Search

Background and Aims: Cover crops have the potential to aid in adapting agricultural systems to climate change impacts through their ecosystem services, such as preventing soil erosion, remediating soil structure, and storing carbon belowground. Though roots are integral to these processes, there is a lack of cover crop root trait data. This study aims to characterize rooting behavior of several commercially available cover crops and assess their potential impact on soil carbon and nitrogen cycling. Methods Twenty-two cover crop cultivars across the grass, legume, and brassica families were grown in O’Fallon, Missouri. Canopy cover was monitored throughout the growing season. Shoot and root biomass samples were collected and analyzed. Results Cereal rye and winter triticale were the most winter hardy cultivars and provide the highest percent canopy cover. Cereal rye and winter triticale also generate the highest amount of shoot and root biomass among treatments but exhibit different rooting behavior. Winter triticale forms coarser roots and exhibits deeper rooting, which may be better suited for carbon sequestration. Similarly, rapeseed and Siberian kale have favorable C:N ratios for nutrient recycling, but rapeseed may invest more into lateral root formation and have a higher potential to “catch” excess nutrients. Conclusion Selection of cover crops for ecosystem services should account for root system architecture and their suitability for these ecosystem services. Differences in root traits among cultivars within the same taxonomic family highlight the potential to engineer cover crop root system architecture to further enhance ecosystem service efficacy.

Soil compaction, in which soil grains are pressed together leaving less pore space for air and water, is a persistent problem in mechanized agriculture. Most plant roots fail to penetrate soil if it is too dense. One might assume that they are physically unable to penetrate the compact soil. However, new research demonstrates a more complex mechanism that requires the build-up of the volatile plant hormone ethylene in the rhizosphere1. Ethylene itself can arrest growth and, in compact soil, it is present in higher concentrations near roots due to its reduced ability to diffuse. Roots that lack the ethylene response pathway grow better through compact soil, demonstrating that it is physically possible to do so. The work suggests new levers for crop improvement in increasingly degraded soils.

Plant cells communicate information for the regulation of development and responses to external stresses. A key form of this communication is transcriptional regulation, accomplished via complex gene networks operating both locally and systemically. To fully understand how genes are regulated across plant tissues and organs, high resolution, multi-dimensional spatial transcriptional data must be acquired and placed within a cellular and organismal context. Spatial transcriptomics (ST) typically provides a two-dimensional spatial analysis of gene expression of tissue sections that can be stacked to render three-dimensional data. For example, X-ray and light-sheet microscopy provide sub-micron scale volumetric imaging of cellular morphology of tissues, organs, or potentially entire organisms. Linking these technologies could substantially advance transcriptomics in plant biology and other fields. Here, we review advances in ST and 3D microscopy approaches and describe how these technologies could be combined to provide high resolution, spatially organized plant tissue transcript mapping.

Phenotyping specific plant traits is difficult when the samples to be measured are architecturally complex. Inflorescence and root system traits are of great biological interest, but these structures present unique phenotyping challenges due to their often complicated and three-dimensional (3D) forms. We describe how a large industrial scale X-ray tomography (XRT) instrument can be used to scan architecturally complex plant structures for the goal of rapid and accurate measurement of traits that are otherwise cumbersome or not possible to capture by other means. The combination of a large imaging cabinet that can accommodate a wide range of sample size geometries and a variable microfocus reflection X-ray source allows noninvasive X-ray imaging and 3D volume generation of diverse sample types. Specific sample fixturing (mounting) and scanning conditions are presented. These techniques can be moderate to high throughput and still provide unprecedented levels of accuracy and information content in the 3D volume data they generate.

A plants’ water and nutrients are primarily absorbed through roots, which in a natural setting is highly dependent on the 3-dimensional configuration of the root system, collectively known as root system architecture (RSA). RSA is difficult to study due to a variety of factors, accordingly, an arsenal of methods have been developed to address the challenges of both growing root systems for imaging, and the imaging methods themselves, although there is no ‘best’ method as each has its own spectrum of trade-offs. Here, we describe several methods for plant growth or imaging. Then, we introduce the adaptation and integration of three complementary methods, root mesocosms, photogrammetry, and electrical resistance tomography (ERT). Mesocosms can allow for unconstrained root growth, excavation and preservation of 3-dimensional RSA, and modularity that facilitates the use of a variety of sensors. The recovered root system can be digitally reconstructed through photogrammetry, which is an inexpensive method requiring only an appropriate studio space and a digital camera. Lastly, we demonstrate how 3-dimensional water availability can be measured using ERT inside of root mesocosms.

