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.     

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.     

阿拉善高原2种荒漠植物根系构型及生态适应性特征

根系构型决定了植物对资源的吸收方式,根系构型的变化是植物对环境的生态适应和有效生存策略。在阿拉善高原西南缘红砂（Reaumuria soongarica）-珍珠猪毛菜（Salsola passerina）混生群落采用传统挖掘法收集两种植物根系,基于量化的根系形态指标,利用几何拓扑学及分形理论分析了根系构型特征,探讨了该地区2种植物对干旱生境的生态适应策略。结果表明：红砂和珍珠猪毛菜根系均以水平分布占优,根系浅层化分布明显,混生的两种植物占据不同的生态位;2种荒漠植物均具有较大的比根长（SRL）和比表面积（SRA）,红砂SRL=21.3 cm/g,SRA=7.6 cm²/g,珍珠SRL=22.4 cm/g,SRA=6.5 cm²/g,有利于水分和养分的获取;红砂根系拓扑指数（TI）、修正拓扑参数（q_a和q_b）分别为0.86、0.52、0.49,珍珠猪毛菜对应参数分别为0.93、0.76、0.73,表明2种植物根系均趋向于鱼尾形分支结构;根系分形维数值（FD_红=1.488、FD_珍=1.422）较小,而分形丰度值（lgK_红=1.855、lgK_珍=1.774）较大,表明2种植物分支相对简单,但空间拓展能力强,有利于对营养空间的占有。上述特征可能是阿拉善西南缘红砂-珍珠猪毛菜群落2种荒漠植物植物对干旱贫瘠生境的重要生态适应策略。     

不同林龄胡杨克隆繁殖根系分布特征及其构型

以中龄林和成熟林胡杨为研究对象,采用挖剖面和根窗的方法,研究胡杨繁殖根系分布、根系构型,以及胡杨根蘖与繁殖根系构型之间的关系。结果表明:(1)细根(d<2 mm)的根长密度、根表面积密度,随深度增加呈现指数函数分布;(2)中龄林细根的根长密度、根表面积密度在0—90 cm各层都是显著大于成熟林的对应指标(P<0.05),成熟林的中等粗根(5 mm0.05),且两种林龄的一级侧根数、分枝角度亦无显著差异(P>0.05);(5)对比两种林龄不同根序上的根蘖芽发现,二级根上不定芽个数均是同组一级根上不定芽个数的3—4倍;基于以上对胡杨根系的功能权衡的分析,得出:细根对胡杨根系构型有重要的影响,在胡杨根系功能权衡中扮演重要角色。     

河西走廊中部两种荒漠植物根系构型特征

在河西走廊中部,采用挖掘法挖取红砂和白刺根系,应用拓扑学与分形理论分析了根系构型的特征.结果表明: 2种荒漠植物根系的拓扑指数均较小,根系分支模式均近似为叉状分支结构.红砂和白刺根系具有较好的分形特征,其分形维数分别为(1.18±0.04)和(1.36±0.06);分形维数、分形丰度与根系平均连接长度均呈显著正相关.2种荒漠植物根系的平均连接长度均较大,以扩大植物的有效营养空间,从而适应干旱贫瘠的土壤环境.2种荒漠植物根系分支前的横截面积等于根系分支后的横截面积之和,验证了Leonardo da Vinci法则.对17个根系构型参数进行主成分分析,根系拓扑指数、根系连接数量、逐步分支率和根系直径4个根系构型参数能很好地表示2种荒漠植物根系构型特征.     

