Five out of the seven genotypes used in this research were selected from the USDA rice mini-core collection (310588, 310723, 311644, 311677, 311795), a collection of 217 genotypes with diverse origins, subgroups, and phenotypic and genotypic characteristics (Agrama et al., 2009; Kumar, 2017). Two additional genotypes outside of the USDA rice mini-core collection selected for this study were a drought tolerant aus genotype Nagina 22 (N22) and a drought sensitive indica genotype Zhe733. Details of each of these genotypes are provided in Table 1 .

We used a non-rectangular hyperbola model (Thornley and Johnson, 1990; Thornley, 1998) in a multilevel Bayesian (MB) framework (Clark and Gelfand, 2006) to estimate model parameters and associated uncertainties. The MBLRC (Multilevel Bayesian Light Response Curve) model has three primary components: (1) the likelihood model which describes the likelihood of the observed net photosynthesis rate (A_N), (2) the process model which describes the photosynthesis response to light (PAR) based on the non-rectangular hyperbola model and process uncertainty associated with random effects, and (3) the prior distributions for model parameters and precision terms. The posterior distribution of all model parameters was obtained by combining these three parts (Wikle, 2003).

The likelihood model: We assumed that the observations of net photosynthesis rate (A_N) are normally distributed for each observation i (i = 1, 2,… n) around mean photosynthesis rate (µ) with precision τ (1/variance):

The process model: The process model describes the mean photosynthesis rate (µ) based on the non-rectangular hyperbola model as follows:

where [Plant[i]] indicates plant-level parameters, A_max is the maximum rate of assimilation (µmol CO₂ m^-2 s^-1), α is the apparent quantum efficiency (µmol CO₂ µmol photon⁻¹), R_d is mitochondrial respiration (µmol CO₂ m^-2 s^-1), and θ (unitless) is the shape parameter for the curve ( Figure 2 ).

The parameter model: Four unknown parameters of interest (A_max , α, R_d , and θ) are allowed to vary by each of the seven genotypes (µ.Parameter[s]), where s indicates the number of genotypes (s = 1,… m). For example, genotype-level parameters are described as:

where τ.Parameter is the precision term associated with the genotype-level mean (µ.Parameter) of the parameter of interest. A_max , α, R_d , and θ were given informative prior distributions with posterior means normally distributed around a mean reported for rice in published literature (e.g., Xu et al., 2019; Lv et al., 2020, see Table 1 in appendix) and large ( ± 200%) variances associated with them.

The observed likelihood, process, and parameter models were combined to generate the posterior distributions of the unknown parameters (Wikle, 2003). The joint posterior was sampled by implementing the Markov Chain Monte Carlo (MCMC) algorithms (Robert and Casella, 2009) in the Bayesian statistical software package WinBUGS (Lunn et al., 2000) by running 3 parallel MCMC chains. Each MCMC chain was run for 10,000 iterations after convergence and the BGR diagnostic tool was used to evaluate convergence of the chains to the posterior distribution (Brooks and Gelman, 1998). The chains were thinned, due to autocorrelation in respiration parameter, every 10^th iteration to obtain an independent sample of 10,000 values per chain (total of 30,000 values) for each parameter from the joint posterior distribution. Model goodness-of-fit was evaluated by using Eq. 1 to generate modeled data for the observed photosynthesis values (Gelman et al., 2021) yielding posterior predictive distributions for each observation. The predicted means of photosynthesis with 95% credible intervals were compared with observed photosynthesis for evaluating the model goodness-of-fit ( Figure 3 ).

The MBLRC model was fitted separately for three growing environments. For hypothesis testing ( µ1 - µ2 = 0) differences in means across different genotypes, methods, and growing environments were calculated by conducting ANOVA and pairwise t-tests (Tukey HSD) on a representative (see Figure S1 in Supplementary Information ) random sample of 50 points for each parameter; random sample was taken to avoid the effect of large sample size on p-values.

The MBLRC model performed well in predicting observed A_N across all growing environments including field (R² = 0.87, Figure 3A ), growth chamber (R² = 0.98, Figure 3B ), and greenhouse (R² = 0.99, Figure 3C ) environments.

The maximum photosynthesis rate (A_max ) varied based on measurement method, and this variation was statistically different between the sequential and non-sequential methods across all genotypes ( Figure 4 ) with exception of 311677 ( Figure 4Q ). While other parameters (α, R_d , and θ) were generally similar between measurement methods with few exceptions ( Figure 4 ). For example, R_d was significantly lower in the non-sequential method in 310723 and α was significantly greater in the non-sequential method in 310723 and Zhe 733.

Consistent with the measurement method results, α remains largely conserved with no difference in parameter means, except one genotype (311795) where parameter (α) means were significantly different between greenhouse and growth chamber ( Figure 5 ). The maximum photosynthesis rate (A_max , µmol CO₂ m^-2 s^-1) was greater under field and growth chamber conditions as compared to the greenhouse conditions across all genotypes ( Figure 5 ). Mitochondrial respiration (R_d , µmol CO₂ m^-2 s^-1) and shape parameters (θ) were similar across all growing conditions. These measurements were conducted during the daytime, so photosynthesis measurements remained greater than zero at all light levels ( Figures 3 , 5 ), and as a result R_d and θ were correlated.

