# Optimization theory explains nighttime stomatal responses

Yujie Wang, William R.L. Anderegg, Martin D. Venturas, Anna T. Trugman, Kailiang Yu, Christian Frankenberg

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## To cite this version:

Yujie Wang, William R.L. Anderegg, Martin D. Venturas, Anna T. Trugman, Kailiang Yu, et al. Optimization theory explains nighttime stomatal responses. New Phytologist, 2021, 230 (4), pp.1550-1561. 10.1111/nph.17267. hal-03230896

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Author Manuscript

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Optimization theory explains nighttime stomatal responses

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Yujie Wang¹*, William R. L. Anderegg², Martin D. Venturas², Anna T. Trugman³, Kailiang Yu⁴, and Christian Frankenberg¹,⁵

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¹ Division of Geological and Planetary Sciences, California Institute of Technology,

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Pasadena, California 91125, USA

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² School of Biological Sciences, University of Utah, Salt Lake City, Utah 84112, USA

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³ Department of Geography, University of California Santa Barbara, Santa Barbara,

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California 93106, USA

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⁴ Le Laboratoire des Sciences du Climat et de l'Environnement,

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IPSL-LSCECEA/CNRS/UVSQ Saclay, Gif-sur-Yvette 91191, France

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⁵ Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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91109, USA

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* Author for correspondence: wyujie@caltech.edu, Telephone: +1 626-395-2021

ORCIDs

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<table><thead><tr><th>Name</th><th>ORCID</th></tr></thead><tbody><tr><td>Y. Wang</td><td>https://orcid.org/0000-0002-3729-2743</td></tr><tr><td>W.R.L. Anderegg</td><td>https://orcid.org/0000-0001-6551-3331</td></tr><tr><td>M.D. Venturas</td><td>https://orcid.org/0000-0001-5972-9064</td></tr><tr><td>A.T. Trugman</td><td>https://orcid.org/0000-0002-7903-9711</td></tr><tr><td>K. Yu</td><td>https://orcid.org/0000-0003-4223-5169</td></tr><tr><td>C. Frankenberg</td><td>https://orcid.org/0000-0002-0546-5857</td></tr></tbody></table>

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Statistics

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<table><tr><td>Summary</td><td>188 words</td></tr><tr><td>Main Text</td><td>6480 words</td></tr><tr><td>Number of Figures</td><td>7</td></tr><tr><td>Number of Tables</td><td>1</td></tr><tr><td>Supporting Information</td><td>5</td></tr></table>

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## SUMMARY

* Nocturnal transpiration is widely observed across species and biomes, and may significantly impact global water, carbon, and energy budgets. However, it remains elusive why plants lose water at night and how to model it at large scales.

* We hypothesized that plants optimize nighttime leaf diffusive conductance ($g_{wn}$) to balance potential daytime photosynthetic benefits and nocturnal transpiration benefits. We quantified nighttime benefits from respiratory reductions because of evaporative leaf cooling. We described nighttime costs as lost of carbon gain during the day because of water use at night. We measured nighttime stomatal responses and tested our model with water birch (*Betula occidentalis* Hook.) saplings grown in a greenhouse.

* The $g_{wn}$ of water birch decreased with drier soil, higher atmospheric CO$_2$, wetter air, lower leaf temperature, and lower leaf respiration rate. Our model predicted all these responses correctly, except for $g_{wn}$ response to air humidity. Our results also suggested that the slow decrease of $g_{wn}$ after sunset could be associated with decreasing leaf respiration.

* The optimality-based nocturnal transpiration model smoothly integrates with daytime stomatal optimization approaches, and thus has the potential to quantitatively predict nocturnal transpiration across space and time.

**Keywords:** evaporative cooling, fitness, nocturnal transpiration, optimization, photosynthesis, respiration, stomatal conductance
# 1 INTRODUCTION

Nocturnal transpiration in land plants has been observed globally across all functional types, biomes, and climates (Resco de Dios et al., 2019; Yu et al., 2019), and typically ranges from 5% to 30% of the daytime transpiration (Caird et al., 2007). However, nocturnal transpiration is often regarded to be at odds with existing optimal stomatal behavior theories, which predict no stomatal opening at night due to the inability to photosynthesize (Cirelli et al., 2016; Yu et al., 2019). Despite numerous studies that observe nocturnal transpiration (Fisher et al., 2007; Novick et al., 2009; Zeppel et al., 2011; Resco de Dios et al., 2015), no theory satisfactorily explains why stomata open at night or why they respond to the environment. As a result, nocturnal transpiration is often omitted in gas exchange simulations (e.g., Mackay et al., 2015; Venturas et al., 2018; Love et al., 2019) and, when present at all, is not mechanistically represented in land surface models (e.g., simply treated as a constant empirical minimal stomatal conductance term; Barnard & Bauerle, 2013; Lombardozzi et al., 2017).

If land surface models do not mechanistically and dynamically simulate nocturnal transpiration, this may lead to biases in predictions of energy and water fluxes during both day and night. Because nocturnal transpiration adds up total water use in a day and thus more rapid soil water depletion, the subsequent photosynthetic carbon gain becomes more limited. Faster soil drying also threatens plants with increased water stress, further impacting the simulation of carbon and water fluxes. Therefore, inaccurately accounting for nocturnal transpiration has the potential to introduce substantial errors in simulated water, carbon, and energy fluxes, the extent of which has not been fully quantified.

Plant nighttime transpiration rates ($E_n$) and nighttime leaf diffusive conductances ($g_{wn} = E_n/D$, where $D$ represents leaf-to-air vapor pressure deficit) do not stay constant throughout the night due to the varying environmental conditions and short term changes in plant physiology during the night. Typically, $g_{wn}$ decreases gradually after sunset, reaches a minimal value at midnight, and then increases before sunrise (Ogle et al., 2012; Resco de Dios et al., 2016). While predawn stomatal opening may be explained as a result of circadian rhythm for increasing early morning photosynthesis, little is known about why stomata close slowly after sunset. Thus, there must be an unknown benefit for the
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slow stomatal closure after sunset. Further, g<sub>wn</sub> typically decreases when soil gets drier (Cavender-Bares et al., 2007; Cirelli et al., 2016), is higher for plants grown at elevated CO<sub>2</sub> (Zeppel et al., 2012), and increases with higher leaf respiration rate (Marks & Lechowicz, 2007; Coupel-Ledru et al., 2016). However, g<sub>wn</sub> is reported to stay unchanged or decrease with drier air in some studies (Cirelli et al., 2016) but increase in others (Barbour et al., 2005; Dawson et al., 2007; Zeppel et al., 2012; Yu et al., 2019). Identifying the physiological and ecological drivers for all these observed nighttime stomatal behaviors requires more investigation.

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Observations that nocturnal transpiration varies with environment and time suggest the following: (i) Plants are actively controlling stomatal aperture at night. (ii) Plants are balancing the upsides for using water at night ("benefits" of nocturnal transpiration) and the downsides of not being able to use the water in the day ("costs" of nocturnal transpiration). The upsides and downsides of nocturnal transpiration fit well into a trade-off framework. However, similar to daytime stomatal optimization theories (Mencuccini et al., 2019; Wang et al., 2020), the difficulty is how to quantify and weigh the "benefits" and "costs" in various forms and measures to the same units.

