Mixing effect on stand yield of Pinus tabulaeformis and Quercus liaotungensis is modulated by site quality and stand density in the Loess Plateau, China

Figures & data

Figure 1. Location of the plots used for investigating the growth of pure and mixed stands of Liaodong oak (Quercus liaotungensis) and Chinese pine (Pinus tabulaeformis) in the Huanglong mountains.

Table 1. Tree characteristics of 120 pure and mixed Liaodong oak (Quercus liaotungensis) and Chinese pine (Pinus tabulaeformis) plots.

Variable	Pure Liaodong oak stands			Pure Chinese pine stands			Chinese pine-Liaodong oak mixed stands
							Total			Liaodong oak			Chinese pine
	Mean (SD)	Max	Min	Mean (SD)	Max	Min	Mean (SD)	Max	Min	Mean (SD)	Max	Min	Mean (SD)	Max	Min
dg (cm)	20.6(2.6)^a	24.5	15.3	20.2(3.9)^a	24.8	13	20.1(3.7)^a	24	13.7	17.9(4.4)^b	23.5	8.9	21.2(2.27)^a	24.2	15.3
$\overline{h}$(m)	11.2(2.4) ^ab	14.9	7.3	11.5(2.8) ^a	15.3	7.6	11.0(2.5)^ab	15.2	6.7	9.8(2.4) ^b	15.1	5.2	11.6(2.5) ^a	15.3	6.8
$\overline{ba}$ (m^2)	0.033(0.005)^a	0.047	0.018	0.032(0.012)^a	0.048	0.013	0.032(0.021)^a	0.045	0.015	0.025(0.015)^b	0.043	0.006	0.035(0.004)^a	0.046	0.019
$\overline{v}$ (m^3)	0.144(0.027)^a	0.184	0.124	0.169(0.035)^b	0.238	0.142	0.160(0.039)^b	0.217	0.116	0.133(0.031)^a	0.178	0.087	0.174(0.037)^b	0.231	0.138
cw (m)	6.1 (0.7)^a	7.3	4.8	3.8 (0.6)^b	4.9	3.1	5.1 (0.9)^c	7.1	3.9	6.4 (1.1)^a	8.4	4.5	4.4 (1.1)^b	6.3	2.8
cl (m)	7.5 (0.5)^a	8.4	6.2	5.8 (0.9)^b	7.3	4.7	6.7 (1.0)^ab	7.9	5.8	7.2 (1.9)^a	9.7	5.5	5.9 (1.3)^b	7.7	4.4
cl/h	0.66 (0.14)^a	0.81	0.47	0.49 (0.07)^b	0.59	0.42	0.58 (0.09)^c	0.69	0.49	0.72 (0.11)^a	0.87	0.52	0.52 (0.18)^b	0.64	0.41

Note: d_g, quadratic mean diameter of the plot; $\overline{h}$, the average tree height of the plot; $\overline{ba}$, the average tree basal area of the plot; $\overline{v}$, the average tree volume of the plot; cw, the average crown width of the plot; cl, the average crown length of the plot; cl/h, the average crown length/tree height ratio of the plot. Different lowercase letters indicate significant differences among forest types. (p < 0.05). All the volume equations are two variables volume equation (DBH, tree height), For broad-leaf species: $V=0.000057887451\times DB{H}^{1.8445849}\times H^{0.98088457}$; For conifer species:$V=0.000060504753\times DB{H}^{1.8077573}\times H^{1.0229567}$; For Chinese pine:$V=0.000066492455\times DB{H}^{1.8655617}\times H^{0.93768879}$; For Liaodong oak: $V=0.000060970532\times DB{H}^{1.6543856}\times H^{1.1426474}$.

Table 2. Stand characteristics of 120 pure and mixed Liaodong oak (Quercus liaotungensis) and Chinese pine (Pinus tabulaeformis) plots.

