Optimizing soil-coring strategies to quantify root-length-density distribution in field-grown maize: virtual coring trials using 3-D root architecture models

Abstract

Background and Aims

Root distribution has a major influence on soil exploration and nutrient and water acquisition by plants. Soil coring is a well-known way to estimate root distribution. However, identifying an optimal core-sampling strategy is important if one is to strike the right balance between the high cost of making field estimates of root length density (RLD) vs. the need for accurate estimates. Virtual assessment of competing soil-coring strategies, based on three-dimensional (3-D) models of root system architecture (RSA), is a highly effective way to find that balance.

Methods

The trajectories of the axile roots of two maize cultivars having contrasting axile root angles were measured in the field using in situ 3-D digitization. Lateral roots were also measured by recording topological and geometrical parameters. Based on the measurement dataset obtained, contrasting 3-D RSA models of individual maize plants were constructed in which the different lateral rooting angles were represented. Using these RSA models the accuracies of various core-sampling strategies for estimating RLD were assessed in a series of virtual experiments.

Key Results

Substantial biases occur if a one-core sampling strategy is used to estimate RLD. The biases largely remain for two-core sampling, although a weighting method can reduce these. However, given that identification of an optimal weighting method is difficult in practice, a new sampling strategy is proposed based on an area-weighting algorithm. In this way low deviations in RLD estimation can be achieved by sampling between rows and also by using larger-diameter (7.5 or 10 cm) cores.

Conclusions

A 3-D root architecture model based on a detailed measurement dataset provides an ideal platform for assessing a range of soil-coring strategies. The improved two-core sampling strategy, based on an area-weighting algorithm, shows considerable promise as a cost-efficient way of obtaining good quality RLD estimates for maize.

INTRODUCTION

Root system architecture (RSA) plays a pivotal role in a plant’s water and nutrient acquisition and thus greatly affects both crop growth and harvest yield (Fitter, 1987; Lynch, 1995; Danjon and Reubens, 2008). The acquisition efficiency of a root system for water and nutrients is strongly affected by the spatial distribution of roots in the soil. Root length density (root length per unit of soil volume, RLD, cm cm^–3) is a very well-known indicator characterizing root distribution in the soil (Waisel et al., 2002), and it is also an important parameter required for several computer simulation models, such as soil water and solute transport/uptake models (Jones et al., 1984; Simunek et al., 1998; Heinen et al., 2003; Pagès et al., 2012). Due to both the complexity and the opaqueness of a soil medium, the study of RLD distribution is difficult. Common methods for quantifying root distribution include both global and local measurement methods. Monolith sampling is a typical global measurement method and it can deliver reliable information for root biomass and also for RLD distribution (Kumar et al., 1993; Gajri et al., 1994; Buczko et al., 2009). However, this global method is utterly destructive and also extremely consumptive of time and thus labour costs. Local measurement methods include auger and core sampling (Chassot et al., 2001; Sharratt and McWilliams, 2005), root mapping (Pagès and Pellerin, 1996) and minirhizotrons (Liedgens and Richner, 2001). Of these, core sampling is the most widely used method for estimating RLD distribution due to its convenience (Bohm, 1979; Kücke et al., 1995; Machado et al., 2003).

Research has shown core sample numbers, sample positions and sample sizes all have strong influences on the variance of the resulting RLD estimates (Rossi and Nuutinen, 2004). Substantial errors can be introduced by an over-simplistic sampling strategy (Van Noordwijk et al., 1985; Kumar et al., 1993; Gajri et al., 1994). Therefore, identifying an optimal core-sampling strategy is very important if one is to make a reasonably accurate estimate of RLD distribution (Van Noordwijk et al., 1985; Bengough et al., 2000; Smit et al., 2000). In general, the sample variance of RLD estimates decreases as the numbers of core samples taken increases (Wiesler and Horst, 1994; Sharratt and McWilliams, 2005). However, taking a large number of cores can involve an unacceptable investment in time and labour cost (Buczko et al., 2009). This limitation is especially pertinent in situations where large numbers of plots must be sampled, for example in a breeding programme. To optimize sampling positions in geometrically regular plantings (i.e. individual plants are evenly spaced and in distinct rows), various strategies are used. These include: (1) sampling at points midway within rows and midway between rows (Van Noordwijk et al., 1985; Kuchenbuch and Barber, 1987; Dwyer et al., 1996; Sharratt and McWilliams, 2005); (2) sampling at different points between rows (Gajri et al., 1994; Ball-Coelho et al., 1998); and (3) sampling at the base of roots (Amato and Ritchie, 2002; Wasson et al., 2014). For example, Gajri et al. (1994) show for maize with a row spacing of 60 cm, and for wheat with a row spacing of 22 cm, the best point for one-core sampling is at the point one-third of the distance from the root base to the midline between rows. Meanwhile, Kumar et al. (1993) report for wheat with a row spacing of 22 cm that RLD is best approximated by taking the average from two core samplings, one from the midpoint within the row and the other from the midline between rows. Buczko et al. (2009), for maize with a row spacing of 75 cm, used a 1: 3 weighting proportion for two-core sampling (one at the midpoint within rows and the other at the midpoint between rows) to estimate RLD. Their results indicate the bias in their RLD estimates is low. Different core sizes have also been used (Kumar et al., 1993; Samson and Sinclair, 1994; Gajri et al., 1994; Kücke et al., 1995; Oikeh et al., 1999; Amato and Ritchie, 2002). Kumar et al. (1993) compared 5-, 7.5- and 10-cm-diameter cores and show that 7.5- and 10-cm-diameter cores give better estimates of the RLD profile than do 5-cm diameter cores.