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A number of theories and hypotheses centered on the causes and consequences of nocturnal transpiration have been proposed to explain why plants lose water at night (Zeppel et al., 2014). Common hypotheses include evaporative cooling, leaky stomata, nutrient uptake, oxygen delivery, CO₂ flush-out, suppression of hydraulic redistribution driven by competition, embolism removal, capacitance refilling, genetic control, and circadian rhythm for early morning stomatal opening (Table 1). These physiological and ecological causes and consequences may be plausible reasons for stomatal opening at night, and some do partially explain the observed nighttime stomatal behaviors (Table 1). However, there is not yet a theory that is able to explain all the observed patterns. Particularly, the contrasting nighttime stomatal responses to air humidity cannot be explained by any of the proposed upsides of nocturnal transpiration.

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The present study asks whether optimality theory that plants balance the benefits and costs of nocturnal transpiration can explain the observed nocturnal transpiration patterns. To answer the question, we proposed a new optimization model following the
trade-off framework to explain why plants regulate stomata at night. We then tested
the model predictions with water birch (Betula occidentalis Hook.) saplings grown in a
greenhouse.

2 MATERIALS AND METHODS

## 2.1 The theory

Water use at night could result in negative consequences to plants as the water
used during the nighttime is unavailable for daytime photosynthesis. As soil water
content declines, soil water potential becomes more negative, and thus the plant
hydraulic system is more stressed and photosynthetic gain decreases. Therefore,
nocturnal transpiration inherently results in a carbon cost separated in time (costs occur
in the subsequent daytime whereas benefits occur in the nighttime). The benefits
associated with nighttime water loss may include nutrient uptake, competition, and
evaporative cooling (a detailed summary in Table 1). Among these physiological and
ecological consequences of nocturnal transpiration, we posit that leaf cooling is a
particularly promising and readily quantifiable benefit that matches the unit of daytime
photosynthetic gain, while it is often neglected in previous nocturnal transpiration
studies.

If leaf cooling is considered a main benefit (B) of nighttime stomatal opening, when B exceeds the potential carbon cost of the nocturnal transpiration (Θ), the plant will use water at night. For instance, when the marginal reduction in respiration resulting from leaf cooling (∂B/∂E_n = -∂R_leaf/∂E_n, where R_leaf is the respiration rate at night, marginal gain of nocturnal transpiration) exceeds the marginal cost of nocturnal transpiration (∂Θ/∂E_n), plants will open stomata more at night until the marginal nighttime cost exceeds the marginal nighttime gain. Otherwise, plants will close the stomata more to avoid overusing the soil water at night. Note that our hypothesis differs from previous theory that highlighted benefit from leaf cooling (e.g., Coupel-Ledru et al., 2016), as our model also accounts for cost in pair with the benefit.

We hypothesized that plants optimize nocturnal transpiration to balance associated
benefit and cost. As the nocturnal transpiration cost is quantified using the daytime carbon gain, it ought to resemble the format of cost function of daytime transpiration (e.g., a carbon risk in plant hydraulic integrity). Therefore, we posited that nighttime transpiration rate is optimal when

where $A_d(E_n)$ is the potential daytime leaf photosynthetic rate at a given transpiration rate $E_n$ (assuming same transpiration rate in the day and at night), $f_f$ is a fitness factor, and $E_{crit}$ is the maximal leaf transpiration rate beyond which leaf desiccates because of hydraulic failure. The formulation “$\partial\Theta/\partial E_n = f_f \cdot A_d/(E_{crit} - E_n)$” is modified from the cost function proposed by Wang et al. (2020). See Fig. 1 for a detailed example of nocturnal transpiration optimization.

The $f_f$ describes the importance of daytime carbon cost relative to nighttime benefits, as leaf cooling may only be one of several potential benefits of nocturnal transpiration. For example, for a plant with sufficient water supply (e.g., with a fixed water table in the root zone), the plant may benefit more from other upsides of nocturnal transpiration (such as nutrient uptake and competition), and $f_f$ ought to be lower. Therefore, $f_f$ ought to be variable depending on the environment. We use $f_f$ ($< 1$) to account for other benefits of nocturnal transpiration ($f_f$ decreases when the other benefits increases).

Note that $\partial R_{leaf}/\partial E_n$ can be computed analytically (see Note S1 for the steps of the derivation) using

where $\lambda$ is the latent heat of vaporization, $c_p$ is the specific heat of dry air at a constant pressure, $g_{be}$ is the boundary layer conductance for sensible energy flux, $f_{view}$ is the mean view factor of the leaves from the air (ratio that radiated energy escape from the canopy, we assume $f_{view} = 1$/LAI, where LAI is the leaf area index), $\epsilon$ is the leaf emissivity (Campbell & Norman, 1998), $\sigma$ is the Stefan-Boltzmann constant, $T_{leaf}$ is leaf temperature in K, $\Delta H_a$ is the activation energy for the temperature dependence of $R_{leaf}$ (Bernacchi et al.,

$$ \frac{\partial B}{\partial E_n} - \frac{\partial \Theta}{\partial E_n} = -\frac{\partial R_{leaf}}{\partial E_n} - f_f \cdot \frac{A_d(E_n)}{E_{crit} - E_n} = 0 \quad (1) $$

$$ \frac{\partial R_{leaf}}{\partial E_n} = \frac{-\lambda}{2c_p g_{be} + 4f_{view} \epsilon \sigma T_{leaf}^3} \cdot R_{leaf} \cdot \frac{\Delta H_a}{RT_{leaf}^2} \quad (2) $$
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2001), and *R* is the ideal gas constant.

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## 2.2 Model prediction

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Our model predicts that if a plant has higher carbon cost (in subsequent daytime; higher $A_d / (E_{crit} - E_n)$, e.g., when soil is drier), it tends to use less water at night. On the other hand, if the plant can save more carbon through reduced respiration at night (higher $-\partial R_{leaf}/\partial E_n$, e.g., when $R_{leaf}$ is higher), it tends to use more water at night. Further, if $f_f$ decreases (e.g., as a result of increased benefit from other upsides), the plant will use more water at night.

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The paragraphs below analyze model predictions for nighttime stomatal responses to the environment, leaf respiration, and fitness factor. We evaluated the model by predicting the nighttime stomatal responses of a leaf or an individual tree to a new environment (e.g., drier soil, elevated atmospheric CO₂ [*C*<sub>a</sub>], drier air, and higher temperature). Note that the predicted responses apply to the scenario where trees have not acclimated their traits to the new environment.

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**Response to soil drought.** When the soil gets drier while other environmental conditions stay unchanged, at the same transpiration rate, the plant's risk of hydraulic failure increases ($A_d / (E_{crit} - E_n)$ increases because $E_{crit}$ decreases, cyan solid line to cyan dashed line, Fig. 2a). The nighttime benefit as a function of $E_n$, however, is not impacted by changes in soil moisture (red solid curve, Fig. 2a). The optimal $E_n$ (intersection of $\partial\Theta/\partial E_n$ and $-\partial R_{leaf}/\partial E_n$) and $g_{wn}$ should decrease with drier soil (from gray dot to black dot, Fig. 2a).

