Stable Isotope Sourcing using Sampling
Erhardt, EB, BO Wolf, M Ben-David, and EJ Bedrick
Open Journal of Ecology 4 (6) pp. 289–298
Online: May 2014
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=46187
DOI: 10.4236/oje.2014.46027
Abstract
Stable isotope mixing models are used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets, plant nutrient use, geochemistry, pollution, and forensics. We describe an algorithm implemented as SISUS software for providing a user-specified number of probabilistic exact solutions derived quickly from the extended mixing model. Our method outperforms IsoSource, a deterministic algorithm for providing approximate solutions to represent the solution polytope. Our method is an approximate Bayesian large sample procedure. SISUS software is freely available at StatAcumen.com/sisus and as an R package at cran.r-project.org/web/packages/sisus.
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Category Archives: stable isotopes
Paper published: Inference for stable isotope mixing models: a study of the diet of dunlin
Inference for stable isotope mixing models: a study of the diet of dunlin
Erhardt, EB and EJ Bedrick
Journal of the Royal Statistical Society: Series C. pp. 579–593
Online: February 4, 2014
http://onlinelibrary.wiley.com/doi/10.1111/rssc.12047/abstract
doi: 10.1111/rssc.12047
Abstract
Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets and plant nutrient use. Statistical methods for inference on the diet proportions by using stable isotopes have focused on the linear mixing model. Existing frequentist methods assume that the diet proportion vector can be uniquely solved for in terms of one or two isotope ratios. We develop large sample methods that apply to an arbitrary number of isotope ratios, assuming that the linear mixing model has a unique solution or is overconstrained. We generalize these methods to allow temporal modelling of the population mean diet, assuming that isotope ratio response data are collected over time. The methodology is motivated by a study of the diet of dunlin, a small migratory seabird.
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Invited talks: Neuroimaging and Statistics at Wright State University, Dayton, OH
I just returned from a fun event-filled couple days at Wright State Univeristy in Dayton, Ohio, visiting statistician Harry Khamis. Harry invited me to give two talks on Friday, November 2nd, 2012: one in Statistics and a second in Neuroscience, arranged by Thomas N. Hangartner. Harry was the model host; I always felt taken care of, my needs met.
I was excited to meet two people from my talks who could use the methods I presented. Prof Nasser H Kashou develops models for HRF functions, which the SimTB might be helpful for. Prof Yvonne Vadeboncoeur uses stable isotopes to study freshwater ecosystems, and we had some exciting discussion about collaborative opportunities.
The links to the papers the talks draw on are at the bottom.
My morning neuroimaging talk (10:15) in the Department of Biomedical, Industrial & Human Factors Engineering (BIE) included two-and-one-half topics: SimTB, subject variability with GICA, and a little data visualization.
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Title Capturing inter-subject variability with group independent component analysis of fMRI data: a simulation study Abstract A key challenge in functional neuroimaging is the meaningful combination of results across subjects. Even in a sample of healthy participants, brain morphology and functional organization exhibit considerable variability, such that no two individuals have the same neural activation at the same location in response to the same stimulus. This inter-subject variability limits inferences at the group-level as average activation patterns may fail to represent the patterns seen in individuals. A promising approach to multi-subject analysis is group independent component analysis (GICA), which identifies group components and reconstructs activations at the individual level. GICA has gained considerable popularity, particularly in studies where temporal response models cannot be specified. However, a comprehensive understanding of the performance of GICA under realistic conditions of inter-subject variability is lacking. In this study we use simulated functional magnetic resonance imaging (fMRI) data to determine the capabilities and limitations of GICA under conditions of spatial, temporal, and amplitude variability. Simulations, generated with the SimTB toolbox, address questions that commonly arise in GICA studies, such as: (1) How well can individual subject activations be estimated and when will spatial variability preclude estimation? (2) Why does component splitting occur and how is it affected by model order? (3) How should we analyze component features to maximize sensitivity to intersubject differences? Overall, our results indicate an excellent capability of GICA to capture between-subject differences and we make a number of recommendations regarding analytic choices for application to functional imaging data. mialab.mrn.org/software/simtbMy afternoon statistics talk (3:00) in the Department of Mathematics and Statistics to a packed room (they had to bring in additional chairs!) included work that extends my published stable isotope sourcing work.
