Silva Fennica

Fig. 1. Locations of nine stands used to study the early development of spruce-birch mixtures. The coordinates of stands varied between 61.162451°–62.56185° north and 24.63745°–28.59488° east. Two plots of 500 m² were measured in each stand. Stand characteristics are described in Tables 1 and 2.

Table 1. Basic site information of nine stands used to study the early development of spruce-birch mixtures. Age is time since planting, TS is temperature sum in degree days (dd), EC is early cleaning, and C/N organic and mineral are carbon-nitrate ratio in different layers of soil. Thickness of organic layer is mean thickness of all samples from each stand.
Stand	Age, years	Planting year	EC year	Site type	TS, dd	Municipality	C/N organic	C/N mineral	Thickness of organic layer, mm
10	8	2013	2017	OMT	1371	Heinola	23.8	21.5	8
12	10	2011	2015	OMT	1371	Heinola	25.3	23.3	11
13	9	2012	2016	MT	1235	Joutsa	27.6	27.1	20
14	8	2013	2017	MT	1383	Puumala	23.3	21.8	21
15	8	2013	2017	MT	1403	Taipalsaari	19.7	19.3	23
16	11	2010	2015	MT	1243	Jämsä	30.5	23.9	33
17	14	2007	2016	MT	1256	Joroinen	19.8	19.6	16
18	12	2009	2016	MT	1287	Heinävesi	27.4	24.9	33
19	14	2007	2014	MT	1260	Leppävirta	28.8	24.3	49

Table 2. Characteristics of nine stands used to study the early development of spruce-birch mixtures by tree species and origin.
Stand	Species	Origin	Stem number, ha⁻¹	% of stems	Basal area, m² ha⁻¹	Mean DBH, cm	Mean height, m	Dominant height, m
11	all	all	2930	100%	0.90	1.7	2.5	3.7
	Scots pine	seed	80	3%	0.06	2.6	2.6	3.0
	Norway spruce	planted	1810	62%	0.56	1.8	2.2	3.4
	Silver birch	seed	790	27%	0.22	1.6	2.9	4.7
	Silver birch	sprout	70	2%	0.01	1.3	2.8	3.0
	Downy birch	seed	170	6%	0.07	2.0	3.5	4.6
	Downy birch	sprout	10	0%	0	1.0	2.6	2.6
12	all	all	3320	100%	3.80	3.6	3.9	5.1
	Scots pine	seed	490	15%	0.98	4.7	3.7	5.3
	Norway spruce	planted	1750	53%	2.29	3.9	3.8	5.8
	Silver birch	seed	360	11%	0.17	2.3	3.9	5.0
	Silver birch	sprout	270	8%	0.14	2.5	4.1	4.8
	Downy birch	seed	130	4%	0.10	2.9	4.4	5.0
	Downy birch	sprout	320	10%	0.15	2.3	4.3	5.2
13	all	all	3180	100%	1.02	1.7	2.6	5.1
	Scots pine	seed	60	2%	0.01	1.3	1.9	1.9
	Norway spruce	planted	1980	62%	0.74	1.9	2.5	4.7
	Silver birch	seed	240	8%	0.07	1.6	2.9	4.1
	Silver birch	sprout	660	21%	0.11	1.2	2.7	3.8
	Downy birch	seed	130	4%	0.08	2.2	3.4	5.2
	Downy birch	sprout	110	3%	0.01	1.1	2.7	3.0
14	all	all	3230	100%	1.60	2.1	2.9	5.6
	Scots pine	seed	130	4%	0.09	2.8	2.6	3.1
	Norway spruce	planted	1760	54%	1.12	2.6	2.9	5.3
	Silver birch	seed	1070	33%	0.35	1.6	3.1	6.6
	Silver birch	sprout	220	7%	0.02	0.9	2.5	3.0
	Downy birch	seed	40	1%	0.02	2.0	3.6	3.6
	Downy birch	sprout	10	0%	0.01	2.1	4.5	4.5
15	all	all	3920	100%	2.63	2.6	3.5	5.5
	Scots pine	seed	260	7%	0.49	4.4	3.3	4.8
	Norway spruce	planted	1840	47%	1.40	3.0	3.2	6.2
	Silver birch	seed	1130	29%	0.54	2.1	3.9	7.5
	Silver birch	sprout	510	13%	0.13	1.7	3.5	5.2
	Downy birch	seed	80	2%	0.05	2.6	4.9	5.1
	Downy birch	sprout	100	3%	0.03	1.7	3.8	4.5
16	all	all	3040	100%	3.78	3.4	3.5	5.8
	Scots pine	seed	110	4%	0.10	3.0	2.5	3.1
	Norway spruce	planted	1950	64%	3.52	4.5	3.8	6.5
	Silver birch	seed	20	1%	0.01	2.2	3.9	3.9
	Silver birch	sprout	900	30%	0.13	1.3	3	4.0
	Downy birch	seed	20	1%	0.02	3.4	4.9	4.9
	Downy birch	sprout	40	1%	0.01	1.5	2.8	2.8
17	all	all	2790	100%	4.77	4.0	4.5	9.5
	Scots pine	seed	0	0%	0	0	0	0
	Norway spruce	planted	1380	49%	3.18	5.0	4.3	7.6
	Silver birch	seed	220	8%	0.39	3.5	5.2	9.4
	Silver birch	sprout	320	11%	0.17	2.0	3.9	5.8
	Downy birch	seed	470	17%	0.75	3.9	5.4	9.5
	Downy birch	sprout	400	14%	0.29	2.4	4.1	7.4
18	all	all	2350	100%	5.98	5.3	5.5	7.7
	Scots pine	seed	110	5%	0.24	4.8	3.9	4.8
	Norway spruce	planted	1400	60%	4.62	6.4	5.7	6.9
	Silver birch	seed	210	9%	0.52	5.2	6.8	8.5
	Silver birch	sprout	390	17%	0.45	3.4	5.2	8.2
	Downy birch	seed	100	4%	0.08	3.0	4.9	5.9
	Downy birch	sprout	140	6%	0.09	2.6	4.5	5.5
19	all	all	2340	100%	4.54	4.6	4.7	7.3
	Scots pine	seed	120	5%	0.49	6.9	4.8	5.3
	Norway spruce	planted	1460	62%	3.61	5.5	4.9	7.5
	Silver birch	seed	170	7%	0.09	2.5	4.3	5.0
	Silver birch	sprout	220	9%	0.18	3.0	4.6	6.4
	Downy birch	seed	120	5%	0.08	2.7	4.7	5.4
	Downy birch	sprout	250	11%	0.11	2.3	4.1	4.6