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**Response to $C_a$.** When atmospheric CO₂ increases while other environmental conditions stay unchanged, at the same transpiration rate, plant hydraulic risk stays unchanged whereas photosynthetic gain increases; and $A_d / (E_{crit} - E_n)$ increases due to higher potential daytime carbon gain (cyan solid line to cyan dashed line, Fig. 1b). The $-\partial R_{leaf}/\partial E_n$ as a function of $E_n$ is not impacted by $C_a$ (red solid curve, Fig. 2). Thus, the optimal $E_n$ and $g_{wn}$ ought to decrease at a higher $C_a$ (from gray dot to black dot, Fig. 2b).

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**Response to atmospheric vapor pressure deficit (VPD).** When only VPD gets higher (air gets drier, both daytime and nighttime), at the same transpiration rate, and
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the hydraulic system risk stays unchanged but photosynthetic rate decreases; and thus $A_d/(E_{crit} - E_n)$ ought to decrease with drier air (cyan solid line to cyan dashed line, Fig. 2c). The VPD, however, does not impact the leaf cooling for a given $E_n$ (red solid curve, Fig. 2c). Thus, the optimal $E_n$ increases with higher VPD. However, $g_{wn}$ may increase, stay constant, or decrease with higher VPD, and the trend depends on whether $E_n$ or leaf-to-air vapor pressure deficit (namely $D$) increases more (e.g., $g_{wn}$ increases with higher VPD when $E_n$ increases more).

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**Response to R<sub>n</sub>.** Holding environmental conditions constant, when $R_{leaf}$ increases, $A_d/(E_{crit} - E_n)$ slightly decreases because of the subtraction of respiration rate in net photosynthetic rate (cyan solid line to cyan dashed line, Fig. 2d), whereas $-\partial R_{leaf}/\partial E_n$ increases proportionally (red solid curve to red dashed curve). As a result, stomata should open more at night due to the higher $R_{leaf}$.

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**Response to temperature.** A warmer temperature (both daytime and nighttime) results in (i) a higher VPD in the air (drier air) and hence lower $A_d/(E_{crit} - E_n)$ (cyan solid line to cyan dashed line, Fig. 2e), and (ii) an exponentially increasing $-\partial R_{leaf}/\partial E_n$ with higher temperature (red solid curve to red dashed curve, Fig. 2e). Thus, the optimal $E_n$ ought to increase at a higher temperature. However, how $g_{wn}$ responds to higher temperature depends on whether $E_n$ or leaf-to-air vapor pressure deficit (namely $D$) increases more.

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**Response to fitness factor.** Holding environmental conditions and respiration rate constant, when $f_f$ decreases, $\partial R_{leaf}/\partial E_n$ and $A_d/(E_{crit} - E_n)$ are not impacted by $f_f$. However, $\partial \Theta/\partial E_n$ decreased with declining $f_f$ proportionally (cyan solid line to cyan dashed line, Fig. 2f). As a result, stomata should open more at night with lower $f_f$.

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In sum, our model predicts that $E_n$ and $g_{wn}$ decrease with drier soil, higher $C_a$, lower $R_{leaf}$, and higher $f_f$. Our model also predicts that $E_n$ increases with drier air and higher temperature, but $g_{wn}$ may either increase or decrease with drier air and higher temperature (assuming constant $f_f$).
## 2.3 Greenhouse measurements

In this study, we used two-year old water birch (Betula occidentalis Hook.) seedlings grown in the greenhouse of the School of Biological Sciences, University of Utah (Salt Lake City, USA). Each sapling was grown in a 5-gallon pot with local sandy clay loam soil starting in October 2016 (Wang et al., 2019). Trees were well watered every day at the end of the day except for during drought treatment. From November 2016 to April 2017, trees were under a supplemental light (Lucalox LU1000, GE Lighting, East Cleveland, Ohio, USA) from 8:00 am to 6:00 pm. Air temperature was ~ 25 °C and relative humidity was ~50% during this period. The plants were then exposed to natural temperature, light, and air humidity variations since May 2017. From July to September 2017, trees (about 1.5 m tall) were used to test how nocturnal transpiration responds to the environment and leaf respiration.

## 2.4 Responses to the environment

Twelve water birch saplings were used for this experiment. Six saplings were used to study how stomata respond to soil drought (subject to drought treatment), and six saplings were used to test the $C_a$, VPD, and temperature responses (well-watered every day). To ensure stable nighttime gas exchange measurements, after sunset, trees to be measured were moved from the greenhouse to the lab where room temperature was controlled at ~25 °C. Leaf gas exchange measurements were conducted during 11:00 pm to 4:00 am. After finishing the measurements, trees were moved back to the greenhouse.

**Drought response.** Six water birch trees were used to test how stomata respond to soil drought at night using a water stress treatment where the trees were left un-watered for four consecutive days. At 11:00 pm–12:00 am of the night before drought treatment, nighttime gas exchange rates were measured for three mature leaves from each tree with a portable photosynthesis system (Li-6800, LICOR Inc., Lincoln, NE, USA). The Li-6800 chamber was set to maintain the leaf temperature at 25 °C and the chamber relative humidity at 50%. Then, trees were bagged for at least 90 minutes to minimize the impact of nighttime transpiration rate on estimating soil water potential from leaf xylem pressure. For each tree, we chose a mature leaf close to the three leaves used for
gas exchange measurements, measured its leaf xylem pressure with a pressure chamber (PMS Instruments, Corvallis, OR, USA; precision ±0.05 MPa), and used as a proxy for soil water potential ($P_{\text{soil}}$). After measuring $P_{\text{soil}}$, bags were removed, and drought stress was initiated on the six trees. We note that there were > 200 leaves per sapling, and thus the leaf removal (≤ 4%) had minimal impact over the physiology of the remain leaves. Nighttime gas exchange rates (measured on the same three leaves) and $P_{\text{soil}}$ were measured for drought-stressed trees for four consecutive nights during the drought treatment.

**C<sub>a</sub> response.** Six well-watered trees (a different set of trees from drought-stressed ones) were used to test how stomata respond to CO<sub>2</sub> at night. Only one mature leaf from each tree was used for the CO<sub>2</sub> response curve. At the beginning of a CO<sub>2</sub> response curve, the Li-6800 chamber was set to a $C_a$ of 0 ppm and relative humidity of 50%. Leaf temperature was maintained at 25 °C throughout the CO<sub>2</sub> response curve. Then the chamber $C_a$ was set to 200, 400, 600, and 800 ppm in steps while the chamber relative humidity maintained at 50%. At each step (from 0 to 800 ppm), gas exchange rates were recorded after $E_n$ reached an equilibrium (typically > 1 hour stabilization when we change CO<sub>2</sub> concentration). A total of six CO<sub>2</sub> response curves were constructed from six trees. For three out of the six CO<sub>2</sub> response curves, an additional 100 ppm step was added between the 0 ppm and 200 ppm steps. The $g_{\text{wn}}$ at the equilibrium was used as the nighttime leaf diffusive conductance at each $C_a$ setting for each tree. The CO<sub>2</sub> response curves of $g_{\text{wd}}$ were also constructed for the same six trees (leaf temperature controlled at 25 °C, chamber relative humidity at 50%, and photosynthesis-active radiation at 1000 µmol m<sup>-2</sup> s<sup>-1</sup>) to compare with the $g_{\text{wn}}$.

