Mesophyll conductance () describes the efficiency with which moves from substomatal cavities to chloroplasts. Despite the stipulated importance of leaf architecture in affecting , there remains a considerable ambiguity about how and whether leaf anatomy influences . Here, we employed nonlinear machine-learning models to assess the relationship between 10 leaf architecture traits and . These models used leaf architecture traits as predictors and achieved excellent predictability of . Dissection of the importance of leaf architecture traits in the models indicated that cell wall thickness and chloroplast area exposed to internal airspace have a large impact on interspecific variation in . Additionally, other leaf architecture traits, such as leaf thickness, leaf density and chloroplast thickness, emerged as important predictors of . We also found significant differences in the predictability between models trained on different plant functional types. Therefore, by moving beyond simple linear and exponential models, our analyses demonstrated that a larger suite of leaf architecture traits drive differences in than has been previously acknowledged. These findings pave the way for modulating by strategies that modify its leaf architecture determinants.
1 INTRODUCTION
Mesophyll conductance, , is a numerical measure of the rate of diffusion of from the substomatal cavities to RuBisCO, the site of carboxylation in the chloroplasts. An increase in mesophyll conductance is thus expected to elevate the rate at which RuBisCO can fix , thereby decreasing the water and nitrogen costs for carbon acquisition and fixation. Therefore, understanding factors controlling is considered important for increasing the availability of at RuBisCO's site of carboxylation, with expected concomitant improvement in the rate of photosynthesis (Zhu et al., 2010).
Relatively few leaf anatomical traits have been linked to interspecific variation in . Existing evidence has indicated that cell wall thickness, , and surface area of chloroplasts exposed to the intercellular airspaces per unit leaf area, , are important determinants of , as these traits negatively and positively correlate with , respectively (Carriquí et al., 2020; Clemente-Moreno et al., 2019; Gago et al., 2019; Tosens et al., 2016; Veromann-Jürgenson et al., 2017, 2020; and references therein). However, there is still considerable ambiguity regarding the extent to which and affect , as their predictive power can be weak or even nonsignificant. For example, Xiong (2023) found that neither of these anatomical traits correlated with in crops, using simple linear regression models. Furthermore, other studies presenting regression analyses on data collected from the literature (Flexas et al., 2021; Knauer et al., 2022b) have generally yielded weak models based on the two aforementioned anatomical traits for different plant functional types (PFTs). Whilst it is true that some exceptional cases have shown very high predictive power, these are based on only very few (e.g., seven) data points, and thus the generalizability of these models remains unexplored (Carriquí et al., 2020; Peguero-Pina et al., 2017). In addition, it remains unclear if other leaf architecture traits, besides and , contribute to explaining the variance of .
The ambiguity surrounding the importance of anatomy is perhaps not surprising if one considers that is a composite parameter that integrates the effects of multiple factors, including cell wall, plasma membrane (via its permeability, affected by aquaporins), cytosol, chloroplast envelope and stroma (Evans, 2021). This problem is further exacerbated by the differences in values obtained by different measuring approaches. As leaf development is often be governed by allometric scaling rules (John et al., 2013), and anatomical traits may have antagonistic and/or complex impacts on , it is likely that simple models based on one or two explanatory variables may be insufficient to robustly capture the relationships between anatomy and . However, to date, the majority of models have applied this approach, describing the relationship between anatomy and have been based on single- and two-variable linear or exponential relationships.
Advances in machine-learning approaches provide one suitable means to obtain data-driven insights into the determinants of . Modern machine-learning approaches can capture nonlinear relationships, and comparisons of models built using different PFTs can test the generalizability of the resulting models. Here, we used machine-learning techniques to address five questions: (1) Can machine-learning approaches be used to improve the predictive power of models describing the relationship between anatomy and across PFTs? (2) Do the best-fitting models vary between different PFTs? (3) Are they generalizable? (4) Do and emerge as important determinants of when several leaf architecture traits are used as inputs into nonlinear models? (5) Can these nonlinear models identify other leaf architecture traits (besides and ) influence ?
To address these questions, we make use of the largest compendium of values along with leaf cell architecture traits published to date, measured over different PFTs and species. These data allow us to also investigate and fully address the extent of generalizability of the developed nonlinear models between different PFTs. Lastly, we show how exhaustive consideration of different combinations of predictors can help in characterizing the role of leaf cell architecture in the control of , and, thereby, photosynthesis. Importantly, we made our models available for exploration with different values for the predictors as an executable file with a graphical user interface as well as a web application linked to our GitHub repository (github.com/MRahimiMajd/leaf_gm_architecture).
2 RESULTS
2.1 Biases in values measured by different methods
Despite the high importance of mesophyll conductance in explaining photosynthesis-related properties, there is no generally accepted method for measuring this parameter. Values for mesophyll conductance in the data set we used Knauer et al. (2022a) are obtained by several methods. For instance, the majority of collected measurements were based on three methods, namely, isotope, fluorescence and curve fitting (see Section 5.1).
