Trends in diameter at breast height (DBH)-height distribution and allometric relationships among major conifer species in the Altay Mountains, Northwest China

doi:10.1016/j.regsus.2026.100386

Abstract

Abstract:

The scaling relationship between diameter at breast height (DBH) and tree height is a fundamental indicator of tree growth dynamics, reflecting biomass allocation strategies in the horizontal and vertical dimensions. While extensive research has examined this relationship in temperate and tropical forests, studies focusing on mountainous coniferous ecosystems in Central Asia, particularly the Altay Mountains in Northwest China, remain limited. This study employed field survey data collected in 2023 from three altitudinal zones within the western, central, and eastern forest regions of the Altay Mountains in Northwest China to systematically assess the DBH-height distribution patterns of Larix sibirica, Abies sibirica, and Picea obovata. Furthermore, 24 statistical DBH-height models, including linear and nonlinear formulations, were evaluated to determine the optimal allometric scaling functions for these species. In the western forest region, L. sibirica was primarily represented by large (DBH of 30.00-50.00 cm) and extra-large (DBH>50.00 cm) individuals, forming a reverse J-shaped DBH frequency distribution. In contrast, the central forest region was dominated by small-diameter trees (DBH<10.00 cm), reflecting active regeneration processes. The eastern forest region, dominated by P. obovata, exhibited a relatively uniform DBH size-class distribution. Tree height distributions also presented distinct regional patterns. L. sibirica in the western forest region followed a bell-shaped height distribution, peaking at mid-altitude. Conversely, P. obovata in the eastern forest region displayed a declining height with increasing altitude. In the central forest region, tree heights predominantly remained below 35.00 m at low altitude, with taller individuals becoming progressively less frequent at mid-altitude and a scattered height distribution observed at high altitude. For DBH-height allometric modeling, the Ratkowsky model provided the best fit for L. sibirica (R²=0.8931), followed by the Loetsch and Prodan models. The Quadratic model showed the highest predictive accuracy for A. sibirica (R²=0.9418), followed by the Linear and Power Function models. The Chapman-Richards model most effectively characterized the growth trajectory of P. obovata (R²=0.8652), followed by the Weibull and Gompertz models. These findings enhance our understanding of the coniferous forest structures and growth dynamics in the Altay Mountains, offering critical insights for forest resource assessment and climate adaptation. The study also provides essential height inputs for biomass and carbon estimation in Central Asian mountain ecosystems.

Key words: Larix sibirica , Abies sibirica, Picea obovata, Diameter at breast height, (DBH)-height allometric scaling, Coniferous forest, Altay Mountains

ZHANG Haiyan, WANG Jian, Ireneusz MALIK, Malgorzata WIATUBA, ZHENG Jianghua. Trends in diameter at breast height (DBH)-height distribution and allometric relationships among major conifer species in the Altay Mountains, Northwest China[J]. Regional Sustainability, 2026, 7(5): 100386.

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Type	Model	Equation	Type	Model	Equation
Linear	Linear	$H=\text{a}+\text{b}D$	Nonlinear	Meyer	$H=1.30+\text{a}\times \left(1-{\text{e}}^{(-\text{b}D)}\right)$
Nonlinear	Quadratic	$H=\text{a}+\text{b}D+\text{c}{D}^{2}$		Modified Logistic	$H=1.30+\frac{\text{a}}{1+{\text{b}}^{-1}\times {D}^{-\text{c}}}$
	Power Function	$H=\text{a}{D}^{\text{b}}$		Prodan	$H=1.30+\frac{{D}^{2}}{\text{a}{D}^{2}+\text{b}D+\text{c}}$
	Burkhart	$H=1.30+\text{a}\times {\text{e}}^{\left(\frac{\text{b}}{D}\right)}$		Ratkowsky	$H=1.30+\text{a}\times {\text{e}}^{{}^{\left(\frac{-\text{b}}{\text{c}+D}\right)}}$
	Curtis	$H=1.30+\text{a}{\left(\frac{D}{1+D}\right)}^{\text{b}}$		Chapman-Richards	$H=1.30+\text{a}{\left(1-{\text{e}}^{-\text{b}D}\right)}^{\text{c}}$
	Exponential	$H=1.30+\text{a}\times {\text{e}}^{\left(\frac{\text{b}}{D+\text{c}}\right)}$		Sibbesen	$H=1.30+\text{a}{D}^{\text{b}{D}^{-\text{c}}}$
	Gompertz	$H=1.30+\text{a}\times {\text{e}}^{\left(-{\text{be}}^{-\text{c}D}\right)}$		Stoffels	$H=1.30+\text{a}{D}^{\text{b}}$
	Korf/Lundqvist	$H=1.30+\text{a}\times {\text{e}}^{\left(-\text{b}{D}^{-\text{c}}\right)}$		Watts	$H=1.30+\left(\frac{\text{a}D}{D+1}\right)+\text{b}D$
	Larson	$H=1.30+{10}^{\text{a}}\times {D}^{\text{b}}$		Weibull	$H=1.30+\text{a}\left(1-{\text{e}}^{-\text{b}{D}^{-\text{c}}}\right)$
	Loetsch	$H=1.30+\frac{{D}^{2}}{{(\text{a}+\text{b}D)}^{2}}$		Wykoff	$H=1.30+{\text{e}}^{\left(\text{a}+\frac{\text{b}}{1+D}\right)}$
	Logarithmic	$H=\text{a}+\text{b}\mathrm{ln}D$		Hossfeld IV	$H=1.30+\text{a}/\left(1+\frac{1}{\text{b}{D}^{\text{c}}}\right)$
	Logistic	$H=1.30+\frac{\text{a}}{1+{\text{be}}^{-\text{c}D}}$		Schumacher	$H=1.30+{\text{ae}}^{(-b{D}^{-1})}$

