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.

Can non-directional male mating preferences facilitate honest female ornamentation?

Recent studies have demonstrated male mate choice for female ornaments in species without sex-role reversal. Despite these empirical findings, little is known about the adaptive dynamics of female signalling, in particular the evolution of male mating preferences. The evolution of traits that signal mate quality is more complex in females than in males because females usually provide the bulk of resources for the developing offspring. Here, we investigate the evolution of male mating preferences using a mathematical model which: (i) specifically accounts for the fact that females must trade-off resources invested in ornaments with reproduction; and (ii) allows male mating preferences to evolve a non-directional shape. The optimal adaptive strategy for males is to develop stabilizing mating preferences for female display traits to avoid females that either invests too many or too few resources in ornamentation. However, the evolutionary stability of this prediction is dependent upon the level of error made by females when allocating resources to either signal or fecundity.

Gaussian operator bases for correlated fermions

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Neighborhood environmental factors correlated with walking near home: Using SPACES

Purpose: The physical environment plays an important role in influencing participation in physical activity, although the specific factors that are correlated with different patterns of walking remain to be determined We examined correlations between physical environmental factors and self-reported walking for recreation and transport near home. Methods: The local neighborhood environments (defined as a 400-m radius from the respondent's home) of 1678 adults were assessed for their suitability for walking. The environmental data were collected during 2000 using the Systematic Pedestrian and Cycling Environmental Scan (SPACES) instrument together with information from other sources. We used logistic regression modeling to examine the relationship between the attributes of the physical environment and the self-reported walking behavior undertaken near home. Results: Functional features were correlated with both walking for recreation (odds ratio (OR) 1.62; 95% confidence interval (Cl): 1.20-2.19) and for transport (OR 1.30; 95% Cl: 0.97-1.73). A well-maintained walking surface was the main functional factor associated with walking for recreation (OR 2.04; 95% Cl: 1.43-2.91) and for transport (OR 2.13; 95% Cl: 1.53-2.96). Destination factors, such as shops and public transport, were significantly correlated with walking for transport (OR 1.80; 95% Cl: 1.33-2.44), but not recreation. Conclusion: The findings suggest that neighborhoods with pedestrian facilities that are attractive and comfortable and where there are local destinations (such as shops and public transport) are associated with walking near home.

Restricted mating dispersal and strong breeding group structure in a mid-sized marsupial mammal (Petrogale penicillata)

Ecological genetic studies have demonstrated that spatial patterns of mating dispersal, the dispersal of gametes through mating behaviour, can facilitate inbreeding avoidance and strongly influence the structure of populations, particularly in highly philopatric species. Elements of breeding group dynamics, such as strong structuring and sex-biased dispersal among groups, can also minimize inbreeding and positively influence levels of genetic diversity within populations. Rock-wallabies are highly philopatric mid-sized mammals whose strong dependence on rocky terrain has resulted in series of discreet, small colonies in the landscape. Populations show no signs of inbreeding and maintain high levels of genetic diversity despite strong patterns of limited gene flow within and among colonies. We used this species to investigate the importance of mating dispersal and breeding group structure to inbreeding avoidance within a 'small' population. We examined the spatial patterns of mating dispersal, the extent of kinship within breeding groups, and the degree of relatedness among brush-tailed rock-wallaby breeding pairs within a colony in southeast Queensland. Parentage data revealed remarkably restricted mating dispersal and strong breeding group structuring for a mid-sized mammal. Breeding groups showed significant levels of female kinship with evidence of male dispersal among groups. We found no evidence for inbreeding avoidance through mate choice; however, anecdotal data suggest the importance of life history traits to inbreeding avoidance between first-degree relatives. We suggest that the restricted pattern of mating dispersal and strong breeding group structuring facilitates inbreeding avoidance within colonies. These results provide insight into the population structure and maintenance of genetic diversity within colonies of the threatened brush-tailed rock-wallaby.

