SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129 NATURE PLANTS | www.nature.com/natureplants 1 The energetic and carbon economic origins of leaf thermoregulation Sean T. Michaletz * , Michael D. Weiser, Nate G. McDowell, Jizhong Zhou, Michael Kaspari, Brent R. Helliker, and Brian J. Enquist *Corresponding author: Michaletz, S.T. ([email protected]) Contents 1. Additional theory linking leaf traits, energy budgets, and carbon economics a. Leaf carbon economics and leaf functional traits b. Leaf traits and temperatures are linked via energy budgets i. Solution of steady state energy budgets ii. Solution of transient energy budgets c. The thermal time constant is a composite leaf functional trait d. Linking leaf carbon economics, functional traits, and energy budgets e. Predicted tradeoff between the thermal breadth of photosynthesis T90 and the thermal time constant τ 2. Leaf thermoregulation varies among plant growth forms 3. Photosynthetic and thermal traits of C3 and C4 plants 4. Additional information on data sources a. Temperature data for evaluating the leaf thermoregulation b. Trait and climate data used for energy budget analyses References Extended Data Figure 1 Extended Data Figure 2 Extended Data Figure 3 Extended Data Figure 4 Extended Data Table 1 Extended Data Table 2 Extended Data Table 3
Contents 1. Additional theory linking leaf traits, energy budgets, and carbon economics
a. Leaf carbon economics and leaf functional traits b. Leaf traits and temperatures are linked via energy budgets
i. Solution of steady state energy budgets ii. Solution of transient energy budgets
c. The thermal time constant is a composite leaf functional trait d. Linking leaf carbon economics, functional traits, and energy budgets e. Predicted tradeoff between the thermal breadth of photosynthesis T90 and the thermal
time constant τ 2. Leaf thermoregulation varies among plant growth forms 3. Photosynthetic and thermal traits of C3 and C4 plants 4. Additional information on data sources
a. Temperature data for evaluating the leaf thermoregulation b. Trait and climate data used for energy budget analyses
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 2
1. Additional theory linking leaf traits, energy budgets, and carbon economics
a. Leaf carbon economics and leaf functional traits
Carbon is a universal currency of leaf economics. Ultimately, leaf energy budgets govern the rates of carbon assimilation that fuel plant growth and reproduction. Carbon economics thus constrains plant demography and influences plant fitness1,2.
Across environments, natural selection has shaped plant form and function so that leaves must have a net positive return on resource investment3. The total mass of carbon assimilated by a leaf over its lifetime must be greater than the total mass of carbon invested in the leaf 4,5. This can be expressed in terms of several key leaf functional traits as1,6-8
01 1 1 1
2 2 2 2
( ) 1
fL
a a ftot tm f
A t dt A LA k k k kG A LLMA k LMA k LMA k k
(S1)
where G is lifetime carbon gain per unit carbon invested (kg C kg C-1), Atot is the cumulative net carbon assimilated during the life lifetime (μmol C m-2 s-1), LMA is the leaf mass-to-area ratio (kg m-2), k1 is the molar mass conversion factor (kg C μmol C-1), k2 is the carbon mass fraction (kg C kg-1), Aa is the time-averaged net carbon assimilation rate per unit leaf area (μmol C m-2 s-
1), aA is the time-averaged net carbon assimilation rate per unit leaf area (μmol C m-2 s-1), Lf is
the functional leaf longevity (s), and mA is the time-averaged net carbon assimilation rate per unit leaf mass (μmol C kg-1 s-1). As we show, all of these traits can ultimately be linked with leaf energy budgets. Further, differences in climate select for unique combinations of LMA, Atot, Aa, Am, and Lf in order to maximize G.
Eq. (S1) shows that selection to maximize G can be achieved in three ways: 1) selection to increase assimilation rate, 2) selection to maximize leaf longevity, or 3) selection to minimize LMA1. As we show, maximizing assimilation rates while simultaneously minimizing LMA must result from selection on leaf traits that govern the thermal and metabolic stability of leaves.
b. Leaf traits and temperatures are linked via energy budgets
Energy budgets equate heat fluxes at leaf surfaces with heat flux to storage in leaf mass (cf. refs9-15), such that
R C E S (S2)
where R (W m-2) is the net radiation flux, C (W m-2) is the convective (sensible heat) flux, and S (W m-2) is the storage flux. The evaporative (latent heat) flux λE (W m-2) is the product of the latent heat of vaporization of water λ (J kg-1) and the transpiration rate E (kg m-2 s-1). As discussed below, the energy balance of Eq. (S2) shows how variation in key leaf functional traits can influence leaf temperatures and physiological rates (e.g. transpiration, photosynthesis, and respiration). Eq. (S2) also provides a strong constraint on trait covariation if natural selection has shaped leaf carbon economics.
Michaletz et al. Supplementary Information 3
The net radiation flux of any object equals the difference between the radiation absorbed (Rabs; W m-2) and emitted (Remit; W m-2), such that
1 4abs emit sun sun longwave sky longwave ground lR R R R R R T (S3)
where αsun (dimensionless) is the leaf absorptivity to total solar radiation, Rsun (W m-2) is the shortwave radiation flux from the sun, αlongwave (dimensionless) is the leaf absorptivity to longwave radiation, Rsky (W m-2) is the longwave radiation flux from the sky, Rground (W m-2) is the longwave radiation flux from the ground, ε (dimensionless) is the leaf emissivity, σ (W m-2 K-4) is the Stefan-Boltzmann constant, and Tl (K) is the leaf temperature. The ratio of projected-to-total leaf area φ (dimensionless; 1/2 for flat leaves and 1/π cylindrical leaves) accounts for emission of radiation from all sides of the leaf.
The convective flux is given by
, ,a p a b h l aC c g T T (S4)
where ρa (kg m-3) is the density of air, cp,a (J kg-1 K-1) is the specific heat capacity of air, and Ta (K) is the air temperature. The boundary layer conductance to heat gb,h (m s -1) is equivalent to the boundary layer conductance gb (m s -1) and varies with leaf size and geometry; for broadleaves, it is given as
0.5
, 0.007b h bUg gL
(S5)
while for needle-leaves it is given as
0.6
, 0.40.004b h bUg gL
(S6)
Here, U (m s-1) is the wind velocity and L (m) is a characteristic dimension taken as broadleaf width or needle-leaf diameter. Since the fitted parameters in Eqns. (S5) and (S6) were obtained for laminar flow conditions, estimates from these relationships can be multiplied by 1.5 when applied to turbulent outdoor conditions10.
The evaporative heat flux is
, ( )a p aw sat l a
cE g e T e
(S7)
where ( )sat se T (Pa) is the saturation vapor pressure evaluated at the leaf temperature Tl (K) and ea is the vapor pressure of air (Pa). The water vapor conductance gw (m s-1) is given by the stomatal conductance gs (m s-1) and boundary layer conductance gb in series, such that
1. Additional theory linking leaf traits, energy budgets, and carbon economics
a. Leaf carbon economics and leaf functional traits
Carbon is a universal currency of leaf economics. Ultimately, leaf energy budgets govern the rates of carbon assimilation that fuel plant growth and reproduction. Carbon economics thus constrains plant demography and influences plant fitness1,2.
Across environments, natural selection has shaped plant form and function so that leaves must have a net positive return on resource investment3. The total mass of carbon assimilated by a leaf over its lifetime must be greater than the total mass of carbon invested in the leaf 4,5. This can be expressed in terms of several key leaf functional traits as1,6-8
01 1 1 1
2 2 2 2
( ) 1
fL
a a ftot tm f
A t dt A LA k k k kG A LLMA k LMA k LMA k k
(S1)
where G is lifetime carbon gain per unit carbon invested (kg C kg C-1), Atot is the cumulative net carbon assimilated during the life lifetime (μmol C m-2 s-1), LMA is the leaf mass-to-area ratio (kg m-2), k1 is the molar mass conversion factor (kg C μmol C-1), k2 is the carbon mass fraction (kg C kg-1), Aa is the time-averaged net carbon assimilation rate per unit leaf area (μmol C m-2 s-
1), aA is the time-averaged net carbon assimilation rate per unit leaf area (μmol C m-2 s-1), Lf is
the functional leaf longevity (s), and mA is the time-averaged net carbon assimilation rate per unit leaf mass (μmol C kg-1 s-1). As we show, all of these traits can ultimately be linked with leaf energy budgets. Further, differences in climate select for unique combinations of LMA, Atot, Aa, Am, and Lf in order to maximize G.
Eq. (S1) shows that selection to maximize G can be achieved in three ways: 1) selection to increase assimilation rate, 2) selection to maximize leaf longevity, or 3) selection to minimize LMA1. As we show, maximizing assimilation rates while simultaneously minimizing LMA must result from selection on leaf traits that govern the thermal and metabolic stability of leaves.
b. Leaf traits and temperatures are linked via energy budgets
Energy budgets equate heat fluxes at leaf surfaces with heat flux to storage in leaf mass (cf. refs9-15), such that
R C E S (S2)
where R (W m-2) is the net radiation flux, C (W m-2) is the convective (sensible heat) flux, and S (W m-2) is the storage flux. The evaporative (latent heat) flux λE (W m-2) is the product of the latent heat of vaporization of water λ (J kg-1) and the transpiration rate E (kg m-2 s-1). As discussed below, the energy balance of Eq. (S2) shows how variation in key leaf functional traits can influence leaf temperatures and physiological rates (e.g. transpiration, photosynthesis, and respiration). Eq. (S2) also provides a strong constraint on trait covariation if natural selection has shaped leaf carbon economics.
Michaletz et al. Supplementary Information 3
The net radiation flux of any object equals the difference between the radiation absorbed (Rabs; W m-2) and emitted (Remit; W m-2), such that
1 4abs emit sun sun longwave sky longwave ground lR R R R R R T (S3)
where αsun (dimensionless) is the leaf absorptivity to total solar radiation, Rsun (W m-2) is the shortwave radiation flux from the sun, αlongwave (dimensionless) is the leaf absorptivity to longwave radiation, Rsky (W m-2) is the longwave radiation flux from the sky, Rground (W m-2) is the longwave radiation flux from the ground, ε (dimensionless) is the leaf emissivity, σ (W m-2 K-4) is the Stefan-Boltzmann constant, and Tl (K) is the leaf temperature. The ratio of projected-to-total leaf area φ (dimensionless; 1/2 for flat leaves and 1/π cylindrical leaves) accounts for emission of radiation from all sides of the leaf.
The convective flux is given by
, ,a p a b h l aC c g T T (S4)
where ρa (kg m-3) is the density of air, cp,a (J kg-1 K-1) is the specific heat capacity of air, and Ta (K) is the air temperature. The boundary layer conductance to heat gb,h (m s -1) is equivalent to the boundary layer conductance gb (m s -1) and varies with leaf size and geometry; for broadleaves, it is given as
0.5
, 0.007b h bUg gL
(S5)
while for needle-leaves it is given as
0.6
, 0.40.004b h bUg gL
(S6)
Here, U (m s-1) is the wind velocity and L (m) is a characteristic dimension taken as broadleaf width or needle-leaf diameter. Since the fitted parameters in Eqns. (S5) and (S6) were obtained for laminar flow conditions, estimates from these relationships can be multiplied by 1.5 when applied to turbulent outdoor conditions10.
The evaporative heat flux is
, ( )a p aw sat l a
cE g e T e
(S7)
where ( )sat se T (Pa) is the saturation vapor pressure evaluated at the leaf temperature Tl (K) and ea is the vapor pressure of air (Pa). The water vapor conductance gw (m s-1) is given by the stomatal conductance gs (m s-1) and boundary layer conductance gb in series, such that
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 4
The psychrometric constant γ (Pa K-1) is
,
0.622p a ac p
(S9)
where pa (Pa) is the air pressure.
The heat flux to storage is given by
, ,l l p l l p ll l
l l
V c m cdT dTSA dt A dt
(S10)
where ρl (kg m-3) is the leaf mass density, Vl (m3) is the leaf volume, cp,l (J kg-1 K-1) is the specific heat capacity of the fresh leaf (including water), Al is the total surface area of the fresh leaf (m2), ml (kg) is the leaf mass including water, and t is time (s).
i. Solution of steady state energy budgets
When leaf temperature is constant in time, steady state conditions prevail and Eq. (S2) is reduced to the surface balance
0R C E (S11)
Eq. (S11) can be solved for leaf temperature using a variety of approaches. The most commonly used approach is the Penman approximation16, which uses a first-order Taylor expansion of the saturation vapor pressure term to rewrite Eqn. (S7) as
,a p aw l a
cE g D s T T
(S12)
where ( ) /sat as de T dT (Pa K-1) is the slope of the saturation vapor pressure curve versus temperature evaluated at Ta, and D (Pa) is the vapor pressure deficit of the air. After substitution of Eqs. (S3), (S4) and (S12) into (S11) and rearrangement, the leaf temperature is given as
,
,, , ,
///
b h wl a
b h wa p a b h b h w
R g g DT Ts g gc g s g g
(S13)
Equation (S13) is a form of the classical derivation for leaf temperature found in many textbooks10-15. The appeal of this relationship is that it is simple, analytically tractable, and provides insight on the causal relationships linking traits and climate to leaf temperatures. For example, the second term on the right describes an increase of leaf temperature above air temperature that is proportional to net radiation, while the third term describes a decrease of leaf temperature that is proportional to the vapor pressure deficit; depending on the relative magnitudes of these terms, leaf temperature will be warmer than, cooler than, or equivalent to air temperature. The leaf temperature excess Tl – Ta (K) is given by
Michaletz et al. Supplementary Information 5
,
,, , ,
///
b h wl a
b h wa p a b h b h w
R g g DT Ts g gc g s g g
(S14)
By setting the leaf temperature excess to zero and simplifying, the theoretical equivalence point temperature can be expressed as17
1/4 1/4
,a p a weq l a abs
c g DT T T R
(S15)
This relationship suggests that the equivalence point temperature is not a constant, but instead varies in space and time due to variation in leaf traits and climate variables, which is supported by empirical data17-19. For example, Teq varies diurnally, increasing through the morning to a maximum during midday and decreasing through the afternoon. Eqn. (S15) gives insight into the conditions required for leaf-air temperature equivalence. The conditions under which Teq can be attained are further explored in ref17.
Despite the advantages of the Penman approximation, it becomes less accurate as leaf-air temperature differences increase, leading to errors greater than 30% at temperature extremes (refs20-24). Thus, while the approach is useful for analyses of equivalence point temperatures (Teq ≡ Tl = Ta; Eqn. (S15)), it is not ideal for analyses that involve large leaf temperature excesses (Tl - Ta; Eqns. (S13) and (S14)).
For analyses of leaf thermoregulation across large air temperature gradients, we must sacrifice analytical tractability for increased accuracy and use a nearly exact, explicit quartic solution to the energy budget21. After substitution of Eqs. (S3), (S4) and (S7) into (S11) and rearrangement, we have
, 1 4, ,
( )a p a w sat l aabs a p a b h l a l
c g e T eR c g T T T
(S16)
Again, the ratio of projected-to-total leaf area φ (dimensionless; 1/2 for flat leaves and 1/π cylindrical leaves) accounts for emission of radiation from all sides of the leaf, since conductances are formulated for projected area following ref10. A quartic solution to Eqn. (S16) can be obtained by approximating the saturation vapor pressure term as the fourth order polynomial
4 3 2( )sat l l l l le T T T T T (S17)
After substitution of Eqn. (S17) into Eqn. (S16) and rearrangement, the energy budget can be expressed in quartic form as
where ρl (kg m-3) is the leaf mass density, Vl (m3) is the leaf volume, cp,l (J kg-1 K-1) is the specific heat capacity of the fresh leaf (including water), Al is the total surface area of the fresh leaf (m2), ml (kg) is the leaf mass including water, and t is time (s).
i. Solution of steady state energy budgets
When leaf temperature is constant in time, steady state conditions prevail and Eq. (S2) is reduced to the surface balance
0R C E (S11)
Eq. (S11) can be solved for leaf temperature using a variety of approaches. The most commonly used approach is the Penman approximation16, which uses a first-order Taylor expansion of the saturation vapor pressure term to rewrite Eqn. (S7) as
,a p aw l a
cE g D s T T
(S12)
where ( ) /sat as de T dT (Pa K-1) is the slope of the saturation vapor pressure curve versus temperature evaluated at Ta, and D (Pa) is the vapor pressure deficit of the air. After substitution of Eqs. (S3), (S4) and (S12) into (S11) and rearrangement, the leaf temperature is given as
,
,, , ,
///
b h wl a
b h wa p a b h b h w
R g g DT Ts g gc g s g g
(S13)
Equation (S13) is a form of the classical derivation for leaf temperature found in many textbooks10-15. The appeal of this relationship is that it is simple, analytically tractable, and provides insight on the causal relationships linking traits and climate to leaf temperatures. For example, the second term on the right describes an increase of leaf temperature above air temperature that is proportional to net radiation, while the third term describes a decrease of leaf temperature that is proportional to the vapor pressure deficit; depending on the relative magnitudes of these terms, leaf temperature will be warmer than, cooler than, or equivalent to air temperature. The leaf temperature excess Tl – Ta (K) is given by
Michaletz et al. Supplementary Information 5
,
,, , ,
///
b h wl a
b h wa p a b h b h w
R g g DT Ts g gc g s g g
(S14)
By setting the leaf temperature excess to zero and simplifying, the theoretical equivalence point temperature can be expressed as17
1/4 1/4
,a p a weq l a abs
c g DT T T R
(S15)
This relationship suggests that the equivalence point temperature is not a constant, but instead varies in space and time due to variation in leaf traits and climate variables, which is supported by empirical data17-19. For example, Teq varies diurnally, increasing through the morning to a maximum during midday and decreasing through the afternoon. Eqn. (S15) gives insight into the conditions required for leaf-air temperature equivalence. The conditions under which Teq can be attained are further explored in ref17.
Despite the advantages of the Penman approximation, it becomes less accurate as leaf-air temperature differences increase, leading to errors greater than 30% at temperature extremes (refs20-24). Thus, while the approach is useful for analyses of equivalence point temperatures (Teq ≡ Tl = Ta; Eqn. (S15)), it is not ideal for analyses that involve large leaf temperature excesses (Tl - Ta; Eqns. (S13) and (S14)).
For analyses of leaf thermoregulation across large air temperature gradients, we must sacrifice analytical tractability for increased accuracy and use a nearly exact, explicit quartic solution to the energy budget21. After substitution of Eqs. (S3), (S4) and (S7) into (S11) and rearrangement, we have
, 1 4, ,
( )a p a w sat l aabs a p a b h l a l
c g e T eR c g T T T
(S16)
Again, the ratio of projected-to-total leaf area φ (dimensionless; 1/2 for flat leaves and 1/π cylindrical leaves) accounts for emission of radiation from all sides of the leaf, since conductances are formulated for projected area following ref10. A quartic solution to Eqn. (S16) can be obtained by approximating the saturation vapor pressure term as the fourth order polynomial
4 3 2( )sat l l l l le T T T T T (S17)
After substitution of Eqn. (S17) into Eqn. (S16) and rearrangement, the energy budget can be expressed in quartic form as
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 6
For Eqn. (S18), leaf temperatures Tl are in units of °C and parameters are defined as
1ek h (S19)
114 ea K h (S20)
1 216 eb K h (S21)
1 314 e tc K h h (S22)
1 41abs e e a t ad R K h h e h T (S23)
,a p a we
c gh
(S24)
and
, ,t a p a b hh c g (S25)
Parameter K1 in Eqns. (S20) to (S23) is the Kelvin-Celsius conversion temperature of 273.15.
ii. Solution of transient energy budgets
When leaf temperature varies in time, transient conditions prevail and Eqs. (S4), (S12) and (S10) can be substituted into Eq. (S2) to give
l e ldT T Tdt
(S26)
Here, Te (K) is an equilibrium leaf temperature that is approached asymptotically through time, and τ (s) is a thermal time constant. The thermal time constant quantifies the thermal response time of a leaf, and also governs the environmental oscillation frequencies that leaf temperature is sensitive to (Extended Data Figure 4). This thermal time constant is a key composite functional trait given by10
,
, , /l p l
l a p a b h r w
m cA c g g g s
(S27)
where gw (m s-1) is the water vapor conductance and gr (m s-1) a radiation “conductance” taken as10,15
Michaletz et al. Supplementary Information 7
3
,
4 ar
a p a
Tgc
(S28)
Notably, τ (s) comprises several important functional traits, including leaf mass ml (kg), specific heat capacity cp,l (J kg-1 K-1), total two-sided surface area Al (m2), size and geometry (Eqs. S4 and S5) and stomatal conductance (Eq. S7). Importantly, all functional traits in Eq. (S27) are for fresh leaves (i.e., including water).
Eq. (S26) can be solved analytically or numerically for various initial and boundary conditions9,25 to predict leaf temperature in a variable environment. For example, for sinusoidal environmental variation, the leaf equilibrium temperature is described by15,25
sin 2 e e eT T T f t (S29)
where eT is the mean equilibrium leaf temperature (K), ΔTe is amplitude of equilibrium temperature oscillation (K), f the frequency (Hz), and t is time (s). For this case, Eq. (S26) is solved to give
sin 2 l e eT T T f t (S30)
where the realized amplitude of leaf temperature eT (K) is given as
cose eT T (S31)
and the phase lag ϕ (dimensionless) is
1tan 2 f (S32)
Substituting Eqs. (S31) and (S32) into (S30) gives
2 sin 2 2 cos 2 1 2
el e
TT T f t f f tf
(S33)
Thus, Eqs. (S26)-(S33) show how leaf temperature dynamics are governed the thermal time constant τ, a composite trait that comprises several additional functional leaf traits. The influence of these leaf traits on τ will be further examined the following section.
c. The thermal time constant is a composite leaf functional trait
Thermal time constants τ (s; Eq. (S27)) are influenced by several key functional traits: leaf mass, specific heat capacity, total surface area, size, geometry, stomatal conductance, leaf mass per area, and leaf dry matter content (i.e., water content). Leaf mass per area (LMA; kg m-
2) is the ratio of leaf dry mass ml,d (kg) to leaf projected area φAl (m2), or , /l d lLMA m A , where φ (dimensionless; taken as 1/2 for flat leaves and 1/π cylindrical leaves) is the ratio of
For Eqn. (S18), leaf temperatures Tl are in units of °C and parameters are defined as
1ek h (S19)
114 ea K h (S20)
1 216 eb K h (S21)
1 314 e tc K h h (S22)
1 41abs e e a t ad R K h h e h T (S23)
,a p a we
c gh
(S24)
and
, ,t a p a b hh c g (S25)
Parameter K1 in Eqns. (S20) to (S23) is the Kelvin-Celsius conversion temperature of 273.15.
ii. Solution of transient energy budgets
When leaf temperature varies in time, transient conditions prevail and Eqs. (S4), (S12) and (S10) can be substituted into Eq. (S2) to give
l e ldT T Tdt
(S26)
Here, Te (K) is an equilibrium leaf temperature that is approached asymptotically through time, and τ (s) is a thermal time constant. The thermal time constant quantifies the thermal response time of a leaf, and also governs the environmental oscillation frequencies that leaf temperature is sensitive to (Extended Data Figure 4). This thermal time constant is a key composite functional trait given by10
,
, , /l p l
l a p a b h r w
m cA c g g g s
(S27)
where gw (m s-1) is the water vapor conductance and gr (m s-1) a radiation “conductance” taken as10,15
Michaletz et al. Supplementary Information 7
3
,
4 ar
a p a
Tgc
(S28)
Notably, τ (s) comprises several important functional traits, including leaf mass ml (kg), specific heat capacity cp,l (J kg-1 K-1), total two-sided surface area Al (m2), size and geometry (Eqs. S4 and S5) and stomatal conductance (Eq. S7). Importantly, all functional traits in Eq. (S27) are for fresh leaves (i.e., including water).
Eq. (S26) can be solved analytically or numerically for various initial and boundary conditions9,25 to predict leaf temperature in a variable environment. For example, for sinusoidal environmental variation, the leaf equilibrium temperature is described by15,25
sin 2 e e eT T T f t (S29)
where eT is the mean equilibrium leaf temperature (K), ΔTe is amplitude of equilibrium temperature oscillation (K), f the frequency (Hz), and t is time (s). For this case, Eq. (S26) is solved to give
sin 2 l e eT T T f t (S30)
where the realized amplitude of leaf temperature eT (K) is given as
cose eT T (S31)
and the phase lag ϕ (dimensionless) is
1tan 2 f (S32)
Substituting Eqs. (S31) and (S32) into (S30) gives
2 sin 2 2 cos 2 1 2
el e
TT T f t f f tf
(S33)
Thus, Eqs. (S26)-(S33) show how leaf temperature dynamics are governed the thermal time constant τ, a composite trait that comprises several additional functional leaf traits. The influence of these leaf traits on τ will be further examined the following section.
c. The thermal time constant is a composite leaf functional trait
Thermal time constants τ (s; Eq. (S27)) are influenced by several key functional traits: leaf mass, specific heat capacity, total surface area, size, geometry, stomatal conductance, leaf mass per area, and leaf dry matter content (i.e., water content). Leaf mass per area (LMA; kg m-
2) is the ratio of leaf dry mass ml,d (kg) to leaf projected area φAl (m2), or , /l d lLMA m A , where φ (dimensionless; taken as 1/2 for flat leaves and 1/π cylindrical leaves) is the ratio of
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 8
projected-to-total leaf area, and Al (m2) is the total surface area of a fresh leaf 26. Leaf dry matter content (LDMC; kg kg-1) is the mass fraction of dry matter in a fresh leaf, or , /l d lLDMC m m , where ml (kg) is the fresh leaf mass including water. LDMC is a key allocation trait relative to leaf carbon economics27,28.
Generally, thermal time constants τ (Eqs. (3) and (S27)) can be written as
,l p l
l
m cCK A h
(S34)
where C (J K-1) is the heat capacitance and K is the thermal conductance (W K-1), and h (W m-2 K-1) is an overall heat transfer coefficient that can take various forms depending on the pertinent energy fluxes10-13,15. For convection, radiation, and transpiration we have
, /a p a h r wh c g g g s (S35)
Here we show how leaf thermal time constants are influenced by two prominent leaf functional traits: leaf mass per area (LMA) and leaf dry matter content (LDMC). Leaf mass per area (LMA; kg m-2) is the ratio of leaf dry mass ml,d (kg) to leaf projected area φA (m2)
,l d
l
mLMA
A (S36)
where φ (dimensionless; taken as 1/2 for flat leaves and 1/π cylindrical leaves) is the ratio of projected-to-total leaf area, and Al (m2) is the total surface area of a fresh leaf26. Leaf dry matter content (LDMC; dimensionless) is the mass fraction of dry matter in a fresh leaf
,l d
l
mLDMC
m (S37)
where ml (kg) is the fresh leaf mass including water. Recognizing that ml/Al = φLMA/LDMC, Eq. (S34) can be rewritten as
,p lcLMALDMC h (S38)
Importantly, the thermal mass in Eq. (S38) includes masses of both leaf dry matter as well as leaf water. Next, we can include the dependence of the specific heat capacity cp,l on leaf water content. From the simple rule of mixtures, we have
, ,1p d p wc LDMC c LDMC c (S39)
where cp,d (J kg-1 K-1) is the specific heat capacity of dry leaf matter and cp,w (J kg-1 K-1) is the specific heat capacity of water in the leaf. Finally, Eq. (S39) is substituted into Eq. (S38) to reveal the influence of LMA and LDMC on thermal time constants
Michaletz et al. Supplementary Information 9
, , ,p w p d p wc c cLMA
LDMC h h
(S40)
This relationship accounts for water content effects on leaf thermal mass29 as well as leaf specific heat capacity.
d. Linking leaf carbon economics, functional traits, and energy budgets
The lifetime carbon gain of a leaf (Eq. (S1)) is the outcome of instantaneous net assimilation rates integrated through time. Since carbon assimilation rates are temperature dependent30, they are ultimately governed by interactions between leaf functional traits and climate variables within leaf energy budgets. In this section, we derive theory linking leaf carbon economics, leaf functional traits, and leaf energy budgets.
We begin by describing the temperature response of photosynthesis. Rates of net photosynthesis generally increase with leaf temperature to a maximum value at some optimal temperature, and then decrease with leaf temperatures above this optimum (see Fig. 3 inset). For convenience, we describe this temperature dependence using a second-order polynomial31 (although more complex functions could also be used32-35). This gives the instantaneous rate of net photosynthesis A(Tl) (μmol C m-2 s-1) evaluated at the leaf temperature Tl as
2( )l l lA T aT bT c (S41)
The fitted parameters a, b, and c can be used to calculate key functional traits, including the optimal temperature for photosynthesis Topt (K)
2opt
bTa
(S42)
the maximum rate of photosynthesis Aopt (μmol C m-2 s-1)
24
4opt
ac bA
a
(S43)
and the thermal breadth of photosynthesis T90 (K)
2
90 2
410
b acTa
(S44)
For steady state conditions, leaf temperature is constant in time so that ( )a lA A T , which is maximized at Aopt when Tl = Topt. Substituting into Eq. (S41) gives
2( )opt opt opt optA T aT bT c (S45)
If we assume that average leaf temperatures are optimal for photosynthesis36-38, we can substitute Eq. (S45) into Eq. (S1) to give a simple expression linking leaf carbon economics, functional traits, and steady state energy budgets
projected-to-total leaf area, and Al (m2) is the total surface area of a fresh leaf 26. Leaf dry matter content (LDMC; kg kg-1) is the mass fraction of dry matter in a fresh leaf, or , /l d lLDMC m m , where ml (kg) is the fresh leaf mass including water. LDMC is a key allocation trait relative to leaf carbon economics27,28.
Generally, thermal time constants τ (Eqs. (3) and (S27)) can be written as
,l p l
l
m cCK A h
(S34)
where C (J K-1) is the heat capacitance and K is the thermal conductance (W K-1), and h (W m-2 K-1) is an overall heat transfer coefficient that can take various forms depending on the pertinent energy fluxes10-13,15. For convection, radiation, and transpiration we have
, /a p a h r wh c g g g s (S35)
Here we show how leaf thermal time constants are influenced by two prominent leaf functional traits: leaf mass per area (LMA) and leaf dry matter content (LDMC). Leaf mass per area (LMA; kg m-2) is the ratio of leaf dry mass ml,d (kg) to leaf projected area φA (m2)
,l d
l
mLMA
A (S36)
where φ (dimensionless; taken as 1/2 for flat leaves and 1/π cylindrical leaves) is the ratio of projected-to-total leaf area, and Al (m2) is the total surface area of a fresh leaf26. Leaf dry matter content (LDMC; dimensionless) is the mass fraction of dry matter in a fresh leaf
,l d
l
mLDMC
m (S37)
where ml (kg) is the fresh leaf mass including water. Recognizing that ml/Al = φLMA/LDMC, Eq. (S34) can be rewritten as
,p lcLMALDMC h (S38)
Importantly, the thermal mass in Eq. (S38) includes masses of both leaf dry matter as well as leaf water. Next, we can include the dependence of the specific heat capacity cp,l on leaf water content. From the simple rule of mixtures, we have
, ,1p d p wc LDMC c LDMC c (S39)
where cp,d (J kg-1 K-1) is the specific heat capacity of dry leaf matter and cp,w (J kg-1 K-1) is the specific heat capacity of water in the leaf. Finally, Eq. (S39) is substituted into Eq. (S38) to reveal the influence of LMA and LDMC on thermal time constants
Michaletz et al. Supplementary Information 9
, , ,p w p d p wc c cLMA
LDMC h h
(S40)
This relationship accounts for water content effects on leaf thermal mass29 as well as leaf specific heat capacity.
d. Linking leaf carbon economics, functional traits, and energy budgets
The lifetime carbon gain of a leaf (Eq. (S1)) is the outcome of instantaneous net assimilation rates integrated through time. Since carbon assimilation rates are temperature dependent30, they are ultimately governed by interactions between leaf functional traits and climate variables within leaf energy budgets. In this section, we derive theory linking leaf carbon economics, leaf functional traits, and leaf energy budgets.
We begin by describing the temperature response of photosynthesis. Rates of net photosynthesis generally increase with leaf temperature to a maximum value at some optimal temperature, and then decrease with leaf temperatures above this optimum (see Fig. 3 inset). For convenience, we describe this temperature dependence using a second-order polynomial31 (although more complex functions could also be used32-35). This gives the instantaneous rate of net photosynthesis A(Tl) (μmol C m-2 s-1) evaluated at the leaf temperature Tl as
2( )l l lA T aT bT c (S41)
The fitted parameters a, b, and c can be used to calculate key functional traits, including the optimal temperature for photosynthesis Topt (K)
2opt
bTa
(S42)
the maximum rate of photosynthesis Aopt (μmol C m-2 s-1)
24
4opt
ac bA
a
(S43)
and the thermal breadth of photosynthesis T90 (K)
2
90 2
410
b acTa
(S44)
For steady state conditions, leaf temperature is constant in time so that ( )a lA A T , which is maximized at Aopt when Tl = Topt. Substituting into Eq. (S41) gives
2( )opt opt opt optA T aT bT c (S45)
If we assume that average leaf temperatures are optimal for photosynthesis36-38, we can substitute Eq. (S45) into Eq. (S1) to give a simple expression linking leaf carbon economics, functional traits, and steady state energy budgets
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 10
2
1
2
1opt opt faT bT c L kGLMA k
(S46)
where the leaf temperature Topt is governed by leaf traits and climate variables in the energy budget of Eq. (S13). Eqs. (S13) and (S46) formalize how selection might operate on leaf functional traits to influence thermoregulation of Tl and maximize G across climate gradients.
For transient conditions, leaf temperature varies in time so that A(Tl) also varies in time. We can rewrite Eq. (S41) to give the instantaneous rate of net photosynthesis ( )lA T t (μmol C m-2 s-1) evaluated at Tl and t as
2( ) ( ) ( )l l lA T t a T t bT t c (S47)
Integrating Eq. (S47) over the functional leaf lifespan gives the cumulative net carbon assimilated over the life of the leaf (Eq. (S1)) as
0
( )fL
tot lt
A A T t dt
(S48)
Substituting Eq. (S48) into Eq. (S1) gives
0 1 1
2 2
( )1
fL
l a ftA T t dt A Lk kGLMA k LMA k
(S49)
where the transient leaf temperature Tl(t) is governed by τ and environmental variation Te as characterized in Eqs. (S26) - (S33).
e. Predicted tradeoff between the thermal breadth of photosynthesis T90 and the thermal time constant τ
Suppose that natural selection operates on the thermal breadth of photosynthesis and the thermal time constant to maximize instantaneous rates of net carbon assimilation. We then predict that the thermal breadth of photosynthesis will correlate with the realized amplitude of leaf temperature, which is a function of the thermal time constant (Eqs. (S31) and (S32)). Consequently, T90 should be proportional to 2 eT (K). From Eqs. (S31) and (S32), this can be formalized as
190 2 2 cos tan 2e eT T T f (S50)
Thus, T90 is predicted to vary inversely with τ, reflecting a tradeoff between leaf photosynthetic stability and leaf thermal stability. The implication is that photosynthesis operates near Aopt across a wide range of temperatures for thermally unstable leaves and across a narrow range of temperatures for thermally stable leaves.
Michaletz et al. Supplementary Information 11
2. Leaf thermoregulation varies among plant growth forms
Patterns of leaf thermoregulation based on short-term from point measurements of various plant growth forms are shown in Extended Data Figure 2.
The fitted slope for cushion plants (1.52; 95% CI = 1.46 – 1.58) was significantly greater than and opposite in direction to slopes of all other growth forms (Extended Data Table 1), indicating that sunlit leaves of cushion plants are greater than and increase at a higher rate than air temperature. Conversely, leaf temperatures of other growth forms increase at a slower rate than air temperature. The fitted slope for trees (0.90; 95% CI = 0.86 – 0.94) was significantly greater than for shrubs (0.70; 95% CI = 0.67 – 0.73), herbs (0.69; 95% CI = 0.68 – 0.70), and succulents (0.77; 95% CI = 0.73 – 0.81), which were not different from each other (Extended Data Table 2). While these data suggest that trees are slightly less homeothermic than other plant growth forms, their slope of thermoregulation is still significantly less than 1 as required for leaf-air temperature equivalence (P = 0.005).
Mean rank sums of leaf temperature by growth form are summarized in Extended Data Table 2. Leaf temperatures varied significantly among growth forms (P < 2.2 x 10-16). Cushion plants generally have lower leaf temperatures than trees, graminoids, and shrubs, which are not significantly different. Shrubs have a higher leaf temperature, and succulents have the highest. Examination of leaf temperature alone doesn’t account for differences in air temperature or thermoregulation among growth forms, however.
Leaf temperature excess (Tl – Ta) accounts for air temperature differences among growth forms and thus better characterizes the degree of thermoregulation of each growth form (Extended Data Table 3). Leaf temperature excesses varied significantly among growth forms (P < 2.2 x 10-16). Graminoids and shrubs (not significantly different) have the smallest departure of leaf temperature, followed by herbs and trees (not significantly different), and succulents and cushions (not significantly different).
3. Photosynthetic and thermal traits of C3 and C4 plants
The classic examples of photosynthesis temperature response suggest the thermal breadth of photosynthesis T90 is larger for C3 plants than for C4 plants30,39,40. If this is a general pattern, then our theory would predict generally smaller time constants for C3 than for C4 plants. For our data, T90 was marginally larger for C3 plants than for C4 plants (P = 0.06), but τ did not vary between the groups (P = 0.50). However, this is not a comprehensive test of the prediction since almost all of our data corresponds to C3 species, with only six T90 values and two τ values corresponding to C4 species from a single genus (Atriplex). Further, more recent analyses suggest that the classic pattern of T90 is strongly mediated by water availability and growth temperature, which can eliminate or even reverse the pattern41,42. If true, this would cause corresponding changes in our predictions. Thus, without additional data, we are at this time unable to draw firm conclusions regarding general differences in photosynthetic and thermal traits between C3 and C4 plants.
where the leaf temperature Topt is governed by leaf traits and climate variables in the energy budget of Eq. (S13). Eqs. (S13) and (S46) formalize how selection might operate on leaf functional traits to influence thermoregulation of Tl and maximize G across climate gradients.
For transient conditions, leaf temperature varies in time so that A(Tl) also varies in time. We can rewrite Eq. (S41) to give the instantaneous rate of net photosynthesis ( )lA T t (μmol C m-2 s-1) evaluated at Tl and t as
2( ) ( ) ( )l l lA T t a T t bT t c (S47)
Integrating Eq. (S47) over the functional leaf lifespan gives the cumulative net carbon assimilated over the life of the leaf (Eq. (S1)) as
0
( )fL
tot lt
A A T t dt
(S48)
Substituting Eq. (S48) into Eq. (S1) gives
0 1 1
2 2
( )1
fL
l a ftA T t dt A Lk kGLMA k LMA k
(S49)
where the transient leaf temperature Tl(t) is governed by τ and environmental variation Te as characterized in Eqs. (S26) - (S33).
e. Predicted tradeoff between the thermal breadth of photosynthesis T90 and the thermal time constant τ
Suppose that natural selection operates on the thermal breadth of photosynthesis and the thermal time constant to maximize instantaneous rates of net carbon assimilation. We then predict that the thermal breadth of photosynthesis will correlate with the realized amplitude of leaf temperature, which is a function of the thermal time constant (Eqs. (S31) and (S32)). Consequently, T90 should be proportional to 2 eT (K). From Eqs. (S31) and (S32), this can be formalized as
190 2 2 cos tan 2e eT T T f (S50)
Thus, T90 is predicted to vary inversely with τ, reflecting a tradeoff between leaf photosynthetic stability and leaf thermal stability. The implication is that photosynthesis operates near Aopt across a wide range of temperatures for thermally unstable leaves and across a narrow range of temperatures for thermally stable leaves.
Michaletz et al. Supplementary Information 11
2. Leaf thermoregulation varies among plant growth forms
Patterns of leaf thermoregulation based on short-term from point measurements of various plant growth forms are shown in Extended Data Figure 2.
The fitted slope for cushion plants (1.52; 95% CI = 1.46 – 1.58) was significantly greater than and opposite in direction to slopes of all other growth forms (Extended Data Table 1), indicating that sunlit leaves of cushion plants are greater than and increase at a higher rate than air temperature. Conversely, leaf temperatures of other growth forms increase at a slower rate than air temperature. The fitted slope for trees (0.90; 95% CI = 0.86 – 0.94) was significantly greater than for shrubs (0.70; 95% CI = 0.67 – 0.73), herbs (0.69; 95% CI = 0.68 – 0.70), and succulents (0.77; 95% CI = 0.73 – 0.81), which were not different from each other (Extended Data Table 2). While these data suggest that trees are slightly less homeothermic than other plant growth forms, their slope of thermoregulation is still significantly less than 1 as required for leaf-air temperature equivalence (P = 0.005).
Mean rank sums of leaf temperature by growth form are summarized in Extended Data Table 2. Leaf temperatures varied significantly among growth forms (P < 2.2 x 10-16). Cushion plants generally have lower leaf temperatures than trees, graminoids, and shrubs, which are not significantly different. Shrubs have a higher leaf temperature, and succulents have the highest. Examination of leaf temperature alone doesn’t account for differences in air temperature or thermoregulation among growth forms, however.
Leaf temperature excess (Tl – Ta) accounts for air temperature differences among growth forms and thus better characterizes the degree of thermoregulation of each growth form (Extended Data Table 3). Leaf temperature excesses varied significantly among growth forms (P < 2.2 x 10-16). Graminoids and shrubs (not significantly different) have the smallest departure of leaf temperature, followed by herbs and trees (not significantly different), and succulents and cushions (not significantly different).
3. Photosynthetic and thermal traits of C3 and C4 plants
The classic examples of photosynthesis temperature response suggest the thermal breadth of photosynthesis T90 is larger for C3 plants than for C4 plants30,39,40. If this is a general pattern, then our theory would predict generally smaller time constants for C3 than for C4 plants. For our data, T90 was marginally larger for C3 plants than for C4 plants (P = 0.06), but τ did not vary between the groups (P = 0.50). However, this is not a comprehensive test of the prediction since almost all of our data corresponds to C3 species, with only six T90 values and two τ values corresponding to C4 species from a single genus (Atriplex). Further, more recent analyses suggest that the classic pattern of T90 is strongly mediated by water availability and growth temperature, which can eliminate or even reverse the pattern41,42. If true, this would cause corresponding changes in our predictions. Thus, without additional data, we are at this time unable to draw firm conclusions regarding general differences in photosynthetic and thermal traits between C3 and C4 plants.
Long term photosynthetically-weighted leaf and air temperature data were compiled from
references111-118. Data were available for trees (Abies balsamea, Acer rubrum, Acer saccharum, Alnus, sp., Betula lenta, Betula papyrifera, Bucida spinosa, Carpinus caroliniana, Carya ovata,
Long term photosynthetically-weighted leaf and air temperature data were compiled from
references111-118. Data were available for trees (Abies balsamea, Acer rubrum, Acer saccharum, Alnus, sp., Betula lenta, Betula papyrifera, Bucida spinosa, Carpinus caroliniana, Carya ovata,
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 14
References
1 Blonder, B., Violle, C., Bentley, L. P. & Enquist, B. J. Venation networks and the origin of the leaf economics spectrum. Ecology Letters 14, 91-100, doi:10.1111/j.1461-0248.2010.01554.x (2011).
2 Kikuzawa, K. The basis for variation in leaf longevity of plants. Vegetatio 121, 89-100, doi:10.1007/BF00044675 (1995).
3 Westoby, M., Falster, D. S., Moles, A. T., Vesk, P. A. & Wright, I. J. PLANT ECOLOGICAL STRATEGIES: Some Leading Dimensions of Variation Between Species. Annual Review of Ecology and Systematics 33, 125-159, doi:doi:10.1146/annurev.ecolsys.33.010802.150452 (2002).
4 Chabot, B. F. & Hicks, D. J. The Ecology of Leaf Life Spans. Annual Review of Ecology and Systematics 13, 229-259, doi:doi:10.1146/annurev.es.13.110182.001305 (1982).
5 Williams, K., Field, C. B. & Mooney, H. A. Relationships Among Leaf Construction Cost, Leaf Longevity, and Light Environment in Rain-Forest Plants of the Genus Piper. The American Naturalist 133, 198-211, doi:10.2307/2462297 (1989).
6 Kikuzawa, K. & Lechowicz, M. J. Toward Synthesis of Relationships among Leaf Longevity, Instantaneous Photosynthetic Rate, Lifetime Leaf Carbon Gain, and the Gross Primary Production of Forests. The American Naturalist 168, 373-383, doi:10.1086/506954 (2006).
7 Falster, D. S. et al. Lifetime return on investment increases with leaf lifespan among 10 Australian woodland species. New Phytologist 193, 409-419, doi:10.1111/j.1469-8137.2011.03940.x (2012).
8 Michaletz, S. T. et al. Plant thermoregulation: Energetics, trait-environment interactions, and carbon economics. Trends in Ecology & Evolution 30, doi:10.1016/j.tree.2015.09.006 (2015).
9 Bergman, T. L., Lavine, A. S., Incropera, F. P. & DeWitt, D. P. Fundamentals of Heat and Mass Transfer. 7th edition., (John Wiley & Sons, Inc., 2011).
10 Jones, H. G. Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology. (Cambridge University Press, 2014).
11 Gates, D. M. Biophysical Ecology. (Springer-Verlag, 1980). 12 Campbell, G. S. & Norman, J. M. An Introduction to Environmental Biophysics.
(Springer Science+Business Media, Inc., 1998). 13 Nobel, P. S. Physicochemical and Environmental Plant Physiology, Fourth Edition.
(Academic Press, 2009). 14 Bonan, G. B. Ecological Climatology: Concepts and Applications. (Cambridge
University Press, 2008). 15 Monteith, J. & Unsworth, M. Principles of Environmental Physics: Plants, Animals, and
the Atmosphere. (Academic Press, 2013). 16 Penman, H. L. Natural Evaporation from Open Water, Bare Soil and Grass. Proceedings
of the Royal Society of London. Series A. Mathematical and Physical Sciences 193, 120-145, doi:10.1098/rspa.1948.0037 (1948).
17 Paw U, K. T. A theoretical basis for the leaf equivalence point temperature. Agricultural Meteorology 30, 247-256, doi:http://dx.doi.org/10.1016/0002-1571(84)90001-3 (1984).
18 Idso, S. B., Reginato, R. J., Jackson, R. D. & Pinter, P. J. Foliage and air temperatures: Evidence for a dynamic “equivalence point”. Agricultural Meteorology 24, 223-226, doi:http://dx.doi.org/10.1016/0002-1571(81)90046-7 (1981).
Michaletz et al. Supplementary Information 15
19 Gates, D. M. Transpiration and leaf temperature. Annual Review of Plant Physiology 19, 211-238 (1968).
20 Tracy, C. R. et al. Errors resulting from linear approximations in energy balance equations. Journal of Thermal Biology 9, 261-264, doi:http://dx.doi.org/10.1016/0306-4565(84)90006-8 (1984).
21 Paw U, K. T. Mathematical analysis of the operative temperature and energy budget. Journal of Thermal Biology 12, 227-233, doi:http://dx.doi.org/10.1016/0306-4565(87)90009-X (1987).
22 Paw U, K. T. A discussion of the Penman form equations and comparisons of some equations to estimate latent energy flux density. Agricultural and Forest Meteorology 57, 297-304, doi:http://dx.doi.org/10.1016/0168-1923(92)90125-N (1992).
23 Paw U, K. T. & Gao, W. Applications of solutions to non-linear energy budget equations. Agricultural and Forest Meteorology 43, 121-145, doi:http://dx.doi.org/10.1016/0168-1923(88)90087-1 (1988).
24 Widmoser, P. A discussion on and alternative to the Penman–Monteith equation. Agricultural Water Management 96, 711-721, doi:http://dx.doi.org/10.1016/j.agwat.2008.10.003 (2009).
25 Nellis, G. F. & Klein, S. A. Heat Transfer. (Cambridge University Press, 2009). 26 Pérez-Harguindeguy, N. et al. New handbook for standardised measurement of plant
functional traits worldwide. Australian Journal of Botany 61, 167-234, doi:http://dx.doi.org/10.1071/BT12225 (2013).
27 Wilson, P. J., Thompson, K. E. N. & Hodgson, J. G. Specific leaf area and leaf dry matter content as alternative predictors of plant strategies. New Phytologist 143, 155-162, doi:10.1046/j.1469-8137.1999.00427.x (1999).
28 Shipley, B. & Vu, T.-T. Dry matter content as a measure of dry matter concentration in plants and their parts. New Phytologist 153, 359-364, doi:10.1046/j.0028-646X.2001.00320.x (2002).
29 Vogel, S. Leaves in the lowest and highest winds: temperature, force and shape. New Phytologist 183, 13-26, doi:10.1111/j.1469-8137.2009.02854.x (2009).
30 Berry, J. & Bjorkman, O. Photosynthetic Response and Adaptation to Temperature in Higher Plants. Annual Review of Plant Physiology 31, 491-543, doi:doi:10.1146/annurev.pp.31.060180.002423 (1980).
31 Duursma, R. A. et al. The peaked response of transpiration rate to vapour pressure deficit in field conditions can be explained by the temperature optimum of photosynthesis. Agricultural and Forest Meteorology 189–190, 2-10, doi:http://dx.doi.org/10.1016/j.agrformet.2013.12.007 (2014).
32 Angilletta Jr, M. J. Estimating and comparing thermal performance curves. Journal of Thermal Biology 31, 541-545, doi:http://dx.doi.org/10.1016/j.jtherbio.2006.06.002 (2006).
33 Dell, A. I., Pawar, S. & Savage, V. M. Systematic variation in the temperature dependence of physiological and ecological traits. Proceedings of the National Academy of Sciences 108, 10591-10596, doi:10.1073/pnas.1015178108 (2011).
34 Deutsch, C. A. et al. Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences 105, 6668-6672, doi:10.1073/pnas.0709472105 (2008).
1 Blonder, B., Violle, C., Bentley, L. P. & Enquist, B. J. Venation networks and the origin of the leaf economics spectrum. Ecology Letters 14, 91-100, doi:10.1111/j.1461-0248.2010.01554.x (2011).
2 Kikuzawa, K. The basis for variation in leaf longevity of plants. Vegetatio 121, 89-100, doi:10.1007/BF00044675 (1995).
3 Westoby, M., Falster, D. S., Moles, A. T., Vesk, P. A. & Wright, I. J. PLANT ECOLOGICAL STRATEGIES: Some Leading Dimensions of Variation Between Species. Annual Review of Ecology and Systematics 33, 125-159, doi:doi:10.1146/annurev.ecolsys.33.010802.150452 (2002).
4 Chabot, B. F. & Hicks, D. J. The Ecology of Leaf Life Spans. Annual Review of Ecology and Systematics 13, 229-259, doi:doi:10.1146/annurev.es.13.110182.001305 (1982).
5 Williams, K., Field, C. B. & Mooney, H. A. Relationships Among Leaf Construction Cost, Leaf Longevity, and Light Environment in Rain-Forest Plants of the Genus Piper. The American Naturalist 133, 198-211, doi:10.2307/2462297 (1989).
6 Kikuzawa, K. & Lechowicz, M. J. Toward Synthesis of Relationships among Leaf Longevity, Instantaneous Photosynthetic Rate, Lifetime Leaf Carbon Gain, and the Gross Primary Production of Forests. The American Naturalist 168, 373-383, doi:10.1086/506954 (2006).
7 Falster, D. S. et al. Lifetime return on investment increases with leaf lifespan among 10 Australian woodland species. New Phytologist 193, 409-419, doi:10.1111/j.1469-8137.2011.03940.x (2012).
8 Michaletz, S. T. et al. Plant thermoregulation: Energetics, trait-environment interactions, and carbon economics. Trends in Ecology & Evolution 30, doi:10.1016/j.tree.2015.09.006 (2015).
9 Bergman, T. L., Lavine, A. S., Incropera, F. P. & DeWitt, D. P. Fundamentals of Heat and Mass Transfer. 7th edition., (John Wiley & Sons, Inc., 2011).
10 Jones, H. G. Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology. (Cambridge University Press, 2014).
11 Gates, D. M. Biophysical Ecology. (Springer-Verlag, 1980). 12 Campbell, G. S. & Norman, J. M. An Introduction to Environmental Biophysics.
(Springer Science+Business Media, Inc., 1998). 13 Nobel, P. S. Physicochemical and Environmental Plant Physiology, Fourth Edition.
(Academic Press, 2009). 14 Bonan, G. B. Ecological Climatology: Concepts and Applications. (Cambridge
University Press, 2008). 15 Monteith, J. & Unsworth, M. Principles of Environmental Physics: Plants, Animals, and
the Atmosphere. (Academic Press, 2013). 16 Penman, H. L. Natural Evaporation from Open Water, Bare Soil and Grass. Proceedings
of the Royal Society of London. Series A. Mathematical and Physical Sciences 193, 120-145, doi:10.1098/rspa.1948.0037 (1948).
17 Paw U, K. T. A theoretical basis for the leaf equivalence point temperature. Agricultural Meteorology 30, 247-256, doi:http://dx.doi.org/10.1016/0002-1571(84)90001-3 (1984).
18 Idso, S. B., Reginato, R. J., Jackson, R. D. & Pinter, P. J. Foliage and air temperatures: Evidence for a dynamic “equivalence point”. Agricultural Meteorology 24, 223-226, doi:http://dx.doi.org/10.1016/0002-1571(81)90046-7 (1981).
Michaletz et al. Supplementary Information 15
19 Gates, D. M. Transpiration and leaf temperature. Annual Review of Plant Physiology 19, 211-238 (1968).
20 Tracy, C. R. et al. Errors resulting from linear approximations in energy balance equations. Journal of Thermal Biology 9, 261-264, doi:http://dx.doi.org/10.1016/0306-4565(84)90006-8 (1984).
21 Paw U, K. T. Mathematical analysis of the operative temperature and energy budget. Journal of Thermal Biology 12, 227-233, doi:http://dx.doi.org/10.1016/0306-4565(87)90009-X (1987).
22 Paw U, K. T. A discussion of the Penman form equations and comparisons of some equations to estimate latent energy flux density. Agricultural and Forest Meteorology 57, 297-304, doi:http://dx.doi.org/10.1016/0168-1923(92)90125-N (1992).
23 Paw U, K. T. & Gao, W. Applications of solutions to non-linear energy budget equations. Agricultural and Forest Meteorology 43, 121-145, doi:http://dx.doi.org/10.1016/0168-1923(88)90087-1 (1988).
24 Widmoser, P. A discussion on and alternative to the Penman–Monteith equation. Agricultural Water Management 96, 711-721, doi:http://dx.doi.org/10.1016/j.agwat.2008.10.003 (2009).
25 Nellis, G. F. & Klein, S. A. Heat Transfer. (Cambridge University Press, 2009). 26 Pérez-Harguindeguy, N. et al. New handbook for standardised measurement of plant
functional traits worldwide. Australian Journal of Botany 61, 167-234, doi:http://dx.doi.org/10.1071/BT12225 (2013).
27 Wilson, P. J., Thompson, K. E. N. & Hodgson, J. G. Specific leaf area and leaf dry matter content as alternative predictors of plant strategies. New Phytologist 143, 155-162, doi:10.1046/j.1469-8137.1999.00427.x (1999).
28 Shipley, B. & Vu, T.-T. Dry matter content as a measure of dry matter concentration in plants and their parts. New Phytologist 153, 359-364, doi:10.1046/j.0028-646X.2001.00320.x (2002).
29 Vogel, S. Leaves in the lowest and highest winds: temperature, force and shape. New Phytologist 183, 13-26, doi:10.1111/j.1469-8137.2009.02854.x (2009).
30 Berry, J. & Bjorkman, O. Photosynthetic Response and Adaptation to Temperature in Higher Plants. Annual Review of Plant Physiology 31, 491-543, doi:doi:10.1146/annurev.pp.31.060180.002423 (1980).
31 Duursma, R. A. et al. The peaked response of transpiration rate to vapour pressure deficit in field conditions can be explained by the temperature optimum of photosynthesis. Agricultural and Forest Meteorology 189–190, 2-10, doi:http://dx.doi.org/10.1016/j.agrformet.2013.12.007 (2014).
32 Angilletta Jr, M. J. Estimating and comparing thermal performance curves. Journal of Thermal Biology 31, 541-545, doi:http://dx.doi.org/10.1016/j.jtherbio.2006.06.002 (2006).
33 Dell, A. I., Pawar, S. & Savage, V. M. Systematic variation in the temperature dependence of physiological and ecological traits. Proceedings of the National Academy of Sciences 108, 10591-10596, doi:10.1073/pnas.1015178108 (2011).
34 Deutsch, C. A. et al. Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences 105, 6668-6672, doi:10.1073/pnas.0709472105 (2008).
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 16
35 Vasseur, D. A. et al. Increased temperature variation poses a greater risk to species than climate warming. Proceedings of the Royal Society of London B: Biological Sciences 281, doi:10.1098/rspb.2013.2612 (2014).
36 Ball, M., Cowan, I. & Farquhar, G. Maintenance of Leaf Temperature and the Optimisation of Carbon Gain in Relation to Water Loss in a Tropical Mangrove Forest. Functional Plant Biology 15, 263-276, doi:http://dx.doi.org/10.1071/PP9880263 (1988).
37 Korner, C. & Diemer, M. In situ photosynthetic responses to light, temperature and carbon dioxide in herbaceous plants from low and high altitude. Functional Ecology 1, 179-194, doi:10.2307/2389420 (1987).
38 Slatyer, R. & Morrow, P. Altitudinal Variation in the Photosynthetic Characteristics of Snow Gum, <I>Eucalyptus pauciflora</I> Sieb. Ex Spreng. I. Seasonal Changes Under Field Conditions in the Snowy Mountains Area of South-Eastern Australia. Australian Journal of Botany 25, 1-20, doi:http://dx.doi.org/10.1071/BT9770001 (1977).
39 Sage, R., Kocacinar, F. & Kubien, D. in C4 Photosynthesis and Related CO2 Concentrating Mechanisms Vol. 32 Advances in Photosynthesis and Respiration (eds Agepati S. Raghavendra & Rowan F. Sage) Ch. 10, 161-195 (Springer Netherlands, 2011).
40 Sage, R. F. & Kubien, D. S. The temperature response of C3 and C4 photosynthesis. Plant, Cell & Environment 30, 1086-1106, doi:10.1111/j.1365-3040.2007.01682.x (2007).
41 Barron-Gafford, G. A., Scott, R. L., Jenerette, G. D., Hamerlynck, E. P. & Huxman, T. E. Temperature and precipitation controls over leaf- and ecosystem-level CO2 flux along a woody plant encroachment gradient. Global Change Biology 18, 1389-1400, doi:10.1111/j.1365-2486.2011.02599.x (2012).
42 Yamori, W., Hikosaka, K. & Way, D. A. Temperature response of photosynthesis in C3, C4, and CAM plants: temperature acclimation and temperature adaptation. Photosynth Res 119, 101-117, doi:10.1007/s11120-013-9874-6 (2014).
43 Ansari, A. & Loomis, W. Leaf temperatures. American Journal of Botany 46, 713-717 (1959).
44 Bregetova, L. G. & Popova, A. J. About temperature regime of leaves of plants in Tadjikistan. Akad. Nauk. Tadzhikskoi SSR, Otdel fiziologii i biofiziki rastenii, Temat. sb. 3, 29-40 (1963).
45 Bukharin, P. D. Leaf temperature and heat resistance in certain cultivated plants. Fiziologiya Rast 5, 117-124 (1958).
46 Clum, H. H. The Effect of Transpiration and Environmental Factors on Leaf Temperatures I. Transpiration. American Journal of Botany 13, 194-216 (1926).
47 Clum, H. H. The Effect of Transpiration and Environmental Factors on Leaf Temperatures II. Light Intensity and the Relation of Transpiration to the Thermal Death Point. American Journal of Botany 13, 217-230 (1926).
48 Collins, B. The atmospheric conditions affecting sporulation of blue mould in tobacco. Australian Journal of Experimental Agriculture 4, 178-184, doi:http://dx.doi.org/10.1071/EA9640178 (1964).
49 Curtis, O. F. Leaf temperatures and the cooling of leaves by radiation. Plant Physiology 11, 343-364 (1936).
Michaletz et al. Supplementary Information 17
50 Doughty, C. E. & Goulden, M. L. Are tropical forests near a high temperature threshold? Journal of Geophysical Research: Biogeosciences 113, G00B07, doi:10.1029/2007JG000632 (2008).
51 Eaton, F. M. & Belden, G. O. Leaf temperatures of cotton and their relation to transpiration, varietal differences, and yields. 1-39 (United States Department of Agriculture, Economic Research Service Technical Bulletin no. 91, 1929).
52 Ehleringer, J. R. & Cook, C. S. Characteristics of Encelia species differing in leaf reflectance and transpiration rate under common garden conditions. Oecologia 82, 484-489, doi:10.1007/BF00319790 (1990).
53 Ehleringer, J. R. & Mooney, H. A. Leaf hairs: Effects on physiological activity and adaptive value to a desert shrub. Oecologia 37, 183-200, doi:10.1007/BF00344990 (1978).
54 Ehrler, W. L. Cotton leaf temperatures as related to soil water depletion and meteorological factors. Agronomy Journal 65, 404-409 (1973).
55 Eller, B. M. Road dust induced increase of leaf temperature. Environmental Pollution (1970) 13, 99-107, doi:http://dx.doi.org/10.1016/0013-9327(77)90094-5 (1977).
56 Ezekiel, W. N. & Taubenhaus, J. J. Leaf temperatures of cotton plants with Phymatotrichum root rot. Science 75, 391-392 (1932).
57 Gale, J. & Poljakoff-Mayber, A. Effect of antitranspirant treatment on leaf temperatures. Plant and Cell Physiology 6, 111-115 (1965).
58 Gates, D., Hiesey, W., Milner, H. & Nobs, M. Temperatures of Mimulus leaves in natural environments and in a controlled chamber. Carnegie Institute Washington Yearbook 63, 418-430 (1964).
59 Gates, D. M. in Water and Plant Life: Problems and Modern Approaches (eds O.L. Lange, L. Kappen, & E.-D. Schlze) 137-147 (Springer-Verlag, 1976).
60 Gates, D. M. Winter Thermal Radiation Studies in Yellowstone Park: Infrared reveals surface phenomena of hot springs and temperatures of vegetation and Old Faithful geyser. Science 134, 32-35, doi:10.1126/science.134.3471.32 (1961).
61 Gates, D. M., Alderfer, R. & Taylor, E. Leaf Temperatures of Desert Plants. Science 159, 994-995, doi:10.1126/science.159.3818.994 (1968).
62 Gates, D. M. & Janke, R. The energy environment of the alpine tundra. Oecol. Plant 1, 39-62 (1966).
63 Gauslaa, Y. Heat resistance and energy budget in different Scandinavian plants. Ecography 7, 5-6, doi:10.1111/j.1600-0587.1984.tb01098.x (1984).
64 Geller, G. N. & Smith, W. K. Influence of leaf size, orientation, and arrangement on temperature and transpiration in three high-elevation, large-leafed herbs. Oecologia 53, 227-234, doi:10.1007/BF00545668 (1982).
65 Gorishina, T. K. Studies of the water and thermal regime of leaves in plants of different ecological types under natural conditions. Vest. Leningr. Gos. Univ. 3, 90-98 (1960).
66 Greathouse, G. A. Effects of the physical environment on the physico-chemical properties of plant saps, and the relation of these properties to leaf temperature. Plant Physiology 7, i4-390 (1932).
67 Harris, D. S., Schapaugh, W. T. & Kanemasu, E. T. Genetic Diversity in Soybeans for Leaf Canopy Temperature and the Association of Leaf Canopy Temperature and Yield1. Crop Sci. 24, 839-842, doi:10.2135/cropsci1984.0011183X002400050002x (1984).
35 Vasseur, D. A. et al. Increased temperature variation poses a greater risk to species than climate warming. Proceedings of the Royal Society of London B: Biological Sciences 281, doi:10.1098/rspb.2013.2612 (2014).
36 Ball, M., Cowan, I. & Farquhar, G. Maintenance of Leaf Temperature and the Optimisation of Carbon Gain in Relation to Water Loss in a Tropical Mangrove Forest. Functional Plant Biology 15, 263-276, doi:http://dx.doi.org/10.1071/PP9880263 (1988).
37 Korner, C. & Diemer, M. In situ photosynthetic responses to light, temperature and carbon dioxide in herbaceous plants from low and high altitude. Functional Ecology 1, 179-194, doi:10.2307/2389420 (1987).
38 Slatyer, R. & Morrow, P. Altitudinal Variation in the Photosynthetic Characteristics of Snow Gum, <I>Eucalyptus pauciflora</I> Sieb. Ex Spreng. I. Seasonal Changes Under Field Conditions in the Snowy Mountains Area of South-Eastern Australia. Australian Journal of Botany 25, 1-20, doi:http://dx.doi.org/10.1071/BT9770001 (1977).
39 Sage, R., Kocacinar, F. & Kubien, D. in C4 Photosynthesis and Related CO2 Concentrating Mechanisms Vol. 32 Advances in Photosynthesis and Respiration (eds Agepati S. Raghavendra & Rowan F. Sage) Ch. 10, 161-195 (Springer Netherlands, 2011).
40 Sage, R. F. & Kubien, D. S. The temperature response of C3 and C4 photosynthesis. Plant, Cell & Environment 30, 1086-1106, doi:10.1111/j.1365-3040.2007.01682.x (2007).
41 Barron-Gafford, G. A., Scott, R. L., Jenerette, G. D., Hamerlynck, E. P. & Huxman, T. E. Temperature and precipitation controls over leaf- and ecosystem-level CO2 flux along a woody plant encroachment gradient. Global Change Biology 18, 1389-1400, doi:10.1111/j.1365-2486.2011.02599.x (2012).
42 Yamori, W., Hikosaka, K. & Way, D. A. Temperature response of photosynthesis in C3, C4, and CAM plants: temperature acclimation and temperature adaptation. Photosynth Res 119, 101-117, doi:10.1007/s11120-013-9874-6 (2014).
43 Ansari, A. & Loomis, W. Leaf temperatures. American Journal of Botany 46, 713-717 (1959).
44 Bregetova, L. G. & Popova, A. J. About temperature regime of leaves of plants in Tadjikistan. Akad. Nauk. Tadzhikskoi SSR, Otdel fiziologii i biofiziki rastenii, Temat. sb. 3, 29-40 (1963).
45 Bukharin, P. D. Leaf temperature and heat resistance in certain cultivated plants. Fiziologiya Rast 5, 117-124 (1958).
46 Clum, H. H. The Effect of Transpiration and Environmental Factors on Leaf Temperatures I. Transpiration. American Journal of Botany 13, 194-216 (1926).
47 Clum, H. H. The Effect of Transpiration and Environmental Factors on Leaf Temperatures II. Light Intensity and the Relation of Transpiration to the Thermal Death Point. American Journal of Botany 13, 217-230 (1926).
48 Collins, B. The atmospheric conditions affecting sporulation of blue mould in tobacco. Australian Journal of Experimental Agriculture 4, 178-184, doi:http://dx.doi.org/10.1071/EA9640178 (1964).
49 Curtis, O. F. Leaf temperatures and the cooling of leaves by radiation. Plant Physiology 11, 343-364 (1936).
Michaletz et al. Supplementary Information 17
50 Doughty, C. E. & Goulden, M. L. Are tropical forests near a high temperature threshold? Journal of Geophysical Research: Biogeosciences 113, G00B07, doi:10.1029/2007JG000632 (2008).
51 Eaton, F. M. & Belden, G. O. Leaf temperatures of cotton and their relation to transpiration, varietal differences, and yields. 1-39 (United States Department of Agriculture, Economic Research Service Technical Bulletin no. 91, 1929).
52 Ehleringer, J. R. & Cook, C. S. Characteristics of Encelia species differing in leaf reflectance and transpiration rate under common garden conditions. Oecologia 82, 484-489, doi:10.1007/BF00319790 (1990).
53 Ehleringer, J. R. & Mooney, H. A. Leaf hairs: Effects on physiological activity and adaptive value to a desert shrub. Oecologia 37, 183-200, doi:10.1007/BF00344990 (1978).
54 Ehrler, W. L. Cotton leaf temperatures as related to soil water depletion and meteorological factors. Agronomy Journal 65, 404-409 (1973).
55 Eller, B. M. Road dust induced increase of leaf temperature. Environmental Pollution (1970) 13, 99-107, doi:http://dx.doi.org/10.1016/0013-9327(77)90094-5 (1977).
56 Ezekiel, W. N. & Taubenhaus, J. J. Leaf temperatures of cotton plants with Phymatotrichum root rot. Science 75, 391-392 (1932).
57 Gale, J. & Poljakoff-Mayber, A. Effect of antitranspirant treatment on leaf temperatures. Plant and Cell Physiology 6, 111-115 (1965).
58 Gates, D., Hiesey, W., Milner, H. & Nobs, M. Temperatures of Mimulus leaves in natural environments and in a controlled chamber. Carnegie Institute Washington Yearbook 63, 418-430 (1964).
59 Gates, D. M. in Water and Plant Life: Problems and Modern Approaches (eds O.L. Lange, L. Kappen, & E.-D. Schlze) 137-147 (Springer-Verlag, 1976).
60 Gates, D. M. Winter Thermal Radiation Studies in Yellowstone Park: Infrared reveals surface phenomena of hot springs and temperatures of vegetation and Old Faithful geyser. Science 134, 32-35, doi:10.1126/science.134.3471.32 (1961).
61 Gates, D. M., Alderfer, R. & Taylor, E. Leaf Temperatures of Desert Plants. Science 159, 994-995, doi:10.1126/science.159.3818.994 (1968).
62 Gates, D. M. & Janke, R. The energy environment of the alpine tundra. Oecol. Plant 1, 39-62 (1966).
63 Gauslaa, Y. Heat resistance and energy budget in different Scandinavian plants. Ecography 7, 5-6, doi:10.1111/j.1600-0587.1984.tb01098.x (1984).
64 Geller, G. N. & Smith, W. K. Influence of leaf size, orientation, and arrangement on temperature and transpiration in three high-elevation, large-leafed herbs. Oecologia 53, 227-234, doi:10.1007/BF00545668 (1982).
65 Gorishina, T. K. Studies of the water and thermal regime of leaves in plants of different ecological types under natural conditions. Vest. Leningr. Gos. Univ. 3, 90-98 (1960).
66 Greathouse, G. A. Effects of the physical environment on the physico-chemical properties of plant saps, and the relation of these properties to leaf temperature. Plant Physiology 7, i4-390 (1932).
67 Harris, D. S., Schapaugh, W. T. & Kanemasu, E. T. Genetic Diversity in Soybeans for Leaf Canopy Temperature and the Association of Leaf Canopy Temperature and Yield1. Crop Sci. 24, 839-842, doi:10.2135/cropsci1984.0011183X002400050002x (1984).
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 18
68 Hatfield, J. L. & Burke, J. J. Energy exchange and leaf temperature behavior of three plant species. Environmental and Experimental Botany 31, 295-302, doi:http://dx.doi.org/10.1016/0098-8472(91)90053-Q (1991).
69 Knapp, A. K. Post-Burn Differences in Solar Radiation, Leaf Temperature and Water Stress Influencing Production in a Lowland Tallgrass Prairie. American Journal of Botany 71, 220-227 (1984).
70 Korner, C. Alpine Plant Life: Functional Plant Ecology of High Mountain Ecosystems. (Springer, 1998).
71 Körner, C. & Cochrane, P. Influence of plant physiognomy on leaf temperature on clear midsummer days in the Snowy Mountains, south-eastern Australia. Acta Oecologia/Oecologia Plantarum 4, 117-124 (1983).
72 Kryuchkov, V. V. Leaf temperature of some plants in the Khibin. Plant Physiol. USSR 8, 502-504 (1962).
73 Larcher, W. Physiological Plant Ecology. (1977). 74 Laurie, S., Bradbury, M. & Stewart, G. R. Relationship between leaf temperature,
compatible solutes and antitranspirant treatment in some desert plants. Plant Science 100, 147-156, doi:http://dx.doi.org/10.1016/0168-9452(94)90070-1 (1994).
75 Le Clerg, E. L. Leaf temperature of lettuce and its relation to tipburn. Phytopathology 22, 851-855 (1932).
76 Leuzinger, S. & Körner, C. Tree species diversity affects canopy leaf temperatures in a mature temperate forest. Agricultural and Forest Meteorology 146, 29-37, doi:http://dx.doi.org/10.1016/j.agrformet.2007.05.007 (2007).
77 Linacre, E. T. A note on a feature of leaf and air temperatures. Agricultural Meteorology 1, 66-72, doi:http://dx.doi.org/10.1016/0002-1571(64)90009-3 (1964).
78 Linacre, E. T. Further notes on a feature of leaf and air temperatures. Archiv für Meteorologie, Geophysik und Bioklimatologie, Serie B 15, 422-436, doi:10.1007/BF02390453 (1967).
79 Lundager, A. Some notes concerning the vegetation of Germania Land, North-East Greenland. Meddr. Gronland 43, 349-414 (1912).
80 Martin, T. A., Hinckley, T. M., Meinzer, F. C. & Sprugel, D. G. Boundary layer conductance, leaf temperature and transpiration of Abies amabilis branches. Tree Physiology 19, 435-443, doi:10.1093/treephys/19.7.435 (1999).
81 Medina, E., Sobrado, M. & Herrera, R. Significance of leaf orientation for leaf temperature in an amazonian sclerophyll vegetation. Radiat Environ Biophys 15, 131-140, doi:10.1007/BF01323262 (1978).
82 Mellor, R. S., Salisbury, F. B. & Raschke, K. Leaf temperatures in controlled environments. Planta 61, 56-72, doi:10.1007/BF01895390 (1964).
83 Miller, E. C. & Saunders, A. R. Some observations on the temperature of the leaves of crop plants. Journal of Agricultural Research 26, 15-43 (1923).
84 Monteith, J. L. & Szeicz, G. Radiative temperature in the heat balance of natural surfaces. Quarterly Journal of the Royal Meteorological Society 88, 496-507, doi:10.1002/qj.49708837811 (1962).
85 Moreland, C. F. Leaf temperatures of sugar cane. Plant Physiology 12, 989-995 (1937). 86 Noffsinger, T. L. Leaf and Air Temperature under Hawaii Conditions. Pacific Science 15,
304-306 (1961).
Michaletz et al. Supplementary Information 19
87 O'Toole, J. C. & Tomar, V. S. Transpiration, leaf temperature and water potential of rice and barnyard grass in flooded fields. Agricultural Meteorology 26, 285-296, doi:http://dx.doi.org/10.1016/0002-1571(82)90046-2 (1982).
88 Pallas, J. E. & Bertrand, A. R. Research in plant transpiration: 1963. (USDA Production Research Report No. 89, 1966).
89 Pearcy, R., Berry, J. & Bartholomew, B. Field measurements of the gas exchange capacities of Phragmites communis under summer conditions in Death Valley. Annu Rep Dep Plant Biol Carnegie Inst, 161-164 (1971).
90 Potter, K., Davidowitz, G. & Woods, H. A. Insect eggs protected from high temperatures by limited homeothermy of plant leaves. Journal of Experimental Biology 212, 3448-3454, doi:10.1242/jeb.033365 (2009).
91 Pruitt, W. O. & Aston, M. J. (eds FA Brooks, WO Pruitt, & DR Nielsen) 69-105 (University of California Davis Final Report Task 3A99-27-005-08, 1963).
92 Reinert, S., Bögelein, R. & Thomas, F. M. Use of thermal imaging to determine leaf conductance along a canopy gradient in European beech (Fagus sylvatica). Tree Physiology 32, 294-302, doi:10.1093/treephys/tps017 (2012).
93 Salisbury, F. & Spomer, G. Leaf temperatures of alpine plants in the field. Planta 60, 497-505, doi:10.1007/BF01894807 (1964).
94 Sellin, A. & Kupper, P. Temperature, light and leaf hydraulic conductance of little-leaf linden (Tilia cordata) in a mixed forest canopy. Tree Physiology 27, 679-688, doi:10.1093/treephys/27.5.679 (2007).
95 Smith, W. K. Temperatures of Desert Plants: Another Perspective on the Adaptability of Leaf Size. Science 201, 614-616, doi:10.1126/science.201.4356.614 (1978).
96 Smith, W. K. & Nobel, P. S. Temperature and Water Relations for Sun and Shade Leaves of a Desert Broadleaf, Hyptis emoryi. Journal of Experimental Botany 28, 169-183, doi:10.1093/jxb/28.1.169 (1977).
97 Smith, W. K. & Nobel, P. S. Influences of Seasonal Changes in Leaf Morphology on Water-Use Efficiency For Three Desert Broadleaf Shrubs. Ecology 58, 1033-1043, doi:10.2307/1936923 (1977).
98 Sumayao, C. R., Kanemasu, E. T. & Brakke, T. W. Using leaf temperature to assess evapotranspiration and advection. Agricultural Meteorology 22, 153-166, doi:http://dx.doi.org/10.1016/0002-1571(80)90042-4 (1980).
99 Tanner, C. B. Plant Temperatures. Agronomy Journal 55, 210-211, doi:10.2134/agronj1963.00021962005500020043x (1963).
100 Tyree, M. T. & Wilmot, T. R. Errors in the calculation of evaporation and leaf conductance in steady-state porometry: the importance of accurate measurement of leaf temperature. Canadian Journal of Forest Research 20, 1031-1035, doi:10.1139/x90-137 (1990).
101 Upchurch, D. R. & Mahan, J. R. Maintenance of constant leaf temperature by plants—II. Experimental observations in cotton. Environmental and Experimental Botany 28, 359-366, doi:http://dx.doi.org/10.1016/0098-8472(88)90060-3 (1988).
102 Vasudeva, R. A. Studies of root rot diseases of cotton in the Punjab. 13. Leaf temperatures of healthy and root-rot affected plants. Ind. J. Agric. Sci. 14, 385-388 (1944).
103 Waggoner, P. E. & Shaw, R. H. Temperature of potato and tomato leaves. Plant Physiology 27, 710-724 (1952).
68 Hatfield, J. L. & Burke, J. J. Energy exchange and leaf temperature behavior of three plant species. Environmental and Experimental Botany 31, 295-302, doi:http://dx.doi.org/10.1016/0098-8472(91)90053-Q (1991).
69 Knapp, A. K. Post-Burn Differences in Solar Radiation, Leaf Temperature and Water Stress Influencing Production in a Lowland Tallgrass Prairie. American Journal of Botany 71, 220-227 (1984).
70 Korner, C. Alpine Plant Life: Functional Plant Ecology of High Mountain Ecosystems. (Springer, 1998).
71 Körner, C. & Cochrane, P. Influence of plant physiognomy on leaf temperature on clear midsummer days in the Snowy Mountains, south-eastern Australia. Acta Oecologia/Oecologia Plantarum 4, 117-124 (1983).
72 Kryuchkov, V. V. Leaf temperature of some plants in the Khibin. Plant Physiol. USSR 8, 502-504 (1962).
73 Larcher, W. Physiological Plant Ecology. (1977). 74 Laurie, S., Bradbury, M. & Stewart, G. R. Relationship between leaf temperature,
compatible solutes and antitranspirant treatment in some desert plants. Plant Science 100, 147-156, doi:http://dx.doi.org/10.1016/0168-9452(94)90070-1 (1994).
75 Le Clerg, E. L. Leaf temperature of lettuce and its relation to tipburn. Phytopathology 22, 851-855 (1932).
76 Leuzinger, S. & Körner, C. Tree species diversity affects canopy leaf temperatures in a mature temperate forest. Agricultural and Forest Meteorology 146, 29-37, doi:http://dx.doi.org/10.1016/j.agrformet.2007.05.007 (2007).
77 Linacre, E. T. A note on a feature of leaf and air temperatures. Agricultural Meteorology 1, 66-72, doi:http://dx.doi.org/10.1016/0002-1571(64)90009-3 (1964).
78 Linacre, E. T. Further notes on a feature of leaf and air temperatures. Archiv für Meteorologie, Geophysik und Bioklimatologie, Serie B 15, 422-436, doi:10.1007/BF02390453 (1967).
79 Lundager, A. Some notes concerning the vegetation of Germania Land, North-East Greenland. Meddr. Gronland 43, 349-414 (1912).
80 Martin, T. A., Hinckley, T. M., Meinzer, F. C. & Sprugel, D. G. Boundary layer conductance, leaf temperature and transpiration of Abies amabilis branches. Tree Physiology 19, 435-443, doi:10.1093/treephys/19.7.435 (1999).
81 Medina, E., Sobrado, M. & Herrera, R. Significance of leaf orientation for leaf temperature in an amazonian sclerophyll vegetation. Radiat Environ Biophys 15, 131-140, doi:10.1007/BF01323262 (1978).
82 Mellor, R. S., Salisbury, F. B. & Raschke, K. Leaf temperatures in controlled environments. Planta 61, 56-72, doi:10.1007/BF01895390 (1964).
83 Miller, E. C. & Saunders, A. R. Some observations on the temperature of the leaves of crop plants. Journal of Agricultural Research 26, 15-43 (1923).
84 Monteith, J. L. & Szeicz, G. Radiative temperature in the heat balance of natural surfaces. Quarterly Journal of the Royal Meteorological Society 88, 496-507, doi:10.1002/qj.49708837811 (1962).
85 Moreland, C. F. Leaf temperatures of sugar cane. Plant Physiology 12, 989-995 (1937). 86 Noffsinger, T. L. Leaf and Air Temperature under Hawaii Conditions. Pacific Science 15,
304-306 (1961).
Michaletz et al. Supplementary Information 19
87 O'Toole, J. C. & Tomar, V. S. Transpiration, leaf temperature and water potential of rice and barnyard grass in flooded fields. Agricultural Meteorology 26, 285-296, doi:http://dx.doi.org/10.1016/0002-1571(82)90046-2 (1982).
88 Pallas, J. E. & Bertrand, A. R. Research in plant transpiration: 1963. (USDA Production Research Report No. 89, 1966).
89 Pearcy, R., Berry, J. & Bartholomew, B. Field measurements of the gas exchange capacities of Phragmites communis under summer conditions in Death Valley. Annu Rep Dep Plant Biol Carnegie Inst, 161-164 (1971).
90 Potter, K., Davidowitz, G. & Woods, H. A. Insect eggs protected from high temperatures by limited homeothermy of plant leaves. Journal of Experimental Biology 212, 3448-3454, doi:10.1242/jeb.033365 (2009).
91 Pruitt, W. O. & Aston, M. J. (eds FA Brooks, WO Pruitt, & DR Nielsen) 69-105 (University of California Davis Final Report Task 3A99-27-005-08, 1963).
92 Reinert, S., Bögelein, R. & Thomas, F. M. Use of thermal imaging to determine leaf conductance along a canopy gradient in European beech (Fagus sylvatica). Tree Physiology 32, 294-302, doi:10.1093/treephys/tps017 (2012).
93 Salisbury, F. & Spomer, G. Leaf temperatures of alpine plants in the field. Planta 60, 497-505, doi:10.1007/BF01894807 (1964).
94 Sellin, A. & Kupper, P. Temperature, light and leaf hydraulic conductance of little-leaf linden (Tilia cordata) in a mixed forest canopy. Tree Physiology 27, 679-688, doi:10.1093/treephys/27.5.679 (2007).
95 Smith, W. K. Temperatures of Desert Plants: Another Perspective on the Adaptability of Leaf Size. Science 201, 614-616, doi:10.1126/science.201.4356.614 (1978).
96 Smith, W. K. & Nobel, P. S. Temperature and Water Relations for Sun and Shade Leaves of a Desert Broadleaf, Hyptis emoryi. Journal of Experimental Botany 28, 169-183, doi:10.1093/jxb/28.1.169 (1977).
97 Smith, W. K. & Nobel, P. S. Influences of Seasonal Changes in Leaf Morphology on Water-Use Efficiency For Three Desert Broadleaf Shrubs. Ecology 58, 1033-1043, doi:10.2307/1936923 (1977).
98 Sumayao, C. R., Kanemasu, E. T. & Brakke, T. W. Using leaf temperature to assess evapotranspiration and advection. Agricultural Meteorology 22, 153-166, doi:http://dx.doi.org/10.1016/0002-1571(80)90042-4 (1980).
99 Tanner, C. B. Plant Temperatures. Agronomy Journal 55, 210-211, doi:10.2134/agronj1963.00021962005500020043x (1963).
100 Tyree, M. T. & Wilmot, T. R. Errors in the calculation of evaporation and leaf conductance in steady-state porometry: the importance of accurate measurement of leaf temperature. Canadian Journal of Forest Research 20, 1031-1035, doi:10.1139/x90-137 (1990).
101 Upchurch, D. R. & Mahan, J. R. Maintenance of constant leaf temperature by plants—II. Experimental observations in cotton. Environmental and Experimental Botany 28, 359-366, doi:http://dx.doi.org/10.1016/0098-8472(88)90060-3 (1988).
102 Vasudeva, R. A. Studies of root rot diseases of cotton in the Punjab. 13. Leaf temperatures of healthy and root-rot affected plants. Ind. J. Agric. Sci. 14, 385-388 (1944).
103 Waggoner, P. E. & Shaw, R. H. Temperature of potato and tomato leaves. Plant Physiology 27, 710-724 (1952).
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 20
104 Wallace, R. H. & Clum, H. H. Leaf temperatures. American Journal of Botany 25, 83-97 (1938).
105 Waterhouse, F. L. Microclimatological profiles in grass cover in relation to biological problems. Quarterly Journal of the Royal Meteorological Society 81, 63-71, doi:10.1002/qj.49708134707 (1955).
106 Wilson, J. W. Observations on the Temperatures of Arctic Plants and Their Environment. The Jounal of Ecology 45, 499-531 (1957).
107 Yan, C. et al. The impact of relative humidity, genotypes and fertilizer application rates on panicle, leaf temperature, fertility and seed setting of rice. The Journal of Agricultural Science 148, 329-339, doi:doi:10.1017/S0021859610000018 (2010).
