Partitioning variation in Douglas-fir xylem properties among multiple scales via a Bayesian hierarchical model
Sonya M. Dunham (1, 2), Lisa M. Ganio (3), Alix I. Gitelman (4) and Barbara Lachenbruch (1)
1. Department of Wood Science and Engineering, Oregon State University, Corvallis, OR 97331-4501, USA / 2. Corresponding author () / 3. Department of Forest Science, Oregon State University, Corvallis, OR 97331-4501, USA / 4. Department of Statistics, Oregon State University, Corvallis, OR 97331-4501, USA / Received February 22, 2007; accepted October 29, 2007; published online May 1, 2008
Summary
Hierarchical biological scales permeate research in tree physiology and represent multiple sources of variation. We discuss
the importance of matching the sampling and analysis scales to biological scales in the data. The advantages of statistical
hierarchical modeling are demonstrated using the relationship between specific conductivity and tracheid diameter of secondary
xylem as an example. The structure and results of three statistical models were compared within a Bayesian context: a simple
linear regression (SLR); a repeated measures analysis (REP); and a hierarchical model (HM). The models share similar mean
structures but differ in how variation is partitioned among scales: the SLR model assumes independence among observations
(variation came from only a single scale); the REP allows multiple observations of each tree to be correlated; and the HM
incorporates features of the REP with an additional variance structure that partitions variation across a broader scale. Our
data included hierarchical scales of position on the tree, tree, fertilization treatment and species (Pseudotsuga menziesii (Mirb.) Franco). The HM gave more precise estimates for model parameters, was more robust to outliers, provided a more detailed
description of covariances within the data at multiple scales compared with the SLR and REP and increased our ability to detect
differences among positions on the tree. The proper statistical analyses increase the value of research by allowing the most
exact interpretation.
