Fractal geometry of bean root systems: correlations between spatial and fractal dimension

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.     

Fractal geometry of root systems: Field observations of contrasting genotypes of common bean (Phaseolus vulgaris L.) grown under different phosphorus regimes

Root growth and architecture are important for phosphorus acquisition due to the relative immobility of P in the soil. Fractal geometry is a potential new approach to the analysis of root architecture. Substantial genetic variation in root growth and architecture has been observed in common bean. Common bean (Phaseolus vulgaris L.) genotypes with contrasting root architecture were grown under moderate and low P conditions in a field experiment. Linear and planar fractal dimension were measured by tracing root intercepts with vertical planes. Linear fractal dimension increased over time in efficient genotypes, but remained fairly constant over time in inefficient genotypes. Planar fractal dimension increased over time for all genotypes, but was higher in efficient than inefficient genotypes at the end of the experiment. Planar fractal dimension of medium P plants was found to correlate with shoot P content indicating fractal dimension to be a possible indicator for root P uptake. The increasing fractal dimension over time indicates that fractal analysis is a sensitive measure of root branching intensity. A less destructive method for acquisition of data that allows for continuous analysis of fractal geometry and thereby screening for more P efficient genotypes in the field is suggested. This method will allow the researcher to conduct fractal analysis and still complete field trials with final yield evaluation.     

Fractal geometry and root system structures of heterogeneous plant communities

Above-ground plant growth is widely known in terms of structural diversity. Likewise, the below-ground growth presents a mosaic of heterogeneous structures of differing complexity. In this study, root system structures of heterogeneous plant communities were recorded as integral systems by using the trench profile method. Fractal dimensions of the root images were calculated from image files by the box-counting method. This method allows the structural complexity of such associations to be compared between plant communities, with regard to their potentials for soil resource acquisition and utilization. Distinct and partly significant differences are found (fractal dimension between 1.46±0.09 and 1.71±0.05) in the below-ground structural complexity of plant communities, belonging to different biotope types. The size of the heterogeneous plant community to be examined has an crucial influence on the fractal dimension of the root system structures. The structural heterogeneity becomes particularly evident (fractal dimensions between 1.32 and 1.77) when analysing many small units of a complex root system association. In larger plant communities, a broad variety of below-ground structures is recorded in its entirety, integrating the specific features of single sub-structures. In that way, extreme fractal dimensions are lost and the diversity decreases. Therefore, the analysis of larger units of root system associations provides a general knowledge of the complexity of root system structures for heterogeneous plant communities.     

Fractal analysis of the root architecture of Gliricidia sepium for the spatial prediction of root branching,size and mass: model development and evaluation in agroforestry

Based on fractal and pipe model assumptions, a static three-dimensional model of the Gliricidia sepium root system was developed, in order to provide a basis for the prediction of root branching, size and mass in an alley cropping system. The model was built from observations about the topology, branching rules, link length and diameter, and root orientation, provided by in situ and extracted root systems. Evaluation tests were carried out at the plant level and at the field level. These tests principally concerned coefficients α and q –- the proportionality factor α between total cross-sectional area of a root before and after branching, and allocation parameter q that defines the partitioning of biomass between the new links after a branching event –- that could be considered as key variables of this fractal approach. Although independent of root diameter, these coefficients showed a certain variability that may affect the precision of the predictions. When calibrated, however, the model provided suitable predictions of root dry matter, total root length and root diameter at the plant level. At the field level, the simulation of 2D root maps was accurate for root distribution patterns, but the number of simulated root dots was underestimated in the surface layers. Hence recommendations were made to improve the model with regard to α and q. This static approach appeared to be well suited to study the root system of adult trees. Compared with explicit models, the main advantage of the fractal approach is its plasticity and ease of use. This revised version was published online in June 2006 with corrections to the Cover Date.     