Although several studies have tried to optimize the core sampling strategy, no consistent conclusion has emerged. This is partly because of defects in the assessment methods. Usually, the field assessment of different core-sampling strategies has been carried out in different plots. Here, contradictory results may occur due to soil variability between plots (Levillain et al., 2011). Soil heterogeneity is well known to introduce substantial variations in root distribution. Thus, ideally, assessment of alternative core-sampling strategies compares plants within a plot where differences in the soil are likely to be least (Hertel and Leuschner, 2002; Ping et al., 2010; Levillain et al., 2011). However, this ideal is impractical because of the destructiveness of core sampling coupled with the collateral disturbance created by sampling.

Three-dimensional (3-D) root models have been developed to quantify the growth and development of RSA (Diggle, 1988; Pagès et al., 1989; Lynch et al., 1997). These 3-D models have also been used to simulate root functional properties such as water and nutrient uptake (Dunbabin et al., 2013; Postma et al., 2014; York et al., 2016). Virtual assessment based on 3-D RSA modelling has great value in the optimization of core-sampling strategies (Miguel et al., 2015). The prerequisite for valid virtual assessment is to build a reliable 3-D RSA model. Because field measurements of RSA are inadequate, the parameters used in RSA models are based mostly on empirical growth rules, or are obtained from measurements made on seedlings in the laboratory. More recently, 3-D RSA models have been constructed based on field datasets (J. Wu et al., 2013, 2015; Wu and Guo, 2014; Q. Wu et al., 2016), which do realistically represent the RSA of individual maize plants.

Maize is one of the world’s most important food crops. The root systems of maize are composed of a range of different root types with different root orders. The root architecture of a field-grown maize plant is relatively complete at tasselling and it has a considerable influence on reproductive growth and yield. The RSA model of Wu and Guo (2014) and J. Wu et al. (2013, 2015) is based on field datasets and provides an ideal platform for assessing various core-sampling strategies for field-grown maize. The objectives of this study were: (1) based on these field datasets, to reconstruct 3-D root models of individual maize plants having different RSAs and to characterize their RLD distributions; and then (2) to assess the accuracies of different core-sampling strategies for RLD estimation.

MATERIALS AND METHODS

Field experiments

Field experiments were conducted in 2011 and 2012 at the Shangzhuang Experimental Station (40°8′N, 116°10′E) of China Agricultural University. The soil type is an aquic cambisol with a sandy clay loam texture (FAO). Maize hybrids ZD958 and XY335 were used. Since 2004, these two cultivars have been planted over the largest areas in China because of their high yields. The axile roots of XY335 are relatively wide and shallow, while those of ZD958 are relatively narrow and deep (J. Wu et al., 2015) (Fig. 1). In the present trial, there were two block replications (each block 16 × 6.5 m) for each test. ZD958 was sown on 15 May 2011 and XY335 was sown on 5 May 2012. The seed was sown in north–south-orientated rows with inter-row and intra-row spacings of 60 and 30 cm, respectively. Based on local practice for maize, a base fertilizer of 120 kg P₂O₅ ha⁻¹ (as superphosphate) and 100 kg K₂O ha⁻¹ (as potassium sulphate) was spread before sowing. A total of 120 kg N ha⁻¹ was applied to each cultivar; 30 % of total N (as urea) was spread as a topdressing at the four-leaf stage and 70 % of total N (also as urea) was spread at the 11-leaf stage.

Fig. 1.

The reconstructed three-dimensional root system architecture models for individual maize plants at the grain-filling stage of two cultivars, ZD958 and XY335, with contrasting axile root angles. The spatial architecture of axile roots was reconstructed using digitized data for the axile roots. The lateral root architecture was reconstructed by matching the scanned data of lateral roots of ZD958 onto the axile roots of both cultivars. Acute and obtuse lateral root angles were set in the reconstruction in which lateral roots with acute angles having a strong preference for the vertical direction and that with obtuse angles having a strong preference for the horizontal direction. Red, yellow and green segments are first-, secondary- and tertiary-order lateral roots, respectively.

