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.

Integrating Visual and Verbal Literacies in the Early Childhood Classroom

Young children have the strong desire to use all of the communicative tools their cultures and families offer them. They want to be able to do all of the things that the powerful people they admire can do, including talking, writing, drawing, using the computer, and otherwise creating and sharing ideas, memories, solutions, even jokes and feelings. Today, we live in a time when the communicative tools are changing rapidly, practically exploding before our eyes in terms of the formats and media available to us in complex combinations not seen before. What do these technological changes mean for how we can support children's development toward literacy? An integrated arts curriculum has long been favored by many educators, but today there are more reasons than ever to implement such a philosophy. From communications theory comes a new understanding of how modern technologies demand that children learn to "read" and "write" messages involving complex combinations and integrations of visual and verbal formats. From psychology come insights about intelligence being multiple not unitary, as well as ecological perception theory offering a well-accepted framework for analyzing the affordances and expressive possibilities of different media. From education come fresh approaches to integrated curriculum, including a philosophy and pedagogy from Reggio Emilia, Italy, that combines well with current thinking by North Americans. Altogether, we have many rationales and exciting strategies at hand for launching young children toward an integrated visual and verbal literacy that involves substance, challenge, and discipline, as well as innovation, creativity, and freedom.