Table 3. Mean values (mean) and standard deviations (SD) of the plot-level variables of crop trees by tree species and origin on 18 sample plots in 9 stands. Data for the same variable marked with different letters are significantly different (p < 0.05). The significance of tree species, origin effect and stand effect was tested by the analysis of variance.
	Spruce	Silver birch		Downy birch		Effect of species and origin		Effect of stand
	planted	seed	sprout	seed	sprout	F	p	F	p
Variable	Mean ± SD	Mean ± SD	Mean ± SD	Mean ± SD	Mean ± SD	F	p	F	p
Mean DBH, cm	3.80 ± 1.72^a	2.37 ± 1.44^bc	1.87 ± 0.85^bc	2.54 ± 1.27^b	1.47 ± 0.96^c	14.09	<0.001	8.02	<0.001
Mean height, m	3.67 ± 1.2^a	3.89 ± 1.64^a	3.56 ± 0.95^a	4 ±1.69^a	2.87 ± 1.71^a	2.36	0.060	5.77	<0.001
Dominant height, m	5.31 ± 1.52^a	5.12 ± 2.18^a	4.33 ± 1.52^ab	4.46 ±2.17^ab	3.3 ± 2.13^b	4.60	0.002	6.37	<0.001
Basal area, m² ha⁻¹	2.32 ± 1.69^a	0.26 ± 0.24^b	0.15 ± 0.14^b	0.13 ± 0.23^b	0.07 ± 0.11^b	31.35	<0.001	2.20	0.036
Stem number, ha⁻¹	1646 ± 291^a	468 ± 426^b	393 ± 289^bc	140 ±148^c	153 ± 164^c	87.49	<0.001	0.94	0.489
Volume, m³ ha⁻¹	7.32 ± 5.8^a	0.92 ± 0.95^b	0.49 ± 0.49^b	0.48 ±0.89^b	0.24 ± 0.39^b	26.46	<0.001	2.42	0.022