108 Drake, B. G. & Salisbury, F. B. Aftereffects of Low and High Temperature Pretreatment on Leaf Resistance, Transpiration, and Leaf Temperature in Xanthium. Plant Physiology 50, 572-575, doi:10.1104/pp.50.5.572 (1972).
109 Loucos, K. E., Simonin, K. A., Song, X. & Barbour, M. M. Observed relationships between leaf H218O Péclet effective length and leaf hydraulic conductance reflect assumptions in Craig–Gordon model calculations. Tree Physiology, doi:10.1093/treephys/tpu110 (2015).
110 Song, X. I. N., Farquhar, G. D., Gessler, A. & Barbour, M. M. Turnover time of the non-structural carbohydrate pool influences δ18O of leaf cellulose. Plant, Cell & Environment 37, 2500-2507, doi:10.1111/pce.12309 (2014).
111 Helliker, B. R. & Richter, S. L. Subtropical to boreal convergence of tree-leaf temperatures. Nature 454, 511-514, doi:http://www.nature.com/nature/journal/v454/n7203/suppinfo/nature07031_S1.html (2008).
112 Song, X., Barbour, M. M., Saurer, M. & Helliker, B. R. Examining the large-scale convergence of photosynthesis-weighted tree leaf temperatures through stable oxygen isotope analysis of multiple data sets. New Phytologist 192, 912-924, doi:10.1111/j.1469-8137.2011.03851.x (2011).
113 Barbour, M. M., Andrews, T. J. & Farquhar, G. D. Correlations between oxygen isotope ratios of wood constituents of Quercus and Pinus samples from around the world. Functional Plant Biology 28, 335-348, doi:http://dx.doi.org/10.1071/PP00083 (2001).
114 Saurer, M., Schweingruber, F., Vaganov, E. A., Shiyatov, S. G. & Siegwolf, R. Spatial and temporal oxygen isotope trends at the northern tree-line in Eurasia. Geophysical Research Letters 29, 7-1-7-4, doi:10.1029/2001GL013739 (2002).
115 Evans, M. N. & Schrag, D. P. A stable isotope-based approach to tropical dendroclimatology. Geochimica et Cosmochimica Acta 68, 3295-3305, doi:http://dx.doi.org/10.1016/j.gca.2004.01.006 (2004).
116 Poussart, P. F., Evans, M. N. & Schrag, D. P. Resolving seasonality in tropical trees: multi-decade, high-resolution oxygen and carbon isotope records from Indonesia and Thailand. Earth and Planetary Science Letters 218, 301-316, doi:http://dx.doi.org/10.1016/S0012-821X(03)00638-1 (2004).
117 Poussart, P. F. & Schrag, D. P. Seasonally resolved stable isotope chronologies from northern Thailand deciduous trees. Earth and Planetary Science Letters 235, 752-765, doi:http://dx.doi.org/10.1016/j.epsl.2005.05.012 (2005).
118 Flanagan, L. B. & Farquhar, G. D. Variation in the carbon and oxygen isotope composition of plant biomass and its relationship to water-use efficiency at the leaf- and
Michaletz et al. Supplementary Information 21
ecosystem-scales in a northern Great Plains grassland. Plant, Cell & Environment 37, 425-438, doi:10.1111/pce.12165 (2014).
119 Wright, I. J. et al. The worldwide leaf economics spectrum. Nature 428, 821-827, doi:http://www.nature.com/nature/journal/v428/n6985/suppinfo/nature02403_S1.html (2004).
120 BIEN: The Botanical Information and Ecology Network. http://bien.nceas.ucsb.edu/bien/. 121 Weston, D. J. & Bauerle, W. L. Inhibition and acclimation of C3 photosynthesis to
moderate heat: a perspective from thermally contrasting genotypes of Acer rubrum (red maple). Tree Physiology 27, 1083-1092, doi:10.1093/treephys/27.8.1083 (2007).
122 Gunderson, C. A., Norby, R. J. & Wullschleger, S. D. Acclimation of photosynthesis and respiration to simulated climatic warming in northern and southern populations of Acer saccharum: laboratory and field evidence. Tree Physiology 20, 87-96, doi:10.1093/treephys/20.2.87 (2000).
123 Osmond, C. B., Bjorkman, O. & Anderson, D. J. Physiological Processes in Plant Ecology: Toward a Synthesis with Atriplex. (Springer-Verlag, 1980).
124 Pearcy, R., Björkman, O., Harrison, A. T. & Mooney, H. A. Photosynthetic performance of two desert species with C4 photosynthesis in Death Valley, California. Carnegie Institute of Washington Yearbook 70, 540-550 (1971).
125 Pearcy, R. Acclimation of photosynthetic and respiratory carbon dioxide exchange to growth temperature in Atriplex lentiformis (Torr.) Wats. Plant Physiology 59, 795-799 (1977).
126 Monson, R., Littlejohn, R., Jr. & Williams, G., III. Photosynthetic adaptation to temperature in four species from the Colorado shortgrass steppe: a physiological model for coexistence. Oecologia 58, 43-51, doi:10.1007/BF00384540 (1983).
127 Paul, M. J., Lawlor, D. W. & Driscoll, S. P. The Effect of Temperature on Photosynthesis and Carbon Fluxes in Sunflower and Rape. Journal of Experimental Botany 41, 547-555, doi:10.1093/jxb/41.5.547 (1990).
128 Zhou, X., Liu, X., Wallace, L. L. & Luo, Y. Photosynthetic and Respiratory Acclimation to Experimental Warming for Four Species in a Tallgrass Prairie Ecosystem. Journal of Integrative Plant Biology 49, 270-281, doi:10.1111/j.1744-7909.2007.00374.x (2007).
129 Tranquillini, W., Havranek, W. M. & Ecker, P. Effects of atmospheric humidity and acclimation temperature on the temperature response of photosynthesis in young Larix decidua Mill. Tree Physiology 1, 37-45, doi:10.1093/treephys/1.1.37 (1986).
130 Mooney, H. A., Björkman, O. & Collatz, G. J. Photosynthetic Acclimation to Temperature in the Desert Shrub, Larrea divaricata: I. Carbon Dioxide Exchange Characteristics of Intact Leaves. Plant Physiology 61, 406-410, doi:10.1104/pp.61.3.406 (1978).
131 Huxman, T. E., Turnipseed, A. A., Sparks, J. P., Harley, P. C. & Monson, R. K. Temperature as a control over ecosystem CO2 fluxes in a high-elevation, subalpine forest. Oecologia 134, 537-546, doi:10.1007/s00442-002-1131-1 (2003).
132 Smith, W. K. & Carter, G. A. Shoot structural effects on needle temperatures and photosynthesis in conifers. American Journal of Botany 75, 496-500 (1988).
133 Way, D. A. & Sage, R. F. Elevated growth temperatures reduce the carbon gain of black spruce [Picea mariana (Mill.) B.S.P.]. Global Change Biology 14, 624-636, doi:10.1111/j.1365-2486.2007.01513.x (2008).
104 Wallace, R. H. & Clum, H. H. Leaf temperatures. American Journal of Botany 25, 83-97 (1938).
105 Waterhouse, F. L. Microclimatological profiles in grass cover in relation to biological problems. Quarterly Journal of the Royal Meteorological Society 81, 63-71, doi:10.1002/qj.49708134707 (1955).
106 Wilson, J. W. Observations on the Temperatures of Arctic Plants and Their Environment. The Jounal of Ecology 45, 499-531 (1957).
107 Yan, C. et al. The impact of relative humidity, genotypes and fertilizer application rates on panicle, leaf temperature, fertility and seed setting of rice. The Journal of Agricultural Science 148, 329-339, doi:doi:10.1017/S0021859610000018 (2010).
108 Drake, B. G. & Salisbury, F. B. Aftereffects of Low and High Temperature Pretreatment on Leaf Resistance, Transpiration, and Leaf Temperature in Xanthium. Plant Physiology 50, 572-575, doi:10.1104/pp.50.5.572 (1972).
109 Loucos, K. E., Simonin, K. A., Song, X. & Barbour, M. M. Observed relationships between leaf H218O Péclet effective length and leaf hydraulic conductance reflect assumptions in Craig–Gordon model calculations. Tree Physiology, doi:10.1093/treephys/tpu110 (2015).
110 Song, X. I. N., Farquhar, G. D., Gessler, A. & Barbour, M. M. Turnover time of the non-structural carbohydrate pool influences δ18O of leaf cellulose. Plant, Cell & Environment 37, 2500-2507, doi:10.1111/pce.12309 (2014).
111 Helliker, B. R. & Richter, S. L. Subtropical to boreal convergence of tree-leaf temperatures. Nature 454, 511-514, doi:http://www.nature.com/nature/journal/v454/n7203/suppinfo/nature07031_S1.html (2008).
112 Song, X., Barbour, M. M., Saurer, M. & Helliker, B. R. Examining the large-scale convergence of photosynthesis-weighted tree leaf temperatures through stable oxygen isotope analysis of multiple data sets. New Phytologist 192, 912-924, doi:10.1111/j.1469-8137.2011.03851.x (2011).
113 Barbour, M. M., Andrews, T. J. & Farquhar, G. D. Correlations between oxygen isotope ratios of wood constituents of Quercus and Pinus samples from around the world. Functional Plant Biology 28, 335-348, doi:http://dx.doi.org/10.1071/PP00083 (2001).
114 Saurer, M., Schweingruber, F., Vaganov, E. A., Shiyatov, S. G. & Siegwolf, R. Spatial and temporal oxygen isotope trends at the northern tree-line in Eurasia. Geophysical Research Letters 29, 7-1-7-4, doi:10.1029/2001GL013739 (2002).
115 Evans, M. N. & Schrag, D. P. A stable isotope-based approach to tropical dendroclimatology. Geochimica et Cosmochimica Acta 68, 3295-3305, doi:http://dx.doi.org/10.1016/j.gca.2004.01.006 (2004).
116 Poussart, P. F., Evans, M. N. & Schrag, D. P. Resolving seasonality in tropical trees: multi-decade, high-resolution oxygen and carbon isotope records from Indonesia and Thailand. Earth and Planetary Science Letters 218, 301-316, doi:http://dx.doi.org/10.1016/S0012-821X(03)00638-1 (2004).
117 Poussart, P. F. & Schrag, D. P. Seasonally resolved stable isotope chronologies from northern Thailand deciduous trees. Earth and Planetary Science Letters 235, 752-765, doi:http://dx.doi.org/10.1016/j.epsl.2005.05.012 (2005).
118 Flanagan, L. B. & Farquhar, G. D. Variation in the carbon and oxygen isotope composition of plant biomass and its relationship to water-use efficiency at the leaf- and
Michaletz et al. Supplementary Information 21
ecosystem-scales in a northern Great Plains grassland. Plant, Cell & Environment 37, 425-438, doi:10.1111/pce.12165 (2014).
119 Wright, I. J. et al. The worldwide leaf economics spectrum. Nature 428, 821-827, doi:http://www.nature.com/nature/journal/v428/n6985/suppinfo/nature02403_S1.html (2004).
120 BIEN: The Botanical Information and Ecology Network. http://bien.nceas.ucsb.edu/bien/. 121 Weston, D. J. & Bauerle, W. L. Inhibition and acclimation of C3 photosynthesis to
moderate heat: a perspective from thermally contrasting genotypes of Acer rubrum (red maple). Tree Physiology 27, 1083-1092, doi:10.1093/treephys/27.8.1083 (2007).
122 Gunderson, C. A., Norby, R. J. & Wullschleger, S. D. Acclimation of photosynthesis and respiration to simulated climatic warming in northern and southern populations of Acer saccharum: laboratory and field evidence. Tree Physiology 20, 87-96, doi:10.1093/treephys/20.2.87 (2000).
123 Osmond, C. B., Bjorkman, O. & Anderson, D. J. Physiological Processes in Plant Ecology: Toward a Synthesis with Atriplex. (Springer-Verlag, 1980).
124 Pearcy, R., Björkman, O., Harrison, A. T. & Mooney, H. A. Photosynthetic performance of two desert species with C4 photosynthesis in Death Valley, California. Carnegie Institute of Washington Yearbook 70, 540-550 (1971).
125 Pearcy, R. Acclimation of photosynthetic and respiratory carbon dioxide exchange to growth temperature in Atriplex lentiformis (Torr.) Wats. Plant Physiology 59, 795-799 (1977).
126 Monson, R., Littlejohn, R., Jr. & Williams, G., III. Photosynthetic adaptation to temperature in four species from the Colorado shortgrass steppe: a physiological model for coexistence. Oecologia 58, 43-51, doi:10.1007/BF00384540 (1983).
127 Paul, M. J., Lawlor, D. W. & Driscoll, S. P. The Effect of Temperature on Photosynthesis and Carbon Fluxes in Sunflower and Rape. Journal of Experimental Botany 41, 547-555, doi:10.1093/jxb/41.5.547 (1990).
128 Zhou, X., Liu, X., Wallace, L. L. & Luo, Y. Photosynthetic and Respiratory Acclimation to Experimental Warming for Four Species in a Tallgrass Prairie Ecosystem. Journal of Integrative Plant Biology 49, 270-281, doi:10.1111/j.1744-7909.2007.00374.x (2007).
129 Tranquillini, W., Havranek, W. M. & Ecker, P. Effects of atmospheric humidity and acclimation temperature on the temperature response of photosynthesis in young Larix decidua Mill. Tree Physiology 1, 37-45, doi:10.1093/treephys/1.1.37 (1986).
130 Mooney, H. A., Björkman, O. & Collatz, G. J. Photosynthetic Acclimation to Temperature in the Desert Shrub, Larrea divaricata: I. Carbon Dioxide Exchange Characteristics of Intact Leaves. Plant Physiology 61, 406-410, doi:10.1104/pp.61.3.406 (1978).
131 Huxman, T. E., Turnipseed, A. A., Sparks, J. P., Harley, P. C. & Monson, R. K. Temperature as a control over ecosystem CO2 fluxes in a high-elevation, subalpine forest. Oecologia 134, 537-546, doi:10.1007/s00442-002-1131-1 (2003).
132 Smith, W. K. & Carter, G. A. Shoot structural effects on needle temperatures and photosynthesis in conifers. American Journal of Botany 75, 496-500 (1988).
133 Way, D. A. & Sage, R. F. Elevated growth temperatures reduce the carbon gain of black spruce [Picea mariana (Mill.) B.S.P.]. Global Change Biology 14, 624-636, doi:10.1111/j.1365-2486.2007.01513.x (2008).
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 22
134 Way, D. A. & Sage, R. F. Thermal acclimation of photosynthesis in black spruce [Picea mariana (Mill.) B.S.P.]. Plant, Cell & Environment 31, 1250-1262, doi:10.1111/j.1365-3040.2008.01842.x (2008).
