A Hierarchical Model for Aggregated Functional Data

In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed individually. We assume that several aggregated curves with linear independent coefficients are available. More specifically, we assume each aggregated curve is an independent partial realization of a Gaussian process with mean modeled through a weighted linear combination of the disaggregated curves. We model the mean of the Gaussian processes as a smooth function approximated by a function belonging to a finite dimensional space ${\cal H}_K$ which is spanned by $K$ B-splines basis functions. We explore two different specifications of the covariance function of the Gaussian process: one that assumes a constant variance across the domain of the process, and a more general variance structure which is itself modelled as a smooth function, providing a nonstationary covariance function. Inference procedure is performed following the Bayesian paradigm allowing experts' opinion to be considered when estimating the disaggregated curves. Moreover, it naturally provides the uncertainty associated with the parameters estimates and fitted values. Our model is suitable for a wide range of applications. We concentrate on two different real examples: calibration problem for NIR spectroscopy data and an analysis of distribution of energy among different type of consumers.Comment: 29 pages, 12 figure

Predicting taxonomic and functional structure of microbial communities in acid mine drainage.

Predicting the dynamics of community composition and functional attributes responding to environmental changes is an essential goal in community ecology but remains a major challenge, particularly in microbial ecology. Here, by targeting a model system with low species richness, we explore the spatial distribution of taxonomic and functional structure of 40 acid mine drainage (AMD) microbial communities across Southeast China profiled by 16S ribosomal RNA pyrosequencing and a comprehensive microarray (GeoChip). Similar environmentally dependent patterns of dominant microbial lineages and key functional genes were observed regardless of the large-scale geographical isolation. Functional and phylogenetic β-diversities were significantly correlated, whereas functional metabolic potentials were strongly influenced by environmental conditions and community taxonomic structure. Using advanced modeling approaches based on artificial neural networks, we successfully predicted the taxonomic and functional dynamics with significantly higher prediction accuracies of metabolic potentials (average Bray-Curtis similarity 87.8) as compared with relative microbial abundances (similarity 66.8), implying that natural AMD microbial assemblages may be better predicted at the functional genes level rather than at taxonomic level. Furthermore, relative metabolic potentials of genes involved in many key ecological functions (for example, nitrogen and phosphate utilization, metals resistance and stress response) were extrapolated to increase under more acidic and metal-rich conditions, indicating a critical strategy of stress adaptation in these extraordinary communities. Collectively, our findings indicate that natural selection rather than geographic distance has a more crucial role in shaping the taxonomic and functional patterns of AMD microbial community that readily predicted by modeling methods and suggest that the model-based approach is essential to better understand natural acidophilic microbial communities