For the present study, three temperate natural mixed conifer–broadleaf forests were selected in Northeastern China: Changbai Mountain (CBS), Xianrendong (XRD) and Maoershan (MES) (Table 1). In August 2018, we sampled a total of 51 typical species (19 in XRD, 17 in CBS and 15 in MES), which spanned a wide range of fine-root size (Supplementary Table 1). At least three mature trees were chosen for each species in each forest ecosystem. Roots at 0–20 cm soil depth were carefully excavated near the base of the selected trees (Guo et al., 2008; Kong et al., 2014). Root branches with intact terminal branch orders were cut, transported in plastic bags in a cooler to the laboratory, and frozen at −20°C until subsequent morphological and chemical analyses.

In the laboratory, the sampled roots were classified into first- and second-order fine roots. Most distal roots were named first-order fine roots, while roots that contained only first-order fine roots were named second-order fine roots (Pregitzer et al., 2002). Here, the term “fine-root size” was defined as the measured values of root length, diameter and area for individual roots. We used branching intensity and ratio as a measure of root number. Branching intensity was defined as the number of first-order roots per centimeter of second-order roots, and branching ratio was defined as the number of first-order roots per second order root (Comas and Eissenstat, 2009; Kong et al., 2014). Branching intensity and ratio were measured for at least 15 second-order roots per individual tree. The collected roots were scanned with an Epson Expression 10000XL scanner (Seiko Epson Corporation, Japan). Measurements were made on the computer screen by mouse clicking on the displayed images using the measuring tools (length of a straight line and a segmented line) provided by ImageJ 1.47 software (National Institutes of Health, United States). Subsamples of fine roots from each species were cleaned and oven-dried at 60°C for 24 h and ground to a fine powder using a ball mill. Carbon and nitrogen concentrations of fine roots were determined with an elemental analyzer (Vario EL Cube; Elementar, Hanau, Germany).

All analyses were run in R version 4.0.3 (R Core Development Team, 2020). We used the Kruskal-Wallis test (kruskal.test function in the “stats” R package) and Kolmogorov-Smirnov test (ks.test function in the “stats” R package) to examine differences in fine-root length, diameter and area and their frequency distributions among the three sampling sites. Post hoc tests were used for mean values of fine-root traits using Fisher’s least significant difference criterion to explore differences among the three sampling sites when the Kruskal-Wallis chi-squared value was statistically significant (p < 0.05). Kernel density estimates were calculated by weighing the distance of all the data points in each specific location along the distribution (geom_density function in the “ggplot2” R package). The coefficient of variation (CV) and the Gini coefficient (G) (a statistic based on sums of absolute deviations of all observations) have both previously been used to quantify relative size inequality measures of plant traits and populations (He et al., 2005; Zhang and Chen, 2015; Rasmussen and Weiner, 2017). However, the coefficient of variation is more sensitive (less robust) to observations in the right-hand tail of the distribution (Bendel et al., 1989). The Gini coefficient (ranging from zero to one) is a single value that describes a specific degree of evenness, measuring the normalized area between a given Lorenz curve and the perfect evenness line (Weiner and Solbrig, 1984). As an indicator based on Lorenz curves, the Gini coefficient can deepen our insight into the overall degree of size inequality associated with fine-root traits and the relationships between fine-root inequality and distribution pattern (He et al., 2005; Wang et al., 2017). We calculated Gini coefficients with the Lc function in the “ineq” R package and plotted Lorenz curves with the ggplot function in the “gglorenz” R package with the blessing of “ggplot2” R package (Buckley and Damgaard, 2012; Chen and Cortina, 2020). We used phylogenetically controlled mixed-effects kinship models (lmekin function in the “coxme” R package) with random effects of tree species to explore the relationships between fine-root size (root length, diameter and area) and fine-root number (branching intensity and branching ratio). Fine-root trait values were log-transformed before analyses. Moreover, a simple correlation analysis (ggcorr function in the “GGally” R package) with the Spearman method and a principal component analysis using the spectral decomposition approach (princomp function in the “stats” R package) with standardization data were employed to assess the correlations between the fine-root size traits and their inequality. Results from the principal component analysis were visualized graphically using fviz_pca_biplot function in the “factoextra” R package.

