A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

Identifying sequence regions undergoing conformational change via predicted continuum secondary structure

Motivation: Conformational flexibility is essential to the function of many proteins, e.g. catalytic activity. To assist efforts in determining and exploring the functional properties of a protein, it is desirable to automatically identify regions that are prone to undergo conformational changes. It was recently shown that a probabilistic predictor of continuum secondary structure is more accurate than categorical predictors for structurally ambivalent sequence regions, suggesting that such models are suited to characterize protein flexibility. Results: We develop a computational method for identifying regions that are prone to conformational change directly from the amino acid sequence. The method uses the entropy of the probabilistic output of an 8-class continuum secondary structure predictor. Results for 171 unique amino acid sequences with well-characterized variable structure (identified in the 'Macromolecular movements database') indicate that the method is highly sensitive at identifying flexible protein regions, but false positives remain a problem. The method can be used to explore conformational flexibility of proteins (including hypothetical or synthetic ones) whose structure is yet to be determined experimentally.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Non-linear principal components analysis: an alternative method for finding patterns in environmental data

The main purpose of this article is to gain an insight into the relationships between variables describing the environmental conditions of the Far Northern section of the Great Barrier Reef, Australia, Several of the variables describing these conditions had different measurement levels and often they had non-linear relationships. Using non-linear principal component analysis, it was possible to acquire an insight into these relationships. Furthermore. three geographical areas with unique environmental characteristics could be identified. Copyright (c) 2005 John Wiley & Sons, Ltd.

Prediction of HLA-DQ3.2 beta ligands: evidence of multiple registers in class II binding peptides

Motivation: While processing of MHC class II antigens for presentation to helper T-cells is essential for normal immune response, it is also implicated in the pathogenesis of autoimmune disorders and hypersensitivity reactions. Sequence-based computational techniques for predicting HLA-DQ binding peptides have encountered limited success, with few prediction techniques developed using three-dimensional models. Methods: We describe a structure-based prediction model for modeling peptide-DQ3.2 beta complexes. We have developed a rapid and accurate protocol for docking candidate peptides into the DQ3.2 beta receptor and a scoring function to discriminate binders from the background. The scoring function was rigorously trained, tested and validated using experimentally verified DQ3.2 beta binding and non-binding peptides obtained from biochemical and functional studies. Results: Our model predicts DQ3.2 beta binding peptides with high accuracy [area under the receiver operating characteristic (ROC) curve A(ROC) > 0.90], compared with experimental data. We investigated the binding patterns of DQ3.2 beta peptides and illustrate that several registers exist within a candidate binding peptide. Further analysis reveals that peptides with multiple registers occur predominantly for high-affinity binders.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.

Segmenting eukaryotic genomes with the generalized Gibbs sampler

Eukaryotic genomes display segmental patterns of variation in various properties, including GC content and degree of evolutionary conservation. DNA segmentation algorithms are aimed at identifying statistically significant boundaries between such segments. Such algorithms may provide a means of discovering new classes of functional elements in eukaryotic genomes. This paper presents a model and an algorithm for Bayesian DNA segmentation and considers the feasibility of using it to segment whole eukaryotic genomes. The algorithm is tested on a range of simulated and real DNA sequences, and the following conclusions are drawn. Firstly, the algorithm correctly identifies non-segmented sequence, and can thus be used to reject the null hypothesis of uniformity in the property of interest. Secondly, estimates of the number and locations of change-points produced by the algorithm are robust to variations in algorithm parameters and initial starting conditions and correspond to real features in the data. Thirdly, the algorithm is successfully used to segment human chromosome 1 according to GC content, thus demonstrating the feasibility of Bayesian segmentation of eukaryotic genomes. The software described in this paper is available from the author's website (www.uq.edu.au/similar to uqjkeith/) or upon request to the author.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Supermodularity and risk aversion

In this paper, we consider the relationship between supermodularity and risk aversion. We show that supermodularity of the certainty equivalent implies that the certainty equivalent of any random variable is less than its mean. We also derive conditions under which supermodularity of the certainty equivalent is equivalent to aversion to mean-preserving spreads in the sense of Rothschild and Stiglitz. (c) 2006 Elsevier B.V. All rights reserved.

Multicriterion differential games with applications to combat problems

In this paper a theory for two-person zero sum multicriterion differential games is presented. Various solution concepts based upon the notions of Pareto optimality (efficiency), security and equilibrium are defined. These are shown to have interesting applications in the formulation and analysis of two target or combat differential games. The methods for obtaining outcome regions in the state space, feedback strategies for the players and the mode of play has been discussed in the framework of bicriterion zero sum differential games. The treatment is conceptual rather than rigorous.