The axile roots (i.e. the main axes of primary, seminal and nodal roots) form the skeleton of a maize root system. To quantify the spatial architecture of field-grown maize, the axile roots of individual maize plants were digitized, starting on 1 September 2011 for ZD958 and on 26 August 2012 for XY335. Two groups (two neighbouring plants in the same row in each group) were selected for each cultivar. A 3Space Fastrak digitizer (Polhemus, Colchester, VT, USA) was used to record the 3-D coordinates of the trajectory of the axile roots. The roots were sampled after digitizing, and each axile root was then scanned using a flat-bed scanner (ScanMaker i800 Plus, Microtek, China) at a resolution of 300 dpi. The proprietary software WinRHIZO Pro 2009b (Régent Instruments Inc., Canada) was used to analyse the scanned root images. Software based on the Visual Basic Application (VBA) language embedded in Microsoft Excel^TM was used to estimate diameter variation along individual axile roots.

To sample individual root systems while retaining relatively complete topological connections between the axile and lateral roots, a custom-made root-core sampling system (Wu and Guo, 2014) was used 77 d after sowing. This extracted the intact root systems of individual adult plants. Two root systems of ZD958 were sampled. The soil in the root system was washed out using a group of fine water jets, and each nodal root (i.e. the shoot-borne crown and brace roots) was dissected out from the exposed root system. There were 55–70 nodal roots for each root system excavated. The branching zone of the axile root for each of the selected nodal roots was cut into 5-cm sections. All laterals in the 5-cm sections were scanned using the flatbed scanner at a resolution of 400 dpi. WinRHIZO Pro software was used to analyse the scanned root images. A program based on VBA was used to batch the files to obtain the topological connections and geometrical data of individual lateral root units (Wu and Guo, 2014; J. Wu et al., 2015). Further detailed information on root measurement is given in the Supplementary Data.

Reconstruction of RSA models of individual plants

To build the RSA model of an individual field-grown maize plant, the spatial deployment of each axile root was reconstructed using the 3-D coordinates of the digitized points (J. Wu et al., 2015). This was smoothed using 3-D cardinal spline interpolation and the geometry was built up using measured diameters of sequential 5-cm sections of the axile root. Next, the measured topological and geometrical information for the lateral roots of the selected nodal roots (source) of ZD958 was matched onto the reconstructed axile root (target) of ZD958 and XY335. The selection criteria for the source nodal root was the closeness of unbranched-zone-diameter to the target nodal root. Acute and obtuse lateral root angles (Supplementary Data Table S1) were set in the 3-D reconstruction of individual root systems for the two cultivars (XY335-Acute and XY335-Obtuse, ZD958-Acute and ZD958-Obtuse), in which lateral roots with acute angles have a strong preference to grow vertically downwards while those with obtuse angles have a strong preference to grow horizontally outwards. Detailed information on lateral root matching is given in Table S1. Visualization of individual RSA models was realized using ParaView software (www.paraview.org). On this basis, individual RSA models with contrasting axile and lateral root angles were built for the two maize cultivars (Fig. 1). A total of 16 RSA models of individual maize plants were constructed based on the digitized axile roots of four plants for each maize cultivar (4 plants × 2 cultivars × 2 lateral root angles).

The reconstructed RSA models are assumed to represent the intact, isolated root systems of 16 individual maize plants. To mimic the interaction of neighbouring root systems in the field, with the RSA models, a cuboid soil column was generated to contain most of the root system of an individual plant and also some of the roots of neighbouring plants. The lateral boundaries of the cuboid were delineated by the midlines between and within the rows and the depth (50 cm) was the maximum depth of the root system, based on actual measurements. For any roots extending beyond the lateral boundaries of the cuboid, the roots were assumed to re-enter the unit from the opposite side to mimic neighbouring interactions (Sinoquet et al., 1991).

Sampling strategies assessed in the virtual experiments

One-core and two-core sampling strategies are commonly used to quantify RLD for maize (Supplementary Data Table S2). To assess the one-core sampling strategy based on the RSA models, we compared five different sampling positions (Fig. 2A). These were: (I) the positions centred at the midpoint between two neighbouring plants in a row, (II) the midpoint between two inter-row neighbouring plants, (III) the point 5 cm from the root base in the inter-row direction, (IV) the point 10 cm from the root base in the inter-row direction and (V) the point 15 cm from the root base in the inter-row direction. Three core diameters (5, 7.5 and 10 cm) were used for each of the five sampling positions. To assess the two-core sampling strategy, only the sample positions in the inter-row direction were considered for the convenience of field operation. Initial assessment of the one-core sampling strategy indicates that RLD was overestimated for the sample position close to the plant (Position III) while it was greatly underestimated for the sample position distant from the plant (Position II), so position III was chosen to represent high RLD soil volume and position V was chosen to represent low RLD soil volume. Different weighting proportions (1: 2, 1: 4, 1: 6, 1: 8 and 1: 10) were applied for the two-core sampling strategy (position III: V) to further improve the precision of its RLD estimate (Van Noordwijk et al., 1985; Buczko et al., 2009). RLD was calculated as (RLD_III×a+RLD_V×b)/(a + b), where a and b are the weighting proportions.

