Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.     

Introducing the Multivariate Dale Model in Population‐Based Genetic Association Studies

Until recently, the most common parametric approaches to study the combined effects of several genetic polymorphisms located within a gene or in a small genomic region are, at the genotype level, logistic regressions and at the haplotype level, haplotype analyses. An alternative modeling approach, based on the case/control principle, is to regard exposures (e.g., genetic data such as derived from Single Nucleotide Polymorphisms – SNPs) as random and disease status as fixed and to use a marginal multivariate model that accounts for inter‐relationships between exposures. One such model is the multivariate Dale model. This model is based on multiple logistic regressions. That is why the model, applied in a case/control setting, leads to straightforward interpretations that are similar to those drawn in a classical logistic modeling framework. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling intraspecific resting egg shape variation in a freshwater fairy shrimp Tanymastix stagnalis (L., 1758) (Crustacea, Branchiopoda)

The shape of the resting eggs of a large branchiopod crustacean, the Anostraca Tanymastix stagnalis , is represented very accurately by analytical expressions. The occurrence of atypical shape of some T. stagnalis eggs may be viewed as a simple change of the analytical expression describing the usual egg shape. Their unusual shape may be explained by a higher embryo volume within an envelope of a given size. Biological implications are briefly discussed and hypothesized in an evolutionary point of view.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 90 , 55–60.     

Gramicidin A-phospholipid model systems

Gramicidin A forms ion-conducting channels which can traverse the hydrocarbon core of lipid bilayer membranes. The structures formed by gramicidin A are among the best characterized of all membrane-bound polypeptides or proteins. In this review a brief summary is given of the occurrence, conformation, and synthesis of gramicidin A, and of its use as a model for ion transport and the interaction of proteins and lipids in biological membranes.     

A physical model of sodium channel gating

Most current models of membrane ion channel gating are abstract compartmental models consisting of many undefined states connected by rate constants arbitrarily assigned to fit the known kinetics. In this paper is described a model with states that are defined in terms of physically plausible real systems which is capable of describing accurately most of the static and dynamic properties measured for the sodium channel of the squid axon. The model has two components. The Q-system consists of charges and dipoles that can move in response to an electric field applied across the membrane. It would contain and may compose the gating charge that is known to transfer prior to channel opening. The N-system consists of a charged group or dipole that is constrained to move only in the plane of the membrane and thus does not interact directly with the trans-membrane electric field but can interact electrostatically with the Q-system. The N-system has only two states, its resting state (channel closed) and its excited state (channel open) and its response time is very short in comparison with that of the Q-system. On depolarizing the membrane the the N-system will not make a transition to its open state until a critical amount of Q-charge transfer has occurred. Using only four adjustable parameters that are fully determined by fitting the equilibrium properties of the model to those of the sodium channel in the squid axon, the model is then able to describe with some accuracy the kinetics of channel opening and closing and includes the Cole and Moore delay. In addition to these predictions of the behaviour of assemblies of channels the model predicts some of the individual channel properties measured by patch clamp techniques.     

Invertebrate predator-prey body size relationships: an explanation for upper triangular food webs and patterns in food web structure?

Summary It has been suggested by Cohen and Newman (1985) that many of the patterns in published food webs can be derived from a stochastic model in which the species are arranged in a trophic hierarchy (the cascade model). We suggest that, if predators are larger than their prey, a trophic hierarchy can be generated on the basis of body size Empirical evidence from the literature shows that there is a positive relationship between predator and prey size for a range of invertebrates and that predators are usually larger than their prey. Using experimental data on an aquatic food web we show that body size can lead to the type of trophic hierarchy used in the cascade model, suggesting that many food web patterns may be a product of body size. This conclusion is discussed with respect to the limitations of the food web data and the relationship between static and dynamic models of web structure.     

Calculation of leaf photosynthetic parameters from light-response curves for ecophysiological applications

Measurement of the light response of photosynthetic CO₂ uptake is often used as an implement in ecophysiological studies. A method is described to calculate photosynthetic parameters, such as the maximum rate of whole electron transport and dissimilative respiration in the light, from the light response of CO₂ uptake. Examples of the light-response curves of flag leaves and ears of wheat (Triticum aestivum cv. ARKAS) are shown.Abbreviations and symbols A net photosynthesis rate - D ¹ rate of dissimilative respiration occurring in the light - f loss factor - I incident PPFD - I effective absorbed PPFD - J rate of whole electron transport - J _m maximum rate of whole electron transport - p ^c intercellular CO₂ partial pressure - PPFD photosynthetic photon flux density - q effectivity factor for the use of light (electrons/quanta) - absorption coefficient - I ^* CO₂ compensation point in the absence of dissimilative respiration (bar) - II conversion factor for calculation of CO₂ uptake from the rate of whole electron transport - convexity factor Gas-exchange rates relate to the projective area and are given in mol·m^-2·s^-1. Electron-transport rates are given in mol electrons·m^-2·s^-1; PPFD is given in mol quanta·m^-2·s^-1.