To examine possible biases in the reported data, we first examined the Pearson correlation between the measured values by different pairs of these methods applied to plants from different PFTs (Figure 1). We observed Pearson correlation coefficients of (Figure 1a) between the values from the fluorescence and curve fitting method, (Figure 1b) for fluorescence and isotope method, and (Figure 1c) between the values from the isotope and curve fitting method. This finding indicated that there are notable biases in the measurements based on different methods.
Correlations of the values over measurement methods. Pearson correlation between the values of the same species measured by different pairs of methods (a) fluorescence—curve fitting, (b) fluorescence—isotope and (c) isotope—curve fitting, considering all variants of these methods. Pearson correlation measure was also used to examine (d) variable J (fluorescence method) with constant J (fluorescence method), (e) variable J (fluorescence method) with EDO (curve fitting method) and (f) variable J (fluorescence method) with sugar (isotope method). For the methods with more than one replicates on a single species, the average was used in the calculation of the Pearson correlation. The solid black lines show the linear regression of the data points. The number of data points (species) in each panel is denoted by . EDO, exhaustive dual optimization.
We were also interested in possible biases originating from the variants of the different measurement methods. To this end, based on the data availability, we determined the correlation between the values of the variable J (fluorescence method) with variable J (fluorescence method), variable J (fluorescence method) with exhaustive dual optimization (curve fitting method) and variable J (fluorescence method) with sugar (isotope method) (Knauer et al., 2022a). We found correlation values of (Figure 1d), (Figure 1e) and (Figure 1f) for the three mentioned pairs, respectively, further supporting the bias in the measurement of based on different method variants.
To access the precision of the measurements over different methods, we analyzed the coefficient of variation (), that is, the ratio of standard deviation to the mean, of for individual species. We then compared the measured values over different pairs of the three methods (i.e., fluorescence, curve fitting and isotope) across the species that include replicated measurements for these methods (Figure 2). These results indicated that differences in the precision of measurements are affected not only by the measurement method, but also by the species measured. For instance, values in Arabidopsis thaliana showed higher for the fluorescence method compared with the other two (Figure 2a–c); in comparison, Solanum lycopersicum displayed a considerably higher for both fluorescence and curve fitting methods (Figure 2a). Generally, however, the values across species and methods were smaller than 1, suggesting small variability. In addition, we found that the smallest values resulted from the isotope method.
Coefficient of variation (CV) of values over species. (a) The lower panel shows the of the values over replicates of the species for the fluorescence (F) and curve fitting (C) methods. The upper panel shows the absolute value of the difference of the of these methods for the corresponding species. The same for the pairs of methods fluorescence (F)—curve fitting (C) and curve fitting (C)—isotope (I) are shown in panels (b) and (c), respectively. To calculate for each pair of methods, we considered the species with at least five measurements from each method. [Color figure can be viewed at wileyonlinelibrary.com]
2.2 Random forest (RF) models accurately predict in terms of structural and anatomical traits
To investigate if machine-learning approaches can lead to better prediction of in terms of leaf architecture traits, we used a recently published comprehensive data set (Knauer et al., 2022a) (see Section 5.1). We then trained RF models for all possible combinations of leaf architecture traits for the global data set (consisting of all PFTs) (see Section 5.2). In the following, we assessed the quantitative and qualitative agreement between the predicted and measured values by the adjusted coefficient of determination, , that controls for the number of predictors, and the Pearson correlation coefficient, , respectively.
We found that some of the RF models (see Section 5.2), showed very good performance (Figure 3), indicating that the structural and anatomical traits used as predictors can explain a substantial percentage of variance in . For instance, the model based on the combination of five anatomical traits, namely, and (model 1 in Figure 3), showed both quantitatively and qualitatively the best performance ( and ). Interestingly, combinations involving some of these five traits were included as predictors in seven of the 10 best-performing models, namely, models , 7, 8 and 10 in Figure 3). Furthermore, the model that considered and (model 14 in Figure 3), the model that considered and (model 3 in Figure 3), and the one based on the combination of and (model 4 in Figure 3) were the best-performing among those trained on two to four anatomical traits as predictors.
Predictive performance of random forest models using different combinations of leaf anatomical traits. The UpSet plot shows the evaluation of predictability of top 30 models for , based on average , consisting of 10 anatomical traits, namely, and , over all available species and PFTs in the data set of Knauer et al. (2022a). The lower panel shows the intersection of traits contributing to the training model. The middle panel indicates the average and between the measured and predicted values of in the test set. The error bars show the standard errors of the predictability measures. The upper panel shows the average Gini importance of the corresponding traits at each combination of the traits. The number of data points in each model is provided above the importance bars. For all models, the average predictability scores were achieved by the RF model in 150 executions, with randomly chosen data elements used for the training set and the remaining used for the test set. PFT, plant functional type; RF, random forest. [Color figure can be viewed at wileyonlinelibrary.com]
The best-performing model ( and ) based on a combination of six traits included: and , while the best-performing model ( and ) on seven traits included: and . Interestingly, the best-performing model ( and ) with eight traits, namely, and ( and ), was considerably weaker in comparison to the top performing models with fewer traits as predictors.
