Results
The final dataset that we used to model carbon assimilation as a function of temperature contained between 17 and 52 assimilation measurements per each of 21 plant species. Changes in the sample chamber concentrations from 400 to 405ppm caused no more than a 0.27 μ mol m-2 s-1 increase in carbon assimilation (Fig. S1 ). The fits of Eq. 1 and Eq. 2 to our temperature-assimilation data are presented in Figure S2 , and the carbon assimilation parameters (Tmax, Popt, Topt, and Ω) estimated from these models are provided in Table S1. The modeled changes in Fv/Fm in response to heat treatments used to calculate Tcrit, T50, and T95 heat tolerances are presented in Figure S3and provided in Table S1. Below we present only values of Topt and Popt estimated using Eq. 1 because they were highly correlated with their respective estimate from Eq. 2. Results for hypotheses 3 and 4 using Popt and Topt from Eq. 2 are provided in Figure S4 .
Figure 3 summarizes the mean Topt, Tmax, Tcrit, T50, and T95 relative to one another for each species and the entire dataset. The mean trait values for the entire dataset show that Tmax is encompassed within the range of temperatures represented by the mean Tcrit and T50. This was not the case for species-level data as Tcritexceeded Tmax for 7 species, but Tmaxnever exceeded T50. The only significant correlations we observed among carbon assimilation parameters involved the Ω parameter, which describes the breadth of the temperature-assimilation curves. We observed that Ω was significantly correlated to Tmax (r = 0.567, p = 0.007; Fig. 4A ), and negatively correlated to Topt (r = 0.489, p = 0.024; Fig. 4B ). No correlations were observed between Topt and Popt estimated with either Eq. 1 or 2.
Figure 5 depicts the phylogenetically controlled correlations between different metrics of heat tolerance for PSII photochemistry and each parameter that describes carbon assimilation as a function of temperature. Tcrit was negatively correlated to T95 (r=-0.486, p= 0.025) and not correlated to T50 (r=-0.089, p= 0.700). Our estimates of T50 and T95 were highly correlated (r= 0.91, p<0.01) and exhibited similar relationships with the carbon assimilation parameters.
We found that Tmax was not correlated with Tcrit, T50, or T95(Fig. 5A-C; r=-0.334, p = 0.138; r=0.270, p = 0.237; r=0.372, p = 0.256), which does not support our hypothesis H1. Tcrit was not correlated with Ω (Fig. 5D;r=-0.190, p = 0.409), but in support of hypothesis H2 we found that T50 and T95 were positively correlated with Ω (Fig. 5E-F; r=0.581, p=0.006; r=0.590, p = 0.005). Our hypothesis H3 was not supported since we found that Tcrit was not correlated with Popt(Fig. 5G ; r = 0.211, p = 0.359), but T50 and T95 were negatively correlated with Popt(Fig. 5H-I; r=-0.495, p=0.022; r =-0.521, p = 0.015). Similar results were obtained using assimilation estimates from Eq. 2 (Fig. S4A-C ). Our hypothesis H4 was not supported as we observed no correlation between Tcrit and Topt from Eq.’s 1 or 2 (Fig. 5J; r = 0.193, p = 0.401; Fig S4D ). Furthermore, we observed that T50 exhibited a marginally significant negative correlation to Topt from Eq. 1 (Fig. 5K; r = -0.432, p = 0.051), and a significant negative correlation to Topt from Eq. 2 (Fig. S4E) . We found T95 that was negatively correlated to Topt from Eq. 1 (Fig. 5L, r = -0.452, p = 0.039) , but not from Eq. 2 (Fig. S4F). Two notable patterns among these relationships are that 1) correlations between Tcrit and each carbon assimilation parameter were in the opposite direction as those observed for T50 and T95, and 2) heat tolerances that signify greater PSII impairment (T95>T50>Tcrit) tend to be more strongly correlated with carbon assimilation parameters, with the exception of Topt from Eq. 2 (Fig. S4D-F ).
When heat tolerances and carbon assimilation traits were not corrected for phylogenetic non-independence, the only significant correlation that persisted was between Ω and Topt. Figure S2suggests Eq. 2 provided a poor fit for our Hamelia patens data. We excluded this species due to a potentially erroneous estimation of Tmax, but exclusion of this species did not change our results, so it remained in our final results. We also log- and square root-transformed our estimates of Topt and Tcrit, respectively to improve assumptions of normality before our phylogenetic corrections, but this had no effect on our results.
Given the poor coordination between Tmax and our predefined estimates of PSII heat tolerance, we wanted to know if there was a predictable level of damage in FV/FM equal to Tmax. We used Eq. 3 to predict the FV/FM at the temperature equal to Tmax for each species. This estimate of FV/FM was then divided by the mean FV/FM values observed for our control treatment temperatures. The mean FV/FM damage represented by Tmax was 0.07 with a range of <0.0 to 0.45. As a point of comparison, our estimate of FV/FM damage at Tcritwas 0.02 (0.00-0.08, 95% C.I.) damage. Based on this information, we re-calculated a heat tolerance equivalent to the temperature that caused FV/FM to decrease by 7% (T07) for each species. After performing the phylogenetic correction explained above, we found that T07 was only correlated with Tcrit(r=0.70, p<0.01).