Title An extended Bayesian stable isotope mixing model for trophic level inference Abstract You are what and where you eat on the food web. We developed an extended Bayesian mixing model to jointly infer organic matter utilization and isotopic enrichment of organic matter sources in order to infer the trophic levels of several numerically abundant fish species (consumers) present in Apalachicola Bay, FL, USA. Bayesian methods apply for arbitrary numbers of isotopes and diet sources but existing models are somewhat limited as they assume that trophic fractionation is estimated without error or that isotope ratios are uncorrelated. The model uses stable isotope ratios of carbon, nitrogen, and sulfur, isotopic fractionations, elemental concentrations, elemental assimilation efficiencies, as well as prior information (expert opinion) to inform the diet and trophic level parameters. The model appropriately accounts for uncertainly and prior information at all levels of the analysis.Neuroscience talk Summary of both SimTB papers. SimTB, a simulation toolbox for fMRI data under a model of spatiotemporal separability Erik B. Erhardt, Elena A. Allen, Yonghua Wei, Tom Eichele, Vince D. Calhoun NeuroImage 59 (2012), pp. 4160-4167 http://www.sciencedirect.com/science/article/pii/S105381191101370X Capturing inter-subject variability with group independent component analysis of fMRI data: A simulation study Elena A. Allen, Erik B. Erhardt, Yonghua Wei, Tom Eichele, Vince D. Calhoun NeuroImage http://www.sciencedirect.com/science/article/pii/S1053811911011712 Data visualization in the neurosciences: overcoming the curse of dimensionality Elena A. Allen, Erik B. Erhardt, Vince D. Calhoun Neuron www.cell.com/neuron/retrieve/pii/S089662731200428X Statistics talk A Bayesian framework for stable isotope mixing models Erik B. Erhardt and Edward J. Bedrick Environmental and Ecological Statistics http://www.springerlink.com/content/vg4v62j8717671p3/ Bio Erik Barry Erhardt, PhD, is an Assistant Professor of Statistics at the University of New Mexico Department of Mathematics and Statistics, where he serves as Director of the statistics consulting clinic. His research interests include Bayesian and frequentist statistical methods for stable isotope sourcing and brain imaging. Erik is a Howard Hughes Medical Institute Interfaces Scholar collaborating in interdisciplinary research and consulting. StatAcumen.com
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Paper published: A Bayesian framework for stable isotope mixing models
A Bayesian framework for stable isotope mixing models
Erik B. Erhardt and Edward J. Bedrick
Environmental and Ecological Statistics
Submitted 19 February 2011
Accepted 28 September 2012
Online 23 October 2012
http://www.springerlink.com/content/vg4v62j8717671p3/
DOI 10.1007/s10651-012-0224-1
Abstract:
Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets and plant nutrient use. Statistical methods for inference on the diet proportions using stable isotopes have focused on the linear mixing model. Existing frequentist methods provide inferences when the diet proportion vector can be uniquely solved for in terms of the isotope ratios. Bayesian methods apply for arbitrary numbers of isotopes and diet sources but existing models are somewhat limited as they assume that trophic fractionation or discrimination is estimated without error or that isotope ratios are uncorrelated. We present a Bayesian model for the estimation of mean diet that accounts for uncertainty in source means and discrimination and allows correlated isotope ratios. This model is easily extended to allow the diet proportion vector to depend on covariates, such as time. Two data sets are used to illustrate the methodology. Code is available for selected analyses.
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Paper published: The 5.1 ka Aridization Event, Expansion of Piñon-Juniper Woodlands
The 5.1 ka Aridization Event, Expansion of Piñon-Juniper Woodlands, and the Introduction of Maize (Zea mays) in the American Southwest
Brandon L. Drake, W. H. Wills, Erik B. Erhardt
The Holocene
Published online before print July 9, 2012, doi: 10.1177/0959683612449758
Accepted 2/13/2012
Lee Drake (UNM Anthropology) exemplifies excellence and I will make every opportunity to work with him again.
Abstract
Pollen analysis is frequently used to build climate and environmental histories. A distinct Holocene pollen series exists for Chaco Canyon, New Mexico. This study reports linear modeling and hypothesis testing of long distance dispersal pollen from radiocarbon-dated packrat middens which reveal strong relationships between piñon pine (Pinus edulis) and ponderosa pine (Pinus ponderosa). Ponderosa pollen dominates midden pollen assemblages during the early Holocene, while a rapid shift to a much higher proportion of piñon to ponderosa pine pollen between 5,440 and 5,100 BP points to an aridization episode. This shift is associated with higher δ18O values in Southwest speleothem records relative to the preceding millenium. The period of aridization is followed by a sharp increase in El Niño/Southern Oscillation events that would have caused highly variable precipitation and lasted until 4,200 BP. Bayesian changepoint analysis suggests that this aridization episode led to stable ecotonal boundaries for at least 3,000 years. The piñon/ponderosa transition may have been caused by punctuated multi-year droughts, analogous to those in the 20th century. The earliest documented instance of Zea mays cultivation on the Colorado Plateau is around ca. 4,290 BP. The introduction of this laborintensive cultigen from Mesoamerica may have been facilitated by changes in the regional ecosystems, specifically by an increase in piñon trees, that promoted increasing human territoriality. Linear modeling and hypothesis testing can complement traditional palynological techniques by adding greater resolution in vegetation patterning to climate/environmental histories.
