Erik Barry Erhardt, PhD

Laurel Goode, Erik Erhardt, Louis Santiago, and Michael Allen.
δ13C of soluble sugars in Tillandsia epiphytes vary in response to shifts in habitat.
Oecologia, Physiological ecology section, 2010.

I met Laurel at SIRFER 2008 where we enjoyed a wide range of stable isotope lectures and lab experience. She first used my software, SISUS, to estimate the proportion of C3 vs CAM photosynthesis of epiphytes. Our work and friendship led to the collaboration where we thought about and developed a model for the environmental factors affecting the phothsynthetic pathways of the species studied.

Abstract

We studied carbon stable isotopic composition (δ13C) of bulk leaf tissue and extracted sugars of four epiphytic Tillandsia species to investigate flexibility in the use of crassulacean acid metabolism (CAM) and C3 photosynthetic pathways. Plants growing in two seasonally-dry tropical forest reserves in Mexico that differ in annual precipitation were measured during wet and dry seasons, and among secondary, mature, and wetland forest types within each site. Dry season sugars were more enriched in 13C than wet season sugars, but there was no seasonal difference in bulk tissues. Bulk tissue δ13C differed by species and by forest type, with values from open-canopied wetlands more enriched in 13C than mature or secondary forest types. The shifts within forest habitat were related to temporal and spatial changes in vapour pressure deficits (VPD). Modeling results estimate a possible 4% increase in the proportional contribution of the C3 pathway during the wet season, emphasizing that any seasonal or habitat-mediated variation in photosynthetic pathway appears to be quite moderate and within the range of isotopic effects caused by variation in stomatal conductance during assimilation through the C3 pathway and environmental variation in VPD. Carbon isotopic analysis of sugars together with bulk leaf tissue offer a useful approach for incorporating short- and long-term measurements of carbon isotope discrimination during photosynthesis.

Statistics, stable isotopes

The Wishart distribution and especially the inverse-Wishart distribution are the source of some confusion because they occasionally appear with alternative parameterizations. Also, the Wishart distribution can be used to model a covariance matrix or a precision matrix (the inverse of a covariance matrix) in different situations, and the inverse-Wishart the same, but the other way round. It’s already becoming complicated. Hal Stern, coauthor of Bayesian Data Analysis (BDA), helped to clarify many issues for me in an email conversation. In this post I hope to clarify the differences in Wishart parameterizations of BDA, the wikipedia pages, and the WinBUGS and OpenBUGS softwares, and show an example in OpenBUGS where the inverse parameterization has to be specified relative to the distribution’s definition for the correct posterior to result.

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Statistics