We hypothesized that the decrease in the performance of RF models with more predictors is a result of (multi)collinearity and the presence of irrelevant predictors. This hypothesis is well grounded on results indicating that, adding irrelevant and highly correlated predictors is not expected to improve model performance (Kuhn & Johnson, 2013). Indeed, we observed high correlations for some pairs of traits, suggesting the presence of collinearity (Figure 4a). For example, and and and as well as and were strongly, moderately, weakly and not correlated, respectively (Figure S1). Thus, (multi)collinearity of the predictors can explain the negative effect of an increasing number of predictors on the performance of our RF models.
Correlation structure of anatomical traits. Pearson correlation between (a) all anatomical traits and (b) the anatomical traits of the best-performing model for cross-validation on the global data set. The correlation was calculated on the available data for each trait pair, regardless of other traits. Missing entries in matrices indicate that the p value of the correlation was larger than the considered significance level of 0.05. [Color figure can be viewed at wileyonlinelibrary.com]
Further, we expected the five traits appearing in our best-performing model (model 1 in Figure 3) not to be highly correlated. Indeed, as expected, we found that all pairs of predictors in the best-performing model showed weak correlations, except for and that exhibited moderate correlations (Figure 4b). We also found that removing from the set of predictors resulted in the second best-performing model (, model 2 in Figure 3), demonstrating that contributes to explaining some of the variance in .
2.3 RF models using structural and anatomical traits can also predict within PFTs
We next investigated the extent to which the performance of the RF models is affected by considering data from individual PFTs. To this end, we summarized the performance of the models on the global data set and on data of individual PFTs using the distribution of predictability scores (Figure 5). Using the data of eight individual PFTs, we found several models with nonnegative . For instance, we found at least one model with positive for woody evergreens, woody evergreen angiosperms, gymnosperms, evergreen gymnosperms, herbaceous, woody angiosperms, herbaceous and extended ferns. Excluding herbaceous, the best models of the mentioned PFTs showed weak to moderate scores, and high values for (Table 1). These results provide further, strong evidence for the effect of leaf anatomy on within PFTs, in agreement with what has already been presented in the literature (e.g., Knauer et al., 2022b).
The predictive performance and total feature importance ratios of the trained models within PFTs. Evaluation of the performance of models in different prediction scenarios based on cross-validation within different PFTs. The upper panels show the violin plots of the average predictability scores ( and ) of the models for the global data set and each PFT. The number of models with positive in each scenario is given above the violin plots. The dashed red lines indicate the maximum predictability scores across all models. The bar charts in the lower panel show the total importance measures, and , of the contributing traits in the models of the global data set and individual PFTs. The position of traits in the bar charts has been sorted from top to bottom based on their total importance. For all the cases, the average predictability scores were achieved by the RF model in 150 repetitions, with randomly chosen data elements used for the training set and the remaining used for the test set. PFT, plant functional type; RF, random forest. [Color figure can be viewed at wileyonlinelibrary.com]
Table 1.
Best-performing models for in cross-validation within different PFTs.
PFT
Global data set
0.63
0.90
599
Woody evergreens
0.42
0.75
72
Woody evergreen angiosperms
0.3
0.74
63
herbaceous
0.37
0.69
49
Evergreen gymnosperms
0.3
0.41
31
Extended ferns
0.22
0.78
7
Woody angiosperms
0.21
0.68
72
herbaceous
0.04
0.51
49
Note: Cross-validation predictability scores of the model with the highest for the global data set and each of seven individual PFTs with at least one model with positive . The number of trained models, , for each data set, is also given in the table.
Abbreviation: PFT, plant functional type.
However, these results raise the question of why there are such differences in the predictive performance scores between the global data set and the PFTs, as well as between the PFTs themselves. To address this issue, we aimed to further examine the differences between the data of the different PFTs. As expected, the data from individual PFTs contained fewer data points compared with the global data set and also differed with respect to the predictors considered. As a result, this allowed the investigation of only a fraction of the possible combinations of the 10 traits as predictors (Table S2).
To investigate the effect of missing traits and combinations, we focused on the most special case, that of herbaceous PFT, which showed very poorly performing models () across the 49 trained models. To this end, we applied the same analyses to the data set of a recently published paper (Xiong, 2023), providing measurements of alongside eight of our anatomical traits for 10 crops. This yielded several models with considerably higher predictive performance for herbaceous plants, that is, moderate and high values, where at least one of the traits involved in each of the top 30 models was missing in our herbaceous data set (Figure S2). The observed effect of missing traits and combinations in this particular case, along with strong correlation values in all PFTs, suggests that increasing the available data for individual PFTs may improve model performance.
