Sparse precision matrix estimation in phenotypic trait evolution models

Phylogenetic trait evolution models allow for the estimation of evolutionary correlations between a set of traits observed in a sample of related organisms. By directly modeling the evolution of the traits along an estimable phylogenetic tree, the model's structure effectively controls for shared evolutionary history. In these models, relevant correlations are usually assessed through the high posterior density interval of their marginal distributions. However, the selected correlations alone may not provide the full picture regarding trait relationships. Their association structure, expressed through a graph that encodes partial correlations, can in contrast highlight sparsity patterns featuring direct associations between traits. In order to develop a model-based method to identify this association structure we explore the use of Gaussian graphical models (GGM) for covariance selection. We model the precision matrix with a G-Wishart conjugate prior, which results in sparse precision estimates. Furthermore the model naturally allows for Bayes Factor tests of association between the traits, with no additional computation required. We evaluate our approach through Monte Carlo simulations and applications that examine the association structure and evolutionary correlations of phenotypic traits in Darwin's finches and genomic and phenotypic traits in prokaryotes. Our approach provides accurate graph estimates and lower errors for the precision and correlation parameter estimates, particularly for conditionally independent traits, which are the target for sparsity in GGMs.Comment: 24 pages, 4 figure

Classification of homogeneous regions of vegetation cover in the State of Rio Grande do Sul, Brazil and its temporal dynamics, using AVHRR GIMMS and MODIS data sets

This study aimed to classify the homogeneous regions of vegetation cover, which occur in Rio Grande do Sul, formed by clustering of pixels with same pattern of temporal variability of the Normalized Difference Vegetation Index (NDVI) of AVHRR GIMMS and MODIS series and to compare their temporal dynamics. We use K means cluster analysis for defi ning homogeneous regions, based on the temporal variability of GIMMS (8 km spatial resolution) and MODIS (1 km spatial resolution) NDVI data sets, using monthly images mean from 2000 to 2008 (overlapping period); and we analyzed the annual pattern of NDVI. Accuracy assessment was done with Landsat images. The results show that the temporal variability of GIMMS and MODIS NDVI allows to delimit similar homogeneous regions in order to mapping the main vegetation cover. MODIS series shows a greater detail in the defi nition of the regions, but with compatibility with those generated by GIMMS. The temporal dynamics show a typical seasonal pattern, with variations of NDVI amplitude between the groups, that allow to monitor phenological changes. The deviations from calibration between times series are linear, which would facilitate a correction in order to construct a long synthetic time series for studies of land cover change

Modelling the covariance structure in marginal multivariate count models: Hunting in Bioko Island.

The main goal of this article is to present a flexible statistical modelling framework to deal with multivariate count data along with longitudinal and repeated measures structures. The covariance structure for each response variable is defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. In order to specify the joint covariance matrix for the multivariate response vector, the generalized Kronecker product is employed. We take into account the count nature of the data by means of the power dispersion function associated with the Poisson–Tweedie distribution. Furthermore, the score information criterion is extended for selecting the components of the matrix linear predictor. We analyse a data set consisting of prey animals (the main hunted species, the blue duiker Philantomba monticola and other taxa) shot or snared for bushmeat by 52 commercial hunters over a 33-month period in Pico Basilé, Bioko Island, Equatorial Guinea. By taking into account the severely unbalanced repeated measures and longitudinal structures induced by the hunters and a set of potential covariates (which in turn affect the mean and covariance structures), our method can be used to indicate whether there was statistical evidence of a decline in blue duikers and other species hunted during the study period. Determining whether observed drops in the number of animals hunted are indeed true is crucial to assess whether species depletion effects are taking place in exploited areas anywhere in the world. We suggest that our method can be used to more accurately understand the trajectories of animals hunted for commercial or subsistence purposes and establish clear policies to ensure sustainable hunting practices