**VPD response.** One mature leaf from each well-watered tree was used for the VPD response curve (same trees as CO<sub>2</sub> response curves, but different leaves). For each VPD response curve, the Li-6800 chamber VPD was ranged from low to high (0.5–3.0 kPa) while maintaining leaf temperature at 25 °C throughout the measurements (see Fig. S1 for an example of the stable leaf temperature). At each VPD setting, leaf-level gas exchange was monitored until reaching an equilibrium, and $g_{\text{wn}}$ at the equilibrium was used as the nighttime leaf diffusive conductance at the VPD setting.

**Temperature response.** One mature leaf from each of the six well-watered trees
was used to test the nighttime stomatal response to leaf temperature (same trees as CO2 and VPD response curves, but different leaves). For each leaf in the Li-6800 chamber, leaf temperature was ranged from low to high (19–35 °C), and the leaf-to-air vapor pressure deficit was maintained at 2.2 kPa throughout the measurements. At each leaf temperature setting, leaf gas exchange was monitored until reaching an equilibrium, and the gwn at the equilibrium was used at the temperature setting. As diffusive coefficient of water vapor increases with higher air temperature, gwn increases with higher temperature if stomatal pore aperture stay unchanged. Thus, we further normalized gwn to a reference temperature at 25 °C (gwn,25) to examine whether stomatal pore aperture changed during the temperature response curve. The temperature correction was made using gwn = gwn,25 · (Tleaf/298.15)1.8, where Tleaf is the leaf temperature in K (Nobel, 2009).

**2.5 Response to leaf respiration**

**Variation among leaves.** Leaf gas exchange rates were measured on different leaves to test how g<sub>wn</sub> varies with leaf respiration. For six consecutive nights, each of the six well-watered trees (same trees as CO<sub>2</sub> response curves) was moved to the lab. During 11:00 pm to 1:00 am, R<sub>leaf</sub> and g<sub>wn</sub> were measured for all the mature and healthy leaves of each tree with the portable photosynthesis system Li-6800. The Li-6800 chamber was set to maintain the chamber relative humidity at 50% and chamber air temperature at 25 °C. The R<sub>leaf</sub> and g<sub>wn</sub> were recorded when the leaf gas exchange was stable (usually within 2 minutes).

**Variation with time.** Leaf gas exchange was monitored on one single leaf per tree continuously to test how nighttime leaf gas exchange changes after sunset. For six consecutive days, each of the six well-watered trees was moved to the lab early in the morning. In the lab, a supplemental light (Lucalox LU1000, GE Lighting, East Cleveland, Ohio, USA) was applied to the tree, and the photosynthesis-active radiation was above 1200 µmol m⁻² s⁻¹ for the sunlit leaves. At the time of sunset, the supplemental light was turned off, and a sunlit leaf was attached to the Li-6800. The Li-6800 chamber was set to maintain a chamber relative humidity at 50% and chamber air temperature at 25 °C. Leaf
gas exchange was monitored continuously for 4–5 hours to test whether R<sub>leaf</sub> and g<sub>wn</sub>
covary after sunset.

**2.6 Model simulation**

We compared our model predictions quantitatively with experimental observations.
To run the model, we used the hydraulic and photosynthetic traits measured on plants
of the same cohort of trees used in this study (data from Wang *et al.*, 2019). The traits
we used were: a mean leaf area index of 4.76 ($f_{view}$ = 0.21), leaf width of 0.1 m, root
Weibull $B$ = 1.879 MPa, root Weibull $C$ = 2.396, root maximal hydraulic conductance of
34.383 mol H<sub>2</sub>O m<sup>-2</sup> s<sup>-1</sup> (per basal area), stem Weibull $B$ = 2.238 MPa, stem Weibull $C$ =
9.380, stem maximal hydraulic conductance of 76.029 mol H<sub>2</sub>O m<sup>-2</sup> s<sup>-1</sup> (per basal area),
leaf Weibull $B$ = 1.897 MPa, leaf Weibull $C$ = 2.203, leaf maximal hydraulic conductance
of 0.0176 mol H<sub>2</sub>O m<sup>-2</sup> s<sup>-1</sup> (per leaf area), leaf maximal carboxylation rate at 25 °C of
61.74 µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>, leaf maximal electron transport rate at 25 °C of 111.13 µmol
CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>, and leaf dark respiration rate at 25 °C of 1.5 µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>. We used
the temperature dependency parameter of respiration rate from Bernacchi *et al*. (2001)
($\Delta H_a$ = 46390 J mol<sup>-1</sup>). Code for the simulations is publicly available for download at
https://github.com/Yujie-WANG/Published-Codes-Yujie-WANG.

Briefly, for any combination of environmental conditions (soil moisture, VPD, and $C_a$) and leaf respiration rate, we solved the unique $E_n$ where $-\partial R_{leaf}/\partial E_n - f_f \cdot A_d / (E_{crit} - E_n) = 0$ (Fig. 1) using the following steps. (1) For a given nighttime transpiration rate $E$, we calculated leaf temperature using known air temperature and a prescribed wind speed of 0.1 m s$^{-1}$. (2) We numerically computed $E_{crit}$, at which leaf hydraulic conductance reached 0.1% of the maximum. (3) We used the same transpiration rate $E$ and leaf temperature for the daytime photosynthesis. With the known leaf temperature and transpiration rate, we were able to calculate leaf stomatal conductance assuming a boundary layer conductance for water vapor of 3 mol m$^{-2}$ s$^{-1}$, and thus photosynthetic rate using the classic photosynthesis model (Farquhar *et al.*, 1980). (4) We computed the $\partial\Theta/\partial E_n$ using an assumed $f_f$. (5) With the calculated leaf temperature, we computed $-\partial R_{leaf}/\partial E_n$ analytically using equation 2. (6) By tuning $E$, we were able to find the
optimal E_n and g_wn. We note that daytime leaf temperature is typically higher than nighttime leaf temperature (and thus higher VPD), so in practice, it is better to use a mean daytime leaf conditions (including temperature and solar radiation) to calculate the daytime photosynthesis in the cost function. Yet, to reduce the uncertainty in the model, we used nighttime leaf temperature and VPD to calculate photosynthetic rate.