In total, 27,573 first-order fine roots from 3848 second-order fine roots across 51 tree species from the three temperate forest ecosystems were collected to assess the distribution and inequality of fine-root size (Supplementary Tables 1, 2). The frequency distributions from the Kolmogorov-Smirnov tests showed marked right-asymmetry for first-order fine-root length, diameter and area for the three forest ecosystems in Northeastern China (Figure 1). The positive skewness indicated that the distributions of first- and second-order fine-root size were right-skewed for almost all species, with a systematic right-hand tail of the distributions (Supplementary Table 2 and Supplementary Figures 1–3). The three forest ecosystems showed a similar frequency distribution pattern in first-order fine-root length, with a unimodal value of about 1.80 mm (Figure 1A). A markedly bimodal frequency distribution of first-order fine-root diameter was observed in MES only, with one peak at about 0.07 mm and a second peak at about 0.14 mm (Figure 1B). The similar unimodal frequency distribution patterns for first-order fine-root area in the three sites were leptokurtic, with the greatest proportion of small first-order fine-roots appearing in CBS (Figure 1C).

There were significant differences in the average length, diameter and area of first-order fine roots among the three forest ecosystems, with the largest roots appearing in XRD and the smallest roots appearing in CBS (Table 2). Fine roots in MES exhibited a higher branching intensity and ratio, while fine roots in XRD showed the lowest branching intensity and ratio (Table 2). Fine roots of the three forest ecosystems had a similar average coefficient of variation (CV) and Gini coefficient (G) of first-order fine-root length and area. However, significant differences in the Gini coefficients of first-order root diameter were detected, with the highest and lowest values being observed in XRD and MES, respectively (Table 2 and Figure 2). Furthermore, large variations in first- and second-order fine-root size were found both within and among species in the three forest ecosystems (Supplementary Tables 1, 2). At the species level, Phellodendron amurense produced the largest first- and second-order roots but had smaller variation and inequality in fine-root size (lower CV and G) and lower branching intensity and ratio within each forest ecosystem (Supplementary Tables 1, 2 and Supplementary Figures 4–6). Sorbaria sorbifolia, Corylus mandshurica and Quercus mongolica had the smaller first- and second-order fine roots but had higher variation and inequality in fine-root size (higher CV and G) (Supplementary Tables 1, 2 and Supplementary Figures 4–6). Ulmus davidiana, C. mandshurica and Ulmus laciniata had the highest branching intensity and ratio across the three forest ecosystems (Supplementary Table 3).

First-order fine-root size showed a consistently linear decline with increasing branching intensity and ratio (Figure 3 and Supplementary Figure 7), although the negative relationship between fine-root diameter and branching ratio was not significant in MES (Supplementary Table 4). First-order fine-root size was strongly positively correlated with the size of second-order roots (Supplementary Figure 8). There were evidently positive correlations among root length, root diameter and root area for both root orders (Supplementary Figure 8). The first two trait axes of the principal component analysis accounted for 42.5 and 15.4% of the total variation, respectively (Figure 4). Branching intensity and ratio and fine-root size-related parameters had high scores on the first axis, while inequality and variation parameters for first-order fine-root diameter and area had high scores on the second axis (Figure 4 and Supplementary Table 5). Additionally, length inequality and variation, nitrogen and carbon content of first-order fine-roots, and specific root length of first- and second-order fine roots had relatively high scores on the third axis (Figure 4 and Supplementary Table 5). Tree species in XRD tended to have higher fine-root size inequality and variation, while those in MES tended to have higher root branching. Fine roots of tree species from CBS scattered on both axes of the principal component analysis (Figure 4).

