Isometric scaling of above- and below-ground biomass at the individual and community levels in the understorey of a sub-tropical forest

Abstract

Background and Aims Empirical studies and allometric partitioning (AP) theory indicate that plant above-ground biomass (M_A) scales, on average, one-to-one (isometrically) with below-ground biomass (M_R) at the level of individual trees and at the level of entire forest communities. However, the ability of the AP theory to predict the biomass allocation patterns of understorey plants has not been established because most previous empirical tests have focused on canopy tree species or very large shrubs.

Methods In order to test the AP theory further, 1586 understorey sub-tropical forest plants from 30 sites in south-east China were harvested and examined. The numerical values of the scaling exponents and normalization constants (i.e. slopes and y-intercepts, respectively) of log–log linear M_A vs. M_R relationships were determined for all individual plants, for each site, across the entire data set, and for data sorted into a total of 19 sub-sets of forest types and successional stages. Similar comparisons of M_A/M_R were also made.

Key Results The data revealed that the mean M_A/M_R of understorey plants was 2·44 and 1·57 across all 1586 plants and for all communities, respectively, and M_A scaled nearly isometrically with respect to M_R, with scaling exponents of 1·01 for all individual plants and 0·99 for all communities. The scaling exponents did not differ significantly among different forest types or successional stages, but the normalization constants did, and were positively correlated with M_A/M_R and negatively correlated with scaling exponents across all 1586 plants.

Conclusions The results support the AP theory’s prediction that M_A scales nearly one-to-one with M_R (i.e. M_A ∝ M_R ^≈1·0) and that plant biomass partitioning for individual plants and at the community level share a strikingly similar pattern, at least for the understorey plants examined in this study. Furthermore, variation in environmental conditions appears to affect the numerical values of normalization constants, but not the scaling exponents of the M_A vs. M_R relationship. This feature of the results suggests that plant size is the primary driver of the M_A vs. M_R biomass allocation pattern for understorey plants in sub-tropical forests.

INTRODUCTION

The relationship between above- and below-ground plant biomass (M_A and M_R, respectively) is of considerable interest to researchers attempting to model global climate change and nutrient cycles as well as those interested in evolutionary organographic relationships across taxonomically and ecologically diverse species (e.g. Niinemets, 1998; Reich et al., 1998; Poorter, 2001; Binkley et al., 2004; Hui and Jackson, 2006; Mokany et al., 2006; Niklas, 2006; Yang et al., 2010). Two methods are commonly used to analyse the M_A vs. M_R biomass allocation pattern (McCarthy and Enquist, 2007; Poorter et al., 2012). The first is derived from the allometric partitioning (AP) theory (Enquist and Niklas, 2002; Niklas, 2004, 2005, 2006), which is based on the metabolic scaling theory of West et al. (1997, 1999). This theory predicts that, for an individual plant under ideal conditions, the M_A vs. M_R biomass allocation pattern will conform to the equation

$$M_{\text{A}}=\beta {\text{M}}_{\text{R}}^{\alpha }$$ (1A)

where β is the normalization constant and α is the scaling exponent. When log-transformed this equation takes the form

$$\log M_{\text{A}}=\log \beta +\alpha \log {\text{M}}_{\text{R}}$$ (1B)

Under ideal conditions, the AP theory predicts that α = 1·0. This isometric prediction is linked to a series of other biomass and metabolic scaling relationships based on the constraints of maximizing photosynthetic capacity and nutrient transport, while minimizing hydrodynamic resistance and transport times (Enquist and Niklas, 2002). For example, stem biomass (M_S) is predicted to scale proportionately with M_R and leaf biomass (M_L) such that α ≈ 1·0 for very small non-woody plants and α ≈ 3/4 for larger plants (e.g. Niklas, 2005, 2006). Indeed, among the various predictions of the AP theory, the isometric scaling relationship between M_A and M_R is perhaps the most frequently presented and tested (e.g. Enquist and Niklas, 2002; Niklas and Enquist, 2002; Niklas, 2004, 2005, 2006).

The AP theory also predicts an isometric M_A and M_R scaling relationship at the community level (Cheng and Niklas, 2007; Yang et al., 2010; Yang and Luo, 2011), which has been tested primarily using data compiled by Cannell (1982) (e.g. Enquist and Niklas, 2002; Niklas, 2005), which primarily pertain to forest tree species. This bias in life form raises concerns because it is possible that arborescent species allocate biomass differently from non-arborescent species, particularly either those lacking wood or those producing small amounts of secondary tissues (Niklas, 2004, 2005, 2006). An additional concern is that the data used to analyse the scaling of individual plants are typically computed by dividing total stand biomass by stand density, which can bias the interpretation of biomass allocations patterns (e.g. Niklas, 2004; McCarthy and Enquist, 2007). Thus, direct measurements at the level of the individual (as well as at the community level) are sparse, but vital for testing the predictions of the AP theory, particularly for understorey plant species which often experience different ambient abiotic conditions compared with coexisting canopy species.

The scarcity of data from understorey species is particularly important because the AP theory considers plant size to be the main driver of biomass allocation patterns (e.g. Enquist and Niklas, 2002). Yet, as noted, the growth and physiological characteristics of understorey plants might differ from those of canopy trees because of size-dependent aspects of biomechanics, resource availability and life history (e.g. Yoda, 1974; Thomas, 1996; Henry and Aarssen, 1999). For example, plant height is reported to scale nearly isometrically with diameter for understorey species and achieve a scaling exponent converging on a 2/3 power function of diameter for canopy trees (Niklas, 1995; Osunkoya et al., 2007).

The second method used to analyse biomass allocation patterns is to calculate M_A/M_R (or M_R/M_A). This parameter is known to be influenced by environmental factors, plant size, competition and a variety of other features (Brouwer, 1962; Poorter, 2001; Poorter et al., 2012). Perhaps for this reason, it is frequently used in optimal partitioning (OP) theory, which predicts that plants will reallocate more biomass to organs that acquire the resource that limits growth the most (Thornley, 1972; Bloom et al., 1985; Shipley and Meziane, 2002). For example, according to OP theory, M_A/M_R is predicted to decrease if growth is limited by soil nutrients, whereas it should increase if growth is limited by light (e.g. Davidson, 1969; Hunt and Burnett, 1973; Poorter et al., 2012).

The predictions of the AP and OP theories are not mutually exclusive, particularly since much of the variation predicted by the latter may be driven by differences in plant size, which is considered to be the main driver in biomass allocation by the AP theory (e.g. Müller et al., 2000; Weiner, 2004, but see Shipley and Meziane, 2002). For example, plants generally have lower M_A/M_R values in their early development and higher M_A/M_R values as they get larger (Litton et al., 2003; Weiner, 2004). By the same token, according to the allometric formula [see Eqn (1)], it follows that β ≈ M_A/M_R when α ≈ 1·0. Thus, variations in the normalization constant may reflect differences in environmental conditions as predicted by both the OP theory and the AP theory (McCarthy and Enquist, 2007; Cheng et al., 2009). Indeed, the normalization constants for M_A vs. M_R relationships typically differ among different experimental treatments as well as among species (e.g. Niklas and Enquist, 2002; Cheng and Niklas, 2007; Yang et al., 2010; Xie et al., 2012).

Based on the synergistic predictions of the AP and the OP theories, we constructed three testable hypotheses with particular reference to understorey species: (1) M_A vs. M_R scaling exponents should be independent of environmental variation and, on average, should conform to an isometric scaling relationship; (2) increasing competition for light during forest succession should increase M_A/M_R (and thus the normalization constants of the M_A vs. M_R scaling relationships) to increase whole-plant light capture, such that (3) normalization constants should covary with M_A/M_R. To test these predictions, we collected and analysed data drawn from 1586 individual plants from 30 sites representing three forest types (i.e. an evergreen broad-leafed forest, a Pinus massoniana forest and a Cunninghamia lanceolata forest) and four different successional stages as indicated by stand ages.

MATERIALS AND METHODS

This study was conducted in Fujian province, south-east China (Table 1), which has a sub-tropical and south sub-tropical monsoon climate with an average annual temperature of 19 °C and a mean precipitation of 1670 mm year⁻¹ (which mainly occurs from May to October). The soils of the study sites are mainly latosolic red soils, red soils, yellow soils and mountain meadow soils (Ren et al., 2011).

Table 1.

Reduced major axis (RMA) regression slopes and y-intercepts (i.e. α and log β, respectively) of the relationships between above-ground biomass (M_A) and below-ground biomass (M_R) for all individual understorey plants in young, immature, premature and mature sub-tropical forests

