Dynamic conditionally linear mixed models for longitudinal data

We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here 'dynamic' means using past responses as covariates and 'conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.     

Generalized character process models: estimating the genetic basis of traits that cannot be observed and that change with age or environmental conditions

The genetic analysis of characters that change as a function of some independent and continuous variable has received increasing attention in the biological and statistical literature. Previous work in this area has focused on the analysis of normally distributed characters that are directly observed. We propose a framework for the development and specification of models for a quantitative genetic analysis of function-valued characters that are not directly observed, such as genetic variation in age-specific mortality rates or complex threshold characters. We employ a hybrid Markov chain Monte Carlo algorithm involving a Monte Carlo EM algorithm coupled with a Markov chain approximation to the likelihood, which is quite robust and provides accurate estimates of the parameters in our models. The methods are investigated using simulated data and are applied to a large data set measuring mortality rates in the fruit fly, Drosophila melanogaster.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

Peak-to-peak dynamics in food chain models

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the forecast concerns the population at the top of the food chain and that peaks variability often increases from bottom to top. All these findings bring naturally to the conclusion that top populations should be sampled in order to have higher chances to detect peak-to-peak dynamics. The analysis is carried out by studying ditrophic food chain models with seasonally varying parameters, tritrophic food chain models with constant parameters, and more complex food chain and food web models.     

On the progressive enrichment of the oxygen isotopic composition of water along a leaf

A model has been derived for the enrichment of heavy isotopes of water in leaves, including progressive enrichment along the leaf. In the model, lighter water is preferentially transpired leaving heavier water to diffuse back into the xylem and be carried further along the leaf. For this pattern to be pronounced, the ratio of advection to diffusion (Péclet number) has to be large in the longitudinal direction, and small in the radial direction. The progressive enrichment along the xylem is less than that occurring at the sites of evaporation in the mesophyll, depending on the isolation afforded by the radial Péclet number. There is an upper bound on enrichment, and effects of ground tissue associated with major veins are included. When transpiration rate is spatially nonuniform, averaging of enrichment occurs more naturally with transpiration weighting than with area-based weighting. This gives zero average enrichment of transpired water, the modified Craig-Gordon equation for average enrichment at the sites of evaporation and the Farquhar and Lloyd (In Stable Isotopes and Plant Carbon-Water Relations, pp. 47-70. Academic Press, New York, USA, 1993) prediction for mesophyll water. Earlier results on the isotopic composition of evolved oxygen and of retro-diffused carbon dioxide are preserved if these processes vary in parallel with transpiration rate. Parallel variation should be indicated approximately by uniform carbon isotope discrimination across the leaf.     

Models in which many cross-bridges attach simultaneously can explain the filament movement per ATP split during muscle contraction

Contractile filaments in skeletal muscle are moved by less than 2 nm for each ATP used. If just one cross-bridge is attached to each thin filament at any instant then this distance represents the fundamental myosin cross-bridge step size (i.e. the distance one cross-bridge moves a thin filament in one ATP-splitting cycle). However, most contraction models assume many cross-bridges are attached at any instant along each thin filament. The purpose of this study was to establish whether the net filament sliding per ATP used could be explained quantitatively in terms of a cross-bridge model in which multiple cross-bridges are attached along each thin filament. It was found that the relationship between net filament sliding per ATP split and the load against which the muscle shortens is compatible with such a model and furthermore predicts that the cross-bridge step size is between 7.5 and 12.5 nm over most of the range of loads. These values were similar for different muscle fibre types.     

Analysis of complex protein-polypeptide systems for proteomic studies

Two-dimensional polyacrylamide gel electrophoresis (2-D PAGE), followed by protein extraction and characterization with chemical sequencing or mass spectrometry (MS), is the most commonly used method to analyze complex protein systems such as cells and organelles. However, it is claimed that 2-D PAGE is a slow and labor-intensive technique and also needs subsequent efforts for one-by-one identification of proteins. Recently, the combined methods of Fourier transform ion cyclotron resonance (FTICR) mass spectrometry, with preceding separation techniques such as capillary isoelectric focusing (CIEF) or liquid chromatography, have been demonstrated as high-throughput techniques suitable for proteomic analysis of protein systems. The studies which employ FTICR MS, aimed at the analysis of complex protein systems, have been reviewed, comparing their performance with that of 2-D PAGE. Also, the possibilities of combining 2-D PAGE and the FTICR MS method to analyze and reconstruct the structures and functions of complex systems are discussed.     

Pigmentation pattern formation in butterflies: experiments and models

Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus.     

Expression of SR-BI receptor and StAR protein in rat ocular tissues

The class-B type-I scavenger receptor (SR-BI) plays a key role in cholesterol homeostasis; it mediates the selective uptake of lipoprotein cholesterol to steroidogenic tissues. We show by RT-PCR, western blot, in situ hybridization and immunohistochemistry analysis that SR-BI is highly expressed in different neuro-retinal and non-neuronal cells types on rat eye. Immunohistochemistry of the steroidogenic acute regulatory protein (StAR) involved in neurosteroid production showed the same expression pattern than SR-BI in rat eye. Our results may suggest a key role of these genes in the ocular cholesterol metabolism for membranes biosynthesis and neurosteroidogenesis.