2.4 Generalizability of models of between PFTs
Next we examined the extent to which values in one PFT can be predicted by the model trained on the data set of another PFT. This approach allowed us to assess if the models are generalizable, that is, their performance remains good on unseen data sets. To tackle this question we employed two strategies.
By the first strategy, we trained RF models in a setting where the data of one PFT was considered as the test set and the remaining data as the training set. This resulted in numerous models with moderate to strong and values (Figure 6a). The prediction of on woody angiosperms, including both evergreen and deciduous species, showed the largest number of models with a positive set as well as the model with the highest predictability across all scenarios (Figure 6a and Table 2). For the two subgroups of these species, woody evergreen angiosperms and woody deciduous angiosperms, we found several models with moderate and strong values. A special case was the scenario with annual herbaceous as the test set, which showed a weak performance for one model and a negative for the rest of the 347 trained models. This finding distinctly contrasts the scenario in which perennial herbaceous was considered as a test set, resulting in several models with moderate to strong predictability scores on only 83 trained models. The prediction of on evergreen gymnosperms and woody evergreens as test sets showed 28 and four models with a positive , respectively. Finally, the scenarios with the (extended) ferns as the test sets also showed 10 models with nonnegative , with the best models showing moderate to strong predictability scores. The data on the remaining PFTs either did not result in a model with nonnegative or did not contain sufficient points to apply the same prediction scenarios (Table S2).
The predictive performance and total feature importance ratios of the trained models between PFTS. The evaluation of the performance of the models in different prediction scenarios with the test sets of individual PFTs and the training sets of (a) nonoverlapping global data set with corresponding test sets and (b) other individual PFTs. Panel (b) contains 15 of the 31 scenarios with at least one model with a positive . The rest of the scenarios are illustrated in Figure S3. The upper panels show the violin plots of the average predictability scores ( and ) of the models for each prediction scenario. The number of models with positive in each scenario is given above the violin plots. The dashed red lines indicate the maximum of predictability scores across all the models. The bar charts in the lower panels show the total importance measures, and , of the contributing traits in the models of each scenario. The position of traits in the bar charts has been sorted from top to bottom based on their total importance. For all models, the average predictability scores and importance ratios were achieved by the RF model in 50 executions with fixed training and test sets. PFT, plant functional type; RF, random forest. [Color figure can be viewed at wileyonlinelibrary.com]
Table 2.
Best-performing models for between PFTs.
Prediction scenario
Nonoverlapping global set—Woody angiosperms
0.67
0.84
371
Nonoverlapping global set— perennial herbaceous
0.62
0.85
83
Nonoverlapping global set—Woody deciduous angiosperms
0.55
0.89
210
Nonoverlapping global set—Extended ferns
0.52
0.76
57
Nonoverlapping global set—Woody evergreen angiosperms
0.51
0.94
387
Nonoverlapping global set—Ferns
0.49
0.79
55
Nonoverlapping global set—Evergreen gymnosperms
0.42
0.84
442
Nonoverlapping global set— herbaceous
0.30
0.81
441
Nonoverlapping global set— herbaceous
0.30
0.81
436
Nonoverlapping global set—Woody evergreens
0.16
0.56
171
Nonoverlapping global set— annual herbaceous
0.09
0.62
347
Woody angiosperms— perennial herbaceous
0.54
0.86
40
Woody angiosperms—Extended ferns
0.45
0.79
30
Woody angiosperms—Ferns
0.42
0.83
30
Woody evergreen angiosperms—Extended ferns
0.40
0.85
23
Woody evergreen angiosperms—Ferns
0.38
0.86
23
annual herbaceous— perennial herbaceous
0.28
0.63
37
Woody evergreen angiosperms—Evergreen gymnosperms
0.28
0.67
35
Woody evergreens—Ferns
0.26
0.66
47
Woody evergreens—Extended ferns
0.27
0.66
43
Woody angiosperms—evergreen gymnosperms
0.27
0.65
55
Extended ferns— perennial herbaceous
0.26
0.84
16
Evergreen gymnosperms— perennial herbaceous
0.21
0.87
23
Evergreen gymnosperms—Woody angiosperms
0.19
0.52
29
Woody evergreens— perennial herbaceous
0.17
0.85
65
Evergreen gymnosperms—Woody evergreen angiosperms
0.16
0.48
30
Note: Predictability scores of the models with the highest for nine prediction scenarios between the nonoverlapping global data set and different PFTs (upper side) and 15 prediction scenarios between different PFTs (lower side), with at least one model with a positive . The number of trained models for each scenario is also given in the table by .
Abbreviation: PFT, plant functional type.
