Convergence in leaf size versus twig leaf area scaling: do plants optimize leaf area partitioning?

Abstract

Background and aims: Corner's rule states that thicker twigs bear larger leaves. The exact nature of this relationship and why it should occur has been the subject of numerous studies. It is obvious that thicker twigs should support greater total leaf area ([Formula: see text]) for hydraulical and mechanical reasons. But it is not obvious why mean leaf size ([Formula: see text]) should scale positively with [Formula: see text] We asked what this scaling relationship is within species and how variable it is across species. We then developed a model to explain why these relationships exist.

Methods: To minimize potential sources of variability, we compared twig properties from six co-occurring and functionally similar species: Acer grandidentatum, Amelanchier alnifolia, Betula occidentalis, Cornus sericea, Populus fremontii and Symphoricarpos oreophilus We modelled the economics of leaf display, weighing the benefit from light absorption against the cost of leaf tissue, to predict the optimal [Formula: see text] combinations under different canopy openings.

Key results: We observed a common [Formula: see text] by [Formula: see text] exponent of 0.6, meaning that [Formula: see text]and leaf number on twigs increased in a specific coordination. Common scaling exponents were not supported for relationships between any other measured twig properties. The model consistently predicted positive [Formula: see text] by [Formula: see text] scaling when twigs optimally filled canopy openings. The observed 0·6 exponent was predicted when self-shading decreased with larger canopy opening.

Conclusions: Our results suggest Corner's rule may be better understood when recast as positive [Formula: see text] by [Formula: see text] scaling. Our model provides a tentative explanation of observed [Formula: see text] by [Formula: see text] scaling and suggests different scaling may exist in different environments.

Keywords: Allometry; Corner’s rule; economics; intraspecific; leaf size; light interception; optimization; self-shading.

Fig. 1.

Key components of the light interception model illustrated by an open canopy with low self-shading (top row) and a denser canopy with higher self-shading. The incoming light environment was modelled as randomly placed leaves at different densities (A, B). Canopy openings were quantified from incoming light in random directions at distances from points with high light (arrows) up to the maximum leaf length (dotted white circles). Under these canopies, mean incoming light decreased exponentially with distance from highest light [see horizontal gradients in (C, D) and ‘zero leaves’ curves in (E, F)]. Twig self-shading reduced available light to leaves lower on the twig and the amount of reduction was a function of canopy openness [see vertical gradients in (C, D) and ‘leaves above’ curves in (E, F)]. Curves in (E, F) indicate available light to three uppermost leaves; black portions correspond to optimal leaf size. For illustration, curves reflect perfect leaf overlap.

Fig. 2.

Mean leaf size versus twig leaf area ($\stackrel{-}{A}$ versus $A_{\mathrm{twig}}$) relationships. SMA scaling exponents were very similar across species and all less than isometric. Scaling coefficients are given in Table 1. Thin background lines are n-isoclines for observed n, which correspond to $\stackrel{-}{A}$ versus $A_{\mathrm{twig}}$ isometry. Triangles represent trees and circles represent shrubs.

Fig. 3.

Mean leaf size and twig leaf area were well correlated with twig diameter and length within species. However, the SMA regressions (shown) had very different exponents. Scaling coefficients and common exponent tests are shown in Table 1. Triangles indicate tree species and circles represent shrubs.

Fig. 4.

Example of optimal $\stackrel{-}{A}$, n and $A_{\text{twig}}$ selection and $\stackrel{-}{A}$ versus $A_{\text{twig}}$ scaling. (A) With constant twig leaf number (n  =  9) and increasing mean leaf size, the total benefit (dashed line) increases faster and then slower than total cost (grey line), leading to an optimal $\stackrel{-}{A}$ (vertical line) which maximizes net gain (solid black line). Shown are model data for twigs under a canopy with ${\mathrm{LAI}}_{\mathrm{can}}$ = 3·8, $f_{\mathrm{eff}}$ = 0·24, $c_0$ = 3·1 and β = 1. (B) For increasing n (numbers at peaks) each n has an optimal $\stackrel{-}{A}$ and across n there is an optimal $\stackrel{-}{A} : n$ pair (1·7:9 here). Model conditions as above. (C) The optimal $\stackrel{-}{A}$ and n (and hence $A_{\text{twig}}$) increases with increasing canopy openness (lighter symbol shades denote greater openness). Model conditions are as above, but twig self-shading varied curvilinearly from $f_{\mathrm{eff},\mathrm{open}}$ = 0·05 to $f_{\mathrm{eff},\mathrm{closed}}$ = 0·5, which produced $b_1$ = 0·64.

Fig. 5.

Self-shading versus canopy openness scenarios (left panels) next to corresponding $\stackrel{-}{A}$ versus $A_{\mathrm{twig}}$ scaling exponents (right panels). We considered scenarios where, as canopy openness increased, twig self-shading was constant (A, B), decreased linearly (C, D) or decreased curvilinearly (E, F). Symbols represent the mean and bars the range. Exponents are shown relative to isometry (grey line) and the observed range (grey bar). Leaf cost per area was either constant (β =1; black circles) or increased with size (β =1·1; open circles). Dashed lines in left-hand panels indicate modelled scenarios that did not meet scaling criteria. Selectively reducing self-shading in more open canopies was necessary to predict the observed exponents.