The symbiosis between crops and arbuscular mycorrhizal fungi (AMF) have become an attractive route towards achieving carbon neutral agriculture and reducing the use of chemical fertilizers. Yet, ou...

Roots are the interface between the plant and the soil and play a central role in multiple ecosystem processes. With intensification of agricultural practices, rhizosphere processes are being disrupted and are causing degradation of the physical, chemical and biotic properties of soil. However, cover crops, a group of plants that provide ecosystem services, can be utilised during fallow periods or used as an intercrop to restore soil health. The effectiveness of ecosystem services provided by cover crops varies widely as very little breeding has occurred in these species. Improvement of ecosystem service performance is rarely considered as a breeding trait due to the complexities and challenges of belowground evaluation. Advancements in root phenotyping and genetic tools are critical in accelerating ecosystem service improvement in cover crops. In this study, we provide an overview of the range of belowground ecosystem services provided by cover crop roots: (1) soil structural remediation, (2) capture of soil resources and (3) maintenance of the rhizosphere and building of organic matter content. Based on the ecosystem services described, we outline current and promising phenotyping technologies and breeding strategies in cover crops that can enhance agricultural sustainability through improvement of root traits.

Background3D imaging, such as X-ray CT and MRI, has been widely deployed to study plant root structures. Many computational tools exist to extract coarse-grained features from 3D root images, such as total volume, root number and total root length. However, methods that can accurately and efficiently compute fine-grained root traits, such as root number and geometry at each hierarchy level, are still lacking. These traits would allow biologists to gain deeper insights into the root system architecture (RSA).ResultsWe present TopoRoot, a high-throughput computational method that computes fine-grained architectural traits from 3D X-ray CT images of field-excavated maize root crowns. These traits include the number, length, thickness, angle, tortuosity, and number of children for the roots at each level of the hierarchy. TopoRoot combines state-of-the-art algorithms in computer graphics, such as topological simplification and geometric skeletonization, with customized heuristics for robustly obtaining the branching structure and hierarchical information. TopoRoot is validated on both real and simulated root images, and in both cases it was shown to improve the accuracy of traits over existing methods. We also demonstrate TopoRoot in differentiating a maize root mutant from its wild type segregant using fine-grained traits. TopoRoot runs within a few minutes on a desktop workstation for volumes at the resolution range of 400^3, without need for human intervention.ConclusionsTopoRoot improves the state-of-the-art methods in obtaining more accurate and comprehensive fine-grained traits of maize roots from 3D CT images. The automation and efficiency makes TopoRoot suitable for batch processing on a large number of root images. Our method is thus useful for phenomic studies aimed at finding the genetic basis behind root system architecture and the subsequent development of more productive crops.

Grapevine 3D inflorescence architecture was comprehensively characterized among 10 wild Vitis species to reveal new phenotypic and evolutionary relationships., Inflorescence architecture provides the scaffold on which flowers and fruits develop, and consequently is a primary trait under investigation in many crop systems. Yet the challenge remains to analyse these complex 3D branching structures with appropriate tools. High information content datasets are required to represent the actual structure and facilitate full analysis of both the geometric and the topological features relevant to phenotypic variation in order to clarify evolutionary and developmental inflorescence patterns. We combined advanced imaging (X-ray tomography) and computational approaches (topological and geometric data analysis and structural simulations) to comprehensively characterize grapevine inflorescence architecture (the rachis and all branches without berries) among 10 wild Vitis species. Clustering and correlation analyses revealed unexpected relationships, for example pedicel branch angles were largely independent of other traits. We identified multivariate traits that typified species, which allowed us to classify species with 78.3% accuracy, versus 10% by chance. Twelve traits had strong signals across phylogenetic clades, providing insight into the evolution of inflorescence architecture. We provide an advanced framework to quantify 3D inflorescence and other branched plant structures that can be used to tease apart subtle, heritable features for a better understanding of genetic and environmental effects on plant phenotypes.

Understanding how an organism's phenotypic traits are conditioned by genetic and environmental variation is a central goal of biology. Root systems are one of the most important but poorly understood aspects of plants, largely due to the three-dimensional (3D), dynamic, and multiscale phenotyping challenge they pose. A critical gap in our knowledge is how root systems build in complexity from a single primary root to a network of thousands of roots that collectively compete for ephemeral, heterogeneous soil resources. We used time-lapse 3D imaging and mathematical modeling to assess root system architectures (RSAs) of two maize (Zea mays) inbred genotypes and their hybrid as they grew in complexity from a few to many roots. Genetically driven differences in root branching zone size and lateral branching densities along a single root, combined with differences in peak growth rate and the relative allocation of carbon resources to new versus existing roots, manifest as sharply distinct global RSAs over time. The 3D imaging of mature field-grown root crowns showed that several genetic differences in seedling architectures could persist throughout development and across environments. This approach connects individual and system-wide scales of root growth dynamics, which could eventually be used to predict genetic variation for complex RSAs and their functions.

Root system architecture (RSA) is a critical aspect of plant growth and competitive ability. Here we used two independently evolved strains of weedy rice, a de-domesticated form of rice, to study the evolution of weed-associated RSA traits and the extent to which they evolve through shared or different genetic mechanisms. We characterised 98 two-dimensional and three-dimensional RSA traits in 671 plants representing parents and descendants of two recombinant inbred line populations derived from two weed × crop crosses. A random forest machine learning model was used to assess the degree to which root traits can predict genotype and the most diagnostic traits for doing so. We used quantitative trait locus (QTL) mapping to compare genetic architecture between the weed strains. The two weeds were distinguishable from the crop in similar and predictable ways, suggesting independent evolution of a 'weedy' RSA phenotype. Notably, comparative QTL mapping revealed little evidence for shared underlying genetic mechanisms. Our findings suggest that despite the double bottlenecks of domestication and de-domestication, weedy rice nonetheless shows genetic flexibility in the repeated evolution of weedy RSA traits. Whereas the root growth of cultivated rice may facilitate interactions among neighbouring plants, the weedy rice phenotype may minimise below-ground contact as a competitive strategy.

We evaluated sixteen traits related to water acquisition and transport, stomatal conductance, and photosynthesis within a diverse panel of maize inbred lines, founders of the U.S. maize nested association mapping (NAM) population, with the aim to determine which traits confer improved growth under water deficit and well-watered conditions. Lasso regression revealed that three key traits explained meaningful and independent proportions of variation in total end-of-season biomass under deficit irrigation (multiple r2 = 0.86): 1) the maximal net CO2 assimilation rate (P = 0.007), 2) the achievable stomatal conductance during the hottest part of the day (P = 0.005), and 3) the width-to-depth ratio of the root system at the seedling stage (P = 0.060), i.e., initial deep root system development facilitated growth. Under well-watered conditions, maximal stomatal conductance in the morning (P = 0.014) and the width-to-depth ratio of the root system (P = 0.043) were identified as key traits contributing to improved performance (multiple r2 = 0.68). Structural equation models revealed that growth under water deficit was linked more strongly to stomatal conductance occurring during the middle of the day (std coef = 0.75; P = 0.006), rather than the maximal stomatal conductance (std coef = −0.25; P = 0.368). In turn, the maintenance of stomatal conductance through the middle of the day depended on the capacity of the xylem tissue to supply water (per unit cross-sectional area) (std coef = 0.48; P = 0.046). Aligned with the transport of water to the stomata and growth, root system depth ( r = 0.77; P = 0.003) and width-to-depth ratio ( r = −0.55; P = 0.064) at seedling stages were also correlated with the capacity of the xylem to transport water, thus suggesting close coordination between root, xylem, and stomatal traits to achieve greater growth under water deficit and well-watered conditions. We propose that maize performance under the drought conditions considered here, could likely be improved via lower stomatal sensitivity to hydraulic and atmospheric cues, greater xylem conductivity, and a deeper, but not necessarily more extensive, root system.