Forest type†	Successional stage*	Site	Latitude	Longitude	n	α (95 % CI)	Log β	r2
BF	YF	Wuping	25°14'N	116°01'E	54	1·06 (0·91–1·22)	−0·14	0·734
		Wuyishan	27°48'N	118°01'E	46	1·04 (0·82–1·31)	−0·25	0·717
	IF	Guangze	26°39'N	117°25'E	105	1·02 (0·96–1·09)	0·36	0·703
		Wuping	25°14'N	116°01'E	102	0·91 (0·82–1·01)	0·23	0·734
		Wuyishan	27°49'N	118°01'E	57	0·97 (0·82–1·14)	0·21	0·717
		Youxi	26°06'N	118°05'E	43	1·45 (1·18–1·78)	−0·54	0·703
	PF	Jianou	26°59'N	119°06'E	47	1·07 (0·91–1·27)	0·036	0·734
		Youxi	27°48'N	118°01'E	52	1·10 (0·94–1·30)	0·18	0·717
	MF	Sanyuan	26°11'N	117°28'E	54	1·11 (0·90–1·38)	0·047	0·703
		Shunchang	26°50'N	117°57'E	59	1·18 (1·06–1·31)	−0·022	0·734
PF	YF	Gutian	26°25'N	118°34'E	36	0·89 (0·73–1·09)	0·23	0·717
		Liancheng	25°36'N	117°08'E	60	0·89 (0·79– 1·00)	0·17	0·703
	IF	Minhou	26°12'N	119°05'E	74	1·03 (0·94–1·14)	0·46	0·734
	PF	Gutian	26°26'N	118°34'E	59	1·06 (0·90–1·25)	0·14	0·717
		Wuyishan	26°45'N	118°03'E	38	0·91 (0·78–1·07)	0·26	0·703
	MF	Anxi	25°17'N	118°02'E	27	1·00 (0·83–1·20)	0·31	0·734
		Liancheng	25°43'N	116°55'E	35	0·98 (0·80–1·21)	0·095	0·717
		Mingxi	26°21'N	117°18'E	39	0·99 (0·81–1·21)	0·059	0·703
CF	YF	Jianyang	27°24'N	117°49'E	45	0·88 (0·72–1·06)	0·18	0·734
		Wuping	25°11'N	115°56'E	59	0·80 (0·69–0·93)	0·17	0·717
		Xianyou	25°26'N	118°29'E	66	0·92(0·79–1·08)	0·35	0·703
		Yongan	25°56'N	117°23'E	16	0·80 (0·50–1·27)	0·82	0·734
	IF	Minhou	26°12'N	119°05'E	79	1·04 (0·94–1·15)	0·33	0·717
		Mingxi	26°21'N	117°12'E	52	1·27 (1·10–1·47)	−0·39	0·703
		Shunchang	26°49'N	117°40'E	57	1·31 (1·11–1·54)	−0·016	0·734
	PF	Jiangle	26°43'N	117°28'E	55	0·99 (0·89–1·10)	0·045	0·717
		Jianyang	27°23'N	117°48'E	25	0·73 (0·55–0·97)	0·80	0·703
	MF	Jianou	27°00'N	118°31'E	52	0·98 (0·84–1·13)	0·11	0·734
		Wuping	25°11'N	115°56'E	66	0·91 (0·80–1·04)	0·28	0·717
		Yongan	25°56'N	117°23'E	27	1·15 (0·92–1·44)	−0·20	0·703

*YF, young forest; IF, immature forest; PF, premature forest; MF, mature forest.

^†BF, broad-leafed forests; CF, Cunninghamia lanceolata forest; PF, Pinus massoniana forest.

Using area distribution and resource quality data of the 2008 China’s National Forest Inventory (NFI), 30 sites were chosen to represent the major forest types in Fujian province. These sites included ten evergreen broad-leafed forests (two young, four immature, two immature and two mature forests), eight Pinus massoniana plantations (two young, one immature, two premature and three mature forests) and 12 Cunninghamia lanceolata plantations (four young, three immature, two premature and three mature forests) (Table 1). The stand ages of the three forest types were determined using case histories in the local forest forestry centre. Because the growth rates and successional processes differed significantly between the conifer and broad-leafed forests selected for study, different age groups were required to achieve comparable successional stages in the two types of forests. Specifically, the stand ages for the conifer forests were <10 years, 11–20 years, 21–25 years and ≥26 years (designated as young, immature, premature and mature forests, respectively), whereas the stand ages for the broad-leafed forests were <40 years, 41–60 years, 61–80 years and ≥81 years (also designated as young, immature, premature and mature forests, respectively).

Three 0·1 ha (50 × 20 m) plots for each site were established in August–October of 2011. Three 2 × 2 m sub-plots were then selected randomly in each plot to investigate the shrub layer of woody plants that were <0·05 m diameter at breast height (DBH) and >0·5 m in height. In addition, in each sub-plot, a 1 × 1 m sample area was selected to investigate grass layer plants, which included all remaining vascular plants (including woody plants <0·5 m tall), i.e. there were nine sub-plots (3 sampled sub-plots × 3 plots) for shrub and grass layer plants in each site. After taking height and base diameter measurements, a direct (destructive) method was used to collect and measure the biomass of understorey plants. In order to collect and measure below-ground (root) biomass accurately, the soil around the base of each plant was dug progressively downward to six depths (i.e. 0–10 cm, 10–20 cm, 20–30 cm, 30–40 cm, 40–50 cm and >50 cm) throughout each 2 × 2 m quadrat. During this process, plants were taxonomically identified and collected starting at the shallow grass layer and progressing downward to the depth of the roots in the shrub layer. Understorey plants connected by rhizomes were carefully excavated to determine their above- and below-ground biomass. Within the shrub layer, the soil around individual plants was collected and sieved (using a mesh size of 0·5 mm) to reduce the loss of fine roots. During this entire process, care was taken to keep roots intact and connected to above-ground parts, particularly those with a rhizomatous growth habit. Previous work in this area indicated that most of the roots within the shrub and grass layers are concentrated within the 0–30 cm soil layer (see Yang et al., 1991). Consequently, we focused on this soil depth during the collection of below-ground biomass.