Fig. 2.

Diagrammatic representation of different core sampling strategies used in the virtual assessment for estimation of root length density of maize. Solid circles indicate the bases of individual root systems. Solid line circles indicate the sampling positions using a 5-cm-diameter core. (A) The sampling positions used for the one-core sampling strategy: position I indicates the midpoint between two neighbouring plants in a row, position II indicates the midpoint between two neighbouring plants between rows, and positions III, IV and V indicate the points 5, 10 and 15 cm away from the root base, respectively, in the inter-row direction. (B) The positions used in the sampling strategy based on an area-weighting algorithm. Circles with different line types indicate the outer and inner diameters of different circular rings.

Initial assessments indicated significant deviations occurred when using either the one-core or the two-core sampling strategy for RLD estimation of maize. Although deviations could be reduced in the two-core sampling by using weighting proportions, it was still difficult to determine the appropriate weighting proportion. Therefore, we propose a new sampling strategy for RLD estimation.

The horizontal plane of a maize plot is assumed to be made of identical rectangular units (of length and width equal to the inter-row and the intra-row distances, respectively), with each occupied by a single maize plant. RLD can then be computed by dividing the total root length of an individual plant by the space occupied by the plant. This procedure is analogous to the calculation of leaf area index (Sinoquet et al., 1991). Previous research indicates there are no significant differences in RLD distribution in different horizontal directions for an individual maize plant (Chopart and Siband, 1999; J. Wu et al., 2015). Assuming an isotropic root distribution, a number of concentric circles were delineated around the plant and core sampling was conducted only in the inter-row direction (Fig. 2B). For the ith annulus with outer radius R_i and inner radius R_i–1, a core was sampled at distance (R_i–1+R_i)/2 from the root base to represent the average RLD (RLD_i) in this toroid (its volume being determined by the dimensions of the annulus and the clipping depth). The total root length of the ith rectangular toroid for a soil horizon with a thickness Δh can be calculated as the product of RLD_i and the volume of this toroid $\left(\pi \times \left(R_i^2-R_{i-1}^2\right)\times \Delta h\times RL{D}_i\right)$. Core sampling was conducted in successive annuli with the first inner circle (R₀) reaching the plant base and the outermost circle (R_n) reaching the inter-row midline. The total root length of a maize plant in the soil horizon is then computed. As all the roots of an isolated maize plant in a defined soil horizon were sampled, as in the RSA model, the intersection with neighbouring root systems was mimicked by the re-entrance of roots exiting the lateral boundaries. The RLD (cm cm^–3) of this horizon can be calculated as:

$$RL{D}_{esti}=({\displaystyle \sum \pi \times (R_i^2-R_{i-1}^2)\text{}\times RL{D}_i)/L\times W(i=1\cdots n)}$$ (1)

where L is the inter-row distance and W is the intra-row distance. As the thickness of the soil horizon was eliminated and RLD was computed by the area weighting (AW) factor of the annulus and the measured RLDs in eqn (1), the proposed strategy is referred to as the AW strategy.

Virtual experiments to assess different sampling strategies

In previous studies estimating RLD profiles using core sampling, different clipping steps for soil depth were used (Kumar et al., 1993; Samson and Sinclair, 1994; Dwyer et al., 1996; Oikeh et al., 1999). We first conducted an initial assessment to determine the appropriate clipping step for virtual core sampling. Different clipping steps (1, 2, 4, 5, 8 and 10 cm) were used to quantify the vertical profiles of total root length (Supplementary Data, Fig. S1). The results indicate that using 1-, 2-, 4- and 5-cm clipping steps can achieve relatively high accuracy estimates of root length profiles. To best balance workload against required accuracy, we used a 5-cm clipping step in the following analysis.

Before conducting assessment of different core sampling strategies with the individual RSA models, we compared the RLD distribution over different soil depths of individual maize plants to check the assumption of isotropic RLD distribution. Virtual core-samplings were conducted at eight different orientations starting from due north and moving clockwise in eight steps of 45°, we also did this at four distances from the root base, 5, 10, 15 and 20 cm and we used a 10-cm-diameter core. The isolated individual RSA models were used for this virtual assessment.

Based on the RSA models of individual maize plants and considering the effects of neighbouring root systems, we estimated RLD using both the one-core and the two-core sampling strategies (Fig. 2A). For the proposed AW strategy, three sample positions were chosen according to inter-row distance. The first sampling position was close to the root base, the third was close to the midline between neighbouring rows and the second was half way between the outer circle of the first annulus and the inner circle of the third annulus (Supplementary Data, Fig. S2A–C). Two-core sampling positions were proposed further for the AW strategy. The first sampling position was close to the root base and the second was half way between the outer circle of the first annulus and the midline between neighbouring rows (Fig. S2D–F). Core diameters of 5, 7.5 and 10 cm were used for each sampling scheme. In total, six sampling schemes were set up in the virtual assessment for the AW strategy (Table 1).

