Forest production efficiency increases with growth temperature

Forest production efficiency (FPE) metric describes how efficiently the assimilated carbon is partitioned into plants organs (biomass production, BP) or—more generally—for the production of organic matter (net primary production, NPP). We present a global analysis of the relationship of FPE to stand-age and climate, based on a large compilation of data on gross primary production and either BP or NPP. FPE is important for both forest production and atmospheric carbon dioxide uptake. We find that FPE increases with absolute latitude, precipitation and (all else equal) with temperature. Earlier findings—FPE declining with age—are also supported by this analysis. However, the temperature effect is opposite to what would be expected based on the short-term physiological response of respiration rates to temperature, implying a top-down regulation of carbon loss, perhaps reflecting the higher carbon costs of nutrient acquisition in colder climates. Current ecosystem models do not reproduce this phenomenon. They consistently predict lower FPE in warmer climates, and are therefore likely to overestimate carbon losses in a warming climate.

aboveground forest production efficiency and how it varies with climate (predominantly temperature, precipitation, and indirectly radiation through the use of latitude in their models). The authors find that FPE increases with temperature across the studies that they compiled. Further the authors find the opposite trend across 8 vegetation models included in the TRENDY project. This result goes against hypotheses included in the TRENDY models where there is increased respiration sensitivity with higher temperature. The authors thus hypothesize that the diverging trend between models and observations is due to acclimation of respiration, a process not included in the TRENDY models. This is a very interesting study and will result in a high number of citations, if for nothing else then the impressive database of FPE studies that the authors invested an enormous amount of work compiling (provided that the authors make it open access, which seems to be their intention based on my reading of the acknowledgements). Still, I have several significant reservations that need to be addressed before publication.
My biggest concern is that in the majority of the panels in Fig. 4 there are very few tropical data points and a large variability at more temperate latitudes. Im worried that the handful of tropical data points could be driving significance trends. In particular, Fig 4d has just 2 points in blue and 3 points in green with |lat| < 20 degrees. If the authors exclude these points, do they still get significant climate relationships? I would like to see the sensitivity of the authors' conclusions to these data points.
Second, though well written overall, I found the organization to be difficult given the format of NC where the methods are at the end. I felt very in the dark about what was meant by 'Micromet' and 'Scaling' and it would be helpful for the authors to include this upfront in the main text. Some structural suggestions are in my line specific comments. Further, Fig. 1, Fig 2a,  My line specific comments are listed below: General methods questions: The authors mention testing the temperature response while holding latitude constant in the discussion but I couldn't find this in the methods.
Its not clear why the authors didn't look at other climate variables. This could explain the significant spread within a particular latitude (fig 4). The choice of climate variables needs to be justified.
The authors need to be clear that FPE is aboveground only. Indeed, this is part of the discussion at the end where boreal root allocation is mentioned, so it should be clear at the beginning in the definition.
L52-53 'Earlier findings -FPE declining with age -are supported by this analysis." This is a weird sentence for the abstract and it detracts from the authors work to put this first. It's a really cool result, but I wouldn't highlight it in the abstract for a general audience like NC. L340 what did the authors do with the data by different authors for the same site?
L352 did the authors look at nutrient status? (they say some of the plots were N fertilized) L368 the authors definition of terms might fit better here as it is integral in your estimation method L374-386 these definitions in some form need to be up in the main text, I felt in the dark without them L388-390 I was not familiar with the Luyssaert method and the latitudinal dependence seems very strange to me so I took a look at the paper. It would be nice for the authors to provide a 1-2 sentence for the latitudinal explanation so other readers can better understand why it is a useful way to estimate error to help them decide if they want to spend the time going to the Luyssaert paper L417 Im a little confused by this because it seems like the gpp methods were separated into different models (different colors, fig 4)? Could the authors help me understand how the random effect (GPPmeth) is different from this binning of different data Table 1: are these coefficients standardized or the raw response coefficients. Judging from the use in Fig 4 they are raw, which makes sense in that context, but it is important to be clear so the reader doesn't compare the sensitivity L492 was CUE calculated as the average over the 20 years? It is unclear how the temporal component factors into the analysis. The statistical modeling part of the TRENDY model analysis needs more explanation Reviewer #3: Remarks to the Author: Review of NCOMMS-20-12586: Forest production efficiency increases with growth temperature by Collalti et al.
