Propagating Uncertainty in Predicting Individuals and Means Illustrated with Foliar Chemistry and Forest Biomass

Yanai, RD
Drake, JE
Buckley, HL
Case, BS
Lilly, PJ
Woollons, RC
Gamarra, JGP
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Springer Science and Business Media LLC

Quantifying uncertainty is important to establishing the significance of comparisons, to making predictions with known confidence, and to identifying priorities for investment. However, uncertainty can be difficult to quantify correctly. While sampling error is commonly reported based on replicate measurements, the uncertainty in regression models used to estimate forest biomass from tree dimensions is commonly ignored and has sometimes been reported incorrectly, due either to lack of clarity in recommended procedures or to incentives to underestimate uncertainties. Even more rarely are the uncertainty in predicting individuals and the uncertainty in the mean both recognized for their contributions to overall uncertainty. In this paper, we demonstrate the effect of propagating these two sources of uncertainty using a simple example of calcium concentration of sugar maple foliage, which does not require regression, then the mass of foliage and calcium content of foliage, and finally an entire forest with multiple species and tissue types. The uncertainty due to predicting individuals is greater than the uncertainty in the mean for studies with few trees—up to 30 trees for foliar calcium concentration and 50 trees for foliar mass and calcium content in the data set we analyzed from the Hubbard Brook Experimental Forest. The most correct analysis will take both sources of uncertainty into account, but for practical purposes, country-level reports of uncertainty in carbon stocks can safely ignore the uncertainty in individuals, which becomes negligible with large enough numbers of trees. Ignoring the uncertainty in the mean will result in exaggerated confidence in estimates of forest biomass and carbon and nutrient contents.

3109 Zoology , 31 Biological Sciences , Generic health relevance , 05 Environmental Sciences , 06 Biological Sciences , Ecology , 3109 Zoology
Ecosystems, ISSN: 1432-9840 (Print); 1435-0629 (Online), Springer Science and Business Media LLC, 1-15. doi: 10.1007/s10021-023-00886-6
Rights statement
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit