Diverging temperature responses of CO2 assimilation and plant development explain the overall effect of temperature on biomass accumulation in wheat leaves and grains

Under rising temperature, the rate of any developmental process increased with temperature more rapidly than that of CO2 assimilation. We found that this discrepancy, summarised by the CO2 assimilation rate per unit of plant development, could explain the observed reductions in biomass accumulation in leaves and grain under high temperatures. This simple model describes the effects of night and day temperature equally well, and offers a simple framework for describing the effects of temperature on plant growth, without any supplementary effect of rising night temperatures.


Introduction
High temperatures decrease biomass accumulation in plant leaves (Vile et al. 2012), cereal grains (Wheeler et al. 1996) and whole plants, with implications for agricultural productivity and ecology under a climate change scenario (Peng et al. 2004). An emerging consensus is that carbon balance is a critical factor in responses of biomass accumulation processes to temperature changes. This view comes from studying temperature responses of grain dry mass (Wardlaw 1994;Wheeler et al. 1996), and leaf dry mass per area (LMA) or its reciprocal, the specific leaf area (Poorter et al. 2009). Most of these studies investigated the effect of very high temperatures within the 'stressing range' where photosynthesis was demonstrated to be negatively affected (Loveys et al. 2002;Vasseur et al. 2011). Accordingly, high CO 2 or light, which increases photosynthesis, can partially offset the impact of high temperature on biomass accumulation in vegetative tissues (Taub et al. 2000;Vasseur et al. 2011) and in grains (Wardlaw 1994;Wheeler et al. 1996).
By contrast, rising temperatures in the 'non-stressing' temperature range increase the rate of photosynthesis (Atkin and Tjoelker 2003;Sage and Kubien 2007). One consequence is accelerated dry weight accumulation in the grain (Wheeler et al. 1996), which reflects faster accumulation of photosynthate. High temperatures also accelerate cell expansion and division, and hasten genetic programs of organ differentiation, consequently shortening the period over which biomass can accumulate (Parent et al. 2010a). These effects are largely independent of variations in carbon fixation (Morita et al. 2005). Temperature during grain filling impacts final single grain weight with effects on both the rate and duration of grain filling (Sofield et al. 1977;Yin et al. 2009). Similarly, temperature influences LMA by impacting photosynthesis and the rates of leaf expansion (Tardieu et al. 1999).
Predicting temperature effects on biomass accumulation requires an understanding of the dynamics of carbon assimilation and plant development responses. The temperature response of respiration and photosynthesis are now well-described under the 'non-stressing' temperature range (Atkin and Tjoelker 2003;Sage and Kubien 2007). These responses are divergent , and both change after exposure to a period of high temperature, i.e. they show acclimation behaviour (Atkin et al. 2006;Campbell et al. 2007). Parent and Tardieu (2012) demonstrated that multiple developmental processes followed a common temperature response curve within a given species. Indeed, rates of processes as diverse as leaf expansion, progression towards flowering or other developmental milestones (e.g. percentage of final grain fill duration per day ¼ grain development rate), shared similar temperature responses and are hereafter referred to as 'development rates'. The temperature responses of these developmental processes followed different patterns to photosynthesis, and other enzymatic reactions involved in primary metabolism (Parent et al. 2010a).
However, in crop temperature response models, different formalisms are currently used to describe development and leaf expansion Kumudini et al. 2014). Predicted responses of development to temperature depend on the chosen equation and its parameterisation, and few models consider equations that accommodate different day and night temperature (example: Crop Heat Unit, reviewed by Kumudini et al. 2014), or different plant stages. There are currently efforts from the community of crop modellers to make these equations converge (Makowski et al. 2015) with suites of tools such as APSIM (Rosenzweig et al. 2013). The same applies to the response of photosynthesis or radiation use efficiency, with several equations used in the various models (reviewed in Parent and Tardieu 2014). While many crop models consider specific leaf area to be a result of leaf expansion and biomass, many others consider SLA as a genetic parameter with leaf expansion being driven by leaf biomass (reviewed in Parent and Tardieu 2014). In addition, there is still debate about specific night temperature effects on biomass or production (Peraudeau et al. 2015;Fang et al. 2015;Glaubitz et al. 2014;Kanno and Makino 2010;Peng et al. 2004).
Due to the different and non-linear temperature response curves of development rate, photosynthesis, and respiration, the relative impacts of these component traits on biomass accumulation (and their temperature dynamics) would depend on the particular growth temperature range. Here, we address these divergences by using rates of respiration, photosynthesis and various developmental processes observed across a range of thermal scenarios in wheat to model the temperature responses of these traits. We then express the net photoassimilate accumulation per 'unit of leaf development' or 'unit of grain development' or 'unit of whole plant development' at a given temperature in terms of the equivalent value at 20 C. As such, this approach provides a framework for describing the relative contributions of photosynthesis and respiration to biomass accumulation across a temperature range, with reference to a standard unit.

Plant growth conditions
All experiments were carried out with the bread wheat (Triticum aestivum) cultivar Apogee. Seeds were sown in plastic pots (8 Â 8 Â 20 cm) filled with a coir-peat-based potting mix. Plants were grown in several identical growth chambers (GC-20 Bigfoot series, BioChambers, Winnipeg, Canada). The light was supplied by fluorescent bulbs (Photosynthetically Active Radiation, PAR ¼ 380 mmol m À2 s À1 ) for 12 h of photoperiod (PP) with an overall daily PAR (3.6 6 0.1 MJ m À2 d À1 ) similar to that observed in the field at vegetative stage (O'Connell et al. 2004). CO 2 naturally varied during the day but daily average CO 2 concentration was similar in all treatments. In each of the three experiments, plants were initially grown under temperatures of 25 C day (T day ) and 20 C night (T night ) and the soil was watered close to the saturation level.
In Experiment 1, plants were transferred to different constant temperatures (11, 17, 20, 23 and 29 C) at the appearance of leaf 6. Leaf temperature, measured with an infrared thermometer (Raynger MX4, Raytek Corporation, Santa Cruz, CA, USA), was close (DT < 1 C) to the air temperature, during both nights and days. Because air relative humidity was stable in all treatments (60 6 5 %), vapour pressure deficit varied from 0.5 kPa at 11 C to 1.8 kPa at 29 C.
In Experiment 2, plants at the appearance of leaf 4 were transferred to several thermal regimes (T day /T night : 20/15, 20/20, 25/15 and 25/20 C) where they remained until anthesis (appearance of first anthers on the main spike).
In Experiment 3, plants at anthesis were transferred to several thermal regimes (T day /T night : 20/15, 20/20, 25/15 and 25/20 C) where they remained until maturity. At heading (head of the main tiller fully emerged), plants were pruned leaving the main tiller with its three youngest leaves. New tillers were then removed weekly.

Leaf measurements
In Experiments 1 and 2, leaf elongation rate (LER) was measured on leaf 6, by measuring leaf length with a ruler, at leaf appearance and again after a further 24 h. In parallel, it was determined that this developmental stage corresponded to the linear phase of elongation under all tested thermal scenarios (data not shown).
In Experiments 1 and 2, photosynthesis rate during the day and respiration rate during the night were analysed on fully-developed leaf 4 when leaf 6 was elongating, using a gas exchange system (LI-6400, Li-Cor, Lincoln, NE). Photosynthesis was measured at least 2 h after the lights were switched on and 2 h before the lights were switched off. Artificial illumination was supplied from a red-blue LED light source with PAR ¼ 380 mmol m À2 s À1 , similar to the growth chambers, or under saturating light (PAR ¼ 2000 mmol m À2 s À1 ). Respiration rate during the night was measured at predawn, during the last 3 h of the night cycle. CO 2 was maintained at 400 ppm (Reference) using the CO 2 mixer (flow rate ¼ 500 mmol s À1 ).
The daily net photosynthesis rate during the day (P N , mol m À2 d À1 ) and daily respiration rate during the night (R, mol m À2 d À1 ) were calculated by integrating the measured instantaneous rates of photosynthesis and respiration during the night during the respective times of light and dark (12 h) to arrive at a daily integral. The overall net CO 2 assimilation rate per day (A N , mol m À2 d À1 ) was calculated: Unless indicated otherwise, values of A N and P N used were those measured at PAR ¼ 380 mmol m À2 s À1 . In Experiment 2, leaves 4, 5, 6 and 7 were collected at anthesis. Leaf length was measured with a ruler, leaf area was measured with a planimeter (PATON electronic belt driven planimeter, CSIRO, Canberra, Australia) and leaf dry weight was determined after 2 days at 85 C.

Data analysis
The R language (R Development Core Team 2005) was used for all statistical analyses and model regressions, namely a comparison of means (function pairwise.t.test with 'BH' method), Pearson correlation tests (function cor.test), linear regression (function lm), non-linear regression (function nls) and analysis of variance (function anova). Data and scripts are available on demand.

Temperature responses
Temperature responses were described by the equation of Johnson et al. (1942), modified by Parent and Tardieu (2012): where F(T) is the considered rate, T is the temperature (Kelvin, K), DH ‡ A (J mol À1 ) is the enthalpy of activation of the process and determines the curvature at low temperature, a (dimensionless) determines how sharp is the decrease in rate at high temperature and is fixed at 3.5 for development processes (Parent and Tardieu 2012), T 0 (K) determines the temperature at which the rate is maximum, and A is the trait scaling coefficient. Temperature responses of LER, P N , and R were calculated by nonlinear regressions on the values measured in Experiment 1. The response of A N to temperature was then calculated from the temperature responses of R and P N , using Eq.1.

Thermal compensation of time and rates
For any measured rate J(T) at temperature T, a temperature compensated rate was calculated as the equivalent rate at 20 C.
with F(T) being the response of development to temperature (here the response of LER). Because developmental time (or thermal time t 20 C ) is the reciprocal of development rate, it results in: Such a procedure was already applied in different studies of developmental processes (Louarn et al. 2010;Parent et al. 2009;Parent et al. 2010b), and was applied here for biomass accumulation processes and net CO 2 assimilation rate (A N ).
In Experiment 2 and 3, F 20 C ð Þ FðTÞ was calculated in each thermal treatment from LER values directly measured in Experiment 2. In the other cases, F 20 C ð Þ FðTÞ was inferred from the regression function LER(T).

Leaf senescence profiles
In Experiment 3, chlorophyll content was measured with a SPAD chlorophyll meter (Minolta, Plainfield, Illinois, USA). Each measurement was the average of 15 readings: 5 taken from along each of the three lastdeveloped leaves. In each treatment, four plants were measured repeatedly: at anthesis and at 7, 13, 19, 25, 31, 38, 42 and 46 days after anthesis.
In each thermal scenario, a bilinear model was fitted to the dataset (see Supporting Information-Methods S1). It comprised a constant value (SPAD 0 ) until a time of senescence (t s ), followed by a linear decrease in content after this point, with a slope a s . Because plants had the same thermal treatment before anthesis, SPAD 0 was fixed for all thermal scenarios and equalled the average value at anthesis for all treatments (SPAD 0 ¼ 57.3). A similar procedure was carried out considering time t and t s as developmental time (t 20 C and t s.20 C , d 20 C ).

Biomass accumulation in the grain
In Experiment 3, the main spikes of four plants per thermal scenario were collected at 7, 13, 19, 25, 31 days after anthesis and at grain maturity, and seed number and average single grain dry weight (GDW) were measured after three days at 85 C. Spikes with fewer than 30 seeds were not used in the analysis (6 in total were discarded from the whole experiment; n ! 3 was used for all sampling dates and thermal treatments).
Curves of biomass accumulation in the grain can be described with a 3 parameter logistic equation (Morita et al. 2005), modified here to obtain the theoretical grain weight at anthesis (W 0 , mg) as a parameter of the following equation (see Supporting Information-Methods S1): is the weight of one seed (mg) at time t (in days) after anthesis, k (in d À1 ) is the slope factor controlling the steepness of the curve and t 0 is the inflection point, or time at which the seed is half the final weight.
Because the plants were transferred to the different thermal treatments at anthesis, W 0 was considered as common in all treatments (W 0 ¼ 1.65 mg, see Supporting Information-Methods S1).
Eq.5 was fitted in each thermal scenario, considering either time or developmental time (t 20 C in d 20 C ). In the last case, the two free parameters are expressed with developmental time units (t 0.20 C in d 20 C ; k 20 C in d 20 C

À1
). Because t 0.20 C values were similar between treatments, a single t 0_20 C value common to all treatments was determined (see Supporting Information-Methods S1). Respective values of t 0 were then calculated in each treatment. In this case, k is the only free parameter.
The grain growth rate GGR(t), was obtained by derivation of Eq.5 (see Supporting Information-Methods S1). The grain growth rate is maximal (GGR max ) at the inflection point, namely t 0 .
with time and model parameters expressed either with time or developmental time units. Note that with t 0.20 C and W 0 fixed, GGR max.20 C depends only on k 20 C (and the reciprocal, k 20 C depends only on GGR max.20 C ). GGR max.20 C alone can therefore explain the kinetics of grain growth rate.
Grain filling duration (t f ) was calculated as the duration between anthesis and the time at which the grain reached 95% of its final weight (see Supporting Information-Methods S1).

Grain growth simulations
For any thermal scenario, a time series (0 to 100 days after anthesis, time step ¼1 d) was built, with corresponding photoperiod PP(t), T day (t), T night (t) and T ave (t). t 20 C (t), P N (t), R(t) were calculated from parameters of Eq.2 (parameter values differing between processes). A N.20 C (t) was calculated from Eq.1 and 3. k 20 C (t) was inferred from the linear relationship between k 20 C and A N.20 C obtained in Experiment 3. GGR 20 C (t) was calculated (see Supporting Information-Methods S1) and individual grain weight was then obtained at each t by numerically integrating GGR 20 C between anthesis and the corresponding t 20 C (t).
Data from the literature Some data were collected from the literature (Alkhatib and Paulsen 1984;Tashiro and Wardlaw 1990;Wardlaw et al. 2002;Wardlaw et al. 1989a,b;Zahedi et al. 2003;Zhao et al. 2007) and are summarized online [see Supporting Information- Table S1]. The positions of the data points were recorded in figures by image analysis (software ImageJ; http://rsbweb.nih.gov/ij/). The grain weight reductions between thermal treatments found in these studies were compared to simulations carried out with the above procedure.

Results
Net CO 2 assimilation rate per unit of plant development decreased when temperature rose In plants where leaf 6 was emerging, rate of leaf 6 elongation (LER) was measured at five constant temperatures in the range 11 to 29 C ( Fig.1a; Experiment 1, n > 8).
The equation of Johnson et al. (1942) modified by Parent and Tardieu (2012) fitted well with experimental data (Fig.1a, close to those previously determined in the meta-analysis of Parent and Tardieu (2012). The temperature response curves of net day photosynthesis (P N ) and dark respiration (R) were also both adequately described by this equation (Fig.1b, n > 4, R 2 ¼ 0.99 and 0.97, respectively). Response of respiration was not far from that of development (DH ‡ A ¼74.9 kJ mol À1 ) but the slope of P N was flatter under rising temperatures, as indicated by the low value of DH ‡ A (19.3 kJ mol À1 ). When measured under saturating light, the response of photosynthesis was steeper (DH ‡ A ¼36.2 kJ mol À1 , not shown) but still less than that of respiration or development. The temperature response curve of the net CO 2 assimilation per day (A N , Fig.1b) was then calculated from P N and R (Eq.1). Temperature response curves were normalized so that they intersected the same value at 20 C (Fig.1c), facilitating the comparison in the absence of any differences in units or magnitude (Parent et al. 2010a). Because leaf elongation is part of the multitude of development processes sharing a common response to temperature (Parent et al. 2010b;Parent and Tardieu 2012), this temperature response of normalized LER was considered as the response of development processes to temperature. It was used to adjust times and rates of other processes by the effect of temperature on general development (developmental time calculation).
The development rate accelerated more than the carbon assimilation rate as temperature increased, until the optimum temperature was reached (26.6 and 25.5 C for LER and A N , respectively). Under saturating light, the two responses were more similar, although development still accelerated more than A N (data not shown). Expressing A N per unit of developmental time (A N.20 C ) can be thought as an amount of carbon assimilated per standard unit of leaf elongation (and by inference, per unit of any developmental process). A N.20 C decreased when the temperature rose across the measured range (Fig.1d), indicating that the amount of assimilated carbon available per unit of development decreased under rising temperatures.
Net CO 2 assimilation rate per unit of leaf development was linked to the dry mass per leaf area for plants grown under different thermal regimes without an additional effect of night temperature Various scenarios of day/night temperature were applied at the appearance of leaf 6 to allow the net CO 2 assimilation rate to be viewed independently of development ( Fig. 2; Experiment 2, n ¼ 6). LER increased about equally under increasing T night or T day (Fig. 2a), and was therefore essentially the same under thermal scenarios (T day / T night ) 20/20 C and 25/15 C. By contrast, R only increased under rising T night and P N only increased under rising T day [see Supporting Information- Table  S2]. Because P N values were much higher than R values and explained most of the variance in A N (not shown), significant differences in A N were only observed when T day differed (Fig. 2b). Therefore, treatment comparisons where only the night temperature differed (20/15 vs. 20/ 20 C, or 25/15 vs. 25/20 C) showed differences in LER with essentially no change in A N . Conversely, the comparison 25/15 vs. 20/20 C showed differences in A N with essentially no change in LER. Overall, these thermal treatments resulted in contrasting CO 2 assimilation rates per unit of developmental time (Fig. 2c), viewed here as the amount of assimilated carbon available per unit of leaf development.
The leaf dry mass per area (LMA), measured at anthesis on leaves 4, 5, 6 and 7, was affected by thermal treatments in all leaves [see Supporting Information- Fig.  S1] even in leaves 4 and 5, which were already partly elongated before applying the different thermal scenarios. Consequently, the average LMA in the 4 measured leaves differed significantly between treatments (Fig. 2d). These differences were mostly due to differences in leaf biomass rather than leaf area (respectively explaining 86.2 % and 2.7 % of the total variance, not shown). A temperature-induced rise in A N while maintaining similar leaf expansion rate would increase the amount of assimilated carbon per unit of leaf area expansion. Accordingly, LMA was significantly greater in the 25/15 C treatment than in the 20/20 C treatment (60.0 6 4.1 versus 41.4 6 3.8 g m À2 , Fig. 2d). Conversely, a temperature-induced increase in LER without any changes in A N would decrease the amount of assimilated carbon per unit of leaf expansion. Accordingly, LMA was less under 20/20 C than 20/15 C (41.46 3.8 versus 51.6 6 2.5 g m À2 ), and less under 25/20 C than 25/15 C (45.4 6 2.9 versus 60.0 6 4.1g m À2 ). Overall, A N.20 C showed a strong positive correlation with LMA (Fig. 2e, R 2 ¼ 0.96; p ¼ 0.022 in a Pearson correlation test). Therefore, A N.20 C integrated the temperature effects on leaf expansion rate and CO 2 assimilation rate to explain differences in LMA observed between these different thermal scenarios.

Rates of progress towards grain maturity and leaf senescence depended only on the temperature response of development
Plants at anthesis were introduced to several temperature scenarios, and then leaf senescence and biomass accumulation in the grain were measured over time ( Fig. 3a and Fig. 4a; Experiment 3; n > 4 for each time point). Chlorophyll content in the three last developed leaves, defined in SPAD units, was at first stable, and then decreased linearly. Fitting a bilinear model enabled the calculation of the time at which the chlorophyll level started to decrease (t s ). This parameter was closely correlated with the average daily temperatures (from 20.0 6 1.7 at 25/20 C to 26.5 6 3.4 d at 20/15 C, Fig. 3a  inset). When time and model parameters were expressed in developmental time units (Fig. 3b), profiles of leaf senescence were similar between thermal treatments (t s.20 C ranging from 21.8 6 3.4 to 23.2 6 3.7 d 20 C ; Fig. 3b inset).
Fitting logistic curves (Eq.5) to the time courses of single grain dry weight (GDW; Fig. 4a) resulted in various values of t 0 , the time at which grain weight reached half of the final dry weight and growth was maximal (Fig. 4a  inset). Its values decreased with rising average   Fig. 4b), values of t 0_20 C were similar across treatments (ranging from 19.8 6 0.3 to 21.6 6 0.7 d 20 C , Fig. 4b inset) as were the values of grain filling duration (from 39.2 to 42.3 d 20 C , not shown).
Overall, rates toward grain maturity and rates of leaf senescence were similar across thermal treatments when expressed in developmental time. Grain filling duration was only dependent on average temperature, and mostly independent of carbon supply.
Maximum rates of biomass accumulation in individual grains were dependent on net CO 2 assimilation but independent of development rates The time courses of biomass accumulation in the grain were adequately described by the logistic model when only one parameter (k) was kept free in each thermal scenario (W 0 and t 0_20 C fixed in all treatments, Fig. 4c, t 0_20 C ¼ 20.2 d 20 C ; see Material and Methods [see Supporting Information-Methods S1]).
As the maximum rate of accumulation of dry weight in single grains (GGR max ) and k are interdependent variables (Eq.6), grain growth responses to temperature are hereafter described in terms of GGR max only (more intuitive than k). GGR max varied between thermal treatments, especially where day temperature differed (Figs 4c and 5a). Because temperature accelerated leaf senescence and progress towards grain maturity similarly, effects of temperature on rates of grain dry weight accumulation could not be attributed to one or the other of these factors.
Relative to the 25/15 C treatment, the 20/20 C treatment showed an increase in CO 2 assimilation (A N ) and GGR max (1.18 6 0.01 to 1.44 6 0.02 mg d À1 , Fig. 5a) but a similar rate of progress toward grain maturity. By contrast, increasing night temperature, i.e. 20/15 vs. 20/20 C, or 25/15 vs. 25/20 C, increased development rate but not A N or GGR max (Fig. 5a). Therefore, GGR max appeared to be only dependent on carbon assimilation rate and largely independent of development rate.
Overall, the two contributors to final grain weight, the rate toward grain maturity and the rate of biomass accumulation in the grain, behaved independently, and correlated with temperature responses of development and of carbon assimilation, respectively. Net CO 2 assimilation rate expressed in developmental units explained the differences in dynamics of grain biomass accumulation When expressed in developmental units, maximum grain growth rate (GGR max.20 C , Fig. 5a) was dependent on both the rate of development and of CO 2 assimilation. GGR max.20 C can be thought as the biomass accumulation per standard unit of grain development. In the same way, A N expressed per unit of developmental time (A N.20 C ) can be thought as the amount of assimilated carbon available per unit of grain development. An increase in CO 2 assimilation for a similar grain development rate increased GGR max.20 C (20/20 vs. 25/15 C; 1.18 to 1.40 mg d 20 C
Overall, by integrating the temperature effects on the rates of grain development and CO 2 assimilation, A N.20 C was able to explain the differences in the grain growth rate and final grain weight observed between the different thermal scenarios.
This relationship was used to simulate final grain weight effects reported in seven different papers for various thermal scenarios involving T day up to 30 C and T night up to 25 C (Fig. 6). The predicted grain weight reductions were not far from the observed ones (R 2 ¼ 0.79), suggesting that the relationship between A N.20 C and grain growth rate could hold true for other genotypes, environmental conditions, and thermal scenarios within the investigated range. However, the model had a tendency to over-estimate the negative effect of rising temperatures (average bias of 16%), indicating a genetic variability for this relationship, or the influence of other physiological processes such as carbon remobilization to the grains.

Discussion
Temperature response patterns of biomass accumulation in leaves and grains as a consequence of the discrepancy between development and carbon assimilation responses Various studies have emphasized a role of altered carbon supply-demand in the effects of high temperature on plant processes (Taub et al. 2000;Vasseur et al. 2011;Vile et al. 2012). Yet, this concept has rarely been tested by concurrently monitoring temperature responses of development, carbon assimilation and biomass accumulation (Poorter et al. 2009), or in a range of temperatures that were not harmful to photosynthesis (Vasseur et al. 2011;Vile et al. 2012). Therefore, we simultaneously monitored the temperature responses of development, respiration and photosynthesis in the non-stressing range. These responses were divergent, resulting in a variation in carbon supply relative to development across various thermal treatments. Under rising temperatures, an increase in photosynthesis increased both LMA and grain weight, while accelerated development reduced leaf and grain weights. We showed that the discrepancy between the temperature responses of development and carbon assimilation could explain the observed patterns of biomass accumulation in wheat leaves and grains across a range of thermal scenarios.
Expressing net CO 2 assimilation and biomass accumulation per unit of development summarizes the effects of temperature on development and carbon assimilation Here, we examined the possibility of using the thermal compensation of time and rates to dissect the factors influencing biomass accumulation. Previously, this concept was applied to enable the effects of other environmental variables on leaf expansion (Parent et al. 2010b), cell expansion profiles in leaf (Parent et al. 2009) or endogenous rhythms (Poire et al. 2010) to be studied independently of the effect of temperature on development.
In the current study, by expressing the rates of processes not classified as 'development processes', such as biomass accumulation in tissues, in terms of rate per unit of development, we were able to quantify the component of the biomass accumulation response that was controlled purely by fluctuations in net carbon assimilation. Expressing the net assimilation rate in terms of developmental time therefore summarized the effects of temperature on photosynthesis, respiration and development. It can be thought as the ratio of the source/development sink, or as the amount of assimilated carbon available per unit of plant development. In addition, a simple model using this trait as the indicator of sourcesink dynamics was able to explain most of the effects of thermal scenarios on grain weight, across different genotypes and environmental conditions. By allowing the contribution of net carbon fixation on biomass accumulation across a temperature range to be followed independently of the effect of temperature on development, this approach makes possible an assessment of the impact of other factors (e.g. light intensity) on biomass accumulation across a range of temperatures. Furthermore, it could provide an approach for quantifying longer lasting heat damage caused by factors such as protein denaturation that are likely encountered at much higher temperatures, independent of reversible responses of a purely thermodynamic nature.
Rising night temperature is likely to decrease biomass production Increasing either night or day temperature would accelerate development by the same degree (Morita et al. 2005;Parent et al. 2010a), but only increases in T night would increase respiration without any compensatory increase in photosynthesis. Simple simulations also indicate that A N.20 C would be more sensitive to an increase in T night than to a similar increase in T day or the 24-h average temperature T ave (not shown). Indeed, our own experiment employing four day/night thermal treatments demonstrated that increasing T night reduced grain biomass more than increasing T day or T ave . In the simulation shown in Supporting Information- Fig. S2, increasing night temperature by 5 C decreased A N.20 C from 1.33 to 1.09 mol m À2 d 20 C À1 (not shown) and therefore decreased final grain weight by 15.3 %. The effect of maximum daily temperature (T max ) and minimum daily temperature (T min ; which occurs during the night) on the performance of wheat and rice in the field has been examined using data across multiple environments. Such studies have revealed greater and more frequent negative impacts of warming during the night than warming during the day (Peng et al. 2004;Welch et al. 2010;Lobell and Ortiz-Monasterio 2007;Cossani and Reynolds 2012). Our findings offer a potential explanation for these differential effects of day and night temperature on crop productivity in the field. In this study, no additional 'hidden' effect of night temperature was detected.

