The experiment was conducted within the Changbai Mountain Nature Reserve (42° 24′N, 127° 47′E) in Jilin province in northeastern China. The Changbai Mountain Nature Reserve has a temperate, continental climate. In this region winters are long and cold, whereas summers are short and cool. The mean annual and growing season temperatures are approximately 3.5° and 15.0°C, respectively. The highest (20.5°C) and lowest (–16.5°C) monthly mean temperatures occur in August and January, respectively. The mean annual precipitation (1982–2012) is approximately 715 mm, 70–80% of which occurs during the growing season between May and October (Zheng et al., 2017). Rainfall data collected at the Forest Ecosystem Research Station of Changbai Mountain at 738 m a.s.l. show that the precipitation in drought years, such as 1985, 1997, 1999, 2001, and 2003 is about 30% less (715 mm) than the long-term mean annual precipitation in the last 30 years (Figure S1). In addition, the total (wet and dry) nitrogen deposition of Jilin province yearly increases by 13.79 kg N ha⁻¹, which is higher than the national average level (12.89 kg N ha⁻¹ year⁻¹) (Lü and Tian, 2007). F. mandschurica in the mixed mature P. koraiensis forest is the dominant broad-leaf tree species, with the mean canopy height of 24.1 m and diameter at breast height of 69.2 cm. The soil bulk density of this study forest is 0.35 g cm⁻³ at 0–10 cm soil depth and 0.68 g cm⁻³ at 10–20 cm soil depth. The soils classified as Eutric cambisol (FAO classification) are developed from volcanic ash.

In September 2009, six 50 × 50 m plots (three reduced precipitation plots and three control plots) were randomly established in the mixed mature P. koraiensis forest. There was a >20 m buffer strip between any two plots. Thirty percent of the plot area was covered with high-light-transmittance (transparency 95%) polycarbonate V-shaped panels to intercept 30% of the throughfall, or approximate 215 mm year⁻¹. A distance of about 1 m from the V-shaped panels to the ground was maintained to keep normal air flow (Figure S2). Each of these six plots was split into two 25 × 50 m subplots with an iron sheet inserted 50 cm deep into the ground. One subplot received additional nitrogen and the other was simultaneously supplied with the same amount of water. Four treatments with three replicates per treatment were developed: control treatment (CK, ambient rainfall without nitrogen addition), nitrogen addition treatment (N), rainfall reduction treatment (W) and the nitrogen addition combined with rainfall reduction treatment (NW). The applied nitrogen level of 50 kg N ha⁻¹ year⁻¹ was about two times the annual total nitrogen deposition in this area (23 kg N ha⁻¹ year⁻¹) (Lü and Tian, 2007). NH₄NO₃ was diluted in 40 L of water and then sprayed onto the forest floor with a backpack sprayer. The control plots including W treatment plots were sprayed with 40 L of water each month during the entire growing season (May to October) to avoid an effect of the treatments on soil moisture.

In August 2015, after 6 years of nitrogen addition and water reduction, soil cores (5 cm internal diameter by 20 cm depth) were collected at five random locations from each plot. The five soil cores from each plot were pooled into one subsample and placed immediately into coolers containing ice. In the laboratory, all samples were kept at –4°C until processing, which was completed within about 1 week. The living F. mandschurica roots were manually picked from soil samples in Petri dishes using forceps and then washed under running water. The roots were dissected into first- and second-order roots according to the protocols described by Pregitzer et al. (2002). Root branching intensity is measured as the number of first-order roots per centimeter of second-order roots. In all, we obtained 967 and 112 first- and second-order roots, respectively. The collected roots were scanned with an Epson Expression 10000XL scanner. Images were analyzed with WinRhizo (Regent Instruments, Inc., Québec, Canada) to determine the count, length, diameter and area of first- and second-order roots.

Owing to non-normality in the data set, non-parametric tests (kruskal.test function) were chosen to examine the treatment effects. We used a TukeyC test to investigate differences among treatments, followed by a least significant difference post-hoc test when p < 0.05. A Kolmogorov-Smirnov test (ks.test function) was used to test the differences in distribution for first-order root length, diameter, and area among treatments. Simple correlations of first-order root length, diameter and area with branching intensity were determined for each treatment using Pearson correlations (cor function). In addition, we used two-way ANOVAs (aov function) to test the effects of nitrogen addition, water reduction and possible interactions between these treatments for each root trait after log-transforming the variables.

