Search

One of the largest and longest standing societal challenges is acquiring enough food to support the human population. Our current era has the added complexities of the population nearing 9 billion, a globalized industrial agricultural production system, and a clearer understanding of how environmentally harmful and unsustainable that system is. While these issues are multifaceted, agriculture is fundamentally coupled with plant and microbial biology and there has been a diversity of avenues pursued by researchers seeking potential solutions and disruptive innovations to address our need to provide healthy food for the world without destroying it in the process. Modern agricultural practices currently require high energetic costs through extensive irrigation, application of synthetic fertilizers and pesticides, and the use of large, mechanized equipment. The lack of biodiversity in large-scale monoculture systems also presents issues in crop nutritional quality, disease pressure, and soil health. Recent advancements in our understanding of plant root systems and the relationships they form with soil microbiota have demonstrated a wealth of potential applications regarding these issues as well as in further illuminating the complex processes at play in plant health and development in an ecological context. It has become increasingly clear that plant roots are essential components to local and global nutrient cycling and drive much of the microbial activity in soils. In order to ensure a future with sustainable, climate-resilient agriculture which enables nutritious diets, we must continue to explore the wealth of knowledge underground. This dissertation seeks to clarify some of the socioeconomic reasons why we grow food the way we do and the limitations of material available for study, as well as underlying biochemical and genetic mechanisms which influence plant root biology and their relationships with microorganisms. The results of this research contribute to the growing body of knowledge in root biology and a paradigm shift in how we understand plants and agriculture to be connected to the wider ecosystem.Chapter 1 seeks to understand the historical and contemporary contexts which influence the scale, scope, and direction of research in agricultural and plant sciences. Analyzing the socioeconomic institution of modern Science, from the conditions leading to the Scientific Revolution in the 16th century to modern day, reveals the conserved influence of western European colonial-imperialism on global agricultural production. From its inception, the institution of Science is shown to be integral to the expansion and maintenance of Western imperial powers materially and socially, by driving critical revenue generation via the enabling and adoption of cash crop agriculture and through controlling the value and direction of intellectual pursuits. From the 19th century we see Science increasingly entangled with emerging capitalist corporate and state interests, which further entrench practices that began with cash crop agriculture and prove to be detrimental to environmental health while distancing crop production from nutritional needs. I describe how these relationships ultimately limit the resources we have available for research in the modern day, hindering our abilities to address the myriad socio-scientific challenges of this century. This clarity is important when making the critical and strategic assessments necessary to direct on-going and future research and teaching efforts. Chapter 2 is an effort to detail that plant roots are essential to plant health and adaptation as well as important contributors to numerous ecological and biogeochemical processes. Despite this, they have been comparatively understudied aspects of plant biology. Recent developments have indicated that a better understanding of root systems can reveal breeding and engineering applications towards plants more well-suited for low-input agricultural systems and frequent stresses. I highlight four co-authored publications concerning the study of root systems: Detailing the limitations and considerations of root system study as well as demonstrations of progress to address these challenges, metabarcoding combined with genomics and data analytics programs to inform the basis of rhizosphere microbiome heritability in Sorghum bicolor, constitutive promoters to fine tune gene expression in synthetic biology with demonstrated function in root systems, and utilizing root system imaging methods and software to inform the effect of a bacterial metabolite on plant-bacterial associations in Arabidopsis thaliana. These studies hope to provide examples of and inspire further efforts to understand root systems, thus enabling improvements in plant performance under new and changing agricultural practices better suited for the world we live in today. Chapter 3 seeks to further illuminate the underlying mechanisms of pectin biosynthesis. Pectin is an abundant component of plant cell walls demonstrated to be important in cell to cell adhesion, plant development, and a variety of signaling pathways. Understanding has so far remained limited due to the wide diversity and redundancy of enzymes involved in the process. The pectin component rhamnogalacturonan I (RG-I) is biosynthesized in part by rhamnosyltransferases (RRTs) in the GT106 family. While it is known that RRTs are expressed in a range of tissues, few studies have demonstrated their function outside of RG-I biosynthesis in seed coat mucilage. In this study we show Lotus japonicus RRT1 contributes to the addition of rhamnose monosaccharide residues to RG-I in root tissues. Mutants