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.

I. Development of the In Situ Reductive Ozonolysis of Alkenes with Tertiary Amine N-Oxides. II. Progress toward the Asymmetric Synthesis of Peroxyplakoric Acid A3.

Ozone, first discovered in the mid 1800’s, is a triatomic allotrope of oxygen that is a powerful oxidant. For over a century, research has been conducted into the synthetic application and mechanism of reactions of ozone with organic compounds. One of the major areas of interest has been the ozonolysis of alkenes. The production of carbonyl compounds is the most common synthetic application of ozonolysis. The generally accepted mechanism developed by Rudolf Criegee for this reaction involves the 1,3-electrocyclic addition of ozone to the π bond of the alkene to form a 1,2,3-trioxolane or primary ozonide. The primary ozonide is unstable at temperatures above -100 °C and undergoes cycloreversion to produce the carbonyl oxide and carbonyl intermediates. These intermediates then recombine in another 1,3-electrocyclic addition step to form the 1,2,4-trioxolane or final ozonide. While the final ozonide is often isolable, most synthetic applications of ozonolysis require a subsequent reductive or oxidative step to form the desired carbonyl compound. During investigations into the nucleophilic trapping of the reactive carbonyl oxide, it was discovered that when amines were used as additives, an increased amount of reaction time was required in order to consume all of the starting material. Surprisingly, significant amounts of aldehydes and a suppression of ozonide formation also occurred which led to the discovery that amine N-oxides formed by the ozonation of the amine additives in the reaction were intercepting the carbonyl oxide. From the observed production of aldehydes, our proposed mechanism for the in situ reductive ozonolysis reaction with amine N-oxides involves the nucleophilic trapping of the carbonyl oxide intermediate to produce a zwitterionic adduct that fragments into 1O2, amine and the carbonyl thereby avoiding the formation of peroxidic intermediates. With the successful total syntheses of peroxyacarnoates A and D by Dr. Chunping Xu, the asymmetric total synthesis of peroxyplakorate A3 was investigated. The peroxyplakoric acids are cyclic peroxide natural products isolated from the Plakortis species of marine sponge that have been found to exhibit activity against malaria, cancer and fungi. Even though the peroxyplakorates differ from the peroxyacarnoates in the polyunsaturated tail and the head group, the lessons learned from the syntheses of the peroxyacarnoates have proven to be valuable in the asymmetric synthesis of peroxyplakorate A3. The challenges for the asymmetric synthesis of peroxyplakorate A3 include the stereospecific formation of the 3-methoxy-1,2-dioxane core with a propionate head group and the introduction of oxidation sensitive dienyl tail in the presence of a reduction sensitive 1,2-dioxane core. It was found that the stereochemistry of two of the chiral centers could be controlled by an anti-aldol reaction of a chiral propionate followed by the stereospecific intramolecular cyclization of a hydroperoxyacetal. The regioselective ozonolysis of a 1,2-disubstituted alkene in the presence of a terminal alkyne forms the required hydroperoxyacetal as a mixture of diastereomers. Finally, the dienyl tail is introduced by a hydrometallation/iodination of the alkyne to produce a vinyl iodide followed by a palladium catalyzed coupling reaction. While the coupling reaction was unsuccessful in these attempts, it is still believed that the intramolecular cyclization to introduce the 1,2-dioxane core could prove to be a general solution to many other cyclic peroxides natural products.