In recent years, an array of new technologies is propelling plant science in exciting directions and facilitating the integration of data across multiple scales. These tools come at a critical time. With an expanding global population and the need to provide food in sustainable ways, we as a civilization will be asking more of plants and plant biologists than ever before. This special issue on emerging technologies in plant science brings together a set of reviews that spotlight a range of approaches that are changing how we ask questions and allow scientific inquiry from macromolecular to ecosystem scales.

The root system is critical for the survival of nearly all land plants and a key target for improving abiotic stress tolerance, nutrient accumulation, and yield in crop species. Although many methods of root phenotyping exist, within field studies, one of the most popular methods is the extraction and measurement of the upper portion of the root system, known as the root crown, followed by trait quantification based on manual measurements or 2D imaging. However, 2D techniques are inherently limited by the information available from single points of view. Here, we used X-ray computed tomography to generate highly accurate 3D models of maize root crowns and created computational pipelines capable of measuring 71 features from each sample. This approach improves estimates of the genetic contribution to root system architecture and is refined enough to detect various changes in global root system architecture over developmental time as well as more subtle changes in root distributions as a result of environmental differences. We demonstrate that root pulling force, a high-throughput method of root extraction that provides an estimate of root mass, is associated with multiple 3D traits from our pipeline. Our combined methodology can therefore be used to calibrate and interpret root pulling force measurements across a range of experimental contexts or scaled up as a stand-alone approach in large genetic studies of root system architecture.

Numerous types of biological branching networks, with varying shapes and sizes, are used to acquire and distribute resources. Here, we show that plant root and shoot architectures share a fundamental design property. We studied the spatial density function of plant architectures, which specifies the probability of finding a branch at each location in the 3-dimensional volume occupied by the plant. We analyzed 1645 root architectures from four species and discovered that the spatial density functions of all architectures are population-similar. This means that despite their apparent visual diversity, all of the roots studied share the same basic shape, aside from stretching and compression along orthogonal directions. Moreover, the spatial density of all architectures can be described as variations on a single underlying function: a Gaussian density truncated at a boundary of roughly three standard deviations. Thus, the root density of any architecture requires only four parameters to specify: the total mass of the architecture and the standard deviations of the Gaussian in the three x , y , z growth directions. Plant shoot architectures also follow this design form, suggesting that two basic plant transport systems may use similar growth strategies.

Summary ●Inflorescence architecture in plants is often complex and challenging to quantify, particularly for inflorescences of cereal grasses. Methods for capturing inflorescence architecture and for analyzing the resulting data are limited to a few easily captured parameters that may miss the rich underlying diversity.●Here, we apply X‐ray computed tomography combined with detailed morphometrics, offering new imaging and computational tools to analyze three‐dimensional inflorescence architecture. To show the power of this approach, we focus on the panicles of Sorghum bicolor, which vary extensively in numbers, lengths, and angles of primary branches, as well as the three‐dimensional shape, size, and distribution of the seed.●We imaged and comprehensively evaluated the panicle morphology of 55 sorghum accessions that represent the five botanical races in the most common classification system of the species, defined by genetic data. We used our data to determine the reliability of the morphological characters for assigning specimens to race and found that seed features were particularly informative.●However, the extensive overlap between botanical races in multivariate trait space indicates that the phenotypic range of each group extends well beyond its overall genetic background, indicating unexpectedly weak correlation between morphology, genetic identity, and domestication history.

Roots remain an underexplored frontier in plant genetics despite their well-known influence on plant development, agricultural performance and competition in the wild. Visualizing and measuring root structures and their growth is vastly more difficult than characterizing aboveground parts of the plant and is often simply avoided. The majority of research on maize root systems has focused on their anatomy, physiology, development and soil interaction, but much less is known about the genetics that control quantitative traits. In maize, seven root development genes have been cloned using mutagenesis, but no genes underlying the many root-related quantitative trait loci (QTLs) have been identified. In this review, we discuss whether the maize mutants known to control root development may also influence quantitative aspects of root architecture, including the extent to which they overlap with the most recent maize root trait QTLs. We highlight specific challenges and anticipate the impacts that emerging technologies, especially computational approaches, may have toward the identification of genes controlling root quantitative traits.