高寒草地甘肃臭草根系分形结构的坡向差异性

根系分形结构是植物根系构型应对环境异质性的表型可塑性结果, 可反映植物对生长环境的适应策略。利用ArcGIS建立研究区域的数字高程模型, 并提取坡向数据, 采用全根挖掘和Win-RHIZO根系分析仪相结合的方法, 研究了祁连山北坡高寒退化草地不同坡向甘肃臭草(Melica przewalskyi)的根系分形结构。结果表明: 随着坡向由北坡向东坡、西坡、南坡转变, 草地群落的密度、高度和土壤含水量逐渐减小, 甘肃臭草种群的密度、高度以及根系分形丰度呈逐渐增大的趋势、分形维数逐渐减小; 不同坡向甘肃臭草根系分形维数和分形丰度间的相关性存在差异(p < 0.05), 南坡和北坡甘肃臭草根系分形维数分形丰度之间存在极显著负相关关系(p < 0.01), 东坡和西坡之间存在显著负相关关系(p < 0.05), 甘肃臭草根系分形维数和分形丰度存在着“此消彼长”的权衡关系; 随着坡向由北坡向东坡、西坡、南坡转变, 甘肃臭草根系分形维数和分形丰度回归方程的标准化主轴(SMA)斜率逐渐增大(p < 0.05), 说明在干旱的南坡, 根系所开发利用的相同体积的土壤内, 根系分支更少、更稀疏。不同坡向甘肃臭草合理权衡根系分形维数和分形丰度的资源配置模式, 体现了植物根系构型构建的资源投资权衡机制。     

Fractal root system of Melica przewalskyi along different aspect in degraded grassland

Aims Fractal root system is phenotypic plasticity result of plant root architecture to respond to environmental heterogeneity, may reflect the growth strategy of plants to adapt to environmental conditions. Our objective was to explore the relationship between root fractal dimension and fractal abundance of fractal root system of Melica przewalskyi population in response to aspect variation in the northwest of China. Methods The study site was located in a degraded alpine grassland on the northern slope in Qilian Mountains, Gansu Province, China. Survey and sampling were carried out at 40 plots which were set up along four slope aspects transects with 20 m distance between adjacent plots. Handheld GPS was used to determine the elevation, longitude and latitude of each plot. ArcGIS was used to set up digital elevation model (DEM). Community traits were investigated and six individuals roots of M. przewalskyi were collected randomly at each plot. The samples were cleaned and divided into different organs, then scanning the root with the Win-RHIZO for measurements of fractal dimension and fractal abundance in laboratory, and their biomass were then measured after being dried at 80 °C in an oven. Important findings With the slope aspect turned from north to east, west, and south, the density, height and soil moisture content of the plant community displayed a pattern of initial decline, the height, density, root fractal abundance of M. przewalskyi increased and the root fractal dimension decreased. The root fractal dimension was negatively associated with the fractal abundance in all aspects, but the relationship varied along the slope aspects gradient; there was a highly significant negative correlation (p < 0.01) between the root fractal dimension and fractal abundance at north slope and south slope aspect, whereas the correlation only reached a significant level (p < 0.05) at the east slope aspect and west slope aspect; indicating that there is a trade-off between the root fractal dimension and fractal abundance. In addition, when the slope aspect changed from north to east, west and south, the standardized major axis (SMA) slope of the regression equation in the scaling relationships between root fractal dimension and fractal abundance increased (p < 0.05), indicating that the roots of M. przewalskyi at the droughty southern slope have less branch and more sparse in the same soil volume of root exploitation and utilization. Consequently, the resource allocation pattern on reasonable trade-off between root fractal dimension and fractal abundance in different slope aspect of M. przewalskyi, reflects the relationship between the income and the cost of construction of plant root architecture.     