In support of our asymmetry distribution hypothesis, we observed noticeably right-skewed distributions of fine-root size (length, diameter and area) at the individual level, with a long tail of larger roots, for the three temperate forest ecosystems and for most of the sampled tree species within each ecosystem in Northeastern China. The preponderance of the right-skewed distribution of plant organ size (small fine-roots in this study) is considered a consequence of the left-wall effect, because the sizes of organs must be greater than zero (Jensen and Zwieniecki, 2013). Similar to leaf size, the strongly right-skewed distributions for fine-root size at the community and species level suggest that most species have experienced natural selection favoring effects of relatively small fine-roots. Stated another way, trees that invest in a small number of coarse roots and many fine roots of small diameter may be better adapted for intensive fine-root growth and high fine-root length densities (Eissenstat, 1992). However, we also noted the diverse skewness and kurtosis of fine-root size among tree species in the three forest ecosystems. For instance, fine-root diameter of P. amurense with the negative skewness demonstrated a left-skewed distribution pattern (i.e., many large fine-roots) in both CBS and MES. These findings, similarly to previous studies, suggest that different tree species appear to present contrasting root types (e.g., species with thinner roots versus species with thicker roots) to enhance nutrient acquisitions in temperate and subtropic forest ecosystems (Liu et al., 2015; Chen et al., 2016; Cheng et al., 2016). Generally, the change in fine-root size is strongly related with tree’s mycorrhizal association, such as arbuscular mycorrhizal or ectomycorrhizal (Bergmann et al., 2020). Like some tree species with thick roots in a subtropical forest (Liu et al., 2015), P. amurense in temperate forests producing the largest roots perhaps also relies more on arbuscular mycorrhizal fungi to forage nutrients. Therefore, the integrated consideration of the tree species composition with contrasting specific fine-root and mycorrhizal traits will improve our insights into the skewed distribution of fine-root size across various tree species.

Apart from asymmetry, we found that the unimodal distribution for fine-root size (except for root diameter in MES) was leptokurtic with a narrow peak, reflecting the occurrence of strong environmental filtering in the three temperate forests in Northeastern China. Environmental filtering plays a major role in shaping trait diversity of fine roots in forests, favoring convergence to an optimal trait value (Wang R. et al., 2018). However, a bimodal platykurtic distribution of fine-root diameter was observed in MES, as previously found for other tree and grass species (Boot and Mensink, 1990; Eissenstat, 1991; Bouma et al., 2001; Anderson et al., 2007). Bimodal trait distributions arise when there are multiple optimal trait values, suggesting the co-existence of contrasting functional strategies or the occurrence of stabilizing niche differences among interacting species (Gross et al., 2013; Le Bagousse-Pinguet et al., 2016). The co-occurrence of species with thick roots versus species with thin roots was observed at the species level in MES temperate forest. This fits with our above discussions on the skewed-distribution of fine-root size, implying that the maintenance of large variances in fine-root size is also strongly related to the species diversity of the forest community or ecosystem. Although there is a growing body of literature on ecological implications of fine-root diameter (Fort and Freschet, 2020; Valverde-Barrantes et al., 2020), more research on root diameter distributions is required to judge the prevalence of the bimodality observed in MES and to understand fully the functional significance of the bimodal distribution in other plant species. In conclusion, the important characteristics of the right-skewed distributions at the individual level in fine-root size traits reported here provide a basis for inferences about mechanisms of exploitation and acquisition in resources, and they avoid the loss of information associated with average metrics of root systems.