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Funded: UNM RAC grant Erhardt/Hanson, Modeling (photo)respiration
We got one! Research Allocation Committee (RAC) Grants are for supporting new research or creative works. The RAC is particularly supportive of projects that may lead to outside funding and/or larger related projects.
PIs: Erik Erhardt and David Hanson
Title: “Frequentist (bootstrap) and Bayesian modeling of (photo)respiration in plants”
Amount: $3982.63, RAC 12-04
Use: To hire statistics graduate student, Mohammad Hattab, to implement and develop modeling that I did last summer in Switzerland.
Purpose:
We are requesting $3982.63 to develop statistical models to estimate (photo)respiration in plants, accounting for sources of uncertainty and prior information. Because current models provide estimates without meaningful assessments of uncertainty, our model will have broad application in understanding photosynthetic pathways and carbon usage in plants, clarifying the precision of our knowledge, conditional on what is already believed. This modeling is an important step towards developing more comprehensive models of photosynthetic parameters. Support from the Resource Allocation Committee will allow us to: (1) develop frequentist (bootstrap) and Bayesian models to analyze existing experimental data, providing inferences on the set of parameters related in the model; (2) design experiments and acquire additional data to distinguish and estimate respiration and photorespiration under a set of scientifically relevant conditions; (3) conduct validations using pre-existing data and estimates; (4) publish our model with results; and (5) develop grant proposals to apply this model more broadly.
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Isotopic signature of photorespiration, poster
Last year David Hanson and I began collaboration continuing his study in leaf respiration. I wrote a custom R package to process data from his tunable diode laser (TDL) and Licor devices to understand how carbon is taken up and respired by leaves. This summer a poster presenting some of what we’ve been learning was presented by graduate student, Dianne Pater, who has been designing and running experiments.
DT Pater, EB Erhardt, and DT Hanson. Isotopic signature of photorespiration. In Joint Annual Meetings of the American Society of Plant Biologists and the Canadian Society of Plant Physiologists, Montreal, CA, August 2010.
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Paper published: δ13C of soluble sugars in Tillandsia epiphytes
In a previous post I discussed this paper and how fun it was to write with Laurel. Here I’m happy to report it’s available electronically (SpringerLink, pdf) and soon in paper.
Laurel K. Goode, Erik B. Erhardt, Louis S. Santiago, Michael F. Allen. Carbon stable isotopic composition of soluble sugars in Tillandsia epiphytes varies in response to shifts in habitat. Oecologia (2010) 163:583–590.
DOI 10.1007/s00442-010-1577-5
Received: 11 March 2009 / Accepted: 25 January 2010 / Published online: 13 February 2010
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Visions
A few important areas of focus, reflecting what I’m doing and where I’m going.
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Professional
Statistics for Stable Isotope applications
My vision is to be the recognized leader of statistical methods in stable isotope sourcing. This will be accomplished through publishing papers from my dissertation work, collaborations leading to publications on methodological extensions, and giving talks in university departments and at courses and conferences.Postdoctoral fellowship at the Mind Research Network
At the MRN my vision is to be an exceptional statistician, a valuable member of Vince Calhoun’s team, and an expert on statistical methods applying to ICA and fMRI. This will be accomplished with thorough discussions and detailed answers to statistical inquiries, active curiosity about others’ work and how I may contribute, and careful study of existing ICA models and sound application of statistical principles. My career goals at the MRN are to develop a broad and deep knowledge of the methods for analysis of fMRI data in particular, and brain imaging data in general, to publish carefully developed extensions in well-written papers, and make contributions to others’ work. This will be accomplished by dissecting the modeling details from published work and uncovering further details by contacting the authors, appealing to theoretical results and experimental confirmation before publicizing new methods, and helping others consider their methods, results, and interpretations.Personal
Dance
My vision is to contribute more to the Albuquerque contra dance community and bring dance to more people, especially youth. This will be accomplished by making opportunities for new callers, writing and calling dances, leading and participating in workshops, helping make more dance and music opportunities to bring the community together, outreach efforts to introduce dance to more people, and always collaborating with our vibrant New Mexico dance community to make it happen.... more
Paper accepted: δ13C of soluble sugars in Tillandsia epiphytes vary in response to shifts in habitat
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.
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