Modelling applicability of fractal analysis to efficiency of soil exploration by roots

BACKGROUND AND AIMS: Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisition of diffusion-limited nutrients. The hypothesis that soil depletion and root competition are more closely correlated with a combination of fractal parameters than by any one alone was tested. MODEL: The geometric simulation model SimRoot was used to dynamically model roots of various architectures growing for up to 16 d in three soil types with contrasting nutrient mobility. Fractal parameters were calculated for whole roots, projections of roots and vertical slices of roots taken at 0, 2.5 and 5 cm from the root origin. Nutrient depletion volumes, competition volumes, and relative competition were regressed against fractal parameters and root length. KEY RESULTS: Root length was correlated with depletion volume, competition volume and relative competition at all times. In analysis of three-dimensional, projected roots and 0 cm slices, log(fractal abundance) was highly correlated with log(depletion volume) when times were pooled. Other than this, multiple regression yielded better correlations than regression with single fractal parameters. Correlations decreased with age of roots and distance of vertical slices from the root origin. Field data were also examined to see if fractal dimension, fractal abundance and lacunarity can be used to distinguish common bean genotypes in field situations. There were significant differences in fractal dimension and fractal abundance, but not in lacunarity. CONCLUSIONS: These results suggest that applying fractal analysis to research of soil exploration by root systems should include fractal abundance, and possibly lacunarity, along with fractal dimension.     

Evolving technologies for growing,imaging and analyzing 3D root system architecture of crop plants

A plant's ability to maintain or improve its yield under limiting conditions,such as nutrient de ficiency or drought,can be strongly in fluenced by root system architecture(RSA),the three-dimensional distribution of the different root types in the soil. The ability to image,track and quantify these root system attributes in a dynamic fashion is a useful tool in assessing desirable genetic and physiological root traits. Recent advances in imaging technology and phenotyping software have resulted in substantive progress in describing and quantifying RSA. We have designed a hydroponic growth system which retains the three-dimensional RSA of the plant root system,while allowing for aeration,solution replenishment and the imposition of nutrient treatments,as well as high-quality imaging of the root system. The simplicity and flexibility of the system allows for modi fications tailored to the RSA of different crop species and improved throughput. This paper details the recent improvements and innovations in our root growth and imaging system which allows for greater image sensitivity(detection of fine roots and other root details),higher ef ficiency,and a broad array of growing conditions for plants that more closely mimic those found under field conditions.     

Visualization of Toyoura sand-grown plant roots by X-ray computer tomography

Plants establish their root system as a three-dimensional structure, which is then used to explore the soil to absorb resources and provide mechanical anchorage. Simplified two-dimensional growth systems, such as agar plates, have been used to study various aspects of plant root biology. However, it remains challenging to study the more realistic three-dimensional structure and function of roots hidden in opaque soil. Here, we optimized X-ray computer tomography (CT)-based visualization of an intact root system by using Toyoura sand, a standard silica sand used in geotechnology research, as a growth substrate. Distinct X-ray attenuation densities of root tissue and Toyoura sand enabled clear image segmentation of the CT data. Sorghum grew especially vigorously in Toyoura sand and it could be used as a model for analyzing root structure optimization in response to mechanical obstacles. The use of Toyoura sand has the potential to link plant root biology and geotechnology applications.     

The response of Spartium junceum roots to slope: anchorage and gene factors

BACKGROUND AND AIMS: Plant anchorage is governed by complex, finely regulated mechanisms that occur at a morphological, architectural and anatomical level. Spanish broom (Spartium junceum) is a woody plant frequently found on slopes--a condition that affects plant anchorage. This plant grows throughout the Mediterranean area where it plays an important role in preventing landslides. Spanish broom seedlings respond promptly to slope by altering stem and root morphology. The aim of this study was to investigate the mechanisms whereby the root system of Spanish broom seedlings adapts to ensure anchorage to the ground. METHODS: Seedlings were grown in tilted and untilted pots under controlled conditions. The root apparatus was removed at different times of growth and subjected to morphological, biomechanical and molecular analyses. KEY RESULTS: In slope-grown seedlings, changes in root system morphology, pulling strength and chemical lignin content, all features related to plant anchorage in the soil, were related to seedling age. cDNA-AFLP analysis revealed changes in the expression of several genes in root systems of slope-grown plants. BLAST analysis showed that some differentially expressed genes are homologues of genes induced by environmental stresses in other plant species, and/or are involved in the production of strengthening materials. CONCLUSION: Plants use various mechanisms/strategies to respond to slope depending on their developmental stage.     

