# Reply to: Disentangling biology from mathematical necessity in twentieth-century gymnosperm resilience trends

Xiangyi Li, Shilong Piao, Kai Wang, Xuhui Wang, Tao Wang, Philippe Ciais, Anping Chen, Xu Lian, Shushi Peng, Josep Peñuelas

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Xiangyi Li, Shilong Piao, Kai Wang, Xuhui Wang, Tao Wang, et al.. Reply to: Disentangling biology from mathematical necessity in twentieth-century gymnosperm resilience trends. Nature Ecology & Evolution, 2021, 5 (6), pp.736-737. 10.1038/s41559-021-01412-4 . hal-04624410

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# Reply to: Disentangling biology from mathematical necessity in twentieth-century gymnosperm resilience trends

Xiangyi Li<fnref n="1" />, Shilong Piao<fnref n="1" />,²✉, Kai Wang<fnref n="1" />, Xuhui Wang<fnref n="1" />, Tao Wang<fnref n="1" />,², Philippe Ciais<fnref n="1" />,³, Anping Chen⁴, Xu Lian<fnref n="1" />, Shushi Peng<fnref n="1" /> and Josep Peñuelas<fnref n="1" />,⁵,⁶

REPLYING TO T. Zheng et al. *Nature Ecology & Evolution* https://doi.org/10.1038/s41559-021-01436-w (2021)

We used a global data set of tree rings to demonstrate an increase in resilience (post-drought recovery rate) and a decrease in drought resistance (sensitivity to drought) for gymnosperms over 1950–2009 driven by plant ecophysiological adaptation to increasing drought. Zheng et al. confirmed our key finding using the same resilience metric, but they argued that our finding would not hold using a different resilience metric. We show that the alternative resilience metric Zheng et al. proposed to use does not include information about different declines in growth rate induced by drought and thus cannot be used for comparing the recovery of tree growth for a large range of drought severity across space and over time. Their metric hence does not fit the purpose of our original study, which aimed to understand the change and adaptation of plant ecophysiological traits under drought.

We recently reported how drought resistance and resilience had changed for gymnosperms since 1950 based on a comprehensive data set of >2,900 tree-ring records<fnref n="1" />. Zheng et al.² repeated our analyses and successfully replicated our result, thus independently confirming our findings of decreased resistance and increased resilience for gymnosperms during 1950–2009. We value their independent validation, which was a commendable effort for replicable science. A recent study by Depardieu et al.³ also reported an increase in drought resilience of a gymnosperm species, confirming our finding.

Zheng et al., however, raised an issue on how resilience should be calculated. In our study<fnref n="1" />, we calculated resilience (Rs) using:

$$Rs^{Li} = \left| \frac{G_d - \overline{G_{mean}}}{G_{d+2} - \overline{G_{mean}}} \right| \quad (1)$$

where $G_d$ and $G_{d+2}$ are the growth rates during a drought year and two years after the drought, respectively, and $G_{mean}$ is the reference normal condition of growth, calculated using the mean growth rate during non-drought years. This equation has been used in other studies, such as ref. ⁴. Zheng et al.² argued that other definitions of resilience, in addition to equation (1), should also be used to assess our findings. Specifically, they suggested a metric proposed by Lloret et al.⁵ (equation (2)), in which resilience is quantified as the

ratio of average growth rates following ($G_{post}$) and prior to ($G_{prev}$) a drought:

$$Rs^{Lloret} = \frac{G_{post}}{G_{prev}} \quad (2)$$

Gymnosperm resilience did not tend to increase when this $Rs^{Lloret}$ metric was applied. We agree that resilience has multiple definitions in the literature, but the metric Zheng et al.² proposed does not serve the purpose of our specific study, and the result based on this metric is ambiguous. Below we elucidate the weaknesses of Zheng and colleagues' method for our study purpose.

First, we defined resilience as 'post-drought recovery rate', as clearly stated in the abstract of ref. <fnref n="1" />. Importantly, recovery begins from the reduced tree growth caused by drought, not from pre-drought growth in normal years. To calculate resilience as the recovery rate, one thus needs to know not only the magnitude of post-drought growth recovery relative to the normal growth rate, but also how much growth was reduced due to the drought, which is what equation (1) describes.

By contrast, however, equation (2) contains no information about different magnitudes of growth rate reduction caused by different droughts, and such a metric is inapplicable to comparison for post-drought recovery across sites, species or time. For example, as shown in Fig. 1, for trees that have experienced different growth reductions but recovered to the same post-drought growth rate, it is clear that those that have undergone more growth rate decline during the drought have higher rates of recovery, that is, they are more resilient, which can also be reproduced by our method (equation (1)). Equation (2), however, would provide the same resilience ($RsA = RsB$; Fig. 1), thus missing the difference.

