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, modelling this within-shoot leaf size variation is necessary.
Within-plant leaf trait variation has been well investigated in canopy
photosynthesis models but less so 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 relationships,
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
(R2 > 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 (R2 > 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.