Table 4. Mean values (mean) and standard deviations (SD) of the tree-level variables of the sample trees by tree species and origin. Data for the same variable marked with different letters are significantly different (p < 0.05). F-test based on estimated marginal means shows the significance of the fixed effects of tree species and origin in the mixed effect models estimated for the given variable. DSH = diameter at stump height, iDSH = increment of diameter at stump height, ih = height increment.
Variable	Spruce	Silver birch		Downy birch		F	p
	Planted	Seed	Sprout	Seed	Sprout
	Mean ± SD	Mean ± SD	Mean ± SD	Mean ± SD	Mean ± SD
All sample trees	N = 136	N = 55	N = 42	N = 25	N = 16	45.20	<0.001
Age (years)	9.1 ± 2.0^a	7.5 ± 2.0^bc	5.3 ± 3.3^d	8.3 ± 1.8^ab	6.7 ± 3.3^cd	27.87	<0.001
DSH (mm)	48.2 ± 21.5^a	36.9 ± 15.0^bc	34.4 ± 16.9^d	43.7 ± 18.7^ab	26.1 ± 17.8^cd	13.67	<0.001
Height (cm)	341 ± 148^a	432 ± 139^b	341 ± 148^a	459 ± 135^b	345 ± 150^a	3.85	0.005
Mean iDSH in the last 4 years (mm)	6.9 ± 2.7^a	6.3 ± 2.6^a	5.7 ± 2.4^a	6.9 ± 3.1^b	5.1 ± 1.8^c	16.34	<0.001
Mean ih in the last 4 years (cm)	45.8 ± 17.5^ab	57.7 ± 11.1^a	55 ± 13.5^a	61.1 ± 14.6^a	54.1 ± 12.8^b
Dominant sample trees	N = 73	N = 42	N = 22	N = 23	N = 12
Age (years)	9.3 ± 2.0^a	7.6 ± 2.1^b	5.8 ± 3.3^c	8.4 ± 1.8^ab	6.9 ± 3.4^bc	24.46	<0.001
DSH (mm)	55.8 ± 23.4^a	40.9 ± 15.5^b	29.0 ± 18.5^b	44.1 ± 19.2^a	31.3 ± 18.7^ab	22.76	<0.001
Height (cm)	379 ± 160^a	453 ± 137^b	380 ± 149^ab	455 ± 126^b	365 ± 135^ab	6.03	<0.001
Mean iDSH in the last 4 years (mm)	7.9 ± 2.9^a	6.9 ± 2.6^ab	6.7 ± 2.4^ab	6.9 ± 3.2^ab	5.8 ± 2.0^b	3.34	0.012
Mean ih in the last 4 years (cm)	49.8 ± 18.5^a	59.4 ± 11.2^b	57.2 ± 14.6^ab	60.8 ± 14.9^b	57.2 ± 13.0^ab	6.06	<0.001

Fig. 2. Height class distribution (5 dm) of spruces and birches in nine stands used to study the early development of spruce-birch mixtures.

Fig. 3. Predicted development and absolute growth rate of diameter at stump height (DSH) based on the Chapman-Richards type growth models fitted for all sample trees and dominant sample trees. Colored areas indicate 95% confidence bands derived from the estimates and standard errors of the fixed parameters (Table 5). The mean value of C/N ratio in organic layer (25.5) was used in predictions.

