Diminishing returns in the scaling of lamina and petiole biomass and its relation to lamina geometric occupancy: evidence from 12 Malus cultivars

BACKGROUND AND AIMS: Leaf biomass allocation involves scaling relationships between photosynthetic surface area and supporting structures. However, whether these relationships remain consistent among closely related cultivars and whether they are associated with leaf geometry remains unclear. This study examined the scaling relationship between lamina fresh mass (ML) and petiole fresh mass (MP), the relationship between lamina area (A) and ML, and the association between lamina geometric occupancy and these scaling patterns across 12 Malus cultivars. METHODS: Lamina geometric occupancy was quantified using the lamina area ratio, defined as the proportion of the reference rectangle formed by lamina length and maximum width occupied by the actual lamina surface. Reduced major axis regression was used to estimate scaling exponents, and leaves were grouped by quantiles of the lamina area ratio to test whether scaling exponents varied with lamina geometric occupancy. KEY RESULTS: The numerical values of both scaling exponents (i.e., α) for the pooled data (n = 3,679 leaves) from the 12 cultivars were significantly smaller than unity (α = 0.9388 for ML vs. MP; α = 0.7846 for A vs. ML), consistent with "diminishing returns". When leaves were grouped by lamina area ratio, the scaling exponent of A vs. ML showed a negative correlation with geometric occupancy, whereas that of ML vs. MP showed a positive but nonsignificant correlation. CONCLUSIONS: The results demonstrate that (1) the "diminishing returns" pattern holds for both relationships across all of the Malus cultivars investigated in this study, and that (2) lamina geometric occupancy is associated with variation in scaling exponents, suggesting that this geometric trait should be considered in future analyses of leaf biomass allocation patterns.