The pairwise comparison of model parameters across different genotypes showed that the quantum yield (α) remained generally similar across all genotypes, but field growing conditions were better suited for quantifying phenotypic difference in A_max parameter as compared to growth chamber and greenhouse environments that showed minimal or no differences in model parameters ( Figure 6 ). Under field conditions Zhe 733 showed the highest A_max followed by Nagina 22 and 310588 (similar A_max ), 310723 and 311644 (similar A_max ), and lastly 311795 and 311677 at the lowest spectrum of A_max values ( Figure 6A ).

Our results show that the non-sequential survey method ( Figure 2A ) captured greater variability compared to sequential method ( Figures 2B, C ). The two methods were very similar in their estimations of α, R_d , and θ, but the non-sequential method resulted in a greater A_max across nearly every genotype surveyed ( Figures 4 , 6 ). However, these results could be the result of differences in pot grown plants acclimated to field conditions and plants grown in the field ( Figures 5 , 6 ). Prior work has shown that plants grown under low light conditions and then moved to high light conditions before measurements increased their photosynthetic capacity (Walters, 2005; Athanasiou et al., 2010). Our results showed greater photosynthesis rate in growth chamber plants that were acclimated to field conditions before measurements as compared to greenhouse plants but increase in photosynthesis was not comparable to the plants grown under field conditions. To confirm that differences in parameter estimates between two methods were only due to the measurement methods, further experiments are needed. Overall, our results suggest that the non-sequential method is equally good or better when estimating the maximum photosynthetic rate of different genotypes to understand the interaction of genes, environment, and management under field conditions as it does not repeatedly measure the same sample, can be done at different days, and is less time consuming because samples are already acclimated to the surrounding environmental conditions.

Light response curves play a vital role in understanding plant characteristics and quantifying photosynthetic acclimation under different conditions (Herrmann et al., 2019). Our results show that the maximum photosynthesis rate (A_max ) varied most significantly across different growing conditions. A_max was greatest in the field plants across all genotypes ( Figure 5 , column 2, Figure 6A ). Plants acclimate to the environment they are in (Walters, 2005; Dyson et al., 2015; Herrmann et al., 2019), and it has been well documented that plants grown at higher light intensities, such as those outside in the field, have greater A_max than those at grown under lower light intensities, such as in a greenhouse (Ögren, 1993; Bailey et al., 2001; Walters, 2005; Perkins et al., 2006; Athanasiou et al., 2010; Du et al., 2020). Prior work has also shown that plants grown at low light and then moved to highlight before measurements increased their photosynthetic capacity (Walters, 2005; Athanasiou et al., 2010). Our results show that the growth chamber plants, which were grown under lower light intensities (600 µmol m^-2 s^-1) and then moved to field conditions before measurements, often had A_max values similar to field plants. The high variability seen in the light response curves of different growth chamber replicates may indicate that some leaves may have been shaded and not fully acclimated to the new light intensity, and thus had lower maximum photosynthesis rate ( Figures 4 , 5 , first column).

We expected a smaller shape parameter (θ) in field plants as θ is generally smaller in plants acclimated to high light (Ögren, 1993). Typically, θ ranges from 0.7 to 0.99 (θ = 1 is a Blackman curve and θ = 0 is a rectangular hyperbola (Ögren and Evans, 1993; Evans et al., 1993)). Ögren (1993) found that when grown under low light, algal cells, and willow (Salix) leaves had lower A_max and higher θ than when grown at high light intensity, a finding that was only partially supported by our results. While our greenhouse plants had lower A_max compared with field and growth chamber plants, θ was generally similar across all growing environments, except 311795 genotype ( Figure 5 ).

Growth chamber plants showed greater variability across replicates within the same genotypes with some replicates showing curves similar to field conditions and some similar to greenhouse conditions ( Figure 5 ). When plants, grown under controlled low light conditions, are allowed to acclimate outside for several days before measurements, photosynthesis measurements may be very similar to field plants. Field curves were different from those conducted on greenhouse plants, but the smallest curves of the growth chamber plants were similar to those of the greenhouse plants ( Figure 5 ). Our results captured a gradient of growing conditions and plasticity of rice genotypes acclimated to those conditions.

The pairwise comparison of model parameters across different genotypes under field conditions showed that Zhe 733 had the highest A_max followed by Nagina 22 and 310588 (similar A_max ), 310723 and 311644 (similar A_max ), and lastly 311795 and 311677 at the lowest spectrum of A_max values ( Figure 6A ). Prior work has shown that Zhe 733 is sensitive to environmental stress (Moldenhauer et al., 2020), and our results showed that the A_max almost doubled under field conditions as compared to the growth chamber, while 311677 remained the same across different light conditions ( Figures 6A, B ). All other genotypes showed little to moderate gain under field conditions compared to growth chamber ( Figures 6A, B ), but all genotypes showed significant increase in A_max under field conditions compared to greenhouse conditions ( Figures 6A, C ).

Photosynthesis model parameters are a critical piece for understanding the gene and environmental interactions of different plant genotypes (Rascher et al., 2000). Photosynthetic parameters generally differ between field and lab experiments (Mishra et al., 2012; Tian-gen et al., 2017), and our results were consistent with the previous studies showing these differences. Field plants are exposed to a variety of light, temperature, and humidity conditions that cannot be easily replicated in a greenhouse. Additionally, greenhouse-grown plants may not have the nutrition, soil depth, etc. to meet their own growth demands. Thus, the photosynthetic parameters and physiological characteristics obtained from greenhouse plants should not be taken as representative of field-grown plants (Tian-gen et al., 2017), but the growth chamber or greenhouse grown plants acclimated to field conditions before measurements may be used for pot experiments.