Tree growth analysis issues, again, part two

This picks up from the previous post on Stephenson et al (2014).  Hoping that you’ve looked at the paper, I’ll try to explain why I have concerns about it. It presents a good opportunity to discuss some important analytical issues, biological and mathematical.

I’ll begin with a criticism that relates more to a general concern with scientific publications: the way statements/claims are made in titles and abstracts.  Many scientists will only ever read the abstract of a given article, or even just the title, so it’s extra important to word things carefully there so as not to create the wrong impression.  And since scientific protocol strongly trains for accuracy and brevity in writing, there’s little room for excuses when failing to do so. Their title reads: “Rate of tree carbon accumulation increases continuously with tree size“. That’s an unambiguous, general statement; they’re basically claiming a new, general finding (law?) regarding tree growth rates, world-wide.  Hmmmm. All I will say to that is, better be able to back something like that up, because a lot of people have been looking at tree growth rates for a long time, and some of them are probably going to look pretty closely at it. Or very closely.

I find quickly enough though, that the paper actually addresses only above-ground tree carbon, not total carbon, an important point easily clarified just by adding that one term to the title.  Moreover, it’s not really a forest carbon flux study either.  Such studies typically use very different approaches that measure carbon dioxide fluxes directly, via continuous (e.g. eddy covariance) or discrete (flask) air sampling techniques (and now, satellite spectroscopy). [Biometric approaches are common, but they are typically better suited for estimating carbon stocks, not fluxes.]  They summarize total system carbon exchanges directly, while synchronously avoiding the very large practical problems involved with biometric approaches, in particular the estimation of below-ground carbon processes.

This is rather a study of above-ground tree growth rates as a function of tree size, species, and global geographic location.  Twenty years ago it might’ve properly been titled Tree growth rates increase continually with size across many taxa worldwide and submitted to Ecology or The American Naturalist.  Now, an increasing number of researchers try to frame their work as being as relevant to the Grand Cause of climate change as they can, which also increases chances of publication in a prestige journal, like say, Nature.  This study exemplifies this by claiming a greater relevance to the carbon cycle than is warranted IMO, for reasons I’ll get into. But since this kind of thing is so common, I’ll just mention it and move on to the specifics that should concern us the most.

I. Background
Their basic approach is a common one in biometrically-based forest carbon studies.  They apply equations that relate above-ground biomass (AGB) to tree diameter (i.e. “allometric” equations), to tree diameter changes measured in monitoring plots by various groups of people worldwide over the last few decades. This was done separately for each of 403 species on several continents, the biomass equations coming from several literature sources.  Anyone experienced in tree biometry will thus be on high alert right away, for several potential issues.  The two most important sources for the equations used, Chave et al (2005) for the tropics, and Jenkins et al (2004); see also here) for North America, are themselves secondary sources, compiling equations from varying more primary sources.  Equations for some North American species were developed by the authors, primarily for evaluation of other sources.

As you might guess, big trees are highly variable and hard to estimate well.  There are thus many allometric equations out there; in their major compilation Jenkins et al (2004) found nearly 350 for whole tree AGB (some excluding stumps) in just North American species alone, excluding Mexico.  Construction of these varies widely in terms of methods used, source location, sample size, date, stand history, etc., and the only way to evaluate their accuracy is to actually measure some trees, often destructively.  This involves measuring/estimating the total volume of bole, branches, bark, and foliage and then multiplying these by standard dry density values.  There’s a lot of measurement error involved, and it’s time consuming, so there’s not a large, publicly available data set to draw on.

For example, both tree growth form (including height, crown form, branch development, self-pruning habits, etc.), and growth rate, are greatly influenced by competitive conditions.  Many allometric equations use stem diameter alone as the biomass/carbon predictor; this practice implicitly assumes a certain, defined competitive growth environment.  But in natural tree stands, the competitive (and abiotic) environments can and do vary wildly over time and space, so the growth conditions of one’s study trees may not be the same as those from which the particular allometric equations used, were derived.  Allometric approaches in trees originated from forestry, where the focus on stem wood (i.e. lumber) production, in settings with highly controlled competition, more uniform resource availabilities, and conducted over the generally shorter time spans of rotation forestry, is a much more focused and precise task than is estimating total biomass/carbon in wild trees.

Notwithstanding these concerns, there is in fact very often good biomass predictability, if sample sizes are high enough and/or important sources of variation are taken into account, because there are indeed strong, genetically based constraints on tree form.

II. Specifics

The specific issues I have with the paper can be conveniently placed into three categories:
(1) Sampling issues
(2) Biological implications of stat/math issues
(3) Results presentation issues

To be continued

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