Efforts to understand the genetic and environmental conditioning of plant morphology are hindered by the lack of flexible and effective tools for quantifying morphology. Here, we demonstrate that persistent-homology-based topological methods can improve measurement of variation in leaf shape, serrations, and root architecture. We apply these methods to 2D images of leaves and root systems in field-grown plants of a domesticated introgression line population of tomato (Solanum pennellii). We find that compared with some commonly used conventional traits, (1) persistent-homology-based methods can more comprehensively capture morphological variation; (2) these techniques discriminate between genotypes with a larger normalized effect size and detect a greater number of unique quantitative trait loci (QTLs); (3) multivariate traits, whether statistically derived from univariate or persistent-homology-based traits, improve our ability to understand the genetic basis of phenotype; and (4) persistent-homology-based techniques detect unique QTLs compared to conventional traits or their multivariate derivatives, indicating that previously unmeasured aspects of morphology are now detectable. The QTL results further imply that genetic contributions to morphology can affect both the shoot and root, revealing a pleiotropic basis to natural variation in tomato. Persistent homology is a versatile framework to quantify plant morphology and developmental processes that complements and extends existing methods.

Phenotypic measurements and images of crops grown under controlled-environment conditions can be analyzed to compare plant growth and other phenotypes from diverse varieties. Those demonstrating the most favorable phenotypic traits can then be used for crop improvement strategies. This article details a protocol for image-based root and shoot phenotyping of plants grown in the greenhouse to compare traits among different varieties. Diverse maize lines were grown in the greenhouse in large 8-gallon treepots in a clay granule substrate. Replicates of each line were harvested at 4 weeks, 6 weeks, and 8 weeks after planting to capture developmental information. Whole-plant phenotypes include biomass accumulation, ontogeny, architecture, and photosynthetic efficiency of leaves. Image analysis was used to measure leaf surface area and tassel size and to extract shape variance information from complex 3D root architectures. Notably, this framework is extensible to any number of above- or below-ground phenotypes, both morphological and physiological. © 2017 by John Wiley & Sons, Inc. Keywords: whole-plant; phenotypes; image-based analysis; shoots; roots

SummaryWe characterized grapevine inflorescence architecture (the rachis and all branches without berries) to describe variation among 10 wild Vitis species, assess phylogenetic signals underlying inflorescence architecture traits, and interpret this variation in the context of breeding objectives.Three-dimensional X-ray tomography scans of grapevine inflorescences were used to measure geometric traits and inflorescence topology using persistent homology, a mathematical approach that can comprehensively measure and compare shapes. We simulated potential space available for berry growth within a given inflorescence architecture by evaluating expanding spheres attached to pedicels, referred to as “berry potential.” Lastly, we performed phylogenetic analysis and mapped trait variation.We detected wide variation in inflorescence architecture features among Vitis species. Hierarchical clustering and correlation analyses revealed relationships among traits. Multivariate analyses identify traits contributing the most to variation and distinguish between species with high accuracy. Phylogenetic analyses revealed 12 morphological traits with strong phylogenetic signal.Morphometric analysis uncovered novel differences in inflorescence architecture among clades and between Vitis species. Cluster density is an important trait for assessing crop quality and forecasting yield; analyses presented here can be used to tease apart subtle, heritable features and environmental influences on this major agronomic trait.

Effective research, education, and outreach efforts by the Arabidopsis thaliana community, as well as other scientific communities that depend on Arabidopsis resources, depend vitally on easily available and publicly-shared resources. These resources include reference genome sequence data and an ever-increasing number of diverse data sets and data types. TAIR (The Arabidopsis Information Resource) and Araport (originally named the Arabidopsis Information Portal) are community informatics resources that provide tools, data, and applications to the more than 30,000 researchers worldwide that use in their work either Arabidopsis as a primary system of study or data derived from Arabidopsis. Four years after Araport's establishment, the IAIC held another workshop to evaluate the current status of Arabidopsis Informatics and chart a course for future research and development. The workshop focused on several challenges, including the need for reliable and current annotation, community-defined common standards for data and metadata, and accessible and user-friendly repositories/tools/methods for data integration and visualization. Solutions envisioned included (a) a centralized annotation authority to coalesce annotation from new groups, establish a consistent naming scheme, distribute this format regularly and frequently, and encourage and enforce its adoption. (b) Standards for data and metadata formats, which are essential, but challenging when comparing across diverse genotypes and in areas with less-established standards (e.g., phenomics, metabolomics). Community-established guidelines need to be developed. (c) A searchable, central repository for analysis and visualization tools. Improved versioning and user access would make tools more accessible. Workshop participants proposed a "one-stop shop" website, an Arabidopsis "Super-Portal" to link tools, data resources, programmatic standards, and best practice descriptions for each data type. This must have community buy-in and participation in its establishment and development to encourage adoption. Published version

