Application of Climate Sensitivity Transfer Matrix Growth Model in Qinghai Province

Abstract

This study utilizes data from the eighth and ninth Chinese National Forest Inventories of Qinghai Province to establish a climate-sensitive transfer matrix growth model for natural forests in Qinghai Province. The model considers tree species diversity (S_d), size diversity (D_c), mean annual temperature (MAT), and mean annual precipitation (MAP) and their impacts on tree growth, mortality, and recruitment. Additionally, the forest stand growth and development were predicted under different climate scenarios (RCP2.6, RCP4.5, RCP8.5) for the next 50 years. The results show that the number of Qinghai spruce (Picea crassifolia Kom.) and White birch (Betula platyphylla Sukaczev) trees per hectare gradually decreases, but the stock volume continues to increase. The number of trees per hectare remains relatively stable (from 2235 to 855), with stock volume increasing annually for the first 30 years of the simulation and then stabilizing (from 76.96 to 798.02). Other tree species groups exhibit a continuous annual increase. Comparing the changes in stock volume and tree numbers under three different climate scenarios, there was no significant difference, and the overall trend remained similar. The finding fills a gap in the research on climate-sensitive transfer matrix growth models for natural forests in Qinghai Province. Compared to single-tree and whole-stand models, this model can predict forest stand growth more quickly and effectively, providing a reliable reference for future forest management. It helps formulate policies to address climate change and promote the sustainable development of forest health. This achievement will contribute to a better understanding of future forest stand growth trends, offering valuable insights for sustainable forest management.

1. Introduction

Qinghai Province, located in northwest China, is an important ecological function zone characterized by fragile ecosystems and high sensitivity to climate change [1,2,3]. Rising temperatures and changes in precipitation patterns have intensified glacier melt, altered river runoff, and affected forest growth and biodiversity [4,5,6]. These impacts highlight the urgent need to understand forest dynamics and to develop scientific strategies for sustainable forest management in the region. Forests play a vital role in maintaining ecological stability, preserving biodiversity, and mitigating global climate change through carbon sequestration [7,8,9]. They also provide essential ecosystem services such as water conservation, soil stabilization, and climate regulation [10,11,12,13]. Therefore, effective forest protection and management in Qinghai are crucial for both regional ecological security and long-term sustainable development.

Therefore, protecting and restoring Qinghai’s forest ecosystems is crucial to address climate change and prevent land degradation. Still, it is also crucial for ensuring ecological security, promoting biodiversity, and improving the quality of life for local people [14]. Therefore, strengthening the protection and management of Qinghai’s forest resources and implementing scientific forest management and restoration measures are essential for achieving sustainable development of the regional ecological environment.

Forests are dynamic biological systems in constant flux; to obtain decision-relevant information, it is crucial to predict these changes. Forest management decisions are based on information about current and future resource conditions. Without long-term field data, forest growth and yield simulation models, which describe forest dynamics (e.g., growth, mortality, recruitment), have been widely used in forest management [15]. Currently, there are three primary forest growth and yield models: whole-stand models, diameter class models, and individual tree models [16,17,18,19]. Whole-stand models focus on the entire stand and are suitable for plantations with a relatively uniform structure and species composition, operating on a more extensive research scale [20,21]. On the other hand, individual tree models are widely used in studying the growth of uneven-aged mixed forests. These models have evolved from fixed parameter models to mixed-effects individual tree growth models, and further to machine learning-based individual tree growth models [22,23,24,25]. For example, Hamidi modeled individual tree growth and mortality for each of the five major tree species in the Hyrcanian forests of northern Iran through a mixed-effects modeling and machine learning approach [26]. However, individual tree models primarily focus on the growth of single trees, which requires exact data collection and increases survey costs. Diameter class models fall between whole-stand models and individual tree models, concentrating on the diameter class level of stands. Compared to individual tree growth models and whole-stand models, diameter class models apply to structurally complex uneven-aged mixed forests while providing similar predictive capabilities as individual tree models. For instance, Rosa used the matrix growth model to evaluate mortality, growth and recruitment in uneven-aged, naturally regenerated maritime pine stands in the central inland region of Portugal [27]. Moreover, modeling the matrix growth model demands less rigorous data collection, thereby reducing survey costs. Consequently, diameter class models have been widely applied in the growth simulation of natural forests [28,29,30,31].

The climatic conditions in Qinghai are crucial for the health and stability of its forest ecosystems [32,33]. It is essential to consider climate factors in forest growth models [34,35]. Climate factors such as temperature, precipitation, and carbon dioxide concentration not only directly affect the growth rate and health of forests but also indirectly influence forest ecosystems by altering the frequency of pest and disease outbreaks, soil moisture, and nutrient cycling [36,37,38]. Therefore, incorporating climate factors into forest growth models can enhance their accuracy and predictive capabilities, providing a more scientific basis for forest management and conservation. This approach helps to accurately assess the impact of climate change on Qinghai’s forest ecosystems. It provides scientific support for developing adaptive management strategies, ensuring the sustainable use of forest resources and regional ecological security. Incorporating climate variables into the models can better simulate and predict forest growth dynamics under various scenarios, offering crucial insights for addressing climate change and protecting the ecological environment.

The transition matrix growth