We varied soil water potential from 0 to -1.5 MPa stepping by 0.1 MPa, while holding atmospheric VPD constant at 1.67 kPa and atmospheric CO2 constant at 400 ppm. At each soil water potential, we calculated optimal g wn using a constant prescribed f f = 0.15 and air temperature of 25 °C, and plotted the predicted curve against experimental observations. We varied Ca from 50 to 800 ppm stepping 50 ppm, while holding soil water saturated (soil water potential of 0) and atmospheric VPD constant at 1.67 kPa. At each Ca, we computed optimal g wn using a constant f f = 0.15 and air temperature of 25 °C. We varied VPD from 0.5 to 3.0 kPa stepping by 0.05 kPa, while holding soil water saturated and Ca constant at 400 ppm. At each VPD, we computed optimal g wn using a constant f f = 0.15 and air temperature of 25 °C. We ranged air temperature from 19 to 35 °C stepping by 1 °C, while holding soil water saturated, VPD = 1.67 kPa, and Ca = 400 ppm. At each air temperature, we computed optimal g wn using a constant f f = 0.15. We varied leaf dark respiration (normalized to 25 °C) from 0.1 to 2.0 µmol CO2 m-2 s-1 stepping by 0.1 µmol CO2 m-2 s-1, while holding soil water saturated, VPD = 1.67 kPa, and Ca = 400 ppm. At each leaf respiration rate setup, we computed optimal g wn using a constant f f = 0.15 and air temperature of 25 °C.

**Fitness factor.** The *f*<sub>*f*</sub> may be variable as the importance of respiratory reduction may change with the environmental conditions. To test how a variable *f*<sub>*f*</sub> improves the model predicted *g*<sub>wn</sub>, we implemented an arbitrarily decreasing *f*<sub>*f*</sub> with increasing VPD: *f*<sub>*f*</sub> = 0.16 – 0.03 · VPD along the VPD steps. We also tested an arbitrarily increasing *f*<sub>*f*</sub> with increasing temperature (T): *f*<sub>*f*</sub> = 0.021 · exp(0.075 · T). As *f*<sub>*f*</sub> represents the other upsides of nocturnal transpiration that are hard to quantify, the estimation of *f*<sub>*f*</sub> has to rely on curve fitting existing data. Yet, *f*<sub>*f*</sub> is not solely an empirical fitting parameter because of its ecological significance, and the *f*<sub>*f*</sub> responses to the environment represent may imply how a plant weighs the benefits from nocturnal transpiration when environmental condition
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# 3 RESULTS

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## 3.1 Responses to the environment

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Nighttime transpiration (i.e., $E_n$) and nighttime leaf diffusive conductance (i.e., $g_{wn}$) decreased with drier soil (Fig. 3a) and higher CO₂ (Fig. 3b), and increased with higher VPD (Fig. 3c). The $g_{wn}$ ranged from 0.014 up to 0.08 mol m⁻² s⁻¹ for well-watered water birch trees and decreased to a range from 0.002 to 0.02 mol m⁻² s⁻¹ when soil dried down (Fig. 3a, each color represented an individual tree, same below). At very low leaf-level $C_a$ (c. 0 ppm), the $g_{wn}$ ranged from 0.09 up to 0.37 mol m⁻² s⁻¹ and averaged at 0.20 mol m⁻² s⁻¹, showing no significant difference with the mean $g_{wd}$ of 0.15 mol m⁻² s⁻¹ in the daytime (leaf-level $C_a$ = 0 ppm; t-test, N = 6, P = 0.30). The maximal stomatal opening at night for a $C_a$ = 0 ppm agreed with our model prediction, as the plants should reduce nighttime respiration rate as much as possible if there is no photosynthetic gain in the day. The $g_{wn}$ increased with atmospheric VPD for all the six leaves from the six well-watered trees (Fig. 3c), opposite of the typically observed decreasing $g_{wd}$ with higher VPD in the daytime.

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The $g_{wn}$ increased when leaf temperature increased from 19 to 35 °C while holding leaf-to-air D constant (Fig. 4a). The increase in $g_{wn}$ resulted from the increased diffusive coefficient of H₂O at a higher temperature and the more open stomatal aperture (as $g_{wn,25}$ also increased, Fig. 4b). All the observed nighttime stomatal behaviors were qualitatively predicted by the model using a constant fitness multiplier except for VPD response (Fig. 2–4). Particularly, our model quantitatively predicted the trends for soil moisture and $C_a$ responses. The disagreement in modeled and observed $g_{wn}$ responses to VPD and temperature may be a result of variable fitness multiplier (namely $f_f$).

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## 3.2 Response to leaf respiration

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The $g_{wn}$ increased with higher nighttime leaf respiration rate for every well-watered tree (Fig. 5). The $R_{leaf}$ and its correlation with $g_{wn}$ differed among trees (Fig. 5). However,
$g_{wn}$ always showed a positive correlation with $R_{leaf}$ ($P < 0.05$, solid regression lines in Fig. 5). Our model using a constant $f_f = 0.15$ was able to quantitatively track the nighttime stomatal responses to higher respiration rate (gray curve in Fig. 5).

After “sunset” (light turned off in the lab), $g_{wn}$ and $R_{leaf}$ covaried for all the six leaves monitored (Fig. 6a). Taking one leaf as an example (red symbols in Fig. 6a), $R_{leaf}$ declined after “sunset” (red symbols in Fig. 6b), and $g_{wn}$ decreased accordingly (gray line in Fig. 6b). This covariation suggested that the slow decline of $g_{wn}$ after sunset was likely a result of slowly decreasing $R_{leaf}$.

We emphasized here that the leaf temperature varied less than 1.3 °C for the tested leaves in Fig. 5 and less than 0.8 °C in Fig. 6. The 1.3 and 0.8 °C temperature variation resulted in about 8.2% and 5.0% change in respiration rates for an individual leaf at 25 °C, respectively (See Note S1 for the computation of $\partial R_{leaf}/\partial T_{leaf}$). Thus, the variation of respiration rate among leaves in Figs. 5 and 6 was not the result of leaf cooling, but was likely the driving force of nocturnal transpiration.

## 3.3 Fitness factor

A constant fitness factor was able to explain quantitative nighttime stomatal responses to soil moisture, CO₂ concentration, and respiration, and qualitative response to temperature (Fig. 3–5). However, the qualitative disagreement in response to nighttime stomatal responses to VPD ($g_{wn}$ trend differed whereas $E_n$ trend agreed) and quantitative disagreement in response to temperature suggest a varying fitness factor in these scenarios. When we adopted a linearly decreasing $f_f$ with higher VPD and a exponentially increasing $f_f$ with higher temperature, the model predicted $g_{wn}$ was able to track the observations quantitatively (Fig. 7).

## 4 DISCUSSION

We proposed a new model that explains several puzzling plant responses associated with why stomata open at night and how stomata respond to nocturnal environment cues. The model uses leaf respiration rate to quantify the benefits of using water at night, as
the transpiration-resulted cooling reduces leaf respiration rate. The water loss at night, if used in the day, would benefit the plant with more photosynthetic gain, namely costs of using water at night. Therefore, nocturnal transpiration can be beneficial to plants if the marginal benefit exceeds the marginal daytime benefit, and plants ought to optimize nighttime stomatal behavior to balance the benefits and costs of nocturnal transpiration.

