Linking the Weibull distribution to Gini coefficients: a bamboo specific framework for intra-culm leaf area...

Quantifying inequality in the leaf area distribution within a single module is critical for elucidating plant resource allocation strategies, but the accuracy of theoretical Gini coefficients derived from statistical distributions remains poorly validated against observed values. To resolve this gap, we analyzed 9,242 leaves from 121 culms of the bamboo Semiarundinaria densiflora, a model system with minimal ontogenetic noise and moderate leaf counts (36-187 leaves per culm) that enables robust Lorenz curve construction. Four candidate distributions were tested: the normal, log-normal, two-parameter Gamma, and two-parameter Weibull distributions. The parameters of the normal and log-normal distributions were estimated directly from sample statistics, whereas the parameters of the Gamma and Weibull distributions were estimated using the maximum likelihood method. Goodness of fit was assessed using the Kolmogorov-Smirnov (K-S) test for distributional validity, and the Akaike's information criterion (AIC) for model selection. Although the Gamma distribution passed the K-S test for a slightly higher percentage of culms (99%) than the Weibull distribution (97.5%), the Weibull distribution was selected as the superior model because it yielded significantly lower AIC values. Crucially, the theoretical Gini coefficients of the Gamma and Weibull distributions (denoted as G_G and G_W , respectively) were tested against the observed Gini coefficients (G_P ) calculated nonparametrically using the polygon method. Linear regression demonstrated that G_W ​ predicted G_P with near isometric accuracy: the intercept's 95% confidence interval included zero (-0.006 to 0.017) and the slope's 95% confidence interval included unity (0.929 to 1.039). In contrast, G_G exhibited significant bias. Notably, pooling leaves across culms violated all distributions due to microhabitat driven multimodality, confirming that intra-culm inequality assessments require organism level analysis. This work provides an empirical validation that the Weibull shape parameter reliably quantifies intra-culm leaf area inequality. By bridging theoretical distribution models with field-derived inequality metrics, our approach provides insights into canopy efficiency, photosynthetic optimization, and hydraulic trade-offs. Future work should test this approach in other grass species and assess its generalizability in plants with contrasting canopy architectures.