Scaling the leaf length-times-width equation to predict total leaf area of shoots

Background and Aims An individual plant consists of different-sized shoots, each of which consists of different-sized leaves. To predict plant-level physiological responses from the responses of individual leaves, modeling this within-shoot leaf size variations is necessary. Within-plant leaf trait variation has been well investigated in canopy photosynthesis models but not so well in plant allometry. Therefore, integration of these two different approaches is needed. Methods We focused on an established leaf-level relationship that the area of an individual leaf lamina is proportional to the product of its length and width. The geometric interpretation of this equation is that different-sized leaf laminas from a single species share the same basic form. Based on this shared basic form, we synthesized a new length-times-width equation predicting total shoot leaf area from the collective dimensions of leaves that comprise a shoot. Furthermore, we showed that several previously established empirical relations, including the allometric relationships between total shoot leaf area, maximum individual leaf length within the shoot, and total leaf number of the shoot, can be unified under the same geometric argument. We tested the model predictions using five species, all of which have simple leaves, selected from diverse taxa (Magnoliids, Monocots, and Eudicots) and from different growth forms (trees, erect herbs and rosette herbs). Key Results For all five species, the length-times-width equation explained within-species variation of total leaf area of a shoot with high accuracy (R  2 > 0.994). These strong relationships existed despite leaf dimensions scaling very differently between species. We also found good support for all derived predictions from the model (R  2 > 0.85). Conclusions Our model can be incorporated to improve previous models of allometry that do not consider within-shoot size variation of individual leaves, providing a cross-scale linkage between individual leaf-size variation and shoot-size variation.