Table 1.

Six sampling schemes for assessing core sampling strategy based on an area-weighting algorithm

Sampling scheme	Core diameter (cm)	Position 1 (cm)	Position 2 (cm)	Position 3 (cm)	R 1 (cm)	R 2 (cm)	R 3 (cm)
1	10	5	15	25	10	20	30
2	7.5	3.75	15	26.25	7.5	22.5	30
3	5	2.5	15	27.5	5	25	30
4	10	5	20	–	10	30	–
5	7.5	3.75	18.75	–	7.5	30	–
6	5	2.5	17.5	–	5	30	–

For the different sampling schemes, sample positions measured from the root base to the midline between neighbouring rows are indicated as Positions 1, 2 and 3. The radii of successive circles are indicated R₁, R₂ and R₃. Three core diameters were used, 5, 7.5 and 10 cm.

The estimated RLD was compared with the reference values of RLD (RLD_refe). RLD_refe of a given soil horizon was calculated by summing the lengths of all root segments of an individual root system within the space defined by the intra- and inter-row distances and the thickness of the soil horizon. In the reconstruction of individual RSA models, each root (axile and different-order laterals) was built up with successive 1-mm-long segments which could be referenced by the 3-D coordinates of their centre points. To estimate the total root length in the sampled cores, the root system was searched to locate root segments with their centre positions in the core volume and their lengths were summed. For different sampling strategies, the bias of RLD estimation (RLD_esti) for each soil horizon was computed as (Van Noordwijk et al., 1985; Kumar et al., 1993; Buczko et al., 2009):

$$Bias=100\times \left|RL{D}_{\text{esti}-}RL{D}_{\text{refe}}\right|/RL{D}_{\text{refe}}$$ (2)

Statistical analyses

The R software (R Development Core Team, 2014) was used for data analysis in which the ggplot2 package (http://ggplot2.org/) was used for data visualization. The dataset of root architecture measurement is available on the public repository https://doi.org/10.6084/m9.figshare.4836890.v5, and is presented in a standard format (RSML) (Lobet et al., 2015).

RESULTS

Vertical distribution of RLD for individual plants

Based on the reconstructed RSA models, the vertical profiles of RLD of individual maize plants were quantified for the four different RSAs (Fig. 3). With increasing soil depth, RLD first increased and then decreased for XY335-Acute, ZD958-Obtuse and ZD958-Acute and the RLD peaked at a depth of 5–10 cm. In contrast, for XY335-Obtuse, RLD decreased with soil depth after a shallow peak in the top 5 cm of soil. For the four RSA types, roots in the depth range 0–10 cm represented 51–67 % of the total root length in the 0–50 cm soil profile, those in the depth range 10–20 cm represented 22–33 % and those in the depth range 20–30 cm represented 8–14 %. For a specific maize cultivar, root length in the top 5-cm soil layer was significantly higher for plants with obtuse lateral angles than those with acute lateral angles. In contrast, root length in the depth range 10–30 cm was significantly lower for plants with obtuse lateral angles than for those with acute lateral angles. Compared with ZD958 and regardless of lateral angle differences, the total root length of XY335 was significantly greater in the top 5 cm but lower at depths below 10 cm.

Fig. 3.

The vertical profiles of root length density (RLD) for individual maize plants having different root-system architectures. For more detail, refer to Fig. 1. Obtuse lateral root angle, red solid circle; acute lateral root angle, green open circle. Significant differences between maize plants with contrasting axile and lateral angles were assessed by standard t-tests.

Horizontal distribution of RLD for individual plants

The horizontal RLD distribution around individual maize plants was computed. With increasing horizontal distance from the root base (0–30 cm), RLD decreased from a maximum of 30–35 cm cm⁻³ (root base) to less than 0.5 cm cm⁻³ (20 cm from the root base) (Fig. 4). The pattern of change in RLD at different depths varied with increasing horizontal distance from the root base but also with other factors. For the 0–10 cm soil depth, RLD decreased very rapidly with increasing distance. For the 10–15 cm soil depth, RLD for plants with acute lateral angles decreased rapidly with increasing distance, while for those with obtuse lateral angles it decreased more slowly. For the 15–30 cm soil depth, RLD first increased slightly with increasing distance but then decreased. For soil depths below 30 cm, RLD was low (<0.5 cm cm⁻³). Overall, the rate of decrease in RLD with increasing horizontal distance from the root base was greater for ZD958 than for XY335.

Fig. 4.

Horizontal distribution of root length density (RLD) at different soil depths for individual maize plants of two cultivars (XY335 and ZD958) with different root system architectures. Only RLDs larger than 0.1 cm² are shown. The y-axis scale is logarithmically transformed. For more detail, refer to Fig. 1.