contained ~19% less rhamnose in their roots and pectin from aboveground tissues had less galactose and more xylose. RG-I in root tissue from Ljrrt1 also had a larger molecular weight and altered structure compared to wild type (WT) Gifu plants, but this was not due to transcriptional differences in other GTs responsible for RG-I biosynthesis. Mutants exhibited altered root morphology, impacted stem and root growth, and impairment of nodule formation when inoculated with Mesorhizobium loti. These findings constitute the first demonstration of RRT function in vascular plants outside of seed coat mucilage and contribute to the increasingly nuanced understanding of RG-I in cell wall biosynthesis and intersecting processes. Chapter 4 is an effort to characterize an unknown subclass of plant GTPase-related signaling proteins which appear to influence symbiotic relationships formed in root systems. Plants possess a unique class of heterotrimeric G? subunits called extra-large GTPases (XLGs) which contribute to numerous developmental and stress responses. XLGs have an uncharacterized N-terminal domain, a G?-like C-terminal domain, and overlapping and distinct functions compared to conventional G? subunits. In this study, we identified homologs of XLG3 in Lotus japonicus responsive to rhizobial and mycorrhizal symbiosis. However, these proteins were approximately one-third the size of conventional XLGs and only aligned to the N-terminal domain, containing a putative NLS and the cysteine-rich domain of unknown function. Multiple sequence alignment and phylogenetic analysis determined SXLGs did not share domains with other mono- or heterotrimeric G-protein classes and exhibited a pattern of duplication and neofunctionalization typical of genes involved in symbiotic signaling pathways. Transient expression of LjSXLGs in tobacco demonstrated their potential for localization to the plasma membrane, nucleus, and nucleolus. Analysis of L. japonicus sxlg2 mutants revealed transient impairment of immature nodule formation in a destructive experimental setup and inhibition of infection events in a nutrient-limited non-destructive experimental setup, with no observed difference in nodule maturation rate. Additionally, sxlg2 mutants showed a potential impairment of the root growth response in N-limited conditions. SXLGs present an ideal opportunity to better understand the evolution, function, and structure of XLGs and are another example of G-protein involvement in symbiotic relationships. Ultimately, this research supports growing efforts to develop more resilient and sustainable agricultural practices through a focus on root systems biology by providing assessments of the technical and methodological resources in the field, demonstrating dynamics of pectin biosynthesis in root tissue, and uncovering new elements of plant symbiotic and G-protein related signaling pathways. These findings will promote further mechanistic and evolutionary discoveries in aspects of root biology that remain filled with questions and unknowns, but also notable potential in the development of roots more amenable to regenerative agricultural approaches, maximizing benefits from microbial associations, and utilization in the biosynthesis of valuable products and biofuels. The situating of historical and contemporary socioeconomic contexts that have heavily influenced the progression of agriculture and plant sciences over the past half a millennium is a critical addition to our ability to wholly assess the materials, practices, and technologies available for further research. This clarity is essential if we truly wish to address the systemic challenges of our era. Technical solutions have limited ability to resolve complex socio-scientific issues without understanding the broader social contexts they were born from and operate in. In the same way that systems biology has begun to permeate many scientific disciplines, our perspectives must shift to accommodate the nuance and complexity of how interconnected this world is

A classic theorem of Gabriel states that, for a finite type Dynkin diagram G, the indecomposable representations of any quiver orienting G are in bijection with reflecting hyperplanes of the associated Coxeter group W. This is the starting point for a rich web of connections between the representation theory of algebras and the combinatorics and geometry of Coxeter groups. Recent work of Iyama, Reading, Reiten, and Thomas constructs a similar correspondence between brick modules of the preprojective algebra Pi_G for a finite type Dynkin diagram G and a combinatorially useful partition of the hyperplanes into cones called shards. A paper of the author, Speyer, and Thomas generalizes this beyond finite type Dynkin diagrams by defining a class of bricks of Pi_G called shard modules which correspond to shards for arbitrary diagrams G. Although harder to understand than in the finite type case, shard modules provide a potential categorical tool for studying infinite Coxeter groups and cluster algebras. In this thesis, we study how the relative position of shards affects the properties of their associated shard modules. We generalize beyond finite type a result of Iyama, Reading, Reiten, and Thomas showing that, when three shards meet in a certain configuration, their shard modules fit into a short exact sequence. We pay specific attention to "stretched" families of graphs obtained by inserting a path into a fixed diagram, describing recurring structure in the shards as the path grows. We use this structure to generalize patterns appearing in the shard modules for the A_n and D_n families of diagrams to any family of diagrams with tails.

