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Fig. 5 Simulations with a coupled leaf gas exchange model (Duursma, 2015), demonstrating the effect of inclusion of the go parameter (Eqn 1) on leaf fluxes (a) Intrinsic water use efficiency (A,/g.) as a function of the photosynthetic photon flux density (PPFD), holding other environmental drivers constant, for thre¢ values of go. (b) The same simulations as in (a), but showing the intercellular CO2 concentration (C;). (c) Leaf transpiration (E_) simulations, where the vapo pressure deficit (VPD) and air temperature (T,i) were covaried based on an empirical relationship (Duursma et a/., 2014), reflecting typical covariation in fielc conditions. (d) The same simulations as in (c), but showing C;. Note how C; increases at high VPD and Tair, only when go > O. For all simulations, itis assumed tha Tieaf is equal to T,;,, and we ignore the differential permeability of the cuticle to COz and HzO (Hanson et al., 2016). When plants are sufficiently water stressed so that stomata are mostly closed, water loss still continues at a rate determined by the minimum conductance. Thus, models that aim to predict when plants desiccate and die must include a minimum conductance term. A classic study by Pisek & Winkler (1953) calculated the ength of time needed to desiccate leaves to some critical low water content, given the minimum transpiration rate and the saturated water content of the leaves. Based on that work, Burghardt & Riederer (2006) reported a direct correlation between gj,i, and the survival time of leaves. Sinclair (2000) presented the minimum conductance as a key drought tolerance trait, and used it as a basis for the prediction of crop mortality during severe drought. More recently, Gleason etal. (2014) and Blackman etal. (2016) have proposed that embolism resistance together with whole-plant capacitance and minimum transpiration rates all contribute to define the time to desiccation. Building on this work, Martin- StPaul etal. (2017) demonstrated, in a whole-plant model of hydraulic failure, that g,,i, was one of the key parameters to explain the drop in water potential below the cavitation threshold, because

Figure 5 Simulations with a coupled leaf gas exchange model (Duursma, 2015), demonstrating the effect of inclusion of the go parameter (Eqn 1) on leaf fluxes (a) Intrinsic water use efficiency (A,/g.) as a function of the photosynthetic photon flux density (PPFD), holding other environmental drivers constant, for thre¢ values of go. (b) The same simulations as in (a), but showing the intercellular CO2 concentration (C;). (c) Leaf transpiration (E_) simulations, where the vapo pressure deficit (VPD) and air temperature (T,i) were covaried based on an empirical relationship (Duursma et a/., 2014), reflecting typical covariation in fielc conditions. (d) The same simulations as in (c), but showing C;. Note how C; increases at high VPD and Tair, only when go > O. For all simulations, itis assumed tha Tieaf is equal to T,;,, and we ignore the differential permeability of the cuticle to COz and HzO (Hanson et al., 2016). When plants are sufficiently water stressed so that stomata are mostly closed, water loss still continues at a rate determined by the minimum conductance. Thus, models that aim to predict when plants desiccate and die must include a minimum conductance term. A classic study by Pisek & Winkler (1953) calculated the ength of time needed to desiccate leaves to some critical low water content, given the minimum transpiration rate and the saturated water content of the leaves. Based on that work, Burghardt & Riederer (2006) reported a direct correlation between gj,i, and the survival time of leaves. Sinclair (2000) presented the minimum conductance as a key drought tolerance trait, and used it as a basis for the prediction of crop mortality during severe drought. More recently, Gleason etal. (2014) and Blackman etal. (2016) have proposed that embolism resistance together with whole-plant capacitance and minimum transpiration rates all contribute to define the time to desiccation. Building on this work, Martin- StPaul etal. (2017) demonstrated, in a whole-plant model of hydraulic failure, that g,,i, was one of the key parameters to explain the drop in water potential below the cavitation threshold, because

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Table 1 Definitions of minimum conductance
Table 1 Definitions of minimum conductance
Fig. 1 Comparison of various estimates of the (presumed) minimum conductance. Error bars are 95% confidence intervals. Gray dots are the original data (but a few data points occur outside the figure range). Different letters denote significant differences (at «=0.05). Zcuti, conductance of isolated cuticles; Zmin, Minimum conductance measured with mass loss of detached leaves; Zdark, leaf conductance during the night or after dark adaptation; Ziow par, leaf conductance during low light (PAR, photosynthetically active radiation); giow a, leaf conductance during periods of very low photosynthesis. See Section II for data sources and methods.