By the second strategy, we investigated prediction scenarios in which the different pairs of nonoverlapping PFTs were considered as the training and test sets for the RF models, respectively. Among all the possible pairs of PFTs, 121 scenarios comprised at least one combination of traits with sufficient training and test data points; of these, 31 resulted in at least one model with positive values (Figures 6b and S3). We found that different groups of woody plants, that is, woody (evergreen/deciduous) angiosperms and evergreen gymnosperms, (annual/perennial) herbaceous plants and (extended) fern plants were included in the training and the test sets of all 31 scenarios.
The models trained on data from selected woody species and tested on the other woody species, herbaceous plants and ferns were generally among the best-performing (Figures 6b and S3 and Table 2).
Woody angiosperm species represented a special case, since: (i) the model trained on the global set (excluding this PFT) resulted in the best-performing model when tested on this PFT (Table 2) and (ii) the model trained on data from this PFT predicted with the best performance on data from perennial herbaceous species (Table 2). In addition, models trained on data from woody plants resulted in 40 models with positive when tested on data from (extended) ferns (Figures 6b and S3). However, the models trained on (extended) ferns could only predict on () herbaceous and woody plants in 8 and 2 models, respectively. On the other hand, the models trained on herbaceous plants could only predict the from the other herbaceous plants (15 models) and woody deciduous plants (two models). The scenarios with the perennial herbaceous as the test sets showed several models with positive , including the one with the best predictability scores. However, this was not the case for the annual herbaceous. This result was in line with the significant difference between the predictability of the models tested on annual herbaceous and perennial herbaceous, both of which were trained on the rest of the global data set (Table 2).
2.5 Importance of anatomical traits in predicting
The relative importance of the traits contributing to the RF models is of particular interest when interpreting the nonlinear relationships between anatomical traits and .
Previous works investigating the relationships between and leaf architecture generally considered and investigated models with one or two traits. They then identified the traits with and without significant regression scores as important and unimportant, respectively (e.g., Flexas et al., 2021; Knauer et al., 2022b; Xiong, 2023). Since we trained models for combinations of 10 traits, we required novel strategies to identify which traits were more important in explaining . To this end, we considered three different aspects to evaluate the importance of traits in predicting : (i) the contribution of a trait in the given model, (ii) the relative importance of a contributing trait in the given model and (iii) the overall impact of a trait in a set of models in terms of its contribution and relative importance, taking into account the performance of the models containing the trait.
The traits contributing to the optimal model can initially be considered as the most important in explaining . However, the contribution of a trait still does not provide details about its share in predicting the in the best-performing model. Therefore, we considered the average impurity-based Gini importance of each trait across different runs of the RF model as its relative importance (Figure 7). The first surprising result was the major share of the importance of one or two traits included in each model. Further, in most models, one trait accounted for at least of the Gini importance and another trait accounted for most of the remaining portion. Interestingly, and were among the important traits in the majority of models. This is in line with several previous works that recognized these traits as the two essential anatomical traits to explain the variation of across PFTs and species (see Section 1). In addition, each of the other eight traits contributed to at least one of the best-performing models. This provides evidence that the 10 investigated anatomical traits contribute to explaining the variance in across plant species.
The importance of the traits in the best models of different prediction scenarios. The average Gini importance of the contributing traits on the optimal models of different prediction scenarios, based on . The position of traits in the bar charts has been sorted from top to bottom based on their relative importance. The prediction scenarios were classified into three groups based on the data splitting methods: (i) cross-validation scenarios, (ii) scenarios with the individual PFTs as the test sets and the nonoverlapping part of the global data set with them as the training set and (iii) scenarios in which the training and test sets are nonoverlapping individual PFTs. PFT, plant functional type. [Color figure can be viewed at wileyonlinelibrary.com]
Next, we investigated the contribution and importance of the traits in models other than the best-performing. Similar to the best-performing, the remaining models with a nonnegative performance showed a large proportion of Gini importance for only one or two traits (e.g., the upper panel of Figure 3). To summarize the importance of each trait over all the models with positive we used two total importance measures and (see Section 5.3). Interestingly, except in three cases (i.e., the scenario trained on the annual herbaceous and tested on perennial herbaceous plants along with the scenarios trained on and herbaceous and tested on woody deciduous angiosperms), one or both of and were again the most important traits based on in all the scenarios (Figures 5, 6a,b and S3). However, the ordering of traits based on importance values assessed by was different: in 10 cases, neither nor were found to be among the top two important traits, and the importance share of the most important traits small compared with the results obtained by . Excluding and , again, all the remaining eight traits showed a considerable contribution of total importance, at least in one of the prediction scenarios, particularly when using . As special cases, and were the most important traits in two scenarios, and and were the most important in one scenario in terms of both measures of total importance.
In summary, our findings indicated that the 10 considered anatomical traits are important in explaining in different prediction scenarios, based on considering the best-performing models or all the models with a positive . We also showed that the relative importance of a few of the traits in explaining is considerably higher than the others. Meanwhile, there are still uncertainties in ranking the importance of the traits due to data limitations. More specifically, except for two prediction scenarios (i.e., cross-validation over the global data set and the scenario with woody angiosperms as the test set and the rest of the global data set as the training set), one or more traits were missing in other scenarios. Therefore, we avoided ranking the contribution of the traits and only highlighted the main trends, such as the major importance of the two traits, namely, and .