Variable	Pure Liaodong oak stands			Pure Chinese pine stands			Chinese pine-Liaodong oak mixed stands
							Total			Liaodong oak			Chinese pine
	Mean (SD)	Max	Min	Mean (SD)	Max	Min	Mean (SD)	Max	Min	Mean (SD)	Max	Min	Mean (SD)	Max	Min
PAIV (m^3 ha^−1 year^−1)	5.23(2.11)^a	9.5	3.05	7.28(0.84)^b	9.24	4.35	6.64(1.88)^b	11.24	3.91	1.58(0.37)	4.22	0.54	5.04(2.36)	9.32	2.17
Annual Ingrowth (%)	0.81(0.37)^a	2.07	0.26	0.32(0.17)^b	1.14	0	0.68(0.37)^a	1.84	0	0.88(0.42)	1.99	0	0.57(0.31)	1.81	0
Annual Mortality (%)	0.70(0.32)^a	1.79	0	0.43(0.15)^b	1.31	0	0.58(0.31)^a	1.61	0.11	0.92(0.37)	1.74	0.17	0.40(0.25)	1.5	0
N (ha^−1)	966(220)^a	1475	550	839(290)^a	1656	475	864(327)^a	1570	476	308(137)	730	144	564(216)	1100	200
SDI	650(201)^a	1137	451	530(86)^a	1027	319	541(187)^a	1051	347	180(56)	320	27	361(141)	604	188
SWC (%)	14.0(1.4)^a	16.2	12.1	13.5(1.2)^a	15.8	11.4	15.7(1.5)^b	17.6	13.1
Soil N (g/kg)	0.087(0.011)^b	0.133	0.058	0.067(0.013)^a	0.113	0.028	0.083(0.016)^b	0.143	0.039
Soil C (g/kg)	1.04(0.13)^b	1.25	0.87	0.81(0.08)^a	0.93	0.68	0.96(0.11)^b	1.12	0.76
Species proportion										37%(10%)	62%	21%	63%(10%)	79%	38%

Note: PAIV, periodic annual volume increment; SDI, stand density index; N, number of trees per unit area; SWC, Soil volumetric water content; Soil N, soil total nitrogen; Soil C, soil carbon content.

Table 3. Fixed effect parameter estimates, standard errors, t values, and p-values for the Chinese pine and Liaodong oak growth models (Equation (8)).

Parameter	Coefficient	Chinese pine			Liaodong oak
		Estimate	SE	p value	Estimate	SE	p value
Intercept	a0	−5.208	0.702	<0.001	−4.218	0.412	<0.001
SF	a1	0.573	0.196	0.007	1.282	0.238	<0.001
SDI	a2	0.879	0.106	<0.001	0.456	0.090	<0.001
dG	a3	0.318	0.213	0.09	−0.467	0.203	0.029
Pi	a4	−0.440	0.341	0.027	1.047	0.240	<0.001

Note: SF, Site form; SDI, Stand density index; d_g, quadratic mean diameter; P_i, stocking proportion of species i.

Table 4. Goodness of fit statistics for the Chinese pine and Liaodong oak growth models (Equation (8)).

Species	RSE	MSE	Sig	Adj. R^2
Chinese pine	0.633	0.151	<0.001	0.940
Liaodong oak	0.759	0.168	<0.001	0.974

Note: RSE, residual standard error; MSE, Mean Square Error; Sig, significance; Adj. R², adjusted coefficient of determination R².

Figure 2. The ratio of different intensities of competition for individuals in pure oak (n = 4572) and pine (n = 4509) forests and pine (n = 5292) and oak (n = 2774) individuals in mixed forests.

Figure 3. The mean annual increment of tree volume (iv)- tree volume (v) relationship for mixed and pure Liaodong oak and Chinese pine.

Figure 4. Relationships between the total basal area of trees larger than the subject trees (BAL) and mean annual increment of tree volume (iv) of Chinese pine and Liaodong oak.

Figure 5. Diameter at breast height (DBH) classes of pure and mixed Chinese pine and Liaodong oak plots.

Figure 6. Influence of mixing on the periodic annual volume increment (PAIV) of different diameter at breast height (DBH) classes of Chinese pine and Liaodong oak.

Figure 7. Modeled stand volume increment (PAIV) of pure and mixed stands of Chinese pine and Liaodong oak with different stand density indices (SDI) and site forms (SF).

Note: The d_g of pine and oak in this figure are 20 cm.

Figure 8. Response of relative mixing response (RMR) to total stand density index (SDI) and site form (SF) at a ratio of 50% Chinese pine.

Note: The d_g of pine and oak in this figure are 20 cm.

Figure 9. The effect of mixing pine (triangle crown) and oak (oval crown) trees (b, d, g, h) on canopy space and the availability of light (blue arrow) of different intensities (a darker arrow color indicates a higher intensity of light) compared with pure pine (a, e) and oak (c, f) stands.