Table 5. Chapman-Richards models (Eq. 1) for under-bark diameter at stump height of all sample trees (8 spruces and 8 birches per plot) and dominant sample trees (4 thickest trees per species and plot). Fitting statistics using only fixed effects are also given. Note: Planted Norway spruce was used as reference.
		All sample trees		Dominant sample trees
		Estimate	S.E.	Estimate	S.E.
Fixed parameter (species)
β₁ (all species)		84.5496	7.8833	111.1110	10.4781
β₁ (silver birch, seed-origin)		0.7415^ns	2.9090	−4.0413^ns	3.2554
β₁ (downy birch, seed-origin)		0.6440^ns	3.9894	−7.1718^ns	4.0967
β₁ (silver birch, sprout-origin)		−3.2092^ns	3.6216	0.0857^ns	4.8827
β₁ (downy birch, sprout-origin)		−8.5849^ns	5.0510	−12.8707	5.3436
β_1,_{C/N organic} (all species)		−1.2090	0.3019	−1.9427	0.4019
β₂ (all species)		0.0791	0.0048	0.0870	0.0061
β₂ (silver birch, seed-origin)		−0.0456	0.0140	−0.0309^ns	0.0160
β₂ (downy birch, seed-origin)		0.0373^ns	0.0198	0.0391	0.0199
β₂ (silver birch, sprout-origin)		−0.0645	0.0168	−0.0899	0.0223
β₂ (downy birch, sprout-origin)		0.0109^ns	0.0214	0.0476	0.0222
β₃ (all species)		1.9984	0.0671	2.1430	0.0900
β₃ (silver birch, seed-origin)		−0.4216	0.0940	−0.4251	0.1204
β₃ (downy birch, seed-origin)		0.2601^ns	0.1766	0.2427^ns	0.1903
β₃ (silver birch, sprout-origin)		−0.7730	0.0975	−0.8384	0.1378
β₃ (downy birch, sprout-origin)		−0.3200^ns	0.1708	−0.2966^ns	0.1974
Random parameters
Stand level	sd(β_1,_k)	--	corr(β_1,_k,β_3,_k)	--	corr(β_1,_k,β_3,_k)
Stand level	sd(β_3,_k)	--	--	--	--
Plot level	sd(β_1,_jk)	5.6840	corr(β_1,_jk,β_3,_jk)	7.7010	corr(β_1,_jk,β_3,_jk)
Plot level	sd(β_3,_jk)	0.1939	0.894	0.2376	0.877
Tree level	sd(β_1,_ijk)	16.6163	corr(β_1,_ijk,β_3,_ijk)	14.9734	corr(β_1,_ijk,β_3,_ijk)
Tree level	sd(β_3,_ijk)	0.3897	0.313	1.7595	0.264
Error term	sd(e_ijk) (spruce)	1.6002		1.7424^a
	sd(e_ijk) (silver birch)	1.4985		1.6261^a
	sd(e_ijk) (downy birch)	1.9117		1.7595^a
Fitting statistics		Random + fixed	Fixed only	Random + fixed	Fixed only
R²		99.4%	77.4%	99.5%	82.4%
Bias, mm (Bias%)		0.02 (0.1%)	−0.11 (−0.5%)	0.03 (0.1%)	−0.16 (−0.6%)
RMSE, mm (RMSE%)		1.40 (6.1%)	8.84 (38.3%)	1.48 (5.8%)	8.60 (33.6%)
^ns Non-significant at 0.05. ^a Based on the likelihood-ratio test, the model estimated with different relative variance weights for each tree species was not significantly better than the one assuming homogeneity of variances.

Table 6. Chapman-Richards models (Eq. 1) for height of all sample trees (8 spruces and 8 birches per plot) and dominant sample trees (4 thickest trees per species and plot). Fitting statistics using only fixed effects are also given. Note: Planted Norway spruce was used as reference.
	All sample trees		Dominant sample trees
	Estimate	S.E.	Estimate	S.E.
Fixed parameter (species)
β₁ (all species)	716.1577	93.2797	833.3473	111.0242
β₁ (silver birch, seed-origin)	192.5226	21.3071	172.7279	25.3613
β₁ (downy birch, seed-origin)	193.3425	29.3316	155.9348	32.1360
β₁ (silver birch, sprout-origin)	203.5790	26.4137	212.1720	35.7630
β₁ (downy birch, sprout-origin)	147.2801	37.8146	117.1191	43.1173
β_{1,C/N organic} (all species)	−13.6956	3.6286	−16.5793	4.3262
β₂ (all species)	−0.0741	0.0065	−0.0747	0.0085
β₂ (silver birch, seed-origin)	−0.0092^ns	0.0197	−0.0475^ns	0.0251
β₂ (downy birch, seed-origin)	−0.1350	0.0351	−0.1878	0.0434
β₂ (silver birch, sprout-origin)	−0.0689	0.0249	−0.1002	0.0347
β₂ (downy birch, sprout-origin)	−0.1438	0.0419	−0.1236	0.0474
β₃ (all species)	1.0550	0.0407	1.0390	0.0423
β₃ (silver birch, seed-origin)	−0.3110	0.0520	−0.3786	0.0555
β₃ (downy birch, seed-origin)	−0.4628	0.0685	−0.5092	0.0673
β₃ (silver birch, sprout-origin)	−0.4500	0.0565	−0.4942	0.0648
β₃ (downy birch, sprout-origin)	−0.5940	0.0774	−0.5385	0.0806
Random parameters
Stand level
sd(β_1,_k)	34.8201	corr(β_1,_k, β_3,_k)	17.8919	corr(β_1,_k, β_3,_k)
sd(β_3,_k)	0.0759	−0.166	0.0726	−0.960
Plot level
sd(β_1,_jk)	42.6272	corr(β_1,_jk, β_3,_jk)	58.9656	corr(β_1,_jk, β_3,_jk)
sd(β_3,_jk)	0.0634	0.970	0.0321	0.748
Tree level
sd(β_1,_ijk)	116.1489	corr(β_1,_ijk, β_3,_ijk)	111.1361	corr(β_1,_ijk, β_3,_ijk)
sd(β_3,_ijk)	0.2177	−0.312	0.1675	−0.204
Error term
sd(e_ijk) (spruce)	11.9095		12.9492
sd(e_ijk) (silver birch)	22.2558		24.2960
sd(e_ijk) (downy birch)	21.7166		22.1014
Fitting statistics	Random + fixed	Fixed only	Random + fixed	Fixed only
R²	98.9%	65.1%	98.8%	69.1%
Bias, mm (Bias%)	−0.17 (−0.1%)	2.13 (1.0%)	−0.23 (−0.1%)	−1.62 (−0.7%)
RMSE, mm (RMSE%)	15.14 (7.0%)	87.19 (40.9%)	17.02 (7.2%)	85.58 (36.0%)
^ns Non-significant at 0.05. ^a Based on the likelihood-ratio test, the model estimated with different relative variance weights for each tree species was not significantly better than the one assuming homogeneity of variances.