Our principal component analysis indicated that the second axis associated with fine-root size inequality is likely a critical dimension of the belowground resource uptake strategy in the multidimensional space of fine-root trait variation. Plant responses to environmental changes depend not only on the mean but also on the plasticity and variation of plant traits (Wang et al., 2017; Zhang et al., 2020). Further analyses extending beyond trait means will permit us to explore original relationships among the traits of interest (Russell et al., 2014). 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). In this study, we detected significant differences in the Gini coefficients of fine-root diameter among the three forest ecosystems, with the highest and lowest values occurring in XRD and MES, respectively. Changes in fine-root size inequality have been attributed to alterations in the mode of competition among fine-root individuals, leading to changes in the shape of the root size frequency distribution of fine-root systems (Wang et al., 2017). Some previous studies have underlined the importance of competition effects on size inequality and vice versa (Chu et al., 2009; Rasmussen and Weiner, 2017). Efficient water availability and higher temperature in XRD are expected to favor larger fine roots growing at relatively higher rates (Kong et al., 2014; Ma et al., 2018), to increase the asymmetric competition in resource utilization by larger fine roots. The harsher environments in MES likely lead to generate many smaller fine roots growing at relatively similar rates, promoting relatively size-symmetric competition among fine-root individuals, and therefore, resource utilization is equal or proportionate to fine-root size (Pagès et al., 1993). Consequently, the biotic factors such as competition, abiotic factors such as nutrient availability and their interactions presented potential effects on size inequality of plant community (Boot and Mensink, 1990; Chu et al., 2009). In addition, we only observed significant differences in size inequality for fine-root diameter, which was always less than that for fine-root length or area in the three forest ecosystems. Therefore, the size inequality of fine-root diameter at the individual root level seems to be a better measure of size inequality, because fine-root diameter is more stable and more directly linked to the functioning of fine-root systems than fine-root length and area (Chen et al., 2013; Kong et al., 2014).

In support of our size-number hypothesis, we found that fine-root size was negatively correlated with fine-root number (branching intensity and ratio), indicating a trade-off across the investigated tree species between building fewer fine roots with a relatively large diameter and forming thinner fine roots in a more highly branched fine-root system. The results reported here may represent generalized trade-off strategies for fine-root deployment at the individual root level within temperate tree species. The fine-root size/number trade-off is in line with the various well-known compromises between size and number of other organs in plant bodies, such as leaf size/number and seed size/number trade-offs (Westoby and Wright, 2003; Milla, 2009), and with compromises between size and number of individuals at the population level (Deng et al., 2008). The leafing premium hypothesis states that high branching intensity should be rewarded in natural selection, based on the pattern that most species are small-leaved and the negative relationship between leaf size and number (Kleiman and Aarssen, 2007; Leigh et al., 2017). Just as the arrangement and location of leaves on a branch influence the capture of CO₂ and sunlight, the position and organization of most distal roots within the root system (branching pattern) regulate their various ecological and functional aspects, such as the resource-foraging strategy and intra-branch competition (Bentley et al., 2013; Kong et al., 2014; McCormack et al., 2020). A high root branching intensity may indeed bring about selective advantages, given the preponderance of small fine-roots in most tree species (e.g., the strongly positive right-skewed fine-root size frequency distribution observed in this study). Trees can enhance resource absorption not only by producing thinner roots but also by enhancing root branching intensity to rapidly exploit resource-rich soil patches at low fertility sites (Holdaway et al., 2011; Beidler et al., 2015). The fine-root size/number trade-off is one of the fundamental adaptation strategies of plants to environmental changes, and it may therefore have particularly important implications for understanding root size evolution (López-Bucio et al., 2003; Rich and Michelle, 2013; Kong et al., 2014).

We observed that larger fine-root diameters were associated with longer length of fine roots, which appears to be a simply physical relationship (Tyree and Ewers, 1991; McCormack et al., 2020), while root diameter could also be related to other functions such as storage, aerenchyma, etc., Gu et al. (2014). Longer roots, with a greater potential to absorb resources, should be connected to roots with a larger diameter, which effectively represent larger pipes with a lower resistance to conduct those resources (Kong et al., 2014; McCormack et al., 2020). Similarly, the strong, positive correlations in fine-root diameter between first- and second-order fine roots observed across tree species and within the same tree species demonstrate that relatively large first-order fine roots tend to arise from relatively large second-order roots.