Our new framework predicts that plants decrease nighttime transpiration rate when soil is drier, atmospheric CO₂ is higher, atmospheric vapor pressure deficit is lower, leaf temperature is lower, and dark respiration is lower. In term of nighttime leaf diffusive conductance, the model predicts decreased conductance at drier soil, higher CO₂, lower temperature, and lower respiration. The nighttime leaf diffusive conductance at higher VPD, however, can be higher or lower depending on the environmental conditions (see sections below). Model prediction of g<sub>wn</sub> responses to the environment and respiration were validated with greenhouse-based measurements of water birch physiological responses. The covariation of nighttime respiration and transpiration also suggests that the decreasing nighttime leaf diffusive conductance after sunset may be the result of decreasing respiration during the night. Future research on how the circadian rhythm relates dynamic regulations of respiration rate will help understand the dynamics of nighttime leaf diffusive conductance.

Build on previous theories of the upsides and downsides of nocturnal transpiration, we proposed an optimization theory that plants regulate nighttime stomata aperture to balance the upsides and downsides. Our model significantly advances previous nocturnal transpiration theories as it (1) quantifies nighttime transpiration rate by optimizing the trade-off between nighttime benefits and daytime benefits (nighttime costs), (2) predicts observed nighttime stomatal responses to the environmental variables, and (3) can be merged seamlessly with existing daytime stomatal optimization models, and (4) allows for mechanistically incorporating nocturnal transpiration in larger scale vegetation models via an analysis of how the fitness factor varies with the environment.
## 4.1 $g_{wn}$ and the environment

Our model predicts nighttime leaf diffusive conductance decreases with increasing CO₂ (Fig. 2b), which is also experimentally validated on water birch sapling. However, trees grown at elevated CO₂ showed the opposite stomatal behavior as the $g_{wn}$ is higher for the trees which were acclimated to elevated CO₂ (Zeppel et al., 2012; Resco de Dios et al., 2016). This different response is probably due to the different physiological traits for the acclimated trees. Typically when $C_a$ increases, leaf area increases (Ainsworth et al., 2002; Ainsworth & Long, 2005; Sperry et al., 2019), Thus, average view factor decreases due to higher leaf area when plants are acclimated to elevated $C_a$, and $\partial R_{leaf}/\partial E_n$ increases according to equation 2. Another reason could be the decreasing fitness factor (i.e., $f_f$) at elevated CO₂ because the plants grow faster and increase nutrient demand. As a result, using water at night may aid in plant nutrients uptake. The increased benefits of nocturnal transpiration translate to a decreased $f_f$ and increased nocturnal transpiration rate. Similarly, plants grown at different environment (e.g., at different soil moisture and air humidity) ought to have different traits, comparison of nighttime stomatal responses needs to be cautious with respect to different plant traits. We note that our proposed model is process- and trait-based, and thus the impacts from changing traits can be accounted for by our model, making it a promising tool to use with vegetation models.

Opposite $g_{wn}$ responses to VPD have been found in various studies (Barbour et al., 2005; Dawson et al., 2007; Zeppel et al., 2012; Cirelli et al., 2016; Yu et al., 2019). Importantly, the contrasting $g_{wn}$ responses to VPD can be explained by our model framework. In our simulation of a fixed fitness multiplier, the model predicted slightly decreasing nighttime leaf diffusive conductance with drier air, which explains some reported decreasing $g_{wn}$ (Cirelli et al., 2016). However, the model predicted increasing $g_{wn}$ when we used a linearly decreasing $f_f$ with drier air, agreeing with the reported increasing $g_{wn}$ with drier air (present study; Barbour et al., 2005; Dawson et al., 2007; Zeppel et al., 2012; Yu et al., 2019). Therefore, it is very likely that $f_f$ decreases with higher VPD (a stress from the environment), which means that the weight from other nocturnal transpiration upsides increases. Similarly, an increasing $f_f$ with higher temperature better explains the increasing $g_{wn}$ with higher temperature (VPD was held constant in our research, and thus the stress to
plant is from the increasing respiration rate), suggesting that the plant weighs respiratory reduction more when leaf temperature increases.

A potential deficit of the model is that the model uses nighttime leaf temperature to estimate the potential photosynthesis in the day. As we mentioned in the "Materials and Methods" section, the use of mean daytime environmental conditions would be more appropriate. Therefore, we verified the argument by using the exact model parameterization but elevating leaf and air temperature by 10 °C. Note that daytime VPD also increased because of temperature (we set atmospheric vapor pressure constant). We re-plotted the model predictions in Fig. 3-5, and the results were in SI Fig. S2-S4. In general, the $g_{wn}$ response to soil moisture and VPD showed little improvement (Fig. S2a,c); the $g_{wn}$ response to $C_a$ was less steep and agreed better with experimental observations (Fig. S2b); the $g_{wn}$ response to temperature was less steep and agreed better with observations (Fig. S3); and the responses to respiration rate became more linear and agreed better with observations. Therefore, experimentally modeling and measuring both the daytime and nighttime leaf gas exchanges will better serve the purpose of modeling nighttime stomatal conductance.

## 4.2 $g_{wn}$ and the fitness factor

Though nocturnal transpiration results in faster soil water consumption and less daytime carbon gain, plants may actually benefit from losing water at night in some circumstances. For example, (1) plants with sufficient water supply (e.g., riparian trees and rainforests) will accumulate more photosynthate if transpiration-resulted leaf cooling occurs at night, and accumulate more nutrients through transpiration flow (Zeppel et al., 2014; Siddiq & Cao, 2018). (2) Understory plants (such as grasses and shrubs) may restrict their competitors' growth by quickly draining the soil, and thus potentially increasing the competitive edge of the understory for scare canopy light (Caird et al., 2007). (3) Deciduous trees and annual plants tend to use water more aggressively to compete with evergreen plants because they cannot use soil water for photosynthesis after they shed the leaves, and using more water (both in the day and night) results in less soil water for their competitors (Zeppel et al., 2014). (4) More drought tolerant plants may out-compete
more vulnerable competitors by draining the soil, and then the vulnerable competitors suffer due to the hydraulic impairment (Yu *et al.*, 2019). (5) Plants with shallow roots (such as grasses and herbs) may transpire more at night to suppress soil water redistribution to deep soil and keep the water in their own root zone (Howard *et al.*, 2009; Neumann *et al.*, 2014; Huang *et al.*, 2017; Yu *et al.*, 2019). Thus, it is expected that plants under higher competition stress will have higher nighttime transpiration rates (due to lower $f_f$). Even though the nocturnal transpiration might make the plants suffering from future drought stress, the fitness benefits that arise could drive plants to take the risk.

Nighttime stomatal behaviors are likely the result of evolutionary adaption to the environment. For example, stomata close more at elevated CO₂ (both during the daytime and nighttime), but plants may not experience great atmospheric CO₂ concentration change throughout their lives. In this case, stomatal response to $C_a$ may not be useful to short-living plants. However, such a response makes plants more competitive in the long run compared to plants that have no response to CO₂, as the former can use water more efficiently and maintain the hydraulic transport capability. Acclimation to local environment (through trait plasticity) would further enhance these benefits, for example, plants that evolved from arid regions tend to lose more water at night when growing in the same environment (Yu *et al.*, 2019). Understanding how plants adapt and acclimate to the environment not only in the daytime but also at nighttime would help advance land surface models, particularly under the unprecedented climate change (Nicotra *et al.*, 2010; IPCC, 2014; Sperry *et al.*, 2019; Trugman *et al.*, 2019).