Collalti et al. assemble and analyze a large global dataset to explore: (1) the range of carbon use efficiency (CUE) and biomass production efficiency (BPE) values present in forests to compare to prior published work; and (2) relationships between these metrics and stand (i.e., age) and environmental (i.e., climate) variables. The overall goal was to build upon prior studies (with much smaller data sets) to test current understanding and use of these concepts in dynamic models. In line with prior studies, they found that there is a wide range in CUE and BPE estimates but that mean values center around 0.47. Moreover, they found that these variables decline with age (also seen in prior studies), while increasing with latitude, precipitation and temperature. This last observed relationship (i.e., declining CUE and BPE with temperature is contrary to current understanding and treatment in models). Much attention, therefore, it given to this point as it is commonly not included in models as such (rather, the opposite is true of most/al current models).
Overall, I found this work to be timely, important and well presented. While the average values presented herein are almost identical to initial work done by Waring et al. some 20+years ago, they are based on well more than 200 observations compared to the 12 used in Waring et al. (which also included many assumptions to estimate CUE that potentially constrained the results). In addition, evidence of declining CUE with stand age was first reported by DeLucia et al. 2007. However, that analysis appeared to be anchored by a single study with an unrealistically high CUE estimate (in excess of 0.8 if I remember correctly), and eliminating that single data point resulted in no relationship whatsoever between stand age and CUE. As such, the current study is a significant advance over the prior studies that were limited by much smaller datasets at the time they were published. Importantly, CUE and BPE are critically important components of the dynamic vegetation models that allow the prediction of future forest C dynamics. If all of those models get any of this wrong to start with, the results of those models are suspect at best. I have no major revision suggestions, but a series of more minor suggestions for the authors to consider. I very much enjoyed reading this article, feel that it is timely and important for the field, and will be of great interest to ecologists and modelers globally. 1) CUE vs. BPE vs. FPE. The authors go to great length to define and outline the terms CUE and BPE, including their differences, assumptions and potential problems. They then show that these two estimates were statistically indistinguishable in their data set, so move to Forest Production Efficiency (FPE) thereafter (and in the title, abstract, etc.). My suggestion is to just use FPE from the very get go, and in defining it talk about its relationship to CUE and BPE. I found the current presentation and use of the three terms to be a bit distracting considering that ultimately FPE was used for most/all analyses. It strikes me that FPE is an overarching term that includes and, in the case of this article, subsumes CUE and BPE.
2) Relationship of FPE and temperature. This is likely to be one of the most important, and potentially controversial, results of this study as it goes against current understand of plant responses to rising temperature, as the authors highlight. With that in mind, I encourage the authors to consider two points. First, the response of forests to long term temperature vs. the response of forests to short term increases in temperature are not necessarily the same thing. You have identified a response of forests that are acclimated to the temperature in which they are growing, vs. a response that may occur over much shorter time scales with contemporary climate change (this latter response is what many models are trying to predict). This is particularly important in forests that are at the high end of their optimum temperature range (e.g., tropical forests), which might well respond differently to rapid increases in temperature compared to temperate or boreal forests. I feel like this deserves more attention in the paper (e.g., couching this result in this context). Second, the relationship observed between FPE and temperature only accounts for 30% of the variation in the data. The authors stress that this was an "unexpectedly high" accounting of variance given the limitations of the data, but it still shows that 70% of that variation is unaccounted for. This also deserves more attention in my opinion for this finding to be more useful to the wider community of scientists. As it stands, the authors leave this as being explained by a higher cost for nutrient acquisition in boreal forests. There is evidence for this, but does that explain the entire result?
3) There are a lot of Methods sprinkled throughout the Results which made that section a bit hard to decipher. Suggest moving all methods to Methods, and focusing on results in Results. To my knowledge, that is the only study that systematically examined each of these competing hypotheses in one model study system. They found that across the competing hypotheses, the age-related decline in NPP was a result of the decline in aboveground wood production being proportionally greater than the decline in canopy photosynthesis. 6) Environmental effects on FPE. Were TAP and MAT correlated in the dataset (typically they are)? If so, how did you handle this to tease apart real vs. potential autocorrelation effects on FPE?