In this study, the term “size” was defined as the measured values of root length, diameter and area for individual first-order roots. We calculated the following two size inequality metrics: Gini coefficient and Lorenz asymmetry coefficient of first-order root length, diameter and area for each treatment. The Gini coefficient is based on the Lorenz curve, which graphically represents a population distribution; a minimum value of zero indicating equal size of all individuals and a maximum value of one indicating maximum inequality within the population (Weiner, 1985; Damgaard and Weiner, 2000; McGown et al., 2015). However, the Gini coefficient does not contain all the information in the Lorenz curve because different Lorenz curves can hold the same Gini coefficient (Weiner and Solbrig, 1984). Thus, the Lorenz asymmetry coefficient is calculated to evaluate whether the observed size inequality is primarily caused by large or small individuals (Damgaard and Weiner, 2000; Magura et al., 2006). When LAC = 1, the Lorenz curve of the population is symmetric; when LAC > 1, most of the size inequality within the population is the result of the largest individuals; when LAC < 1, the size inequality demonstrated within the population is mainly due to a relatively large number of small individuals (Damgaard and Weiner, 2000; Weremijewicz and Janos, 2013). R code developed by Buckley and Damgaard (2012) was used to calculate Gini and Lorenz asymmetry coefficients.

Root diameter is recognized as a key trait in root morphology that can reflect water and nutrient uptake functionality of a root system (Comas and Eissenstat, 2009; Gu et al., 2014). In this study, compared with the CK treatment, the N treatment significantly reduced first-order root diameter, which is in agreement with a study from a F. mandshurica plantation (Wang et al., 2007). Moreover, our previous research conducted in the same sites as this study showed a decreasing average diameter of fine roots at the community level after a 2-year N treatment (Guo et al., 2016). It has been demonstrated that roots with smaller average root diameters tend to have less thickening of exodermal walls than thicker roots and are likely to a exhibit higher nutrient absorptive capacity and have lower construction and maintenance costs (Eissenstat, 1991; Pregitzer et al., 1993). Hence, thinner roots may be more advantageous to tree development, given that trees decrease belowground carbon allocation with increasing nutrient availability (Bae et al., 2015). Furthermore, there is an impressive amount of evidence that root diameter also strongly influences root lifespan (Wells et al., 2002; McCormack et al., 2012). Decreasing diameter (indicating higher turnover) of first-order roots in N treatment plots, together with their lower decomposition rates (Fan and Guo, 2010; Goebel et al., 2011), may imply a greater accumulation of F. mandschurica root necromass with increasing nitrogen deposition in the experimental temperate forest (Clemmensen et al., 2013).

Trees can enhance root resource absorption not only by producing thinner roots but also by enhancing root length and branching intensity to rapidly exploit resource-rich soil patches, a behavior that has been observed for a number of plant species (Ostonen et al., 2007; Kong et al., 2014). We found that the combination of increased nitrogen with reduced rainfall (NW) significantly enhanced first-order root length, a variable that was not influenced by nitrogen addition (N) or rainfall reduction (W) treatments applied separately (Table 1). It is reasonable to speculate that the larger first-order root area in NW treatment plots is primarily caused by longer length rather than by larger diameter. Therefore, under lower water and higher nitrogen availability conditions, F. mandschurica in the mixed mature P. koraiensis forest can increase root surface area to increase the volume of soil explored by producing longer roots that have a larger specific root area. Among functional traits, water and nutrient absorption per unit root mass increase with specific root area if area-related absorption rates remain unchanged (Tyree et al., 1998). This result is consistent with results for Picea abies L., P. sylvestris L., and Betula pendula Roth in a previous study, where the specific root area of mycorrhizal roots (namely first-order roots) increased with site fertility along a broad latitudinal gradient (Ostonen et al., 2007).

Root branching intensity, defined as the number of first-order roots per centimeter of second-order roots, is also a key trait governing the volume of soil explored and thus may affect nutrient acquisition (Comas and Eissenstat, 2009; Kong et al., 2014). In this study, we did not observe effects of nitrogen addition (N), rainfall reduction (W), or their combination (NW) on branching intensity of F. mandschurica compared with CK. However, the NW treatment evidently had negative effects on branching intensity in comparison with the W treatment (Table 1). The different response patterns of fine roots to nitrogen between ambient and reduced water availability suggest that water availability may play an important role in mediating tree root system responses to increased nitrogen availability in the mixed forest. Soil mineral nitrogen is dissolved in the soil solution, and the presence of water affects soil mineral nitrogen mobility and loss (Harpole et al., 2007). Such an interaction may be important in natural forest ecosystems, such as the mixed mature P. koraiensis forest, where fine roots are often subject to multiple covarying resources. Thus, our results suggest that studies of the effects of nitrogen deposition on fine root traits should take into account potential changes in precipitation regime (Harpole et al., 2007; White et al., 2007).

Size inequality of individuals exists in most plant populations, and the associated inequality of plant functional traits may have substantial ecological implications (Metsaranta and Lieffers, 2008; Forde, 2009). The variation in first-order root length, diameter and area within a fine root system can be considered a strategy to reduce ecological niche overlap (e.g., root lifespan overlap) and therefore competition between individual roots, resulting in exploration of a greater volume of soil (Pagès et al., 1993; Nadelhoffer, 2000; Pregitzer et al., 2002). This idea can be summarized: plants don't put all their eggs in one basket (Forde, 2009). One approach for achieving this outcome may be through the generation of differentiations in fine root architecture, morphology and/or vertical distribution among individual plants (Bennett et al., 2002; Forde, 2009).

