To understand the constraints on biological diversity, we analyzed how selection and development interact to control the evolution of inflorescences, the branching structures that bear flowers. We show that a single developmental model accounts for the restricted range of inflorescence types observed in nature and that this model is supported by molecular genetic studies. The model predicts associations between inflorescence architecture, climate, and life history, which we validated empirically. Paths, or evolutionary wormholes, link different architectures in a multidimensional fitness space, but the rate of evolution along these paths is constrained by genetic and environmental factors, which explains why some evolutionary transitions are rare between closely related plant taxa.

Formative cell divisions are critical for multicellular patterning. In the early plant embryo, such divisions follow from orienting the division plane. A major unanswered question is how division plane orientation is genetically controlled, and in particular whether this relates to cell geometry. We have generated a complete 4D map of early Arabidopsis embryogenesis and used computational analysis to demonstrate that several divisions follow a rule that uses the smallest wall area going through the center of the cell. In other cases, however, cell division clearly deviates from this rule, which invariably leads to asymmetric cell division. By analyzing mutant embryos and through targeted genetic perturbation, we show that response to the hormone auxin triggers a deviation from the "shortest wall" rule. Our work demonstrates that a simple default rule couples division orientation to cell geometry in the embryo and that genetic regulation can create patterns by overriding the default rule.

We introduce a class of biologically−motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree−like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research. Reference Modeling and visualization of leaf venation patterns AbstractWe introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodesandauxinsources.Inaddition,aveinconnectiongraphis maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

We integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.Keywords: realistic image synthesis, interactive procedural modeling, plant, positional information, phyllotaxis, Chomsky grammar, L−system, differential turtle geometry, generalized cylinder. Reference The use of positional information in the modeling of plants AbstractWe integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.

E PRESENT a method for generating realistic models of temperate-climate trees and shrubs. This method is based on the biological hypothesis that the form of a developing tree emerges from a self-organizing process dominated by the competition of buds and branches for light or space, and regulated by internal signaling mechanisms. Simulations of this process robustly generate a wide range of realistic trees and bushes. The generated forms can be controlled with a variety of interactive techniques, including procedural brushes, sketching, and editing operations such as pruning and bending of branches. We illustrate the usefulness and versatility of the proposed method with diverse tree models, forest scenes, animations of tree development, and examples of combined interactive-procedural tree modeling.

We introduce a class of biologically−motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree−like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research. Reference Modeling and visualization of leaf venation patterns AbstractWe introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodesandauxinsources.Inaddition,aveinconnectiongraphis maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

We present an empirical model of Arabidopsis (Arabidopsis thaliana), intended as a framework for quantitative understanding of plant development. The model simulates and realistically visualizes development of aerial parts of the plant from seedling to maturity. It integrates thousands of measurements, taken from several plants at frequent time intervals. These data are used to infer growth curves, allometric relations, and progression of shapes over time, which are incorporated into the final threedimensional model. Through the process of model construction, we identify the key attributes required to characterize the development of Arabidopsis plant form over time. The model provides a basis for integrating experimental data and constructing mechanistic models.Plant development is a dynamic process in which the topology and geometry change over time in a seemingly complex manner. This changing form provides the context of gene action while at the same time being under the control of gene action. To understand this process quantitatively, we first need to identify and measure the key attributes of plant form needed to specify the observed growth pattern. This can be achieved by coupling data acquisition with the construction of a model. The needs of the model guide the process of data acquisition, and the choice of parameters is eventually validated by the final appearance of the model (Bell, 1986).We present such a model for Arabidopsis (Arabidopsis thaliana), one of the key organisms used in the study of plant biology. Measurements and staging of wild-type Arabidopsis growth have been described previously to provide standards for comparisons with mutants (e.g. Smyth et al., 1990; Meicenheimer, 2000a, 2002b). Arabidopsis models have previously been constructed by De Visser et al. (2003) for the purpose of simulating a number of flowering mutants, and by Chenu et al. (2004) for the purpose of simulating light acquisition by rosette leaves. We present a more detailed model of the wild-type plant, intended to serve as a stepping stone for the integration of developmental and molecular genetic data, and for the incorporation of developmental mechanisms.Models of plant development can be implemented using a variety of methods (Prusinkiewicz, 1998). We chose the formalism of L-systems (Lindenmayer, 1968;Prusinkiewicz and Lindenmayer, 1990;Karwowski and Prusinkiewicz, 2003), which provides a programming language for describing the models and a convenient method for visualizing the results as growing three-dimensional structures. According to this formalism, a plant is viewed as a developing assembly of individual units, or modules. These modules are characterized by parameters such as length, width, and age, as well as parameters characterizing shape. A methodology for constructing L-system models based on empirical estimates of such parameters has been introduced by Prusinkiewicz et al. (1994).Here we adapt this methodology to model a developing Arabidopsis (Landsberg erecta) plant from seedling to maturity. We cons...

E PRESENT a method for generating realistic models of temperate-climate trees and shrubs. This method is based on the biological hypothesis that the form of a developing tree emerges from a self-organizing process dominated by the competition of buds and branches for light or space, and regulated by internal signaling mechanisms. Simulations of this process robustly generate a wide range of realistic trees and bushes. The generated forms can be controlled with a variety of interactive techniques, including procedural brushes, sketching, and editing operations such as pruning and bending of branches. We illustrate the usefulness and versatility of the proposed method with diverse tree models, forest scenes, animations of tree development, and examples of combined interactive-procedural tree modeling.