Comments on "Forest production efficiency increases with growth temperature" submitted by A. Collalti et al. to Nature Communications
General points Comment 1: This is an interesting peace of work for me and I enjoyed reading the manuscript. In this study, the authors explored the global relationships of forest production efficiency (FPE: i.e. carbon use efficiency and biomass production efficiency), with biological and environmental factors. They constructed a database of observations for productivities (GPP and NPP), biomass production, and explanatory variables. By applying the mixed-effects multivariate linear regression, they found positive relationships with latitude, temperature, and precipitation, and a negative relationship with stand age. The positive relationship with temperature is, as long as I know, a novel finding in terms of both observations and process-based modelling. Then, they discussed underlying mechanisms for the counterintuitive relationship, such as thermal acclimation and nutrient acquisition cost. As demonstrated by the relationships in TRENDY outputs, the contemporary models do not capture the positive relationship between temperature and FPE, implying a serious bias in the present estimation of global carbon budget. In this sense, this study has considerable importance for improving our predictability of the global carbon budget.
Reply 1: We thank the reviewer for this positive assessment.
Comment 2: There remain, however, several technical concerns in this study. I agree that the authors made great effort to compile the database (as shown by global coverage in Figure S1), but it could contain some biases. For example, Table S1 shows that MAT is significantly correlated with age. Although the authors defend the statistical approach adopted in this study , I suppose that the multicollinearity should have affected the results. At least, the authors should show the values of variance inflation factor (VIF) which is also available by R packages.
Reply 2: We thank the reviewer for this comment that gives us the opportunity to clarify.
There are correlations among the explanatory variables, but they are moderate, with only the correlation between MAT and |lat| exceeding 0.7 (0.82). Following the comment, we have calculated the Variance Inflation Factors, both from the vif() function in the R package car, and as the diagonal in the inverse of the correlation matrix, following Harrell (2013), page 65, with similar results. There is no generally accepted level for the VIF, under which data are regarded as unproblematic. In Brown, Tauber and Walczak (2009), J. Ferré argues that a VIF > 10 indicates problems. Other scientists argue for a more cautious approach where the VIF limit is 5 (e.g. Kumar, 2020). But none of these limits indicate problems for our data, since the VIFs are between 1.1 and 3.8 (Line 493 -494).
In general, problems with collinearity become more acute when the model contains interactions. This is not the case in our model. therefore decided to use the p-value method, given that it is of better use for the implemented modelling approach. However, in the "Model selection" paragraph we describe that we compared our model with a log-transformed one and that we used AIC and BIC to quantify the comparison.

 Reviewer# 2
Comment 11: In this manuscript, Collalti et al compiled a database of 244 records across >100 forest sites to look at aboveground forest production efficiency and how it varies with climate (predominantly temperature, precipitation, and indirectly radiation through the use of latitude in their models). The authors find that FPE increases with temperature across the studies that they compiled. Further the authors find the opposite trend across 8 vegetation models included in the TRENDY project. This result goes against hypotheses included in the TRENDY models where there is increased respiration sensitivity with higher temperature. The authors thus hypothesize that the diverging trend between models and observations is due to acclimation of respiration, a process not included in the TRENDY models.