Model	Training set				Testing set
Model	R²	RMSE (m)	AIC	Bias (m)	R²	RMSE (m)	Bias (m)
Linear	0.8093	3.4626	664.7500	0.0000	0.8331	3.2149	0.1848
Quadratic	0.8513	3.0575	600.5600	0.0000	0.8876	2.6382	0.0566
Power Function	0.8403	3.1687	617.5600	-0.0936	0.8675	2.8642	0.0671
Burkhart	0.8394	3.1783	619.1800	0.1789	0.8906	2.6028	0.2688
Curtis	0.8409	3.1632	616.6500	0.1641	0.8915	2.5912	0.2523
Exponential	0.8394	3.1783	621.1800	0.1789	0.8906	2.6028	0.2689
Gompertz	0.8452	3.1202	611.3700	-0.0517	0.8872	2.6425	-0.0958
Korf/Lundqvist	0.8517	3.0541	599.9700	0.0067	0.8895	2.6150	0.1253
Larson	0.8356	3.2149	625.2700	-0.1349	0.8606	2.9377	0.0179
Loetsch	0.8515	3.0555	598.2100	0.0229	0.8925	2.5797	0.1109
Logarithmic	0.7590	3.8930	727.0900	0.0000	0.7817	3.6760	0.1818
Logistic	0.8334	3.2368	630.8800	-0.1021	0.8751	2.7805	-0.2384
Meyer	0.8479	3.0929	604.6900	-0.1261	0.8790	2.7374	-0.0311
Modified Logistic	0.0000	7.9299	1107.5800	0.0000	-0.0041	7.8843	-0.5023
Prodan	0.8518	3.0523	599.6500	-0.0034	0.8904	2.6044	0.0939
Ratkowsky	0.8515	3.0554	600.2000	-0.0117	0.8917	2.5893	0.0624
Chapman-Richards	0.8515	3.0564	600.3600	-0.0209	0.8899	2.6113	0.0413
Sibbesen	0.8518	3.0527	599.7200	0.0024	0.8901	2.6089	0.1087
Stoffels	0.8356	3.2149	625.2700	-0.1349	0.8606	2.9377	0.0179
Watts	0.8148	3.4129	657.0700	-0.0495	0.8380	3.1671	0.1376
Weibull	0.8512	3.0587	600.7800	-0.0297	0.8890	2.6209	0.0253
Wykoff	0.8423	3.1486	616.1800	0.1491	0.8924	2.5805	0.2352
Hossfeld IV	0.0000	7.9299	1107.5800	0.0000	-0.0041	7.8843	-0.5023
Schumacher	0.8394	3.1783	619.1800	0.1789	0.8906	2.6028	0.2688

Model	Training set				Testing set
Model	R²	RMSE (m)	AIC	Bias (m)	R²	RMSE (m)	Bias (m)
Linear	0.9470	1.3356	322.3600	0.0000	0.9383	1.6196	0.1233
Quadratic	0.9503	1.2941	289.6300	0.0000	0.9407	1.5879	0.1160
Power Function	0.9454	1.3565	339.3600	-0.1714	0.9360	1.6494	-0.0338
Burkhart	0.9367	1.4601	420.3200	-0.5240	0.9374	1.6320	-0.3529
Curtis	0.9370	1.4569	417.9300	-0.5347	0.9372	1.6338	-0.3654
Exponential	0.9367	1.4601	422.3200	-0.5240	0.9374	1.6320	-0.3529
Gompertz	0.9283	1.5541	491.0100	-0.5410	0.9318	1.7023	-0.3848
Korf/Lundqvist	0.9373	1.4524	416.5500	-0.5521	0.9367	1.6402	-0.3837
Larson	0.9125	1.7166	598.3700	-0.7073	0.9094	1.9624	-0.5210
Loetsch	0.9312	1.5223	466.2300	-0.6645	0.9282	1.7469	-0.4982
Logarithmic	0.7097	3.1265	1257.9200	0.0000	0.6879	3.6428	0.2999
Logistic	0.9078	1.7614	628.7300	-0.5832	0.9176	1.8719	-0.4181
Meyer	0.8993	1.8412	675.4700	-1.0025	0.8958	2.1052	-0.7973
Modified Logistic	0.2071	5.1669	1812.5100	-0.0001	0.2286	5.7268	0.8482
Prodan	0.9345	1.4848	440.8400	-0.6008	0.9339	1.6769	-0.4429
Ratkowsky	0.9250	1.5893	515.6500	-0.4792	0.9173	1.8755	-0.2581
Chapman-Richards	0.9353	1.4762	434.4100	-0.5687	0.9351	1.6616	-0.4123
Sibbesen	0.9368	1.4584	421.1000	-0.5623	0.9361	1.6484	-0.3993
Stoffels	0.9125	1.7166	598.3700	-0.7073	0.9094	1.9624	-0.5210
Watts	0.9400	1.4209	390.4200	-0.1486	0.9346	1.6679	-0.0189
Weibull	0.9330	1.5016	453.1600	-0.5932	0.9326	1.6924	-0.4423
Wykoff	0.9371	1.4556	418.9600	-0.5457	0.9369	1.6376	-0.3783
Hossfeld IV	0.2071	5.1669	1812.5100	-0.0001	0.2286	5.7268	0.8482
Schumacher	0.9367	1.4601	420.3200	-0.5240	0.9374	1.6320	-0.3529