小麦根系三维形态建模及可视化

作物三维形态建模和可视化技术是数字植物研究的重要组成部分,本文旨在构建基于形态特征参数的小麦根系三维形态模型,并实现小麦根系生长的可视化.基于小麦根系生长的可视化技术框架,首先构建了小麦根轴的三维显示模型,包括根轴生长模型、分枝几何模型和根轴曲线模型;然后结合根系拓扑结构,确定相应的图元,利用根系形态模型输出的形态特征参数,对整个小麦根系进行三维重构;最后基于OpenGL图形平台,综合纹理映射、光照渲染、碰撞检测等真实感处理手段,实现了小麦根系生长的三维可视化表达.结果表明：模型输出的根系真实感较强,能较好地实现不同品种、水分和氮素条件下小麦根系的三维可视化表达.研究结果为进一步建立完整的可视化小麦生长系统奠定了技术基础.     

两种不同根系类型湿地植物的根系生长

实验设计了一个水培系统,利用生活污水培养,对4种“须根型”植物美人蕉、风车草、象草和香根草和4种根茎型植物菖蒲、水鬼蕉、芦苇和水烛的根系生长进行比较研究。该系统由用于盛污水的塑料桶（顶部直径36．5cm,底部直径30．Ocm,高34．5cm）和用于固定植物于水面的泡沫板构成。每桶种植1株植物,每种种5株。水培至10周时,须根型植物的平均根数达到1349条／株,而根茎型植物的平均根数只有549条／株。实验结束（水培第21周）时,须根型植物的平均根生物量为11．3g／株,根茎型植物的平均根生物量为7．4g／株。须根型植物根系中,d〈1mm的细根生物量占根系总生物量的51．9％,而根茎型植物d〈1mm的细根的生物量只占25．1％。根茎型植物的根生物量与地上生物量的比值为0．2,显著高于须根型湿地植物（0．1）。须根型湿地植物的根系表面积（6933cm^2／株）极显著地高于根茎型湿地植物（1897cm^2／株）。根茎型湿地植物根的平均寿命（46．6d）较须根型湿地植物根的平均寿命（34．8d）长。美人蕉的平均根数达1871条／株,根表面积达到22832cm^2／株,远较其他种高。     

The genetic architecture of nodal root number in maize

The maize nodal root system plays a crucial role in the development of the aboveground plant and determines the yield via the uptake of water and nutrients in the field. However, the genetic architecture of the maize nodal root system is not well understood, and it has become the ‘dark matter’ of maize genetics. Here, a large teosinte‐maize population was analyzed, and high‐resolution mapping revealed that 62 out of 133 quantitative trait loci (QTLs), accounting for approximately half of the total genetic variation in nodal root number, were derived from QTLs for flowering time, which was further validated through a transgenic analysis and a genome‐wide association study. However, only 16% of the total genetic variation in nodal root number was derived from QTLs for plant height. These results gave a hint that flowering time played a key role in shaping nodal root number via indirect selection during maize domestication. Our results also supported that more aerial nodal roots and fewer crown roots might be favored in temperate maize, and this root architecture might efficiently improve root‐lodging resistance and the ability to take up deep water and nitrogen under dense planting.     