The use of a “fitness factor” in our model helps account for other benefits of nocturnal transpiration besides the evaporative cooling, by lowering the daytime marginal water use efficiency to match the nighttime respiration benefit. Our proposed model provides a feasible way to model nocturnal transpiration and its response to the environment in vegetation models. Yet, mechanistically modeling nocturnal transpiration at landscape level requires knowing not only how $f_f$ varies spatially, but also how $f_f$ may vary temporally. Currently, it is still unclear (1) whether and how $f_f$ varies with time, (2) whether and how $f_f$ responds to the environment, including plant competitive environment, (3) how $f_f$ differs within and among species, (4) how nocturnal respiration
rate varies spatially and temporally, (5) how cuticular conductance contributes to nighttime transpiration, or (6) how the nutrient dynamics can be improved by nocturnal transpiration and how this process contribute to $f_f$. More in depth research into $f_f$ will helps address the questions and makes it possible to accurately model the nighttime carbon, water, and energy fluxes spatially and temporally.

## 4.3 Conclusion

The proposed nighttime transpiration model explains critical observed nighttime stomatal responses to the environment, and also helps explain the observed dynamic changes with time. The model well serves future research for quantitatively and accurately modeling nocturnal transpiration. Incorporating nocturnal transpiration into larger scale models is eminently feasible by building off daytime stomatal optimization models and leaf respiration, which is already simulated in most all models. More thorough surveys of nocturnal transpiration with respect to dynamic respiration regulation and a variable fitness factor will help improve the modeling of global water and carbon cycles.
## ACKNOWLEDGMENTS

538 YW gratefully acknowledge his PhD supervisor—Dr. John S Sperry for his support in running these experiments, and wishes him the greatest retirement life. YW and CF acknowledge Mountain Philanthropies and Schmidt Futures program for supporting the Climate Modeling Alliance. WRLA acknowledges funding from the David and Lucille Packard Foundation, NSF Grants 1714972, 1802880, and 2003205, and the USDA National Institute of Food and Agriculture, Agricultural and Food Research Initiative Competitive Programme, Ecosystem Services and Agro-ecosystem Management, grant no. 2018-67019-27850. ATT acknowledges funding from the NSF Grant 2003205, the USDA National Institute of Food and Agriculture, Agricultural and Food Research Initiative Competitive Programme Grant No. 2018-67012-31496 and the University of California Laboratory Fees Research Program Award No. LFR-20-652467.

## Author contributions

550 YW, WRLA, and KY planned the research. YW and KY performed experiments. YW analyzed the data, designed the model, and led the writing. YW, WRLA, MDV, ATT, KY, and CF wrote the manuscript.

## SUPPORTING INFORMATION

555 **Notes S1** Derivation of nighttime marginal respiratory saving.

556 **Fig. S1** Example of stable leaf temperature in stomatal response to vapor pressure deficit.

557 **Fig. S2** Fig. 3 with higher daytime temperature.

558 **Fig. S3** Fig. 4 with higher daytime temperature.

559 **Fig. S4** Fig. 5 with higher daytime temperature.
<table><caption>561 **Table 1** A summary of causes and consequences of nocturnal transpiration.</caption><thead><tr><th></th><th>Causes and consequences</th></tr></thead><tbody><tr><td>Theory</td><td><strong>Leaky stomata.</strong> Fully closing the stomata could be energetically expensive so that plants pay the price only when soil is dry.</td></tr><tr><td>References</td><td>Barbour <i>et al.</i> (2005); Cavender-Bares <i>et al.</i> (2007); Dawson <i>et al.</i> (2007); Cirelli <i>et al.</i> (2016)</td></tr><tr><td>Theory</td><td><strong>Nutrient uptake.</strong> Transpiration stream helps deliver nutrients to the leaves.</td></tr><tr><td>References</td><td>Caird <i>et al.</i> (2007); Dawson <i>et al.</i> (2007); Zeppel <i>et al.</i> (2012)</td></tr><tr><td>Theory</td><td><strong>Oxygen delivery.</strong> Oxygen dissolved in the transpiration stream help provide oxygen to the living cells.</td></tr><tr><td>References</td><td>Dawson <i>et al.</i> (2007); Zeppel <i>et al.</i> (2012)</td></tr><tr><td>Theory</td><td><strong>Competition.</strong> Plant ought to achieve higher fitness when suppressing hydraulic redistribution, thereby keeping water in its own root-zone and increasing subsequent carbon uptake, along with potentially having its competitor perform relatively worse.</td></tr><tr><td>References</td><td>Caird <i>et al.</i> (2007); Zeppel <i>et al.</i> (2012); Huang <i>et al.</i> (2017)</td></tr><tr><td>Theory</td><td><strong>Refilling capacitance.</strong> Plants can store water for daily use, especially in the arid environment. The nighttime flow might help this capacitance refilling. Yet, it should be noted that nocturnal transpiration differ from water flow out of the soil, as the latter consists of both nocturnal transpiration and capacitance refilling. As nocturnal transpiration makes fluid pressure more negative, the pressure gradient to refill the capacitance will be lower. Thus, in theory, the refilling progress will be inhibited rather than promoted by nocturnal transpiration.</td></tr><tr><td>References</td><td>Zeppel <i>et al.</i> (2012); Huang <i>et al.</i> (2017)</td></tr></tbody></table>
<table><tr><td>Theory</td><td><strong>Embolism removal.</strong> Cavitated xylem conduits may be refilled at night, and nocturnal transpiration might promote embolism removal. Similar to the capacitance refilling, nocturnal water uptake may help with embolism, but nocturnal transpiration is unlikely to promote embolism removal. The more negative fluid pressure in the xylem will slow down the refilling, if any, rather than speed it up.</td></tr><tr><td>References</td><td>Zeppel et al. (2012)</td></tr><tr><td>Theory</td><td><strong>Circadian rhythm.</strong> Stomatal opening before sunrise facilitates photosynthesis earlier in the day.</td></tr><tr><td>References</td><td>Caird et al. (2007); Dawson et al. (2007); Resco de Dios et al. (2016, 2019)</td></tr><tr><td>Theory</td><td><strong>Preventing CO<sub>2</sub> build-up in leaf.</strong> CO<sub>2</sub> build-up in the leaf might be toxic for leaf metabolism. Thus, nocturnal transpiration benefits the plant by removing the accumulated CO<sub>2</sub>.</td></tr><tr><td>References</td><td>Marks &amp; Lechowicz (2007)</td></tr><tr><td>Theory</td><td><strong>Leaf cooling.</strong> The E<sub>n</sub> ought to lower leaf temperature and hence leaf respiration.</td></tr><tr><td>References</td><td>Coupel-Ledru et al. (2016)</td></tr><tr><td>Theory</td><td><strong>Marginal respiratory cost relative to marginal carbon gain.</strong> Plants could save more photosynthesis by nocturnal-transpiration-resulted leaf cooling. The higher is this saving compared to daytime photosynthesis, the more stomata open (this study).</td></tr></table>
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**Fig. 1** Optimal nocturnal transpiration model framework. (a) When nighttime transpiration rate (E) increases, leaf temperature (*T*<sub>leaf</sub>) decreases due to the increasing latent heat flux out of the leaf. (b) Decreasing *T*<sub>leaf</sub> results in decreasing leaf respiration rate (*R*<sub>leaf</sub>, red curve), which is carbon benefit to the plant. At the same *T*<sub>leaf</sub>, if the nighttime transpiration rate is used in the day, it benefits the plants with higher photosynthetic rate in the daytime (*A*<sub>d</sub>, cyan curve). Also, the faster soil water depletion could result in drier soil, and thus higher risk in plant hydraulic system. Therefore, nocturnal transpiration results in a carbon cost separated in time. (c) We use marginal respiratory reduction caused by evaporative cooling to describe the marginal carbon benefit of nocturnal transpiration (−∂*R*<sub>leaf</sub>/∂*E*<sub>n</sub>, red curve). We used *f*<sub>f</sub>·*A*<sub>d</sub>/(*E*<sub>crit</sub> − *E*<sub>n</sub>) to describe the marginal carbon cost of nocturnal transpiration (see our description of equation 1 for more details about the formulation). When the marginal carbon gain and cost curves intersect, nighttime transpiration rate is optimized (black circle).