Plant light interception can be explained via computed tomography scanning: demonstration with pyramidal cedar (Thuja occidentalis, Fastigiata)

BACKGROUND AND AIMS: Light interception by the leaf canopy is a key aspect of plant photosynthesis, which helps mitigate the greenhouse effect via atmospheric CO(2) recycling. The relationship between plant light interception and leaf area was traditionally modelled with the Beer-Lambert law, until the spatial distribution of leaves was incorporated through the fractal dimension of leafless plant structure photographed from the side allowing maximum appearance of branches and petioles. However, photographs of leafless plants are two-dimensional projections of three-dimensional structures, and sampled plants were cut at the stem base before leaf blades were detached manually, so canopy development could not be followed for individual plants. Therefore, a new measurement and modelling approach were developed to explain plant light interception more completely and precisely, based on appropriate processing of computed tomography (CT) scanning data collected for developing canopies. METHODS: Three-dimensional images of canopies were constructed from CT scanning data. Leaf volumes (LV) were evaluated from complete canopy images, and fractal dimensions (FD) were estimated from skeletonized leafless images. The experimental plant species is pyramidal cedar (Thuja occidentalis, Fastigiata). KEY RESULTS: The three-dimensional version of the Beer-Lambert law based on FD alone provided a much better explanation of plant light interception (R(2) = 0.858) than those using the product LV*FD (0.589) or LV alone (0.548). While values of all three regressors were found to increase over time, FD in the Beer-Lambert law followed the increase in light interception the most closely. The delayed increase of LV reflected the appearance of new leaves only after branches had lengthened and ramified. CONCLUSIONS: The very strong correlation obtained with FD demonstrates that CT scanning data contain fundamental information about the canopy architecture geometry. The model can be used to identify crops and plantation trees with improved light interception and productivity.     

小麦根系特征对干旱胁迫的响应

干旱胁迫时, 小麦(Triticum aestivum)根系率先产生应激响应, 同时向地上部发出信号, 诱导地上部发生生理反应, 从而提高植株抗旱能力。根系构型包括平面几何性状和立体几何结构(即拓扑构型), 具有遗传稳定性和可塑性。干旱胁迫影响根系理化特性, 如根源化学信号、根系细胞酶类和根系渗透作用的响应。根系通过调整其解剖学结构和水分吸收动力等来适应干旱胁迫。该文从根系构型、理化特性和解剖学结构3个方面, 系统阐述了小麦根系特征对干旱胁迫的响应, 并探讨了其与干旱胁迫的关系和当前研究中存在的问题, 以期为相关研究提供参考。     

小麦根系特征对干旱胁迫的响应

干旱胁迫时, 小麦(Triticum aestivum)根系率先产生应激响应, 同时向地上部发出信号, 诱导地上部发生生理反应, 从而提高植株抗旱能力。根系构型包括平面几何性状和立体几何结构(即拓扑构型), 具有遗传稳定性和可塑性。干旱胁迫影响根系理化特性, 如根源化学信号、根系细胞酶类和根系渗透作用的响应。根系通过调整其解剖学结构和水分吸收动力等来适应干旱胁迫。该文从根系构型、理化特性和解剖学结构3个方面, 系统阐述了小麦根系特征对干旱胁迫的响应, 并探讨了其与干旱胁迫的关系和当前研究中存在的问题, 以期为相关研究提供参考。     