Model	Training set				Testing set
Model	R²	RMSE (m)	AIC	Bias (m)	R²	RMSE (m)	Bias (m)
Linear	0.9032	2.5968	1565.1900	0.0000	0.8794	2.8849	-0.2045
Quadratic	0.9094	2.5124	1513.1600	0.0000	0.8957	2.6825	-0.1646
Power Function	0.9044	2.5811	1555.3000	-0.0991	0.8853	2.8142	-0.2839
Burkhart	0.8998	2.6425	1593.7300	0.3210	0.8926	2.7227	0.1226
Curtis	0.9016	2.6185	1578.8000	0.2912	0.8941	2.7040	0.0927
Exponential	0.8998	2.6425	1595.7300	0.3211	0.8926	2.7226	0.1226
Gompertz	0.9140	2.4482	1470.7900	-0.0787	0.9006	2.6197	-0.2834
Korf/Lundqvist	0.9116	2.4822	1493.3600	0.0032	0.8970	2.6666	-0.1959
Larson	0.8975	2.6721	1611.9900	-0.2771	0.8767	2.9176	-0.4726
Loetsch	0.9131	2.4606	1477.0900	-0.0384	0.8979	2.6541	-0.2371
Logarithmic	0.7033	4.5469	2481.6500	0.0000	0.7253	4.3543	0.2051
Logistic	0.9087	2.5219	1519.3200	-0.1528	0.8972	2.6640	-0.3462
Meyer	0.8960	2.6918	1624.0100	-0.4403	0.8818	2.8558	-0.6082
Prodan	0.9137	2.4520	1473.3500	0.0350	0.8997	2.6311	-0.1671
Ratkowsky	0.9134	2.4562	1476.1300	-0.0376	0.8985	2.6466	-0.2401
Chapman-Richards	0.9145	2.4410	1465.9800	-0.0104	0.9002	2.6247	-0.2100
Sibbesen	0.9123	2.4724	1486.9100	0.0147	0.8980	2.6528	-0.1847
Stoffels	0.8975	2.6721	1611.9900	-0.2771	0.8767	2.9176	-0.4726
Watts	0.9026	2.6057	1570.7700	-0.0279	0.8779	2.9030	-0.2416
Weibull	0.9152	2.4306	1459.0100	-0.0176	0.9012	2.6117	-0.2164
Wykoff	0.9034	2.5949	1565.9800	0.2608	0.8954	2.6865	0.0625
Hossfeld IV	0.9145	2.4402	1465.4600	-0.0049	0.9001	2.6253	-0.2055
Schumacher	0.8998	2.6425	1593.7300	0.3210	0.8926	2.7227	0.1226

Species	Optimal model	Evaluation metric				Parameter
Species	Optimal model	R²	RMSE (m)	AIC	Bias (m)	a	b	c
L. sibirica	Loetsch	0.8515	3.0555	598.2100	0.0229	-3.1638	-0.1417
	Prodan	0.8518	3.0523	599.6500	-0.0034	0.0197	0.9271	9.4776
	Ratkowsky	0.8515	3.0554	600.2000	-0.0117	48.3582	40.7618	7.6326
A. sibirica	Quadratic	0.9503	1.2941	289.6300	0.0000	-0.5853	0.6747	-0.0030
	Linear	0.9470	1.3356	322.3600	0.0000	-0.3295	0.5797
	Power Function	0.9454	1.3565	339.3600	-0.1714	0.5372	1.0149
P. obovata	Gompertz	0.9140	2.4482	1470.7900	-0.0787	18.3355	5.9331	0.1283
	Weibull	0.9152	2.4306	1459.0100	-0.0176	19.3807	0.0027	1.9123
	Chapman-Richards	0.9145	2.4410	1465.9800	-0.0104	21.0811	0.0795	2.7814