Intercropping and other forms of mixed cropping are both widely used and beneficial in many agricultural systems. One of the best-known examples is the grass-clover production model in pastures, in which nitrogen-fixation by symbiotic bacteria (e.g. Rhizobium spp.) benefits the grass as well as the host species of clover (Trifolium spp.) or other legume species. This is one example of transgressive overyielding, which refers to situations when the yield of two species growing together exceeds the yield of either of the species growing individually on the same area of land. This doctoral study aimed to investigate the benefits of companion plants in terms of soil biogeochemistry, focusing particularly on species that are companion plants to grasses. Literature is reviewed of plant species competition and co-existence, and rhizosphere biogeochemistry, primarily in the context of pastoral grasslands in the New Zealand High Country. The research project includes an investigation of whether there are nutritional benefits to nitrogen (N) -fixing plants when they grow in combination with grasses, rather than this being simply a relationship that involves spillover of nitrogen from legumes to grasses. This is extended to studies of phosphorus (P) -mobilizing plants and grasses, to investigate whether grasses provide reciprocal nutrients to cluster-rooted plants in the Proteaceae. The hypothesis underlying this study was that rhizosphere processes in grasses may be more adept than clovers at exploiting key trace elements in soils, and that these trace elements can be exchanged for N or P, thus also providing an explanation for species coexistence. Practical investigations consisted of pot experiments, a transplanted-soil core mesocosm experiment and field sampling, primarily concerned with nutrient deficient soils. This experimental work analysed the effects of different species combinations on (i) yield and (ii) plant and soil nutrient status (macronutrients and trace elements). Plant species combinations included both exotic and native species of grasses and legumes. The work was partly carried out on the Lincoln University Campus and at Mt. Grand Station, a university-owned high country pastoral farm in Hawea, Central Otago, from 2019 – 2022, with funding support from the Miss E.L. Hellaby Indigenous Grasslands Research Trust. The results showed that grasses played a critical role in acquisition of soil nutrients when they were growing with companion legumes or proteas in degraded soil. I found that legumes contained more nutrients (e.g. P, potassium sulphur, molybdenum and boron) when they were growing with grasses. Both native tussock grasses and exotic pasture grasses had significant positive impacts on native and exotic legumes in terms of nutrient uptake of a range of elements including Nitrogen and Sulfur. Both legumes and grasses benefited from growing together. Cluster-rooted species of Proteacea and grasses were found to have higher foliar concentrations of nutrients when they were growing together. The findings of this research provide evidence of facilitation between plant species with contrasting root systems when they are growing together in terms of procurement of key plant nutrients. Combinations of species can better exploit soil nutrients under conditions where fertility is constrained. This work is interpreted in the context of pasture production systems, protection of native biodiversity and land sharing by exotic and native species in the New Zealand High Country. The thesis is presented as an introduction to the study, a broad literature review, the inclusion of three published papers 1-3, one recently-submitted manuscript 4, a chapter describing additional work carried out during the PhD study, and a chapter containing the interpretive discussion and conclusions.

