Arboriculture & Urban Forestry 35(6): November 2009 Arboriculture & Urban Forestry 2009. 35(6): 311–320 311 Review of Literature on the Function and Allometric Relationships of Tree Stems and Branches Gregory A. Dahle and Jason C. Grabosky Abstract. The goal of maintenance pruning is the development of a tree canopy that meets a defined objective while minimizing the risk of failure. An in- depth understanding of the primary functions of branches and how they influence canopy form is needed in order to assess the impacts of cultural practices such as pruning or plant spacing on canopy development. Allometric modeling describes the relationship between size and shape of organisms. This paper explores three allometric methods of modeling branch form (pipe model theory, fractal dimensioning, and power laws) and their potential in guiding prun- ing research. Additionally, two principal functions of plants—hydraulic and mechanical—are discussed in light of their impact of stem and branch form. Key Words: Allometry; Biomechanics; Elastic Similarity, Hydraulics; Mechanics; Slenderness Ratio. Arborists prune trees to develop and maintain canopy structure with the overall goal of maximizing canopy benefits while mini- mizing the risk of failure (Harris et al. 2004). It is hoped that the removal of tissue will direct growth in order to develop ‘good’ canopy structure. Good structure is subjective and can be diffi- cult to define. Often the goal is to develop a stable canopy by re- moving undesirable structures and defects, such as co-dominant branching or branch unions with included bark (Gilman 2002; Gilman and Lilly 2008). Pruning can influence canopy form, and damaging wind, ice or cultural practices, such as topping, can de- form a tree’s canopy. Restoration pruning attempts to improve the structure and form of a damaged tree (American National Stan- dards Institute 2008). The ultimate goal of restoration pruning is to return a damaged canopy to a condition where it can provide similar benefits to that of a ‘natural’ canopy with acceptable lev- els of risk of failure. The arborist has limited information on a formal definition of ‘good’ canopy structure and must rely on per- sonal experience and intuition when deciding how to use prun- ing to guide canopy development or restoration. The underlying structure of a canopy rests on individual branch form, yet little is known on how to objectively and reliably predict canopy stability from branch form. The ability to define good canopy structure from branch form or better predict potential weaknesses could help the arborist direct growth and develop a more stable canopy. Sullivan (1896) suggested that in building design, as well as in nature, form follows function. Niklas (1992) suggested that plants balance four functions throughout their lives: photosynthesis, reproduction, hydraulics, and mechanical support. While photo- synthesis and reproduction are important, the hydraulics and me- chanics are directly archived during growth. As a tree matures, the function of stems and branches presumably changes from primar- ily hydraulic (transporting water) to a balance between hydraulic and mechanics (resisting both static and dynamic loads) functions (Farnsworth and Niklas 1995; Woodrum et al. 2003). In order to survive, a tree must be capable of resisting self-applied and exter- nal loads. As a branch increases in size, mechanical support be- comes an increasingly important function particularly if hydrau- lic supply is not limiting (Niklas 1992; Spatz and Brüchert 2000). The ability of trees to modify allocation in the functions of hydraulics and mechanics allows them to adapt overall form over time. Pruning removes tissue in the attempt to direct growth for a desired benefit and therefore shifts canopy form. Knowledge of form placed in a biological context can help the arboricultural community understand how to guide investment in growth and the shift in form. Plant biologists use allometry to describe the relationship between size and shape of organisms. Various allo- metric relationships have been developed to describe and predict growth patterns in trees. It is likely that the application of allomet- ric modeling could aid researchers in the understanding of how a canopy develops and when, or if, a stable canopy form is reached. This review is divided into two sections, beginning with a dis- cussion of woody plant tissue function in terms of the roles of hydraulic and mechanical support in trees. In order to fully dis- cuss these two functions, this paper will also briefly review some important aspects of woody plant anatomy at the tissue and cel- lular level. The second section discusses allometric modeling and reviews three allometric methods of describing tree form (pipe model theory, fractal dimensioning, and power laws), before dis- cussing their potential applicability to arboricultural researchers and practitioners, particularly in terms of areas where additional research is warranted. The intent is to provide an overview of the literature for arboricultural researcher and practitioner, and inform discussions in the growing areas of pruning research, canopy modeling and preferred canopy structure in profession- al tree care, carbon/climate modeling, and risk management. FUNCTION OF WOODY PLANT TISSUE Hydraulics Water is necessary for growth, photosynthesis, metabolic activity such as respiration, and the exchange of gases during transpira- ©2009 International Society of Arboriculture
November 2009
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