星毛委陵菜根系构型对草原退化的生态适应

对轻度、中度、重度和极度退化的草原群落中星毛委陵菜(Potentilla acaulis)根系构型参数及相应的土壤水分、容重和硬度等指标进行了分析, 以研究星毛委陵菜根系构型对草原退化的生态适应性。结果表明: 1)在以大针茅(Stipa grandis)为建群种的典型草原中, 随着退化程度的加剧, 星毛委陵菜在群落中的作用逐渐增强, 其根幅、根深、一级垂向根数、分蘖子株数和水平分蘖根长度显著增加; 2)根表面积、二级侧根长度、总根长和根分叉数4个根系构型参数是解释星毛委陵菜根系构型对草原退化生态适应的首选指标, 解释力依次减小, 累计贡献率为92.34%; 3)直径2 mm以下的根系对单株系星毛委陵菜的根表面积和总根长影响显著; 4)阔腰倒锥体三维根系构型是星毛委陵菜适应草原退化并使之成为建群种的优势构型。     

Modelling the interactions between water and nutrient uptake and root growth

A model of three-dimensional root growth has been developed to simulate the interactions between root systems, water and nitrate in the rooting environment. This interactive behaviour was achieved by using an external-supply/internal-demand regulation system for the allocation of endogenous plant resources. Data from pot experiments on lupins heterogeneously supplied with nitrate were used to test and parameterise the model for future simulation work. The model reproduced the experimental results well (R ² = 0.98), simulating both the root proliferation and enhanced nitrate uptake responses of the lupins to differential nitrate supply. These results support the use of the supply/demand regulation system for modelling nitrate uptake by lupins. Further simulation work investigated the local uptake response of lupins when nitrate was supplied to a decreasing fraction of the root system. The model predicted that the nitrate uptake activity of lupin roots will increase as the fraction of root system with access to nitrate decreases, but is limited to an increase of around twice that of a uniformly supplied control. This work is the first example of a modelled root system responding plastically to external nutrient supply. This model will have a broad range of applications in the study of the interactions between root systems and their spatially and temporally heterogeneous environment.     

Neutral red as a probe for confocal laser scanning microscopy studies of plant roots

BACKGROUND AND AIMS: Neutral red (NR), a lipophilic phenazine dye, has been widely used in various biological systems as a vital stain for bright-field microscopy. In its unprotonated form it penetrates the plasma membrane and tonoplast of viable plant cells, then due to protonation it becomes trapped in acidic compartments. The possible applications of NR for confocal laser scanning microscopy (CLSM) studies were examined in various aspects of plant root biology. METHODS: NR was used as a fluorochrome for living roots of Phaseolus vulgaris, Allium cepa, A. porrum and Arabidopsis thaliana (wild-type and transgenic GFP-carrying lines). The tissues were visualized using CLSM. The effect of NR on the integrity of the cytoskeleton and the growth rate of arabidopsis primary roots was analysed to judge potential toxic effects of the dye. KEY RESULTS: The main advantages of the use of NR are related to the fact that NR rapidly penetrates root tissues, has affinity to suberin and lignin, and accumulates in the vacuoles. It is shown that NR is a suitable probe for visualization of proto- and metaxylem elements, Casparian bands in the endodermis, and vacuoles in cells of living roots. The actin cytoskeleton and the microtubule system of the cells, as well as the dynamics of root growth, remain unchanged after short-term application of NR, indicating a relatively low toxicity of this chemical. It was also found that NR is a useful probe for the observation of the internal structures of root nodules and of fungal hyphae in vesicular-arbuscular mycorrhizas. CONCLUSIONS: Ease, low cost and absence of tissue processing make NR a useful probe for structural, developmental and vacuole-biogenetic studies of plant roots with CLSM.     