In 1996 and 2000 A.G. Helminck gave the first algorithms for computing some of the structure of symmetric spaces. In this thesis we extend these results by designing algorithms for other aspects of the structure of local symmetric spaces. We begin with an involution on the root system. We would like to understand how this involution describes an involution on the Lie algebra. To do so, we consider the concept of lifting. We say an involution θ on the root system Φ can be lifted to an involution θ on the algebra if we can find θ so that θ|Φ = θ. Success gives rise to a method to compute local symmetric spaces. Accomplishing this task requires effort on multiple fronts. On a small scale we consider a correction vector. A correction vector lives in the toral subalgebra of the Lie algebra. A result due to Steinberg establishes a unique Lie algebra automorphism that can always be defined. We can modify this map with the correction vector so that it becomes an involution. On a large scale, computing the correction vector is too cumbersome. We will show how to “break apart†larger involutions on the root system by projecting the roots into the local symmetric space, then “extracting†specific sub-systems. We can correct the involution on each sub-system, then “glue†the pieces together to form the involution on the whole algebra. This process not only vastly improves the timing of the lifting process, but also gives rise to an argument that any involution on the root system can be lifted. We then present an entire computer package written for Mathematica) for working with local symmetric spaces. This package includes the algorithms we devise, as well as “helper†algorithms which are necessary for implementation.

We prove the positivity of Lusztig's q-analogue of weight multiplicity in a purely combinatorial way for rank 2 Lie algebras. Each summand in the polynomial can be interpreted as a linear combination of positive roots. We prove that all negative coefficients are cancelled in the polynomial. Further, the analysis of the root systems allows us to state formulae for every coefficient in Lusztig's q-analogue for rank 2 Lie algebras.

Let R be a reduced root system in a finite dimensional vector space V, N the associated weight lattice, and &phis; the fan of Weyl chambers in N. The pair (N, &phis;) determines a smooth, projective toric variety X = X(R). The action of the Weyl group W on N induces an action of W on X and thus an action on the integral and rational cohomology of X. In work of J. Stembridge, I. Dolgachev and V. Lunts it is shown that in the An and Cn cases, the Weyl group action on the cohomology is a graded permutation representation. An interesting problem, suggested in a paper by J. Stembridge, is to find a concrete basis for this cohomology permuted by W . In this thesis we give a geometric solution to this problem. An immediate consequence is a concrete, and geometrically natural formula for the isotypic Betti numbers of the X(An) cohomology. The key idea is the introduction of natural projection and inclusion maps, which allow us to naturally decompose the cohomology of X( An) and X(Cn). This decomposition allows us to further give an integral basis for the cohomology of X(An) and X(Cn). We also study the X(Bn) variety, describing it geometrically, giving a natural proof of the equivalence of the module structure of its cohomology with the module structure of the cohomology of X( Cn), and giving a proof that for n > 2, the varieties X(Bn) and X(Cn) are not isomorphic.