干旱对杉木幼苗根系构型及非结构性碳水化合物的影响

通过比较不同时期不同强度干旱胁迫下杉木1年生盆栽苗地上部分生长、根系构型以及根系中非结构性碳水化合物含量（TNC）的变化,并分析各指标之间的相关性,探究杉木根系在干旱胁迫下的适应性策略以及抗旱生理机制,以期为杉木造林生产和水分管理提供科学依据和技术指导。结果表明：随着干旱程度的加强,杉木幼苗地上部分干重（SDW）、根干重（RDW）、根长（RL）、根表面积（SA）、根体积（RV）、根尖数（RT）、根系分支角度（Angle）、分形维数（FD）逐渐减小,根冠比（R/T）逐渐增大,根系拓扑指数（TI）、根系平均直径（RD）先增大后减小,比根长（SRL）先减小后增大。而根系连接长度（LL）、TNC、糖淀比在不同时期表现出不同的趋势。连接长度随着干旱胁迫的加强在30 d和60 d时表现出逐渐增加趋势而在90 d时则表现出先减小后增大的趋势。TNC在30 d和60 d时先增大后减小,但90 d时,呈逐渐下降的趋势。糖淀比随着干旱胁迫的加强在30 d和60 d时表现出先增加后减小趋势,90 d时,表现为先减小后增大。干旱胁迫显著影响根系在不同径级的分布长度,且随着胁迫时间的延长不断变化。杉木地上部分生长与根系生长指标（RL、SA、RV、RT、RDW）以及根系构型指标（Angle、FD）之间存在显著的正相关（P < 0.01）,根系平均直径与TNC存在显著的正相关（P < 0.05）。总之,杉木通过增加根系光合产物的积累、提高根系建成成本,增加有限成本下根系的复杂程度和延伸范围,降低根系分支角度,使根系"更陡更深"来适应不同强度的干旱胁迫。     

典型黑土区主要树种根系构型特征及其对固土能力的影响

为量化典型黑土区主要树种根系构型特征,探究其对固土能力的影响,以该区分布较广的榆叶梅、小叶锦鸡儿、白桦、糖槭、红皮云杉、樟子松单株个体为研究对象,采用全根挖掘和WinRHIZO Pro LA2004分析系统相结合对其根系空间分布、几何形态、分形等特征进行测定,同时采用原位整株根系拉拔的方法量化根系垂直拉拔力.结果表明:...     

A density-based approach for the modelling of root architecture: application to Maritime pine (Pinus pinaster Ait.) root systems

Root morphology influences strongly plant/soil interactions. However, the complexity of root architecture is a major barrier when analysing many phenomena, e.g. anchorage, water or nutrient uptake. Therefore, we have developed a new approach for the representation and modelling of root architecture based on branching density. A general root branching density in a space of finite dimension was used and enabled us to consider various morphological properties. A root system model was then constructed which minimizes the difference between measured and simulated root systems, expressed with functions which map root density in the soil. The model was tested in 2D using data from Maritime pine Pinus pinaster Ait. structural roots as input. We showed that simulated and real root systems had similar root distributions in terms of radial distance, depth, branching angle and branching order. These results indicate that general density functions are not only a powerful basis for constructing models of architecture, but can also be used to represent such structures when considering root/soil interaction. These models are particularly useful in that they provide a local morphological characterization which is aggregated in a given unit of soil volume.     

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。     

Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.     

A method to separate plant roots from soil and analyze root surface area

Analysis of the effects of soil management practices on crop production requires knowledge of these effects on plant roots. Much time is required to wash plant roots from soil and separate the living plant roots from organic debris and previous years’ roots. We developed a root washer that can accommodate relatively large soil samples for washing. The root washer has a rotary design and will accommodate up to 24 samples (100 mm diam. by 240 mm long) at one time. We used a flat-bed scanner to digitize an image of the roots from each sample and used a grid system with commercially-available image analysis software to analyze each sample for root surface area. Sensitivity analysis and subsequent comparisons of ‘dirty’ samples containing the roots and all the organic debris contained in the sample and ‘clean’ samples where the organic debris was manually removed from each sample showed that up to 15% of the projected image could be coveredwith debris without affecting accuracy and precision of root surface area measurements. Samples containing a large amount of debris may need to be partitioned into more than one scanning tray to allow accurate measurements of the root surface area. Sample processing time was reduced from 20 h, when hand separation of roots from debris was used, to about 0.5 h, when analyzing the image from an uncleaned sample. The method minimizes the need for preprocessing steps such as dying the roots to get better image contrast for image analysis. Some information, such as root length, root diameter classes and root weights, is not obtained when using this technique. Root length measurements, if needed, could be made by hand on the digital images. Root weight measurement would require sample cleaning and the advantage of less processing time per sample with this method would be lost. The significance of the tradeoff between information not obtained using this technique and the ability to process a greater number of samples with the time and personnel resources available must be determined by the individual researcher and research objectives.     

