Figure 4: The geometric scaling of vein density with leaf size expected because of leaf expansion and mechanisms for its modification.
From: Developmentally based scaling of leaf venation architecture explains global ecological patterns
The first column shows vein orders, and the three columns to the right show scenarios for the scaling of their vein density (=vein length/leaf area) with leaf size. According to the baseline expectation of geometric similarity, in which traits scale with size based on their dimensionality as a length, area or volume (for example, vein length scales with leaf area0.5, and thus vein density with leaf area−0.5), veins are spaced out proportionately with increasing leaf size, given no change in the numbers of veins initiated, in their relative trajectories, or in the shape of the leaf. If vein density declines more than under geometric scaling, this is indicated as 'diminishing scaling' and b<−0.5; with an extreme scenario being independent vein length across a gradient of leaf sizes, with b=−1. Diminishing scaling would occur if larger leaves have fewer veins initiated, or if larger leaves shift in shape (for example, in length/width ratio, or edge complexity, that is, perimeter2 per area), or if vein trajectory changes, either because of changes in procambium development, or later changes in the relative expansion of lamina in different areas of the leaf. If the vein density decreases less than expected under geometric scaling, this is indicated as 'conservative scaling' and b>−0.5; with an extreme scenario being independent vein density, in which b=0. This pattern could arise in the opposite set of conditions as for diminishing scaling.