The segmentation of plant roots from soil and other growing media in X-ray computed tomography images is needed to effectively study the root system architecture without excavation. However, segmentation is a challenging problem in this context because the root and non-root regions share similar features. In this paper, we describe a method based on level sets and specifically adapted for this segmentation problem. In particular, we deal with the issues of using a level sets approach on large image volumes for root segmentation, and track active regions of the front using an occupancy grid. This method allows for straightforward modifications to a narrow-band algorithm such that excessive forward and backward movements of the front can be avoided, distance map computations in a narrow band context can be done in linear time through modification of Meijster et al.'s distance transform algorithm, and regions of the image volume are iteratively used to estimate distributions for root versus non-root classes. Results are shown of three plant species of different maturity levels, grown in three different media. Our method compares favorably to a state-of-the-art method for root segmentation in X-ray CT image volumes., 11 pages

Root systems are branched networks that develop from simple growth properties of their individual roots. Yet a mature maize root system has many thousands of roots that each interact with soil structures, water and nutrient patches, and microbial ecologies in the micro-environments surrounding each root tip. Although the plasticity of root growth to these and other environmental factors is well known, how the many local processes contribute over time to global features of root system architecture is hardly understood. We employ an automated 3D root imaging pipeline to capture the growth of maize roots every four hours throughout seven days of seedling development. We model the contrasting architectures of two maize inbred genotypes and their hybrid to derive key parameters that distinguish complex growth patterns as a function of time. The statistical characteristics of local root growth defined the global system properties despite a large range of trait values. “Computational dissection” of a single root from each root system identified differences in the size of the root branching zone and lateral branching densities, but not radial patterns, that drove the contrasting root architectures from seedling to maturity. X-ray imaging of mature field-grown root crowns showed that seedling growth trajectories persisted throughout development and could predict eventual architectures, suggesting a strong genetic basis. The work connects individual and systemwide scales of root growth dynamics, providing the means for a function-valued approach to understanding the genetic and genetic x environment conditioning of root growth that will enable breeding for enhanced root traits.SIGNIFICANCE STATEMENTWhen and where roots grow determines their ability to capture short-lived and patchy water and nutrient resources to support the aboveground organs of the plant. Roots have no known long-distance external sensing mechanisms, but form branched networks that blindly explore the soil and respond to encountered local stimuli. How global architectures form from the many thousands of these local responses, and how they are controlled genetically are major open questions. Here we quantify differences in local root growth patterns of two inbred genotypes of maize that control contrasting systemwide properties. Measurements at the seedling stage were highly correlated with the complex architectures of mature root systems, paving the way for the development of crops with greater resource uptake capacity.

Current morphometric methods that comprehensively measure shape cannot compare the disparate leaf shapes found in seed plants and are sensitive to processing artifacts. We explore the use of persistent homology, a topological method applied across the scales of a function, to overcome these limitations. The described method isolates subsets of shape features and measures the spatial relationship of neighboring pixel densities in a shape. We apply the method to the analysis of 182,707 leaves, both published and unpublished, representing 141 plant families collected from 75 sites throughout the world. By measuring leaves from throughout the seed plants using persistent homology, a defined morphospace comparing all leaves is demarcated. Clear differences in shape between major phylogenetic groups are detected and estimates of leaf shape diversity within plant families are made. This approach does not only predict plant family, but also the collection site, confirming phylogenetically invariant morphological features that characterize leaves from specific locations. The application of a persistent homology method to measure leaf shape allows for a unified morphometric framework to measure plant form, including shape and branching architectures.