Could temperature acclimation change this pattern?
While temperature changes in the non-stressing range can perturb photosynthesis and respiration in the shortterm, the rates of these two processes can eventually recover completely, due to acclimation (Atkin et al. 2006;Campbell et al. 2007). Acclimation might make net CO 2 assimilation insensitive to any long-term temperature change (Atkin et al. 2006). By contrast, development rate was found to be stably dependent on temperature, and did not acclimate (Parent and Tardieu 2012). Therefore, it is possible that long term responses of biomass accumulation to rising temperature, such as those experienced across the seasons, may only depend on the temperature responses of development, resulting in a greater reduction in biomass (mass per unit of development) than is predicted from the presented model. The model may apply better to day to day fluctuations, such as brief heat waves of several days duration, which commonly occur in the southern Australian wheat belt during the flowering and grain filling period and correlate with significant grain yield losses (Wardlaw and Wrigley 1994).

Diversity of biomass accumulation responses
The temperature response of CO 2 assimilation per unit of plant development can present a large diversity. Firstly, there is a large diversity between plant species for the temperature responses of photosynthesis and respiration rates (Loveys et al. 2002), as well as for temperature acclimation of these processes (Atkin et al. 2006). In addition, there is a large genetic variability for development rate per se (Borras-Gelonch et al. 2010). The temperature response of development, while highly conserved in each species presented also a large variability between species (Parent and Tardieu 2012). It follows that the overall response of the net assimilation per unit of plant development could present a large diversity between genotypes or species.
Grain biomass and yield in a broad sense do not depend only on the total assimilated carbon. A large genetic variability can be found in the ability of plants to mobilize and allocate carbon to the grains (Reynolds et al. 2009). It probably explains why the model overestimated the effects of temperature on grain size in Fig. 6. These processes have their own response to temperature (Poorter et al. 2012) and can therefore present interesting genetic variability. In wheat, improving photosynthesis efficiency and partitioning to the grain are the central targets of the International Wheat Consortium (IWC, Reynolds et al. 2011).
The presented model was intentionally simple, used only to test the presented hypothesis, that the discrepancy between CO 2 assimilation and development responses were responsible for the response of biomass accumulation in tissues. However, the diversity of underlying physiological processes presented above would result in a wide diversity of carbon assimilation per unit of plant development. Experimenters need to be aware of these factors, and this model should be built on or adjusted to account for them, to suit any particular experimental system.

Conclusion
Models based on data collected under controlled conditions were developed to predict net CO 2 assimilation rate per unit of plant development under various temperature scenarios. This unit for expressing biomass accumulation rate (i) summarized the effect of the temperature responses of development, respiration and photosynthesis, (ii) provided a means of comparing rates of biomass accumulation obtained under different growth conditions, independent of the effects of temperature on development, and (iii) represents a potential approach for quantifying irreversible versus reversible responses that may occur in the extremely high temperature range. The model is likely to require modification under certain circumstances, e.g. where acclimation, photosynthate mobilization processes, and genotypic variation are additional factors in temperature responses.

Sources of Funding
This work was supported by the European projects FP7-244374 (DROPS) and FP7-613817 (MODEXTREME) and the Grains Research and Development Corporation (GRDC) project UA00123. ACPFG was also funded by the GRDC, the Australian Research Council, the Government of South Australia and the University of Adelaide.

Contributions by the Authors
Iman Lohraseb carried out most experiments; Nicholas C. Collins contributed to interpretation of the data and preparation of the manuscript; Boris Parent performed most analyses and prepared the manuscript

Conflict of Interest Statement
None declared.

Supporting Information
The following additional information is available in the online version of this article - Figure S1. Mass per leaf area in different leaves and thermal treatments. Figure S2. Simulation of the effect of night temperature on time courses of grain dry weight. Table S1. Summary of data coming from the literature. Table S2. Phenotypic data measured in Experiment 2. Method S1. Fitting procedures and parameters obtained for leaf senescence or growth of individual grain weight.