3 DISCUSSION
Our study aimed to address the relationship between leaf architecture traits and , thus helping assess the suitability of modulating leaf anatomy as a way towards engineer . Several studies have already investigated and attempted to find significant empirical relationships between leaf architecture traits and variability of across plant species. The models reported in the existing studies mainly suggested that two anatomical traits, and , can explain a small proportion of the variability in , as assessed by weak to moderate ; these models were developed often using a limited number of data points (see Section 1). In addition, these modelling efforts generally failed to find a significant relationship between leaf structural traits (e.g., and ) and variation of across PFTs and species (Knauer et al., 2022b). As a result, the existing models tend to not generalize well on unseen data. Further, the existing models are rooted in different linear and nonlinear regression approaches. For instance, different studies have used linear (Carriquí et al., 2020), exponential (Tosens et al., 2016), logarithmic (Tomás et al., 2013; Veromann-Jürgenson et al., 2020, 2017) and power-law (Flexas et al., 2021; Knauer et al., 2022b) models to fit the based on .
However, comprehensive models that consider the majority of measured leaf architecture traits as predictors have not yet been carefully investigated and compared. Here, we asked if nonlinear machine-learning models, with more than two leaf architecture traits as predictors, can be used to improve the predictive power of models describing the relationship between anatomy and . Interestingly, the RF model built based on data for the two anatomical traits, and , found moderately correlated with , demonstrated that increases in any of these traits do not necessarily lead to an increase in (see the rugged surface in Figure S4). Note that the counterintuitive behaviour of at small values for was due to the data used in training of the model, which do not cover this portion of the predictions; namely, measured values of in our data set range from 0.08 to 2.292, while those for range from 0.59 to 36. This was a further motivation to employ multivariate nonlinear models that consider other anatomical and structural traits describing different parts of leaf architecture. In this regard, we created an RF model for each possible combination of 10 leaf architecture traits on the available data across 34 distinct prediction scenarios, representing the global data set, different PFTs and combinations thereof.
Following these strategies, we identified several models, considering both anatomical and structural traits, with strong predictability scores for different prediction scenarios. Particularly, we found that the model trained on all the PFTs can predict based on three anatomical traits (i.e., and ) and two structural traits (i.e., and ) over unseen data with and . This evidence reliably indicated that the leaf architecture is a primary determinant of the variation of within and between PFTs. Furthermore, these findings suggested that a comprehensive analysis of both leaf structure and anatomy is necessary to explain the variation of across species. On the other hand, our analysis indicated that in addition to the best-performing model for each scenario, other models based on different combinations of the traits should also be taken into account. This can result in an exhaustive understanding of different aspects of the effect of leaf architecture on , considering weak to strong (but not perfect) correlations between anatomical and structural traits.
The aim of this study was to also provide robust and generalizable models allowing to assess the extent to which different parts of the leaf architecture associate with across PFTs and species. To this end, we also examined whether and how the models trained on one or more PFTs can predict from other, unseen PFTs. This resulted in the identification of the most robust models tested on completely unseen species. Moreover, this strategy can uncover similarities and differences in the association of with leaf architecture across different PFTs. Our results yielded strong predictability for several models built based on this idea. For instance, the models trained on the global data set, with no overlap with the test sets, could predict on woody angiosperms, herbaceous and (extended) ferns with an . On the other hand, among the models trained and tested on individual PFTs, the ones either trained or tested on woody plants generally showed higher performances. The models trained on data from these plants could predict on other woody plants, herbaceous plants and ferns. However, the models trained on data from ferns and annual herbaceous generalized to a much smaller degree than other PFTs.
Interestingly, our analysis of the data from Xiong (2023) found that only two of the 30 best-performing models contained both and as, with these traits making up only a small fraction of the Gini importance scores (Figure S2). This outcome varies considerably from the analysis based on the Knauer et al. (2022a) data set, including all PFTs (Figure 3). Furthermore, the observation that seems less important in the crop species studied by Xiong (2023) is in stark contrast with a published comparison of anatomy across 15 species, spanning multiple PFTs. Tomás et al. (2013) showed that the slope between (standardized by ) and was much steeper within herbaceous species than for evergreen trees, suggesting that plays a larger role in determining within the herbaceous annual leaves. The importance of in determining has also been difficult to assess from experimental studies. For example, work on tobacco found that the reduction in coinciding with leaf age was strongly correlated with an increase in (Clarke et al., 2021). However, knocking down cell wall mixed-linkage glucan production in rice plants resulted in lower , alongside concurrent reductions to (Ellsworth et al., 2018). As a result of these contrasting observations, it remains unclear if, and to what extent, is influencing within herbaceous annuals.