Genotypic variation in seedling root architectural traits and implications for drought adaptation in wheat (Triticum aestivum L.)

Root system characteristics are of fundamental importance to soil exploration and below-ground resource acquisition. Root architectural traits determine the in situ space-filling properties of a root system or root architecture. The growth angle of root axes is a principal component of root system architecture that has been strongly associated with acquisition efficiency in many crop species. The aims of this study were to examine the extent of genotypic variability for the growth angle and number of seminal roots in 27 current Australian and 3 CIMMYT wheat (Triticum aestivum L.) genotypes, and to quantify using fractal analysis the root system architecture of a subset of wheat genotypes contrasting in drought tolerance and seminal root characteristics. The growth angle and number of seminal roots showed significant genotypic variation among the wheat genotypes with values ranging from 36 to 56 (degrees) and 3 to 5 (plant⁻¹), respectively. Cluster analysis of wheat genotypes based on similarity in their seminal root characteristics resulted in four groups. The group composition reflected to some extent the genetic background and environmental adaptation of genotypes. Wheat cultivars grown widely in the Mediterranean environments of southern and western Australia generally had wider growth angle and lower number of seminal axes. In contrast, cultivars with superior performance on deep clay soils in the northern cropping region, such as SeriM82, Baxter, Babax, and Dharwar Dry exhibited a narrower angle of seminal axes. The wheat genotypes also showed significant variation in fractal dimension (D). The D values calculated for the individual segments of each root system suggested that, compared to the standard cultivar Hartog, the drought-tolerant genotypes adapted to the northern region tended to distribute relatively more roots in the soil volume directly underneath the plant. These findings suggest that wheat root system architecture is closely linked to the angle of seminal root axes at the seedling stage. The implications of genotypic variation in the seminal root characteristics and fractal dimension for specific adaptation to drought environment types are discussed with emphasis on the possible exploitation of root architectural traits in breeding for improved wheat cultivars for water-limited environments.     

Development and validation of a model to describe root length density of maize from root counts on soil profiles

Root length density (RLD) is an important determinant of crop water and nutrient acquisition, but is difficult to measure in the field. On a soil profile, in-situ counts of root impacts per unit surface on soil profiles (NI) can be used to calculate RLD if crop-specific parameters for preferential root orientation (anisotropy) are known. An improved method for field determinations of RLD was developed and validated for maize at sites in Côte d'Ivoire and Burkina Faso. Root anisotropy was measured with cubes of undisturbed soil with 0.1 m sidelength, based on NI observed on three planes oriented perpendicularly to each other. RLD was also measured for the enclosed volume. Repetition of such measurements enabled estimation of the robustness across sites of empirical and geometric models for the relationship between RLD and NI:RLD = NI CO, with CO being the coefficient of root orientation, theoretically equals 2 for an isotropic distribution. Root systems were found to be nearly isotropic, except near the root front (0.3 to 0.5 m), where roots had a preferentially orthotropic orientation. Measured RLD was generally about 50% larger than RLD calculated from observed NI and CO, indicating that at least one of the measurement techniques had a systematic error. The ratio between measured and calculated RLD (CE), which ranged from 0.8 to 2, increased with the age of the plants and decreased with soil depth. CE was therefore introduced as an additional coefficient, resulting in RLD = NI CO CE. The empirical value for CO CE was between 2 and 5. The empirical coefficients CO and CE were the same for the sites in Cote d'Ivoire (oxisol with an iron pan at 0.6 to 0.9 m) and Burkina Faso (alfisol with an iron pan at 0.4 to 0.8 m). The model was validated with independent data sets at both sites, and gave satisfactory predictions of RLD on the basis of NI obtained from single soil planes, which can be easily measured in the field.