This is a very interesting study and will result in a high number of citations, if for nothing else then the impressive database of FPE studies that the authors invested an enormous amount of work compiling (provided that the authors make it open access, which seems to be their intention based on my reading of the acknowledgements). Still, I have several significant reservations that need to be addressed before publication.
Reply 11: We are pleased that the referee found our manuscript interesting and we do confirm our intention to make the database open access to everyone who might be interested. We will publish the data on Zenodo server (already at https://doi.org/10.5281/zenodo.3953478) immediately after the publication of the manuscript.

Comment 12:
My biggest concern is that in the majority of the panels in Fig. 4 there are very few tropical data points and a large variability at more temperate latitudes. I'm worried that the handful of tropical data points could be driving significance trends. In particular , Fig 4d has just 2 points in blue and 3 points in green with |lat| < 20 degrees. If the authors exclude these points, do they still get significant climate relationships? I would like to see the sensitivity of the authors' conclusions to these data points.
Reply 12: We performed the requested analysis and left out the five mentioned records collected on tropical forests. The table below shows that the exclusion does not considerably alter the empirical relationship that was described using the full data set with all the sites: -with tropical sites (AD-test for normality p = 0.0978)

Estimate
Std. Reply 13: We agree with the referee's concern that the specific structure of Nature Communications

papers, with the Methods section at the end, suggests a need for some extra guidance to the reader in the Results section. We have followed the referee's suggestion and included a brief description of the nature of 'scaling', 'micrometeorological' and 'model' terms (Line 119 -121). Thanks for this suggestion which (we think) has improved the manuscript's readability.
Comment 14: Further, Fig. 1, Fig 2a, and Fig 3 are more methods oriented and might be more appropriate for the SI.
Reply 14: We agree that Fig. 1b could be more 'methods oriented' and we have moved this figure to SI (now Fig. S2). However, Figs. 1a, 2a, and 3 describe how FPE (as both CUE and/or BPE) are (potentially) different (Fig. 1a) because of the methods used to estimate them (Fig. 2a), as driven by age (Fig. 2b), and substantially, on average, close to the Waring et al.'s regression (Fig. 3). Fig. 3

Comment 42: L417 I'm a little confused by this because it seems like the gpp methods were separated into different models (different colors, fig 4)? Could the authors help me understand how the random effect (GPPmeth) is different from this binning of different data
Reply 42: The mixed model approach that we used is more powerful than performing the analysis separately in bins. The random effect allows for an intercept specific to the classes of random effect variables, while it keeps the fixed effects (slopes) global to the entire data set. Randomizing an effect thus transfers the variation from the systematic part of the model to the random part, thus incorporating the variation of the variable within the uncertainty of the model. In this way, one analyses the slope (here, the sensitivity of FPE to predictor variables) while correcting for small differences in FPE values across different classes of the random effect. In a binned analysis, by contrast, the slopes would be specific to every bin and the degrees of freedom would be higher. It also means that when using the regression model to make predictions, you need not specify a bin. (The price is a higher uncertainty, as both the uncertainty of bins and the residual variation need to be taken into account).  . 5 and S4). This is now better specified in the revised version (Line 554 -557).

Collalti et al. assemble and analyze a large global dataset to explore: (1) the range of carbon use efficiency (CUE) and biomass production efficiency (BPE) values present in forests to compare to prior published work; and
(2) relationships between these metrics and stand (i.e., age) and environmental (i.e., climate) variables. The overall goal was to build upon prior studies (with much smaller data sets) to test current understanding and use of these concepts in dynamic models. In line with prior studies, they found that there is a wide range in CUE and BPE estimates but that mean values center around 0.47. Moreover, they found that these variables decline with age (also seen in prior studies), while increasing with latitude, precipitation and temperature. This last observed relationship (i.e., declining CUE and BPE with temperature is contrary to current understanding and treatment in models). Much attention, therefore, it given to this point as it is commonly not included in models as such (rather, the opposite is true of most/al current models). Reply 45: We are grateful for the positive assessment by Prof. Litton and have used his comments to be more specific on the still rather vague knowledge of age relationships prior to our study. We hope that this new revised version has also clarified the minor concerns.

