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© 2014 Ricker et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

Growth curves are monotonically increasing functions that measure repeatedly the same subjects over time. The classical growth curve model in the statistical literature is the Generalized Multivariate Analysis of Variance (GMANOVA) model. In order to model the tree trunk radius (r) over time (t) of trees on different sites, GMANOVA is combined here with the adapted PL regression model Q = A·T+E, where for and for , A =  initial relative growth to be estimated, , and E is an error term for each tree and time point. Furthermore, Ei[–b·r]  = , , with TPR being the turning point radius in a sigmoid curve, and at is an estimated calibrating time-radius point. Advantages of the approach are that growth rates can be compared among growth curves with different turning point radiuses and different starting points, hidden outliers are easily detectable, the method is statistically robust, and heteroscedasticity of the residuals among time points is allowed. The model was implemented with dendrochronological data of 235 Pinus montezumae trees on ten Mexican volcano sites to calculate comparison intervals for the estimated initial relative growth . One site (at the Popocatépetl volcano) stood out, with being 3.9 times the value of the site with the slowest-growing trees. Calculating variance components for the initial relative growth, 34% of the growth variation was found among sites, 31% among trees, and 35% over time. Without the Popocatépetl site, the numbers changed to 7%, 42%, and 51%. Further explanation of differences in growth would need to focus on factors that vary within sites and over time.

Details

Title
A New Method to Compare Statistical Tree Growth Curves: The PL-GMANOVA Model and Its Application with Dendrochronological Data
Author
Ricker, Martin; Peña Ramírez, Víctor M; Dietrich von Rosen
First page
e112396
Section
Research Article
Publication year
2014
Publication date
Nov 2014
Publisher
Public Library of Science
e-ISSN
19326203
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1625576730
Copyright
© 2014 Ricker et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.