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.

Impact of Bottom Flange Confinement Reinforcement on Performance of Prestressed Concrete Bridge Girders

For many years AASHTO provided no recommendation to state DOT’s on bottom flange confinement reinforcement for their bridge superstructures. The 1996 edition of AASHTO Standard Specification for Highway Bridges stated that nominal reinforcement be placed to enclose the prestressing steel from the end of the girder for at least a distance equal to the girder’s height. A few years later the 2004 AASHTO LRFD Bridge Design Specification changed the distance over which the confinement was to be distributed from 1.0h to 1.5h, and gave minimum requirements for the amount of steel to be used, No.3 bars, and their maximum spacing, not to exceed 6”. Research was undertaken to study what impact, if any, confinement reinforcement has on the performance of prestressed concrete bridge girders. Of particular interest was the effect confinement had on the transfer length, development length, and vertical shear capacity of the fore mentioned members. First, an analytical investigation was performed on the subject, and then an experimental investigation followed which consisted of designing, fabricating, and testing eight tee-girders and three NU1100 girders with particular attention paid to the amount and distribution of confinement reinforcement placed at the end of each girder. The results of the study show: 1) neither the amount or distribution of confinement reinforcement had a significant effect on the initial or final transfer length of the prestress strands; 2) at the AASHTO calculated development length, no significant impact from confinement was found on either the nominal flexural capacity of bridge girders or bond capacity of the prestressing steel; 3) the effects from varied confinement reinforcement on the shear resistance of girders tested was negligible, however, distribution of confinement did show to have an impact on the prestressed strands’ bond capacity; 4) confinement distribution across the entire girder did increase ductility and reduced cracking under extreme loading conditions.