Each 6-8 month old seedling was detopped, the root system enclosed in a chamber holding labelled (THO, THO and ³⁵S-labelled sulfate) medium, 1.5 bars pressure applied to the medium, and root system exudates collected for up to 116 min., on a series of filter paper discs. Exudate flux rates were generally increasing within about the first 10 min. of collection, then levelled off or dropped slightly. Average flux rates over the interval 12th-48th min. of exudate collection were taken as a basis for comparison. Mean values were; mycorrhizal, 20.62, and nonmycorrhizal, 15.98 mg H₂O/g dry root/min/1.5 bars, the difference not statistically significant. Root system permeabilities, computed from the average flux rates over the 12th-48th min. interval, were highly variable, Coefficient of Variation = 75.94%. There was a highly significant inverse correlation (r = -.5859) between root system permeability and dry weight. Mycorrhizal root systems tended to be more permeable; mean values were: mycorrhizal, .822, and nonmycorrhizal, .638; after adjusting for root dry weight by covariance analysis, mycorrhizal, .842, and nonmychorrhizal, .604 g H₂O/g dry root/hour/bar. The increase with time of THO-C/Co (C/Co is the ratio of radioisotope concentration in the exudate over that in the root medium) was slow; linear in the first hour, then tapering off. THO-C/Co was still increasing at the latest exudate collection. Mean THO-C/Co at the end of the first hour was 0.38, at the 116th min., 0.50. The increase in THO-C/Co with time was probably controlled by exchange and not exudate flux rate. There was a significant inverse correlation (r = -.4674) between time of arrival of THO at the cut end and root system permeability. In the absence however, of a compact radioisotope front, THO appearance at the cut end was not adopted as a reliable indicator of permeability. The presence of mycorrhizas did not substantially alter THO transport into the root system exudates. The increase with time of 35S-C/Co was initially more rapid; the linear increase then tapering off were more rapid and before the end of the 116 min. exudate collection period, ³⁵S-C/Co had levelled off. Appearance of ³⁵S at the cut end and the rate of its transport into the root system exudates did not relate with permeability. ³⁵S- C/ Co in the exudates from mycorrhizal root systems levelled off sooner and at a lower level. Mean plateau ³⁵S-C/Co values were: mycorrhizal, .38, and nonmycorrhizal, .55, the difference statistically significant. Supplementary experiments with killed (by boiling) mycorrhizal root systems confirmed that dead root systems are more permeable. THO-C/Co in the exudates from dead root systems levelled off at about 0.3, before the end of the 116 min. exudate collection period.

A simulation scheme to model three-dimensional plant root architecture and the location, growth and interaction of associated microbial communities has been developed. The scheme expands on previous root architecture models by using the mature root system morphology observed in the field as a spatial envelope to model the system's temporal development. The three-dimensional representation allows a uniquely detailed treatment of the spatial development of microbial populations and their interactions with the root system and with each other. Root morphology and microbial populations are described by different types of "node", each node records a position in three-dimensional space and other details specific to the feature it represents. For example, "Branch" nodes indicate the start of a higher order root, and "Fungal" nodes increase or decrease the level of a fungal population on a root's surface. A large number of probability density functions are required to produce the list of nodes that describe each root. A four-dimensional matrix is used as a convenient abstraction for these functions, the dimensions represent tree type, root order, a "feature" such as branching or microbial infection, and an "attribute" such as length or lifespan. Algorithms for the generation and manipulation of the node lists are given. Specific implementation issues, such as rapid location of roots within the area potentially affected by disease lesion, and visualisation of the simulated root system, are also addressed. Validation of models of complex, irregular entities such as plant root systems is difficult, some techniques, including an objective root distribution index, have been developed and applied in this research. The simulation software includes extensions to allow input and editing of observed root system architectures to simplify the extraction of relevant parameters from such observations. The Pinus radiata / armillaria root-rot pathosystem has been used extensively as a test case for the scheme. The spread of the disease armillaria between roots of seedlings and the control of that spread by antagonistic strains of the soil fungus genus Trichoderma have been successfully modelled. Simulated root architectures are consistent with those observed in the field, and patterns of fungal spread through simulated stands are very similar to those reported in the literature. While this research was initially prompted by the Pinus radiata / armillaria pathosystem, the problems solved, namely representation and manipulation of three-dimensional root architecture and root/microbial spatial interaction, are essentially the same for most plant root ecosystems. The scheme should be a useful tool for the development of biological control programmes, both in formulating an understanding of the dynamics of the ecosystem to be modified, and in optimising the timing and position of biological control agent application. Further development of the scheme should include a generalised root ecosystem description syntax, and a re-implementation of the simulation's internal structure in an object oriented language. This should result in a versatile framework for detailed simulation of plant root microbial ecosystems.