in the number of non-synonymous substitutions, confirming previous results reported elsewhere for other genes. When available, these properties have been partly observed with the secondary symbionts, but with values that are intermediate between Buchnera and free living Proteobacteria. They show high A+T content, but not as high as Buchnera, a non-solved phylogenetic position between Buchnera, and the other γ-Proteobacteria, a loss in codon bias, again not as high as in Buchnera and a significant evolutionary acceleration in the case of the three atpD genes, but not when considering aroQ/pheA genes. These results give support to the hypothesis that they are symbionts at different stages of the symbiotic accommodation to the host.     

Evaluation of 17alpha-E-(trifluoromethylphenyl)vinyl estradiols as novel estrogen receptor ligands

As part of our program to develop novel ligands for the estrogen receptor, we synthesized the series of isomeric 17alpha-(trifluoromethyl)phenylvinyl estradiols using our solid-phase organic synthesis methodology. The compounds were evaluated for their relative binding affinity (RBA) using the ERalpha-LBD and in vivo potency using the immature rat uterotrophic growth assay. The ortho-isomer had the highest RBA values, 48-223, and the highest estrogenicity in vivo. The other isomers had significantly lower affinities and were weaker agonists in the uterotrophic assay. The results suggest that introduction of substituents at the 17alpha-position of estradiol is tolerated by the ER-LBD and permit agonist responses in the intact animal, however, the effect is sensitive to the position of groups on the phenyl ring. This study demonstrates that the 17alpha-position of estradiol is a reasonable site for modification but the position and physicochemical properties of such modifications may significantly affect the affinity and efficacy of the ligand.     

Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution

This study addresses some enduring issues of ontogenetic and evolutionary integration in the form of the hominid cranium. Our sample consists of 38 crania: 20 modern adult Homo sapiens, 14 sub-adult H. sapiens, and four archaic Homo. All specimens were CT-scanned except for two infant H. sapiens, who were imaged by MR instead. For each specimen 84 landmarks and semi-landmarks were located on the midsagittal plane and converted to Procrustes shape coordinates. Integration was quantified by the method of singular warps, a new geometric-statistical approach to visualizing correlations among regions. The two classic patterns of integration, evolutionary and ontogenetic, were jointly explored by comparing analyses of overlapping subsamples that span ranges of different hypothetical factors. Evolutionary integration is expressed in the subsample of 24 adult Homo, and ontogenetic integration in the subsample of 34 H. sapiens. In this data set, vault, cranial base, and face show striking and localized patterns of covariation over ontogeny, similar but not identical to the patterns seen over evolution. The principal differences between ontogeny and phylogeny pertain to the cranial base. There is also a component of cranial length to height ratio not reducible to either process. Our methodology allows a separation of these independent processes (and their impact on cranial shape) that conventional methods have not found.     

Insights on bias and information in group-level studies

Ecological and aggregate data studies are examples of group-level studies. Even though the link between the predictors and outcomes is not preserved in these studies, inference about individual-level exposure effects is often a goal. The disconnection between the level of inference and the level of analysis expands the array of potential biases that can invalidate the inference from group-level studies. While several sources of bias, specifically due to measurement error and confounding, may be more complex in group-level studies, two sources of bias, cross-level and model specification bias, are a direct consequence of the disconnection. With the goal of aligning inference from individual versus group-level studies, I discuss the interplay between exposure and study design. I specify the additional assumptions necessary for valid inference, specifically that the between- and within-group exposure effects are equal. Then cross-level inference is possible. However, all the information in the group-level analysis comes from between-group comparisons. Models where the group-level analysis provides even a small percentage of information about the within-group exposure effect are most susceptible to model specification bias. Model specification bias can be even more serious when the group-level model isn't derived from an individual-level model.