The distribution of RLD of individual maize plants over different soil depths was computed (Fig. 5). Virtual core sampling was also conducted at eight regular orientations (45° apart) at four different distances from the root base using a 10-cm-diameter core, based on the individual root models with different RSAs (16 individual plants) (Fig. 6). No significant differences were found between the RLD profiles in the various orientations (P > 0.05). This supports our earlier assumption of an isotropic RLD distribution, with horizontal orientation.

Fig. 5.

The distribution of root length density (RLD) at different soil depth horizons (2.5–7.5, 12.5–17.5 and 22.5–27.5 cm) of individual maize plants. The RLDs were derived from four different root system architecture models (for more detail, refer to Fig. 1). The effects of neighbouring root systems are considered. The intra-row spacing is 30 cm and the inter-row spacing is 60 cm. The colours map the log transformed RLD values in the legend.

Fig. 6.

Root length density (RLD) distributions at eight different horizontal orientation starting spaced 45° apart from north clockwise (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°) around individual maize plants with different root system architectures (for more detail, refer to Fig. 1). Pairwise Wilcoxon rank sum test was used for comparing means.

Estimation of RLD using the one-core sampling strategy

Based on the reconstructed 3-D RSA models of individual maize plants, the vertical profiles of RLD were estimated using the one-core sampling strategy at the five positions with a 10-cm-diameter core (Table 2).

Table 2.

Mean bias (%) of root length density estimation for 0–50 cm soil depth using a one-core sampling strategy with a 10-cm-diameter core

Sampling position	XY335		ZD958		Mean ± s.d.
	Obtuse	Acute	Obtuse	Acute
I	66	45	53	50	54 ± 9
II	99	99	93	96	97 ± 3
III	303	449	369	475	400 ± 78
IV	96	85	59	50	73 ± 22
V	41	73	60	75	63 ± 16

Sampling position I indicates the midpoint between two neighbouring plants in a row, position II indicates the midpoint between two neighbouring plants between rows, and positions III, IV and V indicate the points 5, 10 and 15 cm away from the root base, respectively, in the inter-row direction. The virtual assessment was made based on the individual root system architecture models of two maize cultivars (XY335 and ZD958) having contrasting axile and lateral root angles (Acute and Obtuse).

Cores sampled at positions midway between plants within rows (I), midway between rows (II) and 15 cm from the root base between rows (V) all greatly underestimated RLD. Mean bias for the full depth 0–50 cm were 54 ± 9 % (I), 97 ± 3 % (II) and 63 ± 16 % (V) (Table 2, Supplementary Data Fig. S3). Meanwhile, the cores sampled at 5 cm (III) and 10 cm (IV) from the root base between rows greatly overestimated RLD. These had mean biases of 400 ± 78 % (III) and 73 ± 22 % (IV). Deviations were observed for the peak position of estimated RLD profiles using the one-core sampling strategy, except for position III (Fig. S3). Using 5- or 7.5-cm-diameter cores, instead of 10 cm, gave broadly similar results (Table S3).

Estimation of RLD using the two-core sampling strategy

Recognizing that RLD was greatly underestimated using the one-core sampling strategy for sampling positions I, II and V but overestimated for positions III and IV, the two core-sampling positions were selected from the above two sets, with the aim of reducing the deviations in RLD estimates. The core-sampling at positions III and V was combined to estimate RLD. The mean RLD for two-core sampling overestimated RLD with a mean bias of 168 ± 32 % (Table 3). Therefore, different weightings were applied to the two-core sampling results to reduce the estimation bias. The mean biases for the full 0–50 cm depth range were 91 ± 16, 30 ± 4, 8 ± 4, 13 ± 4 and 21 ± 7 % using the weightings 1: 2, 1: 4, 1: 6, 1: 8 and 1: 10, respectively (Table 3). No deviations were found for the peak position of the RLD profile estimates using the two-core sampling strategy (data not shown). Again, using 5- and 7.5-cm-diameter cores yielded broadly similar results (Supplementary Data Table S4).

Table 3.

Mean bias (%) of root length density estimation for 0–50 cm soil depth using a two-core sampling strategy (positions III and V) with different weighting proportions

Weighting proportion	XY335		ZD958		Mean ± s.d.
	Obtuse	Acute	Obtuse	Acute
1 : 1	130	188	154	200	168 ± 32
1 : 2	73	100	82	108	91 ± 16
1 : 4	27	31	25	34	30 ± 4
1 : 6	11	10	4	4	8 ± 4
1 : 8	8	16	12	14	13 ± 4
1 : 10	13	25	21	25	21 ± 7

Virtual assessment was made based on root system architecture models of individual maize plants for two cultivars (XY335 and ZD958) with contrasting axile and lateral angles (Acute and Obtuse) and using a 10-cm-diameter core.