"The observed increase in FPE with MAT is new, and is opposite to what would be expected based on the instantaneous responses of photosynthesis and plant respiration as described in textbooks and assumed in many process-based models." (Line 250 -252) and "However, the instantaneous response of autotrophic respiration rate is largely irrelevant here because of the longer time scale" (Line 255 -256) and further "This acclimation takes place on a time scale of days to weeks. Genetic adaptation throughout multiple generations is expected to proceed in the same direction (for definitions and distinctions between acclimation and adaptation see ref. 43)." (Line 259 -261).
Our results and our findings clearly do not refer to short-term temperature responses (as they are based on annual values, or, in some cases, even mean values over different years) but rather they represent much longer-term responses at different temperature. We have now better clarified (Line 285 -286): "Heat tolerance in leaves has also been found to increase linearly with temperature and to decrease with absolute latitude 49 .". Moreover, we discuss the reasons why, in our opinion, TRENDY models (but potentially many other different vegetation models not necessarily included in the TRENDY project) may fail in accounting for the temperature response, through: "we note that the standard approach in today's land ecosystem models as shown here, or more generally in vegetation modelswhere maintenance respiration per unit of respiring tissue is typically determined as a fixed basal rate at a standard temperature (commonly 15 or 20 C°), increasing with the substrate and temperature according to a fixed Q10 factor or Arrhenius-type equation -cannot generate the observed positive response of CUE or BPE to growth temperature observed in our study." (Line 308 -313). We agree that our work gives new insights on the potentially different effects that the expected climate change may have on the long-term on forests at the "extremes" of the temperature range (tropical and boreal forests).
Comment 48: Second, the relationship observed between FPE and temperature only accounts for 30% of the variation in the data. The authors stress that this was an "unexpectedly high" accounting of variance given the limitations of the data, but it still shows that 70% of that variation is unaccounted for. This also deserves more attention in my opinion for this finding to be more useful to the wider community of scientists. As it stands, the authors leave this as being explained by a higher cost for nutrient acquisition in boreal forests. There is evidence for this, but does that explain the entire result?
Reply 48: As we write, it was not expected to be able to explain an even higher fraction of inter site variability in FPE. One can argue that our model considered only a globally common set of interacting effects on FPE, while the residual variance can be possibly attributed to similar global factors, where we lack driver data for a sufficiently large number of data records, and to local factors, determined by the specific situation at the site (e.g., management, specific eco-physiology of the species involved etc.) and, of course, to random variability. At this stage, any further analysis without further information would be speculation. Hence, we confine our analysis to the novel and scientifically relevant results, i.e. the statistically significant global response pattern and the possible underlying mechanisms that constrain it. Reply 49: We agree with the Prof Litton's impression and we choose to amend the text with some basic information on the methods to help the reader understand the matter without the necessity to visit the method section that is generally located after the results section the end in Nat. Comm. papers. Such a guidance on methods in the main text was also suggested by another reviewer (e.g. see comment and Reply 40). Additionally, some of the variability in measured FPE is driven by succinct effects from the "methods" used (in the sense of GPP methods used to obtain the results). We have, therefore, not completely followed the advice of the referee, but if the editors think that we should remove these short methodological clarifications throughout the results sections we will be happy to do so. Comment 50: 4) Lines 77-79: Worth citing Clark et al. 2001 here (Clark, D. A., S. Brown, D. W. Kicklighter, J. Q. Chambers, J. R. Thomlinson, andJ. Ni. 2001. Measuring net primary production in forests: concepts and field methods. Ecological Applications 11:356-370)? They do a nice job of estimating the impact on NPP values when ignoring these components.