Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

Dynamic Routing in Translucent WDM Optical Networks

Translucent WDM optical networks use sparse placement of regenerators to overcome the impairments and wavelength contention introduced by fully transparent networks, and achieve a performance close to fully opaque networks with much less cost. Our previous study proved the feasibility of translucent networks using sparse regeneration technique. We addressed the placement of regenerators based on static schemes allowing only fixed number of regenerators at fixed locations. This paper furthers the study by proposing a suite of dynamical routing schemes. Dynamic allocation, advertisement and discovery of regeneration resources are proposed to support sharing transmitters and receivers between regeneration and access functions. This study follows the current trend in optical networking industry by utilizing extension of IP control protocols. Dynamic routing algorithms, aware of current regeneration resources and link states, are designed to smartly route the connection requests under quality constraints. A hierarchical network model, supported by the MPLS-based control plane, is also proposed to provide scalability. Experiments show that network performance is improved without placement of extra regenerators.

‘Gene shaving’ as a method for identifying distinct sets of genes with similar expression patterns

Background: Large gene expression studies, such as those conducted using DNA arrays, often provide millions of different pieces of data. To address the problem of analyzing such data, we describe a statistical method, which we have called ‘gene shaving’. The method identifies subsets of genes with coherent expression patterns and large variation across conditions. Gene shaving differs from hierarchical clustering and other widely used methods for analyzing gene expression studies in that genes may belong to more than one cluster, and the clustering may be supervised by an outcome measure. The technique can be ‘unsupervised’, that is, the genes and samples are treated as unlabeled, or partially or fully supervised by using known properties of the genes or samples to assist in finding meaningful groupings. Results: We illustrate the use of the gene shaving method to analyze gene expression measurements made on samples from patients with diffuse large B-cell lymphoma. The method identifies a small cluster of genes whose expression is highly predictive of survival. Conclusions: The gene shaving method is a potentially useful tool for exploration of gene expression data and identification of interesting clusters of genes worth further investigation.