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.

Shoot branching is a primary contributor to plant architecture, evolving independently in flowering plant sporophytes and moss gametophytes. Mechanistic understanding of branching is largely limited to flowering plants such as Arabidopsis, which have a recent evolutionary origin. We show that in gametophytic shoots of Physcomitrella, lateral branches arise by re-specification of epidermal cells into branch initials. A simple model co-ordinating the activity of leafy shoot tips can account for branching patterns, and three known and ancient hormonal regulators of sporophytic branching interact to generate the branching pattern- auxin, cytokinin and strigolactone. The mode of auxin transport required in branch patterning is a key divergence point from known sporophytic pathways. Although PIN-mediated basipetal auxin transport regulates branching patterns in flowering plants, this is not so in Physcomitrella, where bi-directional transport is required to generate realistic branching patterns. Experiments with callose synthesis inhibitors suggest plasmodesmal connectivity as a potential mechanism for transport.DOI: http://dx.doi.org/10.7554/eLife.06808.001

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.

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Plants often adapt to adverse conditions via differential growth, whereby limited resources are discriminately allocated to optimize the growth of one organ at the expense of another. Little is known about the decision-making processes that underly differential growth. In this study, we developed a screen to identify decision making mutants by deploying two tools that have been used in decision theory: a well-defined yet limited budget, as well as conflict-of-interest scenarios. A forward genetic screen that combined light and water withdrawal was carried out. This identified BRASSINOSTEROID INSENSITIVE 2 (BIN2) alleles as decision mutants with “confused” phenotypes. An assessment of organ and cell length suggested that hypocotyl elongation occurred predominantly via cellular elongation. In contrast, root growth appeared to be regulated by a combination of cell division and cell elongation or exit from the meristem. Gain- or loss- of function bin2 mutants were most severely impaired in their ability to adjust cell geometry in the hypocotyl or cell elongation as a function of distance from the quiescent centre in the root tips. This study describes a novel paradigm for root growth under limiting conditions, which depends not only on hypocotyl-versus-root trade-offs in the allocation of limited resources, but also on an ability to deploy different strategies for root growth in response to multiple stress conditions.

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

even when the trees are captured in front of complex backgrounds. Moreover, although our neural networks have been trained on synthetic data with data augmentation, we show that our pipeline performs well for real tree photographs. We evaluate the reconstructed geometries with several metrics, including leaf area index and maximum radial tree distances.CCS Concepts: • Computing methodologies → Generative and developmental approaches; Shape analysis; Computer vision problems.

Plant morphogenesis may be characterized by complex feedback mechanisms between signals specifying growth and by the growth of the plant body itself. Comprehension of such feedback mechanisms is an ongoing research task and can be aided with formal descriptions of morphogenesis. In this review, we present a number of established mathematical paradigms that are useful to the formal representation of plant shape, and of biomechanical and biochemical signaling. Specifically, we discuss work from a range of research areas including plant biology, material sciences, fluid dynamics, and computer graphics. Treating plants as organized systems of information processing allows us to compare these different mathematical methods in terms of their expressive power of biological hypotheses. This is an attempt to bring together a large number of computational modeling concepts and make them accessible to the analytical as well as empirical student of plant morphogenesis.