One open question from this study is why models that described annual plants showed weaker performance in comparison to models based on data from other PFTs. One possible explanation is that this is an artefact, caused by the averaging of values derived from different experimental methods. Knauer et al. (2022b) showed that linear regressions between and fit the data considerably better when separate models were built depending on the method used to estimate (i.e., isotope, fluorescence or curve fitting). Whilst bears no importance for our analysis, this indicates that averaging values may not always yield the most reliable results. Estimations of rely on several assumptions (e.g., fractionation factors, the photorespiratory compensation point and methods chosen to estimate respiration). As such, it is conceivable that combining independent estimations of may have introduced unforeseen errors into the data set that may interfere with model construction. Given that there is a bias towards research on annual species (which the majority of the world's staple crop species belong), a greater number of measurements have been recorded, per species, for this PFT. Consequently, within the data set collated by Knauer et al. (2022a) annual herbaceous species had 538 measurements for 52 species, whereas the ratio of measurements to species was for all other PFTs. This remains to be tested, but it may also explain why models could be built to describe the relationship between anatomy and based on data from Xiong (2023), as these were derived from a single source and were not subject to the same averaging.
4 CONCLUSIONS AND FUTURE WORK
By using a well-established machine-learning approach, that of RF, we demonstrated that one can obtain models based on leaf architecture traits that achieve excellent predictability of . In addition, we showed that these models are generalizable, particularly if trained with data from specific PFTs. We also presented a systematic approach for determining the importance of anatomical and structural traits based on the Gini importance of traits in best-performing models and two total importance measures that consider all models with a positive in each prediction scenario. Using the systematic approach, we found that not only and are two critical traits in explaining the variation of across plant species, but also the remaining eight structural and anatomical traits considered play a role in explaining . In future work, we envision that approaches based on ensemble learning, where predictions from multiple machine-learning approaches are aggregated, may further boost the performance of the models. These approaches can particularly focus on exploring and making use of variability of using natural variability within species, particularly crops. Given the link between and classical models of photosynthesis, accurate machine-learning models also pave the way for exploring the link between structural and anatomical leaf traits and photosynthesis via their effect on . Ultimately, the modelling results and future directions outlined here provide tractable means for identifying factors that can contribute to modulating towards the improvement of agronomically relevant traits.
5 METHODS
5.1 Data and preprocessing
To identify and analyze the relationships between anatomical traits and , we used a recently published comprehensive data set (Knauer et al., 2022a) providing leaf structural, anatomical, biochemical and physiological traits measured on the same set of plants. This is currently the largest available data for , which collected measurements from 563 peer-reviewed studies over 617 species partitioned to 13 major PFTs, namely, evergreen gymnosperms, deciduous gymnosperms, woody evergreen angiosperms, woody deciduous angiosperms, semideciduous angiosperms, CAM plants, ferns, fern allies, mosses, perennial herbaceous, annual herbaceous, annual herbaceous and perennial herbaceous.
Since most of the individual PFTs do not contain enough data points to train a model for many of the possible combinations of the traits as predictors, we also formed five more groups from the union of the above PFTs. This was performed according to the shared functional characteristics among the PFTs. The groups involved the following: woody evergreens (union of woody evergreen angiosperms and evergreen gymnosperms), woody angiosperms (union of woody evergreen angiosperms, woody deciduous angiosperms and semideciduous angiosperms), extended ferns (union of ferns and fern allies), herbaceous (union of perennial herbaceous and annual herbaceous) and () herbaceous (union of annual herbaceous, perennial herbaceous, perennial herbaceous and annual herbaceous). This strategy allowed us to not only increase the data available for model training, but also to compare the findings for different groups and their subgroups. This modelling strategy also facilitated the investigation of whether or not the combination of data from PFTs increases the generalizability of the models.
In our analyses, we used values standardized to the temperature of and the atmospheric pressure of 1 bar (), as provided in the data set (see Knauer et al., 2022b). The data set contains information about all the published methods for estimating in each study. Except for a few cases, all collected measurements were based on one of three methods: isotope (Caemmerer & Evans, 1991; Evans et al., 1986; Evans & Von Caemmerer, 2013; Lloyd et al., 1992; Mizokami et al., 2015; Scartazza et al., 1998; Tazoe et al., 2009, 2011), fluorescence (Bernacchi et al., 2002; Epron et al., 1995; Harley et al., 1992; Loreto et al., 1992; Maxwell et al., 1997; Yin & Struik, 2009; Yin et al., 2009) and curve fitting (Ethier & Livingston, 2004; Ethier et al., 2006; Gu et al., 2010; Sharkey, 2015; Sharkey et al., 2007). To have only one value for each individual experiment, we aggregated the repeated data by calculating per-species as the average of its values measured with the different methods. After aggregation, we used all the remaining data with no additional filters.