Fig. 1 Comparison of various estimates of the (presumed) minimum conductance. Error bars are 95% confidence intervals. Gray dots are the original data (but a few data points occur outside the figure range). Different letters denote significant differences (at «=0.05). Zcuti, conductance of isolated cuticles; Zmin, Minimum conductance measured with mass loss of detached leaves; Zdark, leaf conductance during the night or after dark adaptation; Ziow par, leaf conductance during low light (PAR, photosynthetically active radiation); giow a, leaf conductance during periods of very low photosynthesis. See Section II for data sources and methods.
Fig. 2 Analysis of a literature compilation of minimum conductance (gin) estimates, as measured with mass loss of detached leaves. (a) Histogram (probability density) of all estimates (after averaging by species, n = 221), with alog-normal distribution curve (mean = 4.89, SD = 2.67). (b) Zmin averaged by phylogenetic order (including only the top 10 orders in the database). Bars are 95% confidence intervals. Numbers above the figure refer to the number of species. Different letters denote significant differences (at «= 0.05, adjusted for multiple comparisons) and gray symbols are species-level data. (c) Zmin estimates for crops only, averaged by genotype. Bars denote the range, illustrating the wide range in g,i, among genotypes for a particular crop species. Numbers above the figure refer to the number of genotypes included.
Fig. 2 Analysis of a literature compilation of minimum conductance (gin) estimates, as measured with mass loss of detached leaves. (a) Histogram (probability density) of all estimates (after averaging by species, n = 221), with alog-normal distribution curve (mean = 4.89, SD = 2.67). (b) Zmin averaged by phylogenetic order (including only the top 10 orders in the database). Bars are 95% confidence intervals. Numbers above the figure refer to the number of species. Different letters denote significant differences (at «= 0.05, adjusted for multiple comparisons) and gray symbols are species-level data. (c) Zmin estimates for crops only, averaged by genotype. Bars denote the range, illustrating the wide range in g,i, among genotypes for a particular crop species. Numbers above the figure refer to the number of genotypes included.
Fig. 3 Minimum conductance (gmin) measured by mass loss of detached leaves on a variety of Hakea species, a genus native to Australia. Plants were grown in containers in a grow house, and supplied with ample water or subjected to long-term (8 months) mild drought stress. Bars are labeled by leaf form (broadleaf (B) or needle-like (N)) and ordered by gmin in the well- watered treatment. For drought-treated plants, gin was higher for species with needle-like leaves (Wilcoxon test, P=0.02), but not for well-watered plants (P=0.14).
Fig. 3 Minimum conductance (gmin) measured by mass loss of detached leaves on a variety of Hakea species, a genus native to Australia. Plants were grown in containers in a grow house, and supplied with ample water or subjected to long-term (8 months) mild drought stress. Bars are labeled by leaf form (broadleaf (B) or needle-like (N)) and ordered by gmin in the well- watered treatment. For drought-treated plants, gin was higher for species with needle-like leaves (Wilcoxon test, P=0.02), but not for well-watered plants (P=0.14).
Fig. 4 Minimum conductance (gimin) measured with mass loss of detached leaves on Eucalyptus parramattensis grown in whole-tree chambers. Trees were grown following ambient conditions or in an elevated temperature treatment (+ 3°C) (see Drake et a/., 2018). Measurements of gmin were carried out at five different temperatures on replicate leaves. There was no consistent effect of measurement temperature on gmin, but leaves of trees grown in elevated temperature showed, on average, a45% reduction in gimin (P<0.01, linear mixed-effects model). Error bars denote 95% confidence intervals.
Fig. 4 Minimum conductance (gimin) measured with mass loss of detached leaves on Eucalyptus parramattensis grown in whole-tree chambers. Trees were grown following ambient conditions or in an elevated temperature treatment (+ 3°C) (see Drake et a/., 2018). Measurements of gmin were carried out at five different temperatures on replicate leaves. There was no consistent effect of measurement temperature on gmin, but leaves of trees grown in elevated temperature showed, on average, a45% reduction in gimin (P<0.01, linear mixed-effects model). Error bars denote 95% confidence intervals.