岷江干旱河谷25种植物一年生植株根系功能性状及相互关系

相同条件下相同生长期的植物根系生长与适应策略及其差异性还不清楚。因此,采集岷江干旱河谷地区25种乡土植物(木本15/草本10种)的种子于2009年3月播种在同一干旱环境中,9月测定了1年生植株的最大根深(RDmax)、根幅(RW)与根生物量(RB),计算了总根长(TRL)、比根长(SRL)及细/粗根生物量比(RBf/c),分析了它们之间的关系,进行了根系功能组划分。结果表明:1)25种植物1年生植株RDmax与RW变异较小,总变异率为14.9%和20.7%;TRL和SRL变异相对较大,分别为28.5%和34.7%,草本植物SRL明显大于木本植物;RB和RBf/c种间变异较大,总变异率分别为50.1%和70.5%;2)25种植物的RDmax、RW、RB和TRL间呈显著正相关关系,表明根系较深的物种RW较大,TRL和RB也较高;SRL与RDmax呈极显著负相关关系,与RBf/c呈极显著正相关关系,表明根系垂直分布较浅的物种细根发达,SRL较大;3)主成分分析显示,25种植物可分为3个功能组:第1组具有较大RDmax、RW和RB,资源利用持续时间较长;第2组具有较大TRL、SRL和RBf/c,资源利用效率较高;第3组根系功能性状没有一致的突出特点,可能通过降低自身生理机能适应生存条件。综合分析表明,岷江干旱河谷区25种植物1年生植株根系的功能性状变异明显,可塑性大,历经长期自然选择压力而形成了不同的环境适应策略,但生长型并不必然表达出1年生植株根系功能性状的差异性。     

Automated image analyses for separating plant roots from soil debris elutrated from soil cores

Historically, destructive root sampling has been labor intensive and requires manual separation of extraneous organic debris recovered along with the hydropneumatic elutriation method of separating plant roots from soils. Quantification of root system demographics by public domain National Institute of Health (NIH-Image) and Root Image Processing Laboratory (RIPL) image processing algorithms has eliminated much of the labor-intensive manual separation. This was accomplished by determining the best length to diameter ratio for each object during image analyses. Objects with a length to diameter ratio less than a given threshold are considered non-root materials and are rejected automatically by computer algorithms. Iterative analyses of length to diameter ratios showed that a 15:1 ratio was best for separating images of maize (Zea mays L.) roots from associated organic debris. Using this threshold ratio for a set of 24 soil cores, a highly significant correlation (r² = 0.89) was obtained between computer image processed total root length per core and actual root length. A linear relationship (r² = 0.80) was observed between root lengths determined by NIH-Image analyses and lengths determined independently by the RIPL imaging system, using the same maize root + debris samples. This correlation demonstrates that computer image processing provides opportunities for comparing root length parameters between different laboratories for samples containing debris.     

Fine root tradeoffs between nitrogen concentration and xylem vessel traits preclude unified whole‐plant resource strategies in Helianthus

Recent work suggests variation in plant growth strategies is governed by a tradeoff in resource acquisition and use, ranging from a rapid resource acquisition strategy to a resource‐conservative strategy. While evidence for this tradeoff has been found in leaves, knowledge of root trait strategies, and whether they reflect adaptive differentiation across environments, is limited. In the greenhouse, we investigated variation in fine root morphology (specific root length and tissue density), chemistry (nitrogen concentration and carbon:nitrogen), and anatomy (root cross‐sectional traits) in populations of 26 Helianthus species and sister Phoebanthus tenuifolius. We also compared root trait variation in this study with leaf trait variation previously reported in a parallel study of these populations. Root traits varied widely and exhibited little phylogenetic signal, suggesting high evolutionary lability. Specific root length and root tissue density were weakly negatively correlated, but neither was associated with root nitrogen, providing little support for a single axis of root trait covariation. Correlations between traits measured in the greenhouse and native site characteristics were generally weak, suggesting a variety of equally viable root trait combinations exist within and across environments. However, high root nitrogen was associated with lower xylem vessel number and cross‐sectional area, suggesting a tradeoff between nutrient investment and water transport capacity. This led to correlations between root and leaf traits that were not always consistent with an acquisition–conservation tradeoff at the whole‐plant level. Given that roots must balance acquisition of water and nutrients with functions like anchorage, exudation, and microbial symbioses, the varied evidence for root trait covariation likely reflects the complexity of interacting selection pressures belowground. Similarly, the lack of evidence for a single acquisition–conservation tradeoff at the whole‐plant level likely reflects the vastly different selection pressures shaping roots and leaves, and the resources they are optimized to obtain.