Second, the formulation of equation (2) does not help us to understand how trees adapt to changes in drought severity and frequency by varying their ecophysiological traits, because drought severity will become the primary factor determining both resistance and resilience. This equation will naturally lead to a 'positive' (but often false) relationship between drought resistance and resilience: for sites and years with higher drought severity, trees will

<footnote n="1">¹Sino-French Institute for Earth System Science, College of Urban and Environmental Sciences, Peking University, Beijing, China. ²Key Laboratory of Alpine Ecology and Biodiversity, Institute of Tibetan Plateau Research, Center for Excellence in Tibetan Earth Science, Chinese Academy of Sciences, Beijing, China. ³Laboratoire des Sciences du Climat et de l'Environnement, CEA CNRS UVSQ, Gif-sur-Yvette, France. ⁴Department of Biology and Graduate Degree Program in Ecology, Colorado State University, Fort Collins, CO, USA. ⁵CSIC, Global Ecology Unit CREAF-CSIC-UAB, Bellaterra, Barcelona, Catalonia, Spain. ⁶CREAF, Cerdanyola del Vallès, Barcelona, Catalonia, Spain. ✉e-mail: slpiao@pku.edu.cn</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1 | Conceptual diagram of the decline in tree growth during drought and its post-drought recovery.** The orange (extreme A) and blue (extreme B) curves represent changes in rates of tree growth during and after extreme droughts A and B, respectively. The grey dashed line represents the growth rate prior to drought, and the red dashed line is the post-drought growth rate. The vertical brown dashed line represents the difference of tree growth reduction between the two extreme drought events. In calculating resilience as the recovery rate, the metric used by Zheng et al. did not include information for different magnitudes of growth reduction during extremes A and B, and relied simply on the growth rate prior to drought (grey dashed line) and after drought (red dashed line). With the metric used by Zheng and colleagues, resilience under extreme A (RsA) would be the same as that under extreme B (RsB), that is, $RsA = RsB$. Note that recovery begins from the lowest point of each curve, but RsA is clearly higher than RsB.</figcaption></figure>

be more severely affected and thus have both low ‘resistance’ and low post-drought ‘resilience’, and vice versa. The decrease in gymnosperm Rs<sup>Lloret</sup> during 1950–2009 derived by Zheng et al.<sup>2</sup> using equation (2) was thus likely due to an increase in drought severity<sup>6</sup>, but not necessarily lower post-drought recovery.

Trees have lower rates of post-drought recovery when they are affected by larger drought damage. Without other environmental factors enhancing tree growth in normal years, such as rising CO<sub>2</sub> levels<sup>7,8</sup>, we would not expect the increase in the rate of gymnosperm recovery under the increasing drought damage during 1950–2009. Our finding of an increase in the rate of gymnosperm recovery thus provides the opportunity to look at the role of other evolving environmental factors on enhancing the capacity for the recovery of post-drought tree growth, which could not be achieved with the Rs<sup>Lloret</sup> used by Zheng and colleagues<sup>2</sup>.

In addition, Zheng et al.<sup>2</sup> worried that the formulation of equation (1) could mathematically lead to a negative autocorrelation between resistance and resilience. Assuming that the autocorrelation is the main cause of the observed negative relationship between gymnosperm resistance and resilience, one would expect that both resistance and resilience are driven by the same dominant forces. By contrast, however, we found that changes in gymnosperm resilience

and resistance were driven by different plant traits and that ecophysiological mechanisms could be responsible for these phenomena. Specifically, the change in resistance was driven by multiple hydraulic traits affecting the capacity of trees to cope with hydraulic failure, but the change in resilience was mainly driven by foliar economic traits associated with the demand of an enhanced photosynthetic rate and more carbon acquisition (figure 2 in ref. <sup>1</sup>). The autocorrelation was thus unlikely to be the main cause of the temporal patterns of resistance and resilience identified in our study.

In conclusion, we appreciate the effort of Zheng et al.<sup>2</sup> in replicating our analyses and welcome the opportunity to address their questions. The equation used by Zheng et al. for calculating resilience, however, does not fit the scope of our study, which aimed to discover how trees adjust ecophysiological traits for coping with changing drought. The decreasing trend of Rs<sup>Lloret</sup> reported by Zheng et al. could be simply a result of the trend of increasing drought over the past half-century and obscures any signal of plant adaptation under increasing drought.

Received: 8 September 2020; Accepted: 10 February 2021; Published online: 5 April 2021

## References

1. Li, X. et al. Temporal trade-off between gymnosperm resistance and resilience increases forest sensitivity to extreme drought. *Nat. Ecol. Evol.* **4**, 1075–1083 (2020).

2. Zheng, T. et al. Disentangling biology from mathematical necessity in twentieth-century gymnosperm resilience trends. *Nat. Ecol. Evol.* https://doi.org/10.1038/s41559-021-01436-w (2021).

3. Depardieu, C. et al. Adaptive genetic variation to drought in a widely distributed conifer suggests a potential for increasing forest resilience in a drying climate. *New Phytol.* **227**, 427–439 (2020).

4. Isbell, F. et al. Biodiversity increases the resistance of ecosystem productivity to climate extremes. *Nature* **526**, 574–577 (2015).

5. Lloret, F. et al. Components of tree resilience: effects of successive low growth episodes in old ponderosa pine forests. *Oikos* **120**, 1909–1920 (2011).

6. Dai, A. Increasing drought under global warming in observations and models. *Nat. Clim. Change* **3**, 52–58 (2013).

7. Keenan, T. F. et al. Increase in forest water-use efficiency as atmospheric carbon dioxide concentrations rise. *Nature* **499**, 324–327 (2013).

8. Piao, S. et al. Characteristics, drivers and feedbacks of global greening. *Nat. Rev. Earth Environ.* **1**, 14–27 (2020).

## Acknowledgements

This study was supported by the National Natural Science Foundation of China (no. 41988101).

## Author contributions

S. Piao, X. Li and A.C. wrote the first draft of the reply with help from P.C., J.P., K.W., X.W., T.W., X. Lian and S. Peng; X. Li created the figure; P.C., J.P., K.W., X.W., T.W., X. Lian and S. Peng contributed to the revision of the reply.

## Competing interests

The authors declare no competing interests.

## Additional information

Correspondence and requests for materials should be addressed to S.P.

Peer review information *Nature Ecology & Evolution* thanks Nate Mcdowell and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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