Fig. 4. Predicted development and absolute growth rate of height based on the Chapman-Richards type growth models fitted for all sample trees and dominant trees. Colored areas indicate 95% confidence bands derived from the estimates and standard errors of the fixed parameters (Table 6). The mean value of C/N ratio in organic layer (25.5) was used in predictions.

Table 7. Statistically significant differences (p < 0.05) among the species- and origin-specific fixed parameters of Chapman-Richards models (Eq. 1) for under-bark diameter at stump height and height of all sample trees (8 spruces and 8 birches per plot) and dominant sample trees (4 thickest trees per species and plot). Parameter estimates for the same model and parameter marked with different letters are significantly different (p < 0.05).
Model for			Spruce	Silver birch, seed-origin	Downy birch, seed-origin	Silver birch, sprout-origin	Downy birch, sprout-origin
Diameter at stump height	All sample trees	β₁	a	a	a	a	a
		β₂	a	b	a	b	a
		β₃	ab	c	b	d	ac
	Dominant sample trees	β₁	a	ab	ac	ad	bcd
		β₂	a	a	b	c	b
		β₃	ab	c	b	d	ac
Height	All sample trees	β₁	a	b	b	b	b
		β₂	a	a	b	b	b
		β₃	a	b	c	c	c
	Dominant sample trees	β₁	a	b	b	b	b
		β₂	a	a	bc	ab	ac
		β₃	a	b	b	b	b

Fig. 5. Simulated height development of Norway spruce, silver birch and downy birch in a mixed spruce-birch stand (Eq. 1, Table 6); carbon-nitrogen ratio of 25.5 was used. Spruce is planted, and birches regenerate naturally from seeds and sprouts. EC is performed at the beginning of 4th growing season after spruce planting.

Fig. 6. Height developments simulated by the models of this study (Eq. 1, Table 6); the earlier studies are illustrated with gray lines. A = spruce in a mixed spruce-birch stand (Huuskonen et al. 2023), B = spruce in a pure spruce stand on fresh site (Siipilehto et al. 2014), C = spruce in a pure spruce stand (Saksa et al. 2005), D = spruce in a pure spruce stand (Elfving 1982), E = silver birch in a mixed spruce-birch stand (Huuskonen et al. 2023), F = sprout-origin silver birch, stump diameter 5 cm (Björkdahl 1983), G = downy birch in a mixed spruce-birch stand (Huuskonen et al. 2023), H = sprout-origin downy birch, stump diameter 5 cm (Björkdahl 1983), I = sprout-origin silver birch, stump diameter 2.5 cm (Björkdahl 1983), J = sprout-origin downy birch, stump diameter 2.5 cm (Björkdahl 1983), and K = seed-origin birch (Elfving 1982).

Fig. 7. Development of stump height diameter simulated by the models of this study (Eq. 1, Table 5) and earlier studies: A = spruce in a mixed spruce-birch stand (Huuskonen et al. 2023), B = spruce in a mixed pine-spruce stand (Bianchi et al. 2021), C = silver birch in a mixed spruce-birch stand (Huuskonen et al. 2023), and D = downy birch in a mixed spruce-birch stand (Huuskonen et al. 2023).

Fig. 8. Average of Ripley’s L₁₂-functions of spruce and birch on 18 sample plots in nine mixed spruce-birch stands. Colored area represents the confidence level of 999 Montecarlo simulations.