Fig. 6 Simulations with the Sureau model demonstrating the effect of gmin on the desiccation tolerance of plants. The Sureau model simulates water transport in the soil-plant-atmosphere continuum, and includes a detailed representation of capacitance in stem and leaf tissues. (a) Soil relative extractable water (REW; 1 =field capacity, O = permanentwilting point) for the two simulations, using a minimum conductance (gmin) of 2 or 4 mmol m~? s~'—all other parameters were equal. (b) Water potential in the soil and leaf as the dry-down progresses. (c) Progression of percent loss conductivity (PLC) of the xylem. Dashed line is ata PLC of 88%, indicating possible mortality.
Fig. 6 Simulations with the Sureau model demonstrating the effect of gmin on the desiccation tolerance of plants. The Sureau model simulates water transport in the soil-plant-atmosphere continuum, and includes a detailed representation of capacitance in stem and leaf tissues. (a) Soil relative extractable water (REW; 1 =field capacity, O = permanentwilting point) for the two simulations, using a minimum conductance (gmin) of 2 or 4 mmol m~? s~'—all other parameters were equal. (b) Water potential in the soil and leaf as the dry-down progresses. (c) Progression of percent loss conductivity (PLC) of the xylem. Dashed line is ata PLC of 88%, indicating possible mortality.
Fig. 7 (a) Example linear regression of stomatal conductance (g,) against a combination of terms, in this case the linearized version of the model of Medlyn et al. (2011) applied to a leaf gas exchange dataset of Martin-StPaul et a/. (2012). This example shows a very good fit between g, and the stomatal index, and was selected from the database of Lin et a/. (2015). The solid line is the regression line, and the shaded area is the 95% confidence interval for the mean. (b) The correlation between the estimated slope (g,) and intercept (go) of the regression shown in (a). The dotted ellipse is a bivariate 95 % confidence interval for slope and intercept. The symbols represent 1000 bootstrap samples of the coefficients.
Fig. 7 (a) Example linear regression of stomatal conductance (g,) against a combination of terms, in this case the linearized version of the model of Medlyn et al. (2011) applied to a leaf gas exchange dataset of Martin-StPaul et a/. (2012). This example shows a very good fit between g, and the stomatal index, and was selected from the database of Lin et a/. (2015). The solid line is the regression line, and the shaded area is the 95% confidence interval for the mean. (b) The correlation between the estimated slope (g,) and intercept (go) of the regression shown in (a). The dotted ellipse is a bivariate 95 % confidence interval for slope and intercept. The symbols represent 1000 bootstrap samples of the coefficients.
Fig. 8 Statistical uncertainty in the estimation of go from regression, demonstrated with two parameter databases. (a) We fitted the linearized form of the Medlyn et al. (2011) model to each of the datasets in the Lin et a/. (2015) leaf gas exchange database, showing that, for poorly fitted relationships (low R?) inflated estimates of go are obtained. Vertical lines are 95% confidence intervals. The gray line is a fitted loess smoother with 95 % confidence interval. Note the wide confidence intervals and frequent negative values. (b) Similar to (a), but using the published compilation by Miner et al. (2017). The gray line is a fitted loes: smoother with 95% confidence interval. (c) Using the fits from (a), a demonstration that the standard error (SE) of go is much higher when the coefficient o' variation (CV) of the predictor (i.e. right-hand side of the equation being fitted) is lower.
Fig. 8 Statistical uncertainty in the estimation of go from regression, demonstrated with two parameter databases. (a) We fitted the linearized form of the Medlyn et al. (2011) model to each of the datasets in the Lin et a/. (2015) leaf gas exchange database, showing that, for poorly fitted relationships (low R?) inflated estimates of go are obtained. Vertical lines are 95% confidence intervals. The gray line is a fitted loess smoother with 95 % confidence interval. Note the wide confidence intervals and frequent negative values. (b) Similar to (a), but using the published compilation by Miner et al. (2017). The gray line is a fitted loes: smoother with 95% confidence interval. (c) Using the fits from (a), a demonstration that the standard error (SE) of go is much higher when the coefficient o' variation (CV) of the predictor (i.e. right-hand side of the equation being fitted) is lower.
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Environmental ScienceEcosystem ModelingMedicineAtmospheric sciencesPlant Water RelationsStomatal Conductance
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