Estimation of RLD using the sampling strategy based on the AW algorithm

The proposed AW sampling strategy was applied for the estimation of RLD (Table 4). When sampling three cores in the inter-row orientation using 10-, 7.5- and 5-cm-diameter cores (Schemes 1, 2 and 3), the mean biases of the RLD estimates from the reference RLD for the full 0–50 cm soil profile were 15 ± 4, 13 ± 7 and 38 ± 5 %, respectively. When using two-core sampling in the inter-row orientation with 10-, 7.5- or 5-cm-diameter cores (Schemes 4, 5 and 6), the mean biases for the full 0–50 cm soil profile were 16 ± 4, 17 ± 3 and 46 ± 7 %, respectively. Therefore, relatively low deviations in RLD estimation can be achieved by sampling two cores between rows and also by using larger-diameter (7.5- and 10-cm) cores. No deviations were observed in the peak position for estimated RLD profiles using the AW sampling strategy (data not shown).

Table 4.

Mean bias (%) of root length density estimation for the 0–50 cm soil depth using the sampling strategy based on area-weighting algorithm

Sampling scheme	Core diameter (cm)	Sampling number	XY335		ZD958		Mean ± s.d.
			Obtuse	Acute	Obtuse	Acute
1	10	3	13	19	10	16	15 ± 4
2	7.5	3	15	22	8	8	13 ± 7
3	5	3	37	45	33	35	38 ± 5
4	10	2	19	20	12	12	16 ± 4
5	7.5	2	20	19	15	13	17 ± 3
6	5	2	52	50	42	41	46 ± 7

The virtual assessment was conducted based on root system architecture models of individual maize plants of two cultivars (XY335 and ZD958) with contrasting axile and lateral angles (Acute and Obtuse). Different sampling schemes are determined by sampling number, position and core diameter (for further details refer to Table 1).

DISCUSSION

This study describes a range of virtual experiments carried out to assess several alternative core-sampling strategies that various researchers have used to estimate RLD. The study was based on 3-D root models of actual maize plants of contrasting RSAs. The results show substantial deviations between sample estimates of RLD and actual RLD. Deviations were particularly large for the one-core sampling strategy. Although the two-core sampling strategy gained some improvement, the deviations were still too large in many cases. In contrast, much more satisfactory results were obtained using the proposed new two-core sampling strategy based on an AW algorithm, in which core sampling was conducted only in the inter-row direction using larger-diameter (7.5- or 10-cm) cores. The new two-core sampling strategy shows considerable promise as a cost-efficient way of obtaining good-quality RLD estimates for maize.

RSA modelling and RLD distribution estimation

The spatial distribution of roots of an individual maize plant is defined both by the axile roots, which form the skeleton of the root system, and by the lateral roots, which comprise the major part of the root system. The spatial configuration of the axile roots of each RSA model was reconstructed using 3-D coordinates collected by field digitization (J. Wu et al., 2015). The architecture of the lateral roots associated with the axile roots was also reconstructed from field measurements (Wu and Guo, 2014). The resulting RSA models were thus faithful to the actual root architecture of particular mature maize plants in the field. Two cultivars were used in the virtual experiments, XY335 whose root system is relatively wide and shallow, and ZD958 whose root system is relatively narrow and deep. The growth trajectory of lateral roots is highly susceptible to the soil environment (soil structure, soil fertility, soil water content, soil temperature, etc.) (Hodge, 2004, 2006; Croft et al., 2012; Füllner et al., 2012). Two substantially different lateral angles (obtuse vs. acute) were used here in the root model reconstruction. Therefore, the root models cover a wide spectrum of root architecture variation – essential for assessing a range of core-sampling strategies for use in the field.

Relatively high RLDs were observed in the topsoil (0–10 cm) with the individual RSA models. This confirms the field observations of others (Chassot et al., 2001; Kuchenbuch et al., 2009; Peng et al., 2012). In our virtual study, a maximal soil depth of 50 cm was used. Our own field observations have shown that most roots are distributed in the 0–50 cm soil layer. Maximal root system depths have previously been reported as 50–90 cm (Dwyer et al., 1996; Oikeh et al., 1999; Amato and Ritchie, 2002; Gao et al., 2010). It is known that maximal root system depth is affected by factors such as soil fertility (Chassot et al., 2001), precipitation and tillage (Sharratt and McWilliams, 2005), soil structure (Amato and Ritchie, 2002) and soil temperature (Füllner et al., 2012). The relatively shallow root distribution in this study is probably the result of readily availability water through the season with irrigation in the early growth stages and good summer rainfall in the main growth stage.

The RLD distribution of the different RSA models varied both vertically and horizontally. RLD decreased with horizontal distance from the root base and also with soil depth (Fig. 4). The spatial variability of RLD in the upper soil layers was substantially larger than in the deeper layers (Fig. 5). Similar phenomena have been observed by others (Bengough et al., 2000; Yu et al., 2007). There was no preferred orientation of RLD distribution in individual plants (Fig. 6), which agrees with previous studies (Chopart and Siband, 1999) and supports the underlying assumption in our study of isotropic RLD distribution upon which the proposed AW sampling strategy is based.