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<figure><img src="image_7.png" /><figcaption>**Fig. 2** Mechanism of nighttime stomatal response to the environment and dark respiration ($R_{leaf}$). The x-axis plots the nighttime transpiration rate ($E_n$). The y-axis plots the marginal benefit at night ($-\partial R_{leaf}/\partial E_n$, red curves) and the marginal cost as calculated in the daytime ($f_f \cdot A_d/(E_{crit} - E_n)$, cyan lines, $f_f$ is the fitness factor multiplier). The optimal solution is where the marginal benefit and marginal cost curves intersect. (a) When soil gets drier, $A_d/(E_{crit} - E_n)$ increases (from cyan solid line to cyan dashed line) whereas $-\partial R_{leaf}/\partial E_n$ curve stays unchanged. The optimal $E_n$ and nighttime leaf diffusive conductance ($g_{wn}$) decrease with drier soil (shift from the gray dot to black dot). (b) When atmospheric CO$_2$ ($C_a$) increases, $A_d/(E_{crit} - E_n)$ increases (from cyan solid line to cyan dashed line) whereas $-\partial R_{leaf}/\partial E_n$ curve stays unchanged. The optimal $E_n$ and $g_{wn}$ decrease with higher $C_a$. (c) When the air gets drier, $A_d/(E_{crit} - E_n)$ decreases (from cyan solid line to cyan dashed line) whereas $-\partial R_{leaf}/\partial E_n$ curve stays unchanged. The optimal $E_n$ increases with drier air, but the $g_{wn}$ may increase or decrease to provide the optimal $E_n$. (d) When $R_{leaf}$ increases, $A_d/(E_{crit} - E_n)$ decreased slightly in the tested case, whereas $-\partial R_{leaf}/\partial E_n$ increases (from red solid curve to red dashed curve). The optimal $E_n$ and $g_{wn}$ increase with higher $R_{leaf}$. (e) When temperature increases, $A_d/(E_{crit} - E_n)$ decreases (from cyan solid line to cyan dashed line) whereas $-\partial R_{leaf}/\partial E_n$ increases (from red solid curve to red dashed curve). The optimal $E_n$ increases with higher temperature, but the $g_{wn}$ may increase or decrease. (f) When the fitness factor decreases, both $A_d/(E_{crit} - E_n)$ and $\partial R_{leaf}/\partial E_n$ stay unchanged, but $\partial \Theta/\partial E_n$ decreases. The optimal $E_n$ and $g_{wn}$ increase with lower $f_f$.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 3** Nighttime leaf diffusive conductance (g<sub>wn</sub>) responses to the environmental cues. Each color represents a mature leaf from a tree. (a) The g<sub>wn</sub> response to soil water potential (P<sub>soil</sub>) in six drought-stressed trees. The light gray curve plots our model predicted g<sub>wn</sub> using a constant fitness multiplier. (b) The g<sub>wn</sub> response to atmospheric CO<sub>2</sub> (C<sub>a</sub>) in six well-watered trees. (c) The g<sub>wn</sub> response to atmospheric vapor pressure deficit (VPD) for the same six well-watered trees as in CO<sub>2</sub> response.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 4** Nighttime leaf diffusive conductance (g<sub>wn</sub>) response to leaf temperature (T<sub>leaf</sub>). Each color represents data from a mature leaf from a well-watered tree. (a) The g<sub>wn</sub> is not corrected by temperature. The light gray curve plots our model predicted g<sub>wn</sub> using a constant fitness multiplier. (b) The g<sub>wn</sub> is normalized to 25 °C (g<sub>wn,25</sub>).</figcaption></figure>
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<figure><img src="image_10.png" /><figcaption>**Fig. 5** Nighttime leaf diffusive conductance ($g_{wn}$) and leaf respiration ($R_{leaf}$) covary for mature leaves. Each symbol represents a leaf, and each corresponding color represents a well-watered tree. Each colored solid line plots the linear regression of $g_{wn} \sim R_{leaf}$ from each tree, and each shaded region indicates the confidence interval ($P < 0.05$ for all fittings). The light gray curve plots our model predicted $g_{wn}$ using a constant fitness multiplier. The purple color line plots the linear regression of all leaves.</figcaption></figure>
**Fig. 6** Nighttime leaf diffusive conductance (g<sub>wn</sub>) and leaf respiration rate (R<sub>leaf</sub>) covary with time after sunset. Each color represents a well-watered tree, and each symbol plots the gas exchange of a mature leaf every 30 seconds. (a) Correlation between g<sub>wn</sub> and R<sub>leaf</sub>. The solid lines plot linear regression of g<sub>wn</sub> ~ R<sub>leaf</sub> in a time series (P < 0.05). (b) An example of how g<sub>wn</sub> and R<sub>leaf</sub> change with time (same data as the red symbols in (a)). The red symbols plot g<sub>wn</sub>, and the gray curve plots R<sub>leaf</sub>.

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<figure><img src="image_12.png" /><figcaption>**Fig. 7** Comparison of nighttime leaf diffusive conductance (g<sub>wn</sub>) at different leaf-to-air vapor pressure deficit (D) and temperature versus model predictions using variable fitness multiplier. (a) The g<sub>wn</sub> response to leaf-to-air vapor pressure deficit from six well-watered trees (data same as Fig. 3c). The light gray curve plots our model predicted g<sub>wn</sub> using a variable fitness multiplier depending on D. The red line plots the linear regression of all data, and shaded region plots the confidence interval. (b) The g<sub>wn</sub> response to leaf temperature (T<sub>leaf</sub>) at a constant D (data same as Fig. 4a). The light gray curve plots our model predicted g<sub>wn</sub> using a variable fitness multiplier depending on T<sub>leaf</sub>.</figcaption></figure>

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E (mmol H₂O m⁻² s⁻¹)

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$T_{\text{leaf}}$ (°C)

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R<sub>n</sub> (µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>)

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R<sub>n</sub> (µmol CO<sub>2</sub> m<sup>-2</sup> s<sup>-1</sup>)

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