Traditionally, variations in plant quantitative traits have been described and analyzed using the statistical standard deviation and skewness coefficient. In 1984, the Gini coefficient, widely applied in economics, was first introduced in plant ecology to estimate the inequality distribution (Weiner and Solbrig, 1984). Our results of different Gini coefficients clearly demonstrated distinct responses of size inequality of first-order root length, diameter and area and of branching intensity among different treatments (Table 2). Nitrogen addition treatments increased the size inequality (higher Gini coefficients) of F. mandschurica first-order root length, diameter and area compared with the CK treatment (Table 2), a response similarly observed in a previous study of P. contorta Loudon (Lieffers and Titus, 1989). However, the responses in size inequality of root traits to soil nitrogen availability may be modified by interactions with other environmental variables, such as soil water condition (Table 2). The results reported here suggest that the nitrogen–water interaction has a striking effect on the frequency distribution of first-order root length and area (Figures 1A, C), characterized by a lower branching intensity (Table 1) and a lower Gini coefficient of first-order root length in NW treatment plots (Table 2). The increasing degree of uniformity in first-order root length, as reflected by decreasing inequality (lower Gini coefficient; Table 2), indicates that F. mandschurica might enhance the development of shorter roots to make root length more uniform under the combination of greater nitrogen and water availability. Thus, our observations that the responses of roots to the multifactor treatment differed from simple combinations of single-factor responses further indicate a non-additive effect of nitrogen addition and water induced on size inequality of tree fine roots (Niu et al., 2009). In addition, we found that the Gini coefficients of first-order diameter and branching intensity were always less than those of first-order length and area in all treatment plots (Table 2), together with a stable first-order diameter and branching intensity in all treatments (Figure 1D), meaning that root diameter and branching could be characterized as more stable than root length and area (Chen et al., 2013; Kong et al., 2014). Therefore, roots might adapt to changes in soil nitrogen or water through variation (Gini coefficient) of root diameter at individual level (Table 2) while maintaining invariable mean values at the population level (Table 1).

As one of the metrics that describes the shape of the size distribution, the Lorenz asymmetry coefficient is sensitive to minor changes in size distributions and may therefore be helpful in identifying changes in various fine root systems of forest ecosystems. After 6 years of water and nitrogen management, the Lorenz asymmetry coefficient of first-order root diameter in NW treatment plots (1.16) was higher than that in CK treatment plots (0.91; Table 2). The result of a Lorenz asymmetry coefficient of more than one suggests that the first-order roots of F. mandschurica exhibit a greater degree of asymmetry (higher Gini coefficient), with a greater proportion of thicker first-order roots in NW treatment plots than in CK treatment plots (Figure 1A). However, the discrepancies in first-order root diameter between NW and CK treatment plots were not observed based on statistic average values of first-order root diameter (Table 1). Thus, the ecological interpretations of patterns of fine root responses to soil environmental changes should include the inequality of root traits by considering the Gini coefficient and Lorenz asymmetry coefficient.

Moreover, there is a large body of studies focused on the effects of individual interactions, such as competition, on size distributions, which indicates that changes in size inequality may often be attributed to an alteration in the competition mode during different root development stages (He et al., 2005; Chu et al., 2009; Forde, 2009; McGown et al., 2015). Competitive interactions between root individuals can be placed along a continuum from completely size-symmetric competition (resource utilization is equal or proportionate to root size) to completely size asymmetric competition (resource utilization is dominated by larger roots) (Schwinning and Weiner, 1998). In general, size asymmetric competition occurs in shoot competition within plants for light. For instance, leaves located at the top of the tree canopy can pre-empt the utilization of light energy by leaves lower in the tree canopy (Schenk, 2006). Size asymmetric root competition involves nutrient and water assimilation (Rewald and Leuschner, 2009). It has been hypothesized that in heterogeneous soils, such as this experimental field (Wang et al., 2010; Xu et al., 2010) the chance of encountering and using soil resource patches may increase nonlinearly with root system size, potentially causing size asymmetric root competition (Schwinning and Weiner, 1998). In this work, we observed larger average values of first-order root length (Table 1) and a higher frequency distribution of longer first-order root length (Figure 1A) in NW treatment plots, where asymmetric competition may occur because of improved chances of acquiring resources conferred by the longer roots (Schenk, 2006). In turn, first-order root length can be expected to increase with increasing branching intensity when competition is asymmetric (NW treatment), whereas first-order length should decrease with increasing branching intensity when competition is symmetric, such as in the CK, N, and W treatment plots (Figure 1D).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.