Virtual assessment of core sampling strategies

Generally, the accuracy of core sampling for the estimation of RLD increases with core-sample number (Buczko et al., 2009). However, the higher the number of core samples the greater the investment in time and cost. Researchers must always balance the need for measurement accuracy with the limitations in available finance/time (Ping et al., 2010; Levillain et al., 2011). Our assessments show that RLD estimation bias was very large when using a one-core sample strategy (Table 2). Therefore, we infer that using a one-core sampling strategy is not a good option for estimating RLD profiles for maize in the field.

Large biases in RLD estimations for two-core sampling strategies have also been reported (Buczko et al., 2009). This has led researchers to used various weighting proportions for the two core-samples to reduce deviation (Van Noordwijk et al., 1985; Buczko et al., 2009). Buczko et al. (2009) found a lower variance was obtained using 1: 3 weighting for within-row vs. between-row cores. Our assessment results indicate locating sampling cores at the midway point within rows or at the midway point between rows (Fig. 2) both resulted in substantial underestimations of RLD (Table 2 and Supplementary Data Fig. S3). Therefore, deviations may still not be reduced to an acceptable level by using weighting proportions for the two cores. Based on the assessment results of the one-core sampling strategy, two positions were selected for using the two-core sampling strategy with different weighting proportions. The results show that RLD estimation bias can be dramatically reduced by using the weighting proportions 1: 6 or 1: 8. RLD estimation bias was also relatively low using the weighting proportions 1: 4 or 1: 10 (Table 3). This study indicates the accuracy of RLD estimation using a two-core sampling strategy depends largely on the selection of weighting proportions. RLD was high in the soil volume close to the plant and much lower in the soil volume distant from the plant (Figs 1 and 4). As the soil volume with lower RLD was much larger, it is plausible the RLD estimation bias was reduced when using relatively low weighting proportions. It is likely the optimal weighting proportion varies for row crops having different row and plant spacings. Optimal weighting factors can only be determined for row crops when detailed information on root distribution is available (Van Noordwijk et al., 1985). However, this is not realistic in most situations. Therefore, we conclude that using a two-core sampling strategy for RLD estimation based on optimal weighting factors is not always feasible in a real-world situation.

Because of the serious drawbacks of one-core and two-core sampling strategies, we propose a new core-sampling strategy based on an AW algorithm. The proposed AW algorithm is based on an assumption of isotropic root distribution. This assumption finds support in previous research (Chopart and Siband, 1999; J. Wu et al., 2015). With this, the assessment results show the bias in the RLD estimation was still large when using small-diameter cores (5 cm) (Table 4), but that it can be substantially reduced by using larger-diameter cores (7.5 or 10 cm). The failure with small-diameter cores was probably a result of a too-small sampling volume, which fails to satisfactorily represent the average RLD of the corresponding rectangular toroid. Sampling three cores between rows using larger-diameter cores (10 or 7.5 cm) gave a satisfactory accuracy for the RLD estimates (Table 4). Also, the accuracy of the RLD estimate remained satisfactory when using the improved two-core sampling strategy, based on the AW algorithm. The proposed new sampling strategy is very promising for estimating RLD distribution in field-grown maize and other crops. Nevertheless, further field measurements and model simulations are required to confirm and further improve this sampling strategy for various RSAs, including for tap root systems and for different development stages of RSA.

The planting density used in the field and virtual trials (56 000 plants ha⁻¹) is close to that commonly used for the two maize cultivars (Chen et al., 2013; Niu et al., 2013). High planting density is used increasingly with modern maize cultivars for high grain yield (Sangoi et al., 2002). Accordingly, the effectiveness of the isotropic root distribution assumption for individual plants growing under high planting density conditions as well as for other soil conditions (e.g. different soil types) requires evaluation in further research.

SUPPLEMENTARY DATA

Supplementary data are available online at www.aob.oxfordjournals.org and consist of the following. Detailed information on root measurement and lateral root matching. Table S1: Parameters used in the ViRoot software for the 3-D architecture reconstruction of lateral roots of individual maize plants. Table S2: Sampling strategies and core diameters used by other researchers to estimate root length density profile. Table S3: Mean bias of root length density estimation of the 0–50 cm soil depth using the one-core sampling strategy with 5- and 7.5-cm-diameter cores. Table S4: Mean bias of root length density estimation in the 0–50 cm soil profile using the two-core sampling strategy with different weighting proportions. Fig. S1: Vertical profiles of estimated total root length per unit depth of soil layer with different clipping depths. Fig. S2: Schematic diagram of the sampling schemes used in the assessment of the sampling strategy based on the area-weighting algorithm. Fig. S3: Vertical profiles of root length density estimated using a one-core sampling strategy with a 10-cm-diameter core at five different positions.