135 Wang, K.-Y., Kellomäki, S. & Laitinen, K. Acclimation of photosynthetic parameters in Scots pine after three years exposure to elevated temperature and CO2. Agricultural and Forest Meteorology 82, 195-217, doi:http://dx.doi.org/10.1016/0168-1923(96)02329-5 (1996).
136 Wertin, T. M., McGuire, M. A., van Iersel, M., Ruter, J. M. & Teskey, R. O. Effects of elevated temperature and [CO2] on photosynthesis, leaf respiration, and biomass accumulation of Pinus taeda seedlings at a cool and a warm site within the species’ current range. Canadian Journal of Forest Research 42, 943-957, doi:10.1139/x2012-050 (2012).
137 Atkin, O. K., Scheurwater, I. & Pons, T. L. High thermal acclimation potential of both photosynthesis and respiration in two lowland Plantago species in contrast to an alpine congeneric. Global Change Biology 12, 500-515, doi:10.1111/j.1365-2486.2006.01114.x (2006).
138 Silim, S., Ryan, N. & Kubien, D. Temperature responses of photosynthesis and respiration in Populus balsamifera L.: acclimation versus adaptation. Photosynth Res 104, 19-30, doi:10.1007/s11120-010-9527-y (2010).
139 Fares, S., Mahmood, T., Liu, S., Loreto, F. & Centritto, M. Influence of growth temperature and measuring temperature on isoprene emission, diffusive limitations of photosynthesis and respiration in hybrid poplars. Atmospheric Environment 45, 155-161, doi:http://dx.doi.org/10.1016/j.atmosenv.2010.09.036 (2011).
140 Wertin, T. M., McGuire, M. A. & Teskey, R. O. Higher growth temperatures decreased net carbon assimilation and biomass accumulation of northern red oak seedlings near the southern limit of the species range. Tree Physiology 31, 1277-1288, doi:10.1093/treephys/tpr091 (2011).
141 Yamori, W., Noguchi, K., Hikosaka, K. & Terashima, I. Phenotypic plasticity in photosynthetic temperature acclimation among crop species with different cold tolerances. Plant physiology 152, 388-399 (2010).
142 Leigh, A. et al. Do thick leaves avoid thermal damage in critically low wind speeds? New Phytologist 194, 477-487, doi:10.1111/j.1469-8137.2012.04058.x (2012).
143 Michaletz, S. T., Cheng, D., Kerkhoff, A. J. & Enquist, B. J. Convergence of terrestrial plant production across global climate gradients. Nature 512, 39-43, doi:10.1038/nature13470
144 New, M., Lister, D., Hulme, M. & Makin, I. A high-resolution data set of surface climate over global land areas. Climate research 21, 1-25 (2002).
Michaletz et al. Supplementary Information 23
Extended Data Figure 1 | Relationship between photosynthesis rate and leaf temperature illustrating the maximum photosynthesis rate Aopt (dashed gray line), the optimal temperature for photosynthesis Topt (dashed gray line), and the thermal breadth of photosynthesis T90 (solid gray arrow and green area).
134 Way, D. A. & Sage, R. F. Thermal acclimation of photosynthesis in black spruce [Picea mariana (Mill.) B.S.P.]. Plant, Cell & Environment 31, 1250-1262, doi:10.1111/j.1365-3040.2008.01842.x (2008).
135 Wang, K.-Y., Kellomäki, S. & Laitinen, K. Acclimation of photosynthetic parameters in Scots pine after three years exposure to elevated temperature and CO2. Agricultural and Forest Meteorology 82, 195-217, doi:http://dx.doi.org/10.1016/0168-1923(96)02329-5 (1996).
136 Wertin, T. M., McGuire, M. A., van Iersel, M., Ruter, J. M. & Teskey, R. O. Effects of elevated temperature and [CO2] on photosynthesis, leaf respiration, and biomass accumulation of Pinus taeda seedlings at a cool and a warm site within the species’ current range. Canadian Journal of Forest Research 42, 943-957, doi:10.1139/x2012-050 (2012).
137 Atkin, O. K., Scheurwater, I. & Pons, T. L. High thermal acclimation potential of both photosynthesis and respiration in two lowland Plantago species in contrast to an alpine congeneric. Global Change Biology 12, 500-515, doi:10.1111/j.1365-2486.2006.01114.x (2006).
138 Silim, S., Ryan, N. & Kubien, D. Temperature responses of photosynthesis and respiration in Populus balsamifera L.: acclimation versus adaptation. Photosynth Res 104, 19-30, doi:10.1007/s11120-010-9527-y (2010).
139 Fares, S., Mahmood, T., Liu, S., Loreto, F. & Centritto, M. Influence of growth temperature and measuring temperature on isoprene emission, diffusive limitations of photosynthesis and respiration in hybrid poplars. Atmospheric Environment 45, 155-161, doi:http://dx.doi.org/10.1016/j.atmosenv.2010.09.036 (2011).
140 Wertin, T. M., McGuire, M. A. & Teskey, R. O. Higher growth temperatures decreased net carbon assimilation and biomass accumulation of northern red oak seedlings near the southern limit of the species range. Tree Physiology 31, 1277-1288, doi:10.1093/treephys/tpr091 (2011).
141 Yamori, W., Noguchi, K., Hikosaka, K. & Terashima, I. Phenotypic plasticity in photosynthetic temperature acclimation among crop species with different cold tolerances. Plant physiology 152, 388-399 (2010).
142 Leigh, A. et al. Do thick leaves avoid thermal damage in critically low wind speeds? New Phytologist 194, 477-487, doi:10.1111/j.1469-8137.2012.04058.x (2012).
143 Michaletz, S. T., Cheng, D., Kerkhoff, A. J. & Enquist, B. J. Convergence of terrestrial plant production across global climate gradients. Nature 512, 39-43, doi:10.1038/nature13470
144 New, M., Lister, D., Hulme, M. & Makin, I. A high-resolution data set of surface climate over global land areas. Climate research 21, 1-25 (2002).
Michaletz et al. Supplementary Information 23
Extended Data Figure 1 | Relationship between photosynthesis rate and leaf temperature illustrating the maximum photosynthesis rate Aopt (dashed gray line), the optimal temperature for photosynthesis Topt (dashed gray line), and the thermal breadth of photosynthesis T90 (solid gray arrow and green area).
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 24
Extended Data Figure 2 | Leaf thermoregulation for different plant growth forms. a,b, Leaf temperature (a) and leaf temperature excess (b; Tl – Ta) from short-term point measurements of 1504 individual leaves from 185 taxa. Taxa and data sources are given in Supplementary Information. Solid lines are OLS regression fits of data plotted in Fig. 2a and Extended Data Fig. 1a. Black dashed lines, true poikilothermy (Tl = Ta).
Michaletz et al. Supplementary Information 25
Extended Data Figure 3 | Effects of covariation in the thermal time constant τ and the thermal breadth of the photosynthesis T90 on instantaneous photosynthesis rate and lifetime total carbon gain. Here we consider 16 taxa that have unique values of τ and T90. a,b,Thermal breadth data were adjusted to a common optimal temperature for photosynthesis (a; data from refs39,41,121-131,133-141) so that leaf temperature dynamics could be forced using a common environment (b). b,c, Differences in τ and T90 lead to differences in leaf temperature dynamics (b) and instantaneous photosynthesis rates (c). d, However, simulated lifetime net carbon gain integrated over the functional life span of each leaf was invariant with functional leaf longevity (P = 0.30, r2 = 0.08) (d), consistent with empirical data6. These results show that the tradeoff between τ (thermal stability) and T90 (metabolic stability) shown in Fig. 4 provides a mechanism that enables plants to minimize LMA while maintaining photosynthetic stability and maximizing both time-averaged and time-integrated photosynthesis rates, irrespective of functional leaf longevity. Thermal time constants were calculated from global trait databases119,120 using Eq. (5) and an overall heat transfer coefficient h that included convection, radiation, and transpiration (see Supplementary Information). Leaf temperatures were calculated using Eq. (4) with environmental forcing (amplitude and frequency)142 that is consistent with empirical data10,11.
Extended Data Figure 2 | Leaf thermoregulation for different plant growth forms. a,b, Leaf temperature (a) and leaf temperature excess (b; Tl – Ta) from short-term point measurements of 1504 individual leaves from 185 taxa. Taxa and data sources are given in Supplementary Information. Solid lines are OLS regression fits of data plotted in Fig. 2a and Extended Data Fig. 1a. Black dashed lines, true poikilothermy (Tl = Ta).
Michaletz et al. Supplementary Information 25
Extended Data Figure 3 | Effects of covariation in the thermal time constant τ and the thermal breadth of the photosynthesis T90 on instantaneous photosynthesis rate and lifetime total carbon gain. Here we consider 16 taxa that have unique values of τ and T90. a,b,Thermal breadth data were adjusted to a common optimal temperature for photosynthesis (a; data from refs39,41,121-131,133-141) so that leaf temperature dynamics could be forced using a common environment (b). b,c, Differences in τ and T90 lead to differences in leaf temperature dynamics (b) and instantaneous photosynthesis rates (c). d, However, simulated lifetime net carbon gain integrated over the functional life span of each leaf was invariant with functional leaf longevity (P = 0.30, r2 = 0.08) (d), consistent with empirical data6. These results show that the tradeoff between τ (thermal stability) and T90 (metabolic stability) shown in Fig. 4 provides a mechanism that enables plants to minimize LMA while maintaining photosynthetic stability and maximizing both time-averaged and time-integrated photosynthesis rates, irrespective of functional leaf longevity. Thermal time constants were calculated from global trait databases119,120 using Eq. (5) and an overall heat transfer coefficient h that included convection, radiation, and transpiration (see Supplementary Information). Leaf temperatures were calculated using Eq. (4) with environmental forcing (amplitude and frequency)142 that is consistent with empirical data10,11.
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 26
Extended Data Figure 4 | Leaf thermal response as a function of oscillation frequency and thermal time constant. The leaf thermal response is quantified as the ratio of realized to equilibrium amplitude /e eT T (dimensionless), which can be related to oscillation frequency f (Hz) and thermal time constant τ (s) via rearrangement of Eq. (S31). a,b, Eq. (S31) is plotted as a function of (a) the product of oscillation frequency and thermal time constant fτ (dimensionless) and (b) oscillation frequency for thermal time constants taken as the median and median ± 1 median absolute deviation calculated from global leaf trait119,120 and growing season climate143,144 data. When τ and/or f are small, the thermal response will approach 1 and the leaf temperature will follow the effective temperature Te almost exactly. When τ and/or f are large, the thermal response will approach 0 and the leaf will not respond to oscillations in the effective temperature. The grey line in panel (b) indicates the frequency of 0.0025 Hz used to force model predictions in Extended Data Figure 3; this value is typical for plant leaves10,11,142.
Michaletz et al. Supplementary Information 27
Extended Data Table 1 | Pairwise tests for common slope of thermoregulation between plant growth forms.
Shrub Herb Succulent Tree Graminoid Cushion < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001Shrub 0.9999 0.5709 0.0005 1.0000 Herb 0.3056 < 0.0001 0.9999 Succulent 0.1802 0.7829 Tree 0.0070Reported values are P values. Bold indicates a significant difference at α = 0.05.
Extended Data Figure 4 | Leaf thermal response as a function of oscillation frequency and thermal time constant. The leaf thermal response is quantified as the ratio of realized to equilibrium amplitude /e eT T (dimensionless), which can be related to oscillation frequency f (Hz) and thermal time constant τ (s) via rearrangement of Eq. (S31). a,b, Eq. (S31) is plotted as a function of (a) the product of oscillation frequency and thermal time constant fτ (dimensionless) and (b) oscillation frequency for thermal time constants taken as the median and median ± 1 median absolute deviation calculated from global leaf trait119,120 and growing season climate143,144 data. When τ and/or f are small, the thermal response will approach 1 and the leaf temperature will follow the effective temperature Te almost exactly. When τ and/or f are large, the thermal response will approach 0 and the leaf will not respond to oscillations in the effective temperature. The grey line in panel (b) indicates the frequency of 0.0025 Hz used to force model predictions in Extended Data Figure 3; this value is typical for plant leaves10,11,142.
Michaletz et al. Supplementary Information 27
Extended Data Table 1 | Pairwise tests for common slope of thermoregulation between plant growth forms.
Shrub Herb Succulent Tree Graminoid Cushion < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001Shrub 0.9999 0.5709 0.0005 1.0000 Herb 0.3056 < 0.0001 0.9999 Succulent 0.1802 0.7829 Tree 0.0070Reported values are P values. Bold indicates a significant difference at α = 0.05.
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPLANTS.2016.129
Michaletz et al. Supplementary Information 28
Extended Data Table 2 | Mean rank sums of leaf temperature by plant growth form.
Growth form Mean rank sum Groups Cushion 443.59 a Tree 671.66 b Graminoid 711.08 b Herb 735.88 b Shrub 903.09 c Succulent 1171.57 d A Kruskal-Wallis test indicated global significance (χ2(5) = 144.04, P < 2.2 x 10-16). Letters identify groups that are significantly different at α = 0.05.
Michaletz et al. Supplementary Information 29
Extended Data Table 3 | Mean rank sums of leaf temperature excess (Tl – Ta) by plant growth form.
Growth form Mean rank sum Groups Graminoid 523.92 a Shrub 635.55 a Herb 749.21 b Tree 814.30 b Succulent 1040.52 c Cushion 1233.16 c A Kruskal-Wallis test indicated global significance (χ2(5) = 216.34, P < 2.2 x 10-16). Letters indicate groups that are significantly different at α = 0.05.
Extended Data Table 2 | Mean rank sums of leaf temperature by plant growth form.
Growth form Mean rank sum Groups Cushion 443.59 a Tree 671.66 b Graminoid 711.08 b Herb 735.88 b Shrub 903.09 c Succulent 1171.57 d A Kruskal-Wallis test indicated global significance (χ2(5) = 144.04, P < 2.2 x 10-16). Letters identify groups that are significantly different at α = 0.05.
Michaletz et al. Supplementary Information 29
Extended Data Table 3 | Mean rank sums of leaf temperature excess (Tl – Ta) by plant growth form.
Growth form Mean rank sum Groups Graminoid 523.92 a Shrub 635.55 a Herb 749.21 b Tree 814.30 b Succulent 1040.52 c Cushion 1233.16 c A Kruskal-Wallis test indicated global significance (χ2(5) = 216.34, P < 2.2 x 10-16). Letters indicate groups that are significantly different at α = 0.05.