The data sets include measurements for 31 anatomical traits. However, in addition to the two frequently reported traits ( and ), we selected eight other anatomical and structural traits that have received the most attention in the literature in terms of published data (Table S1): Leaf dry mass per area (), leaf density (), leaf thickness (), mesophyll thickness (), cytosol thickness (), chloroplast thickness (), surface area of mesophyll cells exposed to the intercellular airspaces per unit leaf area () and fraction of intercellular airspaces in leaf mesophyll (). In this way, we kept all the data samples with a value for standardized and at least one of the mentioned anatomical traits, resulting in 882 data samples from 453 species and all the mentioned PFTs. The number of data samples and species for individual PFTs and groups is provided in Table S2.
To investigate the performance of selected models, we used the data set from Xiong (2023) consisting of eight anatomical and structural traits and measured for 10 crops. The measurements of in this data set were obtained using online carbon isotope discrimination and chlorophyll fluorescence methods, and we used the provided by the second method in our analyses.
To perform the model training based on data for each PFT, we then constructed all possible combinations of traits for the global data set (consisting of all PFTs) and for each of the individual PFTs, respectively. In each combination, we removed the data samples with a missing value in one or more traits. We then kept only the combinations with at least 50 data samples, with no missing data, and ignored the rest. This strategy allowed us to avoid data imputation, which may bias the findings given that the measurements are made across different plant species. Future studies may consider investigating the effect of bias by relying on recently proposed imputation techniques (Ellington et al., 2015; Lee & Beretvas, 2023; Scherer & Emslander, 2023). This resulted in 599 combinations for the set of all PFTs, each containing from 1 to 10 anatomical traits as independent variables and the corresponding standardized as a response variable (Table S2). We also ensured that the training set was larger than the test set, to achieve generalizable models.
5.2 The model
The RF model in a regression setting (Breiman, 2001) was used to predict by the anatomical traits, used as predictors. To achieve a robust result for the prediction scenarios within PFTs, for each combination of predictors we performed the training in a Monte-Carlo cross-validation setting (Smyth, 1996), by running 150 independent executions with randomly chosen data points for the training set and the remaining used for the test set. We also run the RF model 150 times for prediction scenarios between PFTs, with fixed training and test sets, to capture the effect of different random seeds controlling the bootstrapping and feature sampling in the trees (Raste et al., 2022). The training models and splitting data were implemented using the Python package Scikit-learn (Pedregosa et al., 2011). The source code ensuring the reproducibility of our analyses is available on GitHub: github.com/MRahimiMajd/leaf_gm_architecture.
The predictive performance of the models was assessed quantitatively and qualitatively by using the coefficient of determination () and Pearson correlation (), respectively. The coefficient of determination () is used as a quantitative measure of how much variance in is explained by the anatomical traits, employed as predictors. However, our models have different numbers of independent variables (i.e., anatomical traits as predictors). To capture the effect of this difference on the performance of models, we relied on the , which adjusts the value based on the number of predictors (Hocking, 1976).
5.3 Measures of predictor importance in RF models
To assess the relative importance of a trait contributing to an RF model, we used the impurity-based feature importance (Gini importance). Since the RF model is an ensemble of decision trees (obtained by node splitting), Gini importance measures the total reduction of the impurity of the RF model attributed to that feature, averaged over all trees in the ensemble (Pedregosa et al., 2011). For a single run or an ensemble of runs, we ensure that the (average) values of the relative importance of the contributing traits always sum up to one, as explained in the following.
For the case where we have several models with different combinations of traits as predictors, we are interested in obtaining a total importance for each trait across all these models. In our analyses, the number of models is given by the number of possible combinations of traits. However, poorly performing models do not provide any information about trait importance. Thus, by excluding these models, based on a threshold for the measure of performance, the number of models that include a given trait can simply be used as a measure of total importance for the trait. While seemingly sound, this measure does not discriminate between models of weak, moderate and strong performance. To address this issue, we also employ the quality of the regression and the Gini importance of the traits in each model to define two total importance measures: the total contribution importance () and the total Gini importance (). More specifically, of a trait is defined as the average of values of all models with positive , including the trait. This measure captures the contribution of the traits in the models weighted by the performance of the models. The follows the same steps, but the values for each model are also multiplied by the Gini importance of the traits before averaging these values. This total importance measure captures more detail about the impact of the traits on achieving models of good performance while considering the importance of features in the RF model. Having the average values for each trait, we normalize them such that the sum of the importance values of all the traits equals one. In our analyses, we set the threshold at which a model contributes to the total importance measures as . This threshold indicates that the model explains the variance of better than the average of its values (Chicco et al., 2021).
ACKNOWLEDGEMENTS
The authors would like to thank Dr. Dongliang Xiong for kindly sharing the data on anatomical and structural leaf architecture traits from crops. All authors acknowledge the funding support by the NovoNordisk Foundation, Data Science Initiative, project DIRECTION (Grant NNF 21OC0068884 to Zoran Nikoloski and Johannes Kromdijk). Open Access funding enabled and organized by Projekt DEAL.
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
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