From an anatomical perspective, smaller fine roots have a less suberized and less lignified hypodermis than larger fine roots, characteristics that are associated with higher construction and maintenance costs (Fitter et al., 1991; Pregitzer et al., 1993; Fort and Freschet, 2020). The lower within-root structural investment for smaller fine roots of temperate tree species allows shorter life spans/quicker turnover and greater plasticity in root growth proliferation (Eissenstat, 1991, 1992), conferring them advantages in seasonally more variable environments (such as MES in this study) in terms of temperature, moisture and nutrient supply (Chen et al., 2013). For instance, small roots with a thinner cortical thickness are likely to have less hydraulic resistance to the lateral transport of resources from the root surface to the vascular bundle (Valverde-Barrantes et al., 2020). From an ecological perspective, roots with a high branching intensity (namely small roots) are capable of rapid and extensive proliferation into resource-rich patches in heterogeneous forest soils (Hodge, 2004; Kong et al., 2014). Moreover, our result of intensive root branching also increases the specific root length of the pool of first- and second-order roots, which are presumed to have high respiration rates and high resource uptake activities (Rewald et al., 2011, 2014; McCormack et al., 2015). It has previously been demonstrated that small roots enhance small-scale foraging and nutrient absorption in the arid temperate zone (Chen et al., 2013). Fine-root clusters with more root tips and branching can accommodate greater colonization by mycorrhizal fungi, which in turn improve the nutrient and water absorption capacity of fine-root systems (Comas and Eissenstat, 2009; Ekblad et al., 2016). In addition, branching pattern differences have various effects on the ability of a fine-root system to capture relatively mobile versus immobile soil nutrients (Beidler et al., 2015). A large number of small fine roots are needed to acquire less mobile soil resources rapidly, improving competitive ability (Robinson et al., 1999) but leading to decreases in exploitation efficiency (Berntson, 1994). Radial resistance in fine roots is an important limitation to water and nutrient uptake; therefore, fine roots with a small diameter have a shorter path length for water and nutrient movement to the xylem than large-diameter fine roots (Purushothaman et al., 2013; Wang W. et al., 2018). As a result of selection favoring minimization of transport distances and maximization of exchange surfaces, the formation of very fine roots can be a prime strategy to increase the soil–root exchange surface at a minimal cost (Kong et al., 2017).

In our study, as fine-root length increased the proliferation of root tips decreased, which may be related to the exploitation potential, i.e., the volume of soil exploited per unit volume of fine roots (Chen et al., 2016; McCormack et al., 2020). Compared with small fine roots, large fine roots are more efficient at assimilating diffuse resources through more extensive soil exploration, because low root branching intensity reduces the overlap of depletion zones of neighboring branches and inter-root individual competition (Berntson, 1994; Beidler et al., 2015). Thus, decreased frequency of root tip proliferation events along a length of fine root may be indicative of a more exploratory growth strategy (Beidler et al., 2015). In other words, there is a clear trade-off between the exploitation efficiency and exploitation potential in fine-root systems. Small fine roots in MES will show a high exploitation efficiency (intensive) but low exploitation potential and are associated with a greater specific root length, more root branching and shorter root life span (fast absorption strategy) (Comas and Eissenstat, 2009; Liese et al., 2017). Inversely, large fine roots in XRD will exhibit a high exploitation potential (extensive) but low exploitation efficiency and are associated with lower specific root length, less root branching and longer root life span (slow absorption strategy) (Zadworny and Eissenstat, 2011; Fort and Freschet, 2020). Together with the similar functional associations identified in leaves, the intensive–extensive continuum in fine-root systems is a key feature of trees and should be considered in order to gain a thorough understanding of the belowground ecological strategies of trees, the assembly processes of forest communities, and the functioning of forest ecosystems (Reich, 2014).