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. National Science Foundation through NSF [DBI-1300426] University of Tennessee, Knoxville, Knoxville, TN, United States This work was assisted through participation in the Morphological Plant Modeling: Unleashing geometric and topological potential within the plant sciences Investigative Workshop at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville, Knoxville, TN, United States.

Genetic contributions to plant morphology are not partitioned between shoots and roots. Yet, shoot and root architectures are rarely measured in the same plants. Even if shoot and root architectures are both studied, the application of mathematical methods flexible enough to accommodate the disparate topologies and shapes within a plant, and across scales, are lacking. Here, we advocate the use of persistent homology, a mathematical method robust to noise, invariant with respect to orientation, capable of application across diverse scales, and importantly, compatible with diverse functions to quantify disparate plant morphologies, architectures, and textures. To demonstrate the usefulness of this method, we apply persistent homology approaches to the shape of leaves, serrations, and root architecture as measured in the same plants of a domesticated tomato Solanum pennellii near-isogenic introgression line population under field conditions. We find that genetic contributions to morphology affect the plant in a concerted fashion, affecting both the shoot and root, revealing a pleiotropic basis to natural variation in tomato.

Developmental processes that control root system architecture are critical for soil exploration by plants, allowing for uptake of water and nutrients. Conversion of the auxin precursor indole-3-butyric acid (IBA) to active auxin (indole-3-acetic acid; IAA) modulates lateral root formation. However, mechanisms governing IBA-to-IAA conversion have yet to be elucidated. We identified TRANSPORTER OF IBA1 (TOB1) as a vacuolar IBA transporter that limits lateral root formation. Moreover, TOB1, which is transcriptionally regulated by the phytohormone cytokinin, is necessary for the ability of cytokinin to exert inhibitory effects on lateral root production. The increased production of lateral roots in tob1 mutants, TOB1 transport of IBA into the vacuole, and cytokinin-regulated TOB1 expression provide a mechanism linking cytokinin signaling and IBA contribution to the auxin pool to tune root system architecture.

Plant morphology is inherently mathematical in that morphology describes plant form and architecture with geometrical and topological descriptors. The geometries and topologies of leaves, flowers, roots, shoots and their spatial arrangements have fascinated plant biologists and mathematicians alike. Beyond providing aesthetic inspiration, quantifying plant morphology has become pressing in an era of climate change and a growing human population. Modifying plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems with fewer natural resources. In this white paper, we begin with an overview of the mathematical models applied to quantify patterning in plants. We then explore fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leafs in air streams. We end with a discussion concerning the incorporation of plant morphology into educational programs. This strategy focuses on synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. This white paper arose from bringing mathematicians and biologists together at the National Institute for Mathematical and Biological Synthesis (NIMBioS) workshop titled “Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences” held at the University of Tennessee, Knoxville in September, 2015. Never has the need to quantify plant morphology been more imperative. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Field-based, high-throughput phenotyping enables the detailed characterization of plant populations under relevant conditions, providing valuable biological insight into the life history of plants. ### Glossary FB-HTP : field-based, high-throughput phenotyping EM : electromagnetic radiation 3D : three-dimensional UAS : unmanned aircraft system QTL : quantitative trait locus GPR : ground-penetrating radar ERT : electrical resistivity tomography EQ : entity quality IPPN : International Plant Phenotyping Network CGM : crop growth model * ### Glossary FB-HTP : field-based, high-throughput phenotyping EM : electromagnetic radiation 3D : three-dimensional UAS : unmanned aircraft system QTL : quantitative trait locus GPR : ground-penetrating radar ERT : electrical resistivity tomography EQ : entity quality IPPN : International Plant Phenotyping Network CGM : crop growth model

Quantifying plant morphology is a very challenging task that requires methods able to capture the geometry and topology of plant organs at various spatial scales. Recently, the use of persistent homology as a mathematical framework to quantify plant morphology has been successfully demonstrated for leaves, shoots, and root systems. In this paper, we present a new data analysis pipeline implemented in the R package archiDART to analyse root system architectures using persistent homology. In addition, we also show that both geometric and topological descriptors are necessary to accurately compare root systems and assess their natural complexity.