A simple method to localise pleiotropic susceptibility loci using univariate linkage analyses of correlated traits

Univariate linkage analysis is used routinely to localise genes for human complex traits. Often, many traits are analysed but the significance of linkage for each trait is not corrected for multiple trait testing, which increases the experiment-wise type-I error rate. In addition, univariate analyses do not realise the full power provided by multivariate data sets. Multivariate linkage is the ideal solution but it is computationally intensive, so genome-wide analysis and evaluation of empirical significance are often prohibitive. We describe two simple methods that efficiently alleviate these caveats by combining P-values from multiple univariate linkage analyses. The first method estimates empirical pointwise and genome-wide significance between one trait and one marker when multiple traits have been tested. It is as robust as an appropriate Bonferroni adjustment, with the advantage that no assumptions are required about the number of independent tests performed. The second method estimates the significance of linkage between multiple traits and one marker and, therefore, it can be used to localise regions that harbour pleiotropic quantitative trait loci (QTL). We show that this method has greater power than individual univariate analyses to detect a pleiotropic QTL across different situations. In addition, when traits are moderately correlated and the QTL influences all traits, it can outperform formal multivariate VC analysis. This approach is computationally feasible for any number of traits and was not affected by the residual correlation between traits. We illustrate the utility of our approach with a genome scan of three asthma traits measured in families with a twin proband.

The roles of natural and sexual selection during adaptation to a novel environment

The net effect of sexual selection on nonsexual fitness is controversial. On one side, elaborate display traits and preferences for them can be costly, reducing the nonsexual fitness of individuals possessing them, as well as their offspring, In contrast, sexual selection may reinforce nonsexual fitness if an individual's attractiveness and quality are genetically correlated. According to recent models, such good-genes mate choice should increase both the extent and rate of adaptation. We evolved 12 replicate populations of Drosophila serrata in a powerful two-way factorial experimental design to test the separate and combined contributions of natural and sexual selection to adaptation to a novel larval food resource. Populations evolving in the presence of natural selection had significantly higher mean nonsexual fitness when measured over three generations (13-15) during the course of experimental evolution (16-23% increase). The effect of natural selection was even more substantial when measured in a standardized, monogamous mating environment at the end of the experiment (generation 16; 52% increase). In contrast, and despite strong sexual selection on display traits, there was no evidence from any of the four replicate fitness measures that sexual selection promoted adaptation. In addition, a comparison of fitness measures conducted under different mating environments demonstrated a significant direct cost of sexual selection to females, likely arising from some form of male-induced harm. Indirect benefits of sexual selection in promoting adaptation to this novel resource environment therefore appear to be absent in this species, despite prior evidence suggesting the operation of good-genes mate choice in their ancestral environment. How novel environments affect the operation of good-genes mate choice is a fundamental question for future sexual selection research.

Interactions between behaviour and plasma steroids within the scramble mating system of the promiscuous green turtle, Chelonia mydas

We measured plasma androgen (combined testosterone and 5 alpha-dihydrotestosterone) (A) and corticosterone (B) in the promiscuous green turtle (Chelonia mydas) during courtship in the southern Great Barrier Reef. This study examined if reproductive behaviors and intermale aggression induced behavioral androgen and adrenocortical responses in reproductively active male and female green turtles. Associations between reproductive behavior and plasma steroids were investigated in green turtles across the population and within individuals. Levels across a range of both asocial and social behaviors were compared including (a) free swimming behavior; (b) initial courtship interactions; (c) mounted behavior (male and female turtles involved in copulatory activities); (d) intermale aggression (rival males that physically competed with another male turtle or mounted males recipient to these aggressive interactions); and (e) extensive courtship damage (male turtles that had accumulated excessive courtship damage from rival males). Behavioral androgen responses were detected in male turtles, in that plasma A was observed to increase with both attendant and mounted behavior. Male turtles who had been subjected to intermale aggression or who had accumulated severe courtship damage exhibited significantly lower plasma A than their respective controls. No pronounced adrenocortical response was observed after either intermale aggression or accumulation of extensive courtship damage. Female turtles exhibited a significant increase in plasma B during swimming versus mounted behavior, but no change in plasma A. We discuss our results in terms of how scramble polygamy might influence behavioral androgen interactions differently from more typical combative and territorial forms Of male polygamy. (C) 1999 Academic Press.