title: Convergence in leaf size versus twig leaf area scaling: do plants optimize leaf area partitioning?
abstract: OBJECTIVE
  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.
  
  
  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.
authors.affiliation: Department of Biology, University of Utah, Salt Lake City, UT 84112, USA ddsmith3@wisc.edu.
authors.forename: Duncan D
authors.initials: DD
authors.lastname: Smith
authors.affiliation: Department of Biology, University of Utah, Salt Lake City, UT 84112, USA.
authors.forename: John S
authors.initials: JS
authors.lastname: Sperry
authors.affiliation: Department of Biology, University of Utah, Salt Lake City, UT 84112, USA.
authors.forename: Frederick R
authors.initials: FR
authors.lastname: Adler
mesh_terms: D031002:Acer / Q000033:anatomy & histology / Q000502:physiology; D029662:Betula / Q000033:anatomy & histology / Q000502:physiology; D001696:Biomechanical Phenomena; D029768:Cornus / Q000033:anatomy & histology / Q000502:physiology; D008954:Models, Biological; D018515:Plant Leaves / Q000033:anatomy & histology* / Q000502:physiology; D018547:Plant Stems / Q000033:anatomy & histology* / Q000502:physiology; D032107:Populus / Q000033:anatomy & histology / Q000502:physiology; D027824:Rosaceae / Q000033:anatomy & histology / Q000502:physiology; D031240:Symphoricarpos / Q000033:anatomy & histology / Q000502:physiology
keywords: Allometry; Corner’s rule; economics; intraspecific; leaf size; light interception; optimization; self-shading