Plant physiology

Research

Using L-systems for modeling source–sink interactions, architecture and physiology of growing trees: the L-PEACH model
Blackwell Publishing, Ltd.

M. T. Allen1, P. Prusinkiewicz2 and T. M. DeJong1
1

Department of Plant Sciences, University of California, Davis, CA 95616, USA; 2Department of Computer Science, University of Calgary, Alberta, T2N 1N4,

Canada

Summary
Authorfor correspondence: Theodore M. DeJong Tel: +1 530 7521843 Fax: +1 530 7528502 Email: tmdejong@ucdavis.edu Received: 18 October 2004 Accepted: 23 November 2004

• Functional–structural plant models simulate the development of plant structure, taking into account plant physiology and environmental factors. The L-PEACH model is based on the development of peach trees. It demonstrates theusefulness of Lsystems in constructing functional–structural models. • L-PEACH uses L-systems both to simulate the development of tree structure and to solve differential equations for carbohydrate flow and allocation. New L-systembased algorithms are devised for simulating the behavior of dynamically changing structures made of hundreds of interacting, time-varying, nonlinear components. • L-PEACHincorporates a carbon-allocation model driven by source–sink interactions between tree components. Storage and mobilization of carbohydrates during the annual life cycle of a tree are taken into account. Carbohydrate production in the leaves is simulated based on the availability of water and light. Apices, internodes, leaves and fruit grow according to the resulting local carbohydrate supply. • L-PEACHoutputs an animated three-dimensional visual representation of the growing tree and user-specified statistics that characterize selected stages of plant development. The model is applied to simulate a tree’s response to fruit thinning and changes in water stress. L-PEACH may be used to assist in horticultural decisionmaking processes after being calibrated to specific trees. Key words: carbonpartitioning, functional–structural plant modeling, L-system, modeling plant growth and development. New Phytologist (2005) 166: 869–880 © New Phytologist (2005) doi: 10.1111/j.1469-8137.2005.01348.x

Introduction
Historically, two of the most difficult aspects of functional– structural plant modeling have been developing a systematic approach for dealing with carbon allocation, and making carbonallocation respond to context-explicit, environmental and endogenous signals within a dynamically growing plant. Carbon allocation in plants has been the subject of intense study and debate among plant physiologists for many years (Gifford & Evans, 1981; Brouwer, 1983; Farrar & Gunn, 1998), but there is still no generally accepted theory to explain its underlying mechanisms. Allometric relationships incarbon

allocation between roots and shoots clearly exist (Niklas & Enquist, 2002), but the processes involved in creating them are still not well understood. Although the concepts of source and sink strength have appeared in the literature for decades (Warren-Wilson, 1967), there remains a lack of consensus regarding their role in the process of carbon allocation because of the complexquantitative interactions between ‘sources’ and ‘sinks’ in a whole-plant system (Farrar, 1993). Consequently, carbohydrate partitioning remains a central problem of processbased models of plant growth. Most early integrated simulation models of plant growth avoided the issue by using empirically derived partitioning coefficients or functional balance/allometric

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relationship rules (Loomis et al., 1979) to arrive at reasonable model outcomes. However, such approaches are more difficult to apply to models of perennial species, in which indeterminate, multiyear growth makes interactions between carbon partitioning, growth and architecture too complicated to capture using empirical formulae (Le Roux et al., 2001). PEACH (Grossman & DeJong, 1994) was...