In the laboratory, understorey plants were separated into the above- (stem and leaf) and below-ground (root) parts. A fine meshed screen (mesh size 0·5 mm) was used to wash soil from roots. The above- and below-ground biomass was oven-dried at 65 °C to determine dry biomass. Because of the significant difference existing among individuals in each of the woody species (e.g. seedlings vs. sapling vs. more mature individuals), all plants in the three 2 × 2 m sub-plots in each site were used to analyse individual level above- and below-ground biomass allocation patterns (n = 30). In addition, all the plants in each of the three 2 × 2 m sub-plots were used to examine community level biomass allocation patterns (n = 90).

The data for leaf, stem, above-ground and below-ground biomass (M_L, M_S, M_A and M_R, respectively) were log₁₀-transformed [see Eqn (1B)]). Because functional rather than predictive relationships were sought (see Sokal and Rohlf, 1981; Niklas, 1994), Model Type II (reduced major axis, RMA) regression protocols were used to determine the scaling exponent and allometric constant of log–log linear relationships, i.e. α and log β, respectively. The software package ‘Standardised Major Axis Tests and Routines’ (SMATR; Falster et al., 2003; see also Warton and Weber, 2002) was used to determine whether the numerical values of α and log β differ between contrasted data sub-sets (the equivalent of ordinary least square standard analyses of covariance, ANCOVA). The significance level for testing slope heterogeneity was P < 0·05 (i.e. slope heterogeneity is rejected if P > 0·05).

RESULTS

The numerical values of M_A, M_R and M_A/M_R exhibited large variations across the 30 sites, ranging from 0·03 to 6010·27 g for M_A, 0·01 to 1848·89 g for M_R, and 0·04 to 36·00 for M_A/M_R at the individual plant level and ranging from 32·67 to 3474·58 g m⁻² for M_A, 26·35 to 1405·15 g m⁻² for M_R, and 0·41 to 4·44 for M_A/M_R at the community level (Table 2; Fig. 1). The mean values of M_A, M_R and M_A/M_R were 80·58 g, 44·81 g and 2·44, respectively, across all plants, and 457·76 g m⁻², 327·93 g m⁻² and 1·57, respectively, at the whole community level (Table 2).

Table 2.

Mean values of above-ground biomass (M_A), below-ground biomass (M_R) and M_A/M_R for understorey plants in three forest types in Fujian province, south-east China for all individual plants and at the community level

Forest type†	Successional stage*	Individual plant level					Community level
		n	MA	MR	MA/MR	Range	n	MA	MR	MA/MR	Range
BF	YF	100	29·77	40·14	1·29a	0·04–10·57	6	203·52	331·41	0·67a	0·41–0·99
	IF	307	138·11	54·30	2·79b	0·04–30·12	12	934·75	434·30	2·08b	0·55–3·51
	PF	99	105·14	55·25	2·28bc	0·07–8·14	6	505·21	315·39	1·79b	1·08–3·68
	MF	113	44·48	25·83	1·97ac	0·09–10·23	6	276·47	169·05	1·71b	1·31–2·29
	All	619	98·24	46·97	2·32	0·04–30·12	30	570·94	336·89	0·85	0·27–2·46
PF	YF	96	34·95	37·48	1·84a	0·11–7·22	6	232·23	342·05	0·79a	0·49–1·28
	IF	74	84·07	18·80	5·69b	0·25–36·00	3	651·14	197·77	3·09b	2·49–4·17
	PF	97	66·37	55·02	2·13a	0·06–8·67	9	471·35	440·88	1·28a	0·72–2·35
	MF	101	122·26	79·66	2·13a	0·10–25·62	6	374·91	242·14	1·62a	0·95–2·83
	All	368	77·07	49·92	2·56	0·06–36·00	24	409·93	336·10	0·91	0·24–2·04
CF	YF	186	55·45	43·23	2·51a	0·08–34·00	12	357·34	294·09	1·44a	0·49–3·24
	IF	188	54·98	21·31	2·94b	0·05–29·33	9	325·83	203·25	2·09ab	0·71–4·44
	PF	80	37·23	25·21	2·50ab	0·17–16·00	6	226·75	151·20	1·66a	0·87–2·44
	MF	145	103·44	65·94	1·90a	0·09–10·36	9	627·85	563·86	1·15ac	0·62–1·63
	All	599	64·48	39·44	2·49	0·05–34·00	36	395·33	315·01	0·84	0·23–2·04
All		1586	80·58	44·81	2·44	0·04–36·00	90	457·76	327·93	1·57	0·41–4·44

*YF, young forest; IF, immature forest; PF, premature forest; MF, mature forest.

^†BF, broad-leafed forests; CF, Cunninghamia lanceolata forest; PF, Pinus massoniana forest. Note: Different letters in the M_A/M_R line mean significant difference at P < 0·05.

Fig. 1.

Relationships between above-ground biomass (M_A) and below-ground biomass (M_B) for all individual of understorey layer plants in young, immature, premature and mature forests. (A) Broad-leafed forest; (B) Cunninghamia lanceolata forest; (C) Pinus massoniana forest; (D) across the entire data sets.

The numerical values of M_A, M_R and M_A/M_R also varied markedly among the different successional stages within the three forest types (Table 2). For example, across individual plants, the mean values of M_A ranged from 29·77 g for young forest sites to 138·11 g for immature forest sites, and, at the community level, from 169·05 g m⁻² for mature evergreen broad-leafed forest sites to 434·30 g m⁻² for immature forest sites (Table 2). In contrast, the mean values of M_A, M_R and M_A/M_R were less variable across the three forest types (Table 2). Across all plants in the data set, M_A ranged from 64·48 g in C. lanceolata forests to 98·24 g in broad-leafed forests. At the community level, M_A ranged from 315·01 g m⁻² in the C. lanceolata forests to 336·89 g m⁻² in the evergreen broad-leafed forests (Table 2). Furthermore, the mean values of M_A/M_R at the community level were lower than those at the individual plant level across the different successional stages and forest types (Table 2).

Across the 50 regressions for individual plants (Tables 1 and 3–5), the mean α ± s.e. of M_A vs. M_R was 1·02 ± 0·02, which is statistically indistinguishable from an isometric scaling relationship. Forty of these regressions had α-values that were indistinguishable from the predicted value of 1·0 (Table 1; Figs 1 and 2A). However, (S)MATR analyses and numerical comparisons of 95 % confidence intervals (CIs) identified ten regression slopes differing statistically from 1·0. These were the three evergreen broad-leafed immature forests of Youxi (P = 0·001), the mature forest of Shunchang (P = 0·004), all mature plants (P = 0·001), one P. massoniana forest (P = 0·03) (Table 3), five young C. lanceolata forests of Wuping (P = 0·004), the immature forests of Mingxi (P = 0·002) and Shunchang (P = 0·002), the premature forest of Jiangyang (P = 0·032) (Table 1), the entire immature forest data set (P = 0·008, respectively) (Table 3) and the data set for all understorey plants from immature forests (P = 0·004) (Table 3). Four of the ten regression analyses had 95 % CIs that fell either significantly below or above the numerical range of 0·97–1·03, which was statistically compatible with isometry. These were the premature C. lanceolata forest of Jiangyang (95 % CIs = 0·55–0·97) (Table 1), the young forest of P. massoniana (95 % CIs = 0·82–0·99), the immature forest of C. lanceolata (95 % CIs = 1·02–1·20) and all understorey plants in immature forests (95 % CIs = 1·01–1·09) (Table 3). The scaling exponents of the M_A vs. M_R relationship did not differ significantly among the three forest types at the community level (Table 4; Figs 2B and 3). The scaling exponent of M_A vs. M_R of understorey plants at the community level in Fujian province was indistinguishable from that for all individual plants (P > 0·05) (Fig. 3).

Table 3.

Reduced major axis (RMA) regression slopes and y-intercepts (i.e. α and log β, respectively) of the relationships between above-ground biomass (M_A) and below-ground biomass (M_B) for all individual understorey plants in young, immature, premature and mature forests

Successional stages*	Forest type†	n	α (95 % CI)	Log β (95 % CI)	r2
YF	BF	100	1·05 (0·92–1·19)	−0·19 (−0·37 to −0·0054)	0·585
	PF	96	0·90 (0·82–0·99)	0·19 (0·071–0·30)	0·783
	CF	186	0·95 (0·87–1·03)	0·20 (0·083–0·32)	0·629
	All	382	0·96 (0·91–1·02)	0·093 (0·013–0·17)	0·651
IF	BF	307	1·01 (0·96–1·06)	0·25 (0·18–0·31)	0·813
	PF	74	1·03 (0·94–1·14)	0·46 (0·34–0·57)	0·822
	CF	188	1·11 (1·03–1·20)	0·088 (–0·013 to 0·19)	0·718
	All	569	1·05 (1·01, 1·09)	0·21 (0·16–0·26)	0·777
PF	BF	99	1·06 (0·94–1·19)	0·15 (–0·032 to 0·34)	0·671
	PF	97	0·97 (0·88–1·08)	0·19 (0·052–0·34)	0·727
	CF	80	1·05 (0·94–1·16)	0·15 (0·013–0·28)	0·770
	All	276	1·03 (0·97–1·09)	0·16 (0·081–0·25)	0·753
MF	BF	113	1·16 (1·06–1·28)	–0·012 (–0·14 to 0·12)	0·763
	PF	101	1·01 (0·90–1·13)	0·12 (–0·068 to 0·30)	0·673
	CF	145	0·96 (0·88–1·05)	0·17 (0·047–0·30)	0·734
	All	359	1·03 (0·97–1·09)	0·097 (0·016–0·18)	0·734

Isometric α-values are shown in bold.

*YF, young forest; IF, immature forest; PF, premature forest; MF, mature forest.

^†BF, broad-leafed forests; CF, Cunninghamia lanceolata forest; PF, Pinus massoniana forest.

Fig. 2.

Log–log bivariate plots of above- vs. below-ground (root) biomass (M_A vs. M_R) at the level of individual plants and at the community level. (A) Comparison between this study and global data set (K Niklas, unpubl. res.) at the individual level. The raw data unit is g dry mass per individual; (B) comparison between this study and Chinese forests data sets at the community level (provided by Luo 1996). The raw data unit is g dry mass m⁻¹.

Table 4.

Reduced major axis (RMA) regression slopes and y-intercepts (i.e. α and log β, respectively) of the relationships between above-ground biomass (M_A) and below-ground biomass (M_B) for all individual understorey plants in the three forest types

Forest type	n	α (95 % CIs)	Log β (95 % CIs)	r2
Broad-leafed forest	619	1·04 (1·00–1·08)	0·13 (0·077–0·19)	0·753
P. massoniana forest	368	0·95 (0·90–1·00)	0·25 (0·18–0·32)	0·749
C. lanceolata forest	599	1·03 (0·98–1·07)	0·12 (0·062–0·18)	0·734
All	1586	1·01 (0·99–1·04)	0·15 (0·12–0·19)	0·744

Isometric α-values are shown in bold.

Fig. 3.

Log–log bivariate plots of above- vs. below-ground (root) biomass (M_A vs. M_R) at the level of all individual plants (n = 1586) and the community level (n = 90). The raw data have comparable numerical values when log transformed despite differences in their original units, i.e. g dry mass per individual and g dry mass m⁻¹.

At the level of individual plants, the scaling exponent for M_A vs. M_R of understorey plants across the entire data set was 1·01 (95 % CIs of 0·99–1·04; n = 1586, r²= 0·744), which was indistinguishable from 1·0 (P = 0·264). In addition, the slopes of the individual data sets hovered around 1·0 and did not vary significantly among the different forest successional stages (P = 0·137) (Table 3; Fig. 1). Likewise, the slopes of M_A vs. M_R were 1·04, 0·95 and 1·03 for understorey plants in the broad-leafed forest, the P. massoniana forest and the C. lanceolata forest, respectively, which were all indistinguishable from 1·0 (P = 0·070, 0·059 and 0·24, respectively) (Table 4; Fig. 1). At the community level, the slope of the M_A vs. M_R scaling relationship for understorey plants was 0·99 (95 % CIs = 0·85–1·16; n = 90, r²= 0·476) (Table 5; Fig. 3).

Table 5.

Reduced major axis (RMA) regression slopes and y-intercepts (i.e. α and log β, respectively) of the relationships between above-ground biomass (M_A) and below-ground biomass (M_B) for understorey plants at the community level

Forest type	n	α (95 % CIs)	Log β (95 % CIs)	r2
Broad-leafed forest	30	1·23 (0·95–1·59)	–0·40 (–1·19 to 0·39)	0·540
P. massoniana forest	24	0·90 (0·62–1·32)	0·34 (–0·53 to 1·20)	0·229
C. lanceolata forest	36	0·83 (0·66–1·05)	0·53 (0·067–0·99)	0·558
All	90	0·99 (0·85–1·16)	0·15 (–0·23 to 0·52)	0·476

Isometric α-values are shown in bold.

Substantial variation in the numerical values of normalization constants (i.e. log β) was observed across the 50 different M_A vs. M_R regression curves for individual plants (Tables 1, 3 and 4) and for the four regression curves at the community level (Table 5), i.e. the absolute values of M_A differed substantially with respect to M_R across the different sites, successional stages and species. However, the normalization constant for M_A vs. M_R at the individual plant level was indistinguishable from that of the community level across the entire data set (Fig. 3; Tables 4 and 5).

Although the main objective of this study was to test the scaling relationships between M_A and M_R at the community and individual plant level, the relationships among leaf, stem and root biomass (i.e. M_L, M_S and M_R, respectively) were also investigated (Fig. 4). M_L scaled as the 0·96 (95 % CIs = 0·92–1·01) and as the 0·90 (95 % CIs = 0·78–1·05) power of M_R at the individual plant level and at the community level, respectively. M_L also scaled as the 0·97 (95 % CIs = 0·93–1·02) and 0·84 (95 % CIs = 0·75–0·95) power of M_S, respectively, whereas M_S scaled as the 0·99 (95 % CIs = 0·95–1·03) and 1·07 (95 % CIs = 0·94–1·22) power of M_R at the individual plant level and community level, respectively (Fig. 4).

Fig. 4.

M_L, M_S and M_R relationships for understorey plants in sub-tropical forests in China at the individual and community level. Solid lines are reduced major axis regression curves of log-transformed data. At the individual level: (A) M_L vs. M_R; (C) M_S vs. M_R; (E) M_L vs. M_S; at the community level: (B) M_L vs. M_R; (D) M_S vs. M_R; (F) M_L vs. M_S.

Finally, the mean values of M_A/M_R were correlated positively with the numerical values of normalization constants, but showed no significant relationship with the scaling exponents of the 30 M_A vs. M_R scaling relationships at the individual plant level (Fig. 5A, B). As noted, if M_A = β M_R^α, it follows that β = M_A/M_R^α. Therefore, if α is on average invariant and close to unity, it also follows that β ≈ M_A/M_R. In this context, using the mean values of M_A and M_R for all of the plants in each of the 30 sites, we observed significant negative correlations between β and α (β = 1·142α^−3·493, r²= 0·608) and between β and M_R^α (β = 41·042 M_R^−α+ 0·424, r²= 0·454) (Fig. 5C, D). In addition, no significant correlation between β and M_A or M_R was detected (Fig. 5E, F). We interpret these results to indicate that variations in β are primarily the result of site-specific environmental effects on plant size and on the allocation of biomass to M_A relative to M_R.

Fig. 5.

The relationship between scaling parameters and individual-level M_A/M_R. (A) normalization constant vs. M_A/M_R; (B) scaling exponent vs. M_A/M_R; (C) scaling normalization constant vs. scaling exponent; (D) normalization constant vs. M_R^α; (E) normalization constant vs. M_A; (F) normalization constant vs. M_R.

DISCUSSION

A number of factors are known to influence our perception of the relationship between above- and below-ground biomass at the community level and at the level of individual plants. These include, but are not limited to, sampling protocols, community successional stage, life form and species composition. Our data show that the average M_A/M_R of understorey plants in sub-tropical forests at the community level is 1·57, which indicates that more biomass is allocated to shoots compared with roots. This value is lower than that reported for canopy tree species in sub-tropical forests, but higher than that in sub-tropical grasslands reported by Mokany et al. (2006) (i.e. M_A/M_R = 4·55 and M_A/M_R = 0·53, respectively). Sampling protocols might account for these differences, because the individuals collected in this study were plants with DBH <5 cm, including woody plants and grasses, and because trees generally have higher M_A/M_R than grasses (e.g. Jackson et al., 1996; Mokany et al., 2006). Alternatively, differences in species composition may account for differences in M_A/M_R. The community level M_A/M_R in our data set is smaller than that for all individual plants (Table 2), which might reflect the relative contributions of small vs. larger plants to overall community biomass frequency distribution. In general, large woody plants typically have large M_A/M_R quotients and also contribute disproportionately larger amounts of biomass to total community biomass, whereas small plants typically have small M_A/M_R and contribute smaller amounts of biomass to total community biomass (e.g. Müller et al., 2000; Weiner, 2004). These relationships hold true despite the fact that size-frequency distributions show that smaller plants typically numerically outnumber larger woody plants (e.g. Niklas et al., 2003; Wang et al., 2009).

Although differences in M_A/M_R can reflect differences in abiotic gradients between the canopy and forest floor, our data are somewhat counterintuitive in light of the predictions of the OP theory, according to which plants should allocate more biomass to their shoots as succession progresses (as an adaptation to progressively less intense light conditions). Yet, our data show that M_A/M_R is smallest in young broad-leafed forests, in P. massoniana forests and in the mature C. lanceolata forest, and largest in the immature forests of all tree forest types. Furthermore, no significant variation in M_A/M_R was observed in all of the premature and mature forests regardless of forest type (Table 2). These results are comparable with those of Cairns et al. (1997) and Yang and Luo (2011) who report that M_A/M_R does not change with stand age across forest ecosystems worldwide.

We have reason to believe that the apparent stability of M_A/M_R at the community level can be attributed to a turnover in species composition that results in a more or less uniform acclimation to changing light conditions. For example, understorey species that are less adapted to shading might be gradually replaced by more shade-tolerant species during community succession (Connell and Slatyer, 1977), particularly since early successional species have higher light saturation than late successional understorey species (e.g. Bazzaz, 1979). Thus, the apparent stability of M_A/M_R for understorey plants in later successional stages might be the result of a change in species composition in response to light-level changes at the community level. We cannot rule out changes in soil nutrient levels as a contributing factor to the stabilization of M_A/M_R (Walker and Syers, 1976; Cleveland et al., 2006). However, we did not detect any correlation between M_A/M_R and N, P or N:P soil concentrations (data not shown).

Our data reveal statistically significant scaling relationships for M_A vs. M_R both at the level of individual plants (across all species) and at the whole community level (r²= 0·744, P < 0·001 and r²= 0·476, P < 0·001, respectively) (Tables 1 and 3–5). Taken at face value, this indicates that the root biomass of understorey plants can be estimated based on above-ground biomass measurements. Likewise, our data show that root biomass can also be reliably calculated for canopy layer plants based on above-ground biomass measurements (see also Cheng et al., 2007), in large part because above-ground biomass scales nearly isometrically with respect to below-ground biomass for both understorey and canopy species (Enquist and Niklas, 2002; Niklas and Enquist, 2002; Cheng and Niklas, 2007). However, in this context, it is important to note that the y-intercepts of M_A vs. M_R regression curves (i.e. β-values) varied across the comparisons made here (see below). This variation can be site or community specific, which indicates that predictions of M_R based on measurements of M_A are problematic at best unless they are based on robust local sampling of both M_A and M_R to obtain statistically reliable estimates of β-values.

We also freely acknowledge the methodological difficulties associated with precise measurements of root biomass (e.g. Jackson et al., 1996; Vogt et al., 1998; Mokany et al., 2006). For example, the seasonal variations in peak root biomass can be easily missed (Lauenroth, 2000), just as it is easy to underestimate root biomass owing to a disproportionate loss of fine roots as root systems are excavated or washed free of soil (Oliveira et al., 2000). Although we tried to measure root biomass accurately, it is likely that M_R was underestimated such that the scaling exponent of M_A vs. M_R might exceed unity in some of our study sites (e.g. Enquist and Niklas, 2002).

Nevertheless, there are good reasons to assert that an isometric M_A vs. M_R relationship exists and that it is insensitive to differences in forest type or succession stage, particularly in light of other studies. For example, regression analyses of a new global data set that includes data from managed and field grown trees, crop plants, grasses, forbs and herbs (K Niklas, unpubl. res.) show that the M_A vs. M_R scaling relationship is governed by a slope of 1·01 (95 % CIs = 1·003 and 1·013; n = 3452, r²= 0·977, P < 0·001), which is indistinguishable from the slope reported here (Fig. 2A). Likewise, above-ground biomass in the understorey plants in forests scaled with respect to below-ground biomass in a manner strikingly similar to that of China’s canopy forest plants (Luo, 1996) (Fig. 2B).

Returning to the importance of β-values when estimating below-ground biomass, we emphasize the influence of site-specific variation on biomass allocation patterns both within and across plant taxa, especially during ontogeny (Bazzaz, 1997; Weiner, 2004). For example, OP theory predicts that plants respond to environmental variation by changing M_A/M_R in a manner that adjusts for deficiencies in nutrients, water or light to maximize growth (Bloom et al., 1985; Shipley and Meziane, 2002). Thus, plants are predicted to allocate more biomass to roots in response to low-nutrient conditions or water stress and to shift biomass allocation to shoots under low light conditions. Accordingly, M_A/M_R will change in response to the most limiting resource in a specific site. This prediction is of particular interest because AP theory predicts that the numerical values of the normalization constant (i.e. β-values) of the M_A vs. M_R scaling relationship will positively correlate with M_A/M_R when the scaling exponent for the M_A vs. M_R scaling relationship is ≈ 1·0, i.e. normalization constants are predicted to be site specific and to change across successional stages. We observed significant variation in the normalization constants of M_A vs. M_R regression curves across different sites, successional stages and species (Tables 1, 3 and 4). Across the 30 sites, these constants ranged from −0·54 to 0·82 (Table 1) and reached their maximum in P. massoniana forests and a minimum in C. lanceolata forests (Table 5). We also observed a significant correlation between the numerical values of β and α (r²= 0·608) (Fig. 5C). This correlation emerges from the mathematical relationships among α, β and M_A/M_R. Noting that M_A = β M_R^α, it follows that β = M_A/M_R^α such that the numerical value of β must increase as the numerical value of α decreases, even if α decreases slightly, provided that M_A and M_R are, on average, isometrically related to one another.

Conclusions

We tested the hypothesis that the biomass allocation patterns of understorey plants abide by the same isometric scaling relationships reported for canopy tree species. This hypothesis is supported by the data drawn from 30 sites in a sub-tropical ecosystem showing that the isometric scaling relationships hold true at the level of individual plants and at the level of entire communities. Such facts indicate that the proportional allocation of above-ground biomass with respect to below-ground biomass is comparatively constant across all comparisons. Although positively correlating with M_A/M_R, normalization constants of the M_A vs. M_R do not support the hypothesis that normalization constants should increase with successional stage reflecting the accompanied light competition. Indeed, significant differences were observed for the normalization constants of the M_A vs. M_R scaling relationship across different sites, forest types and successional stages, which indicates that the absolute amount of biomass allocated to above-ground vs. below-ground organs is site specific (as gauged by M_A/M_R and the numerical values of the normalization constants of M_A vs. M_R). The data also indicate that plant size is the main driver of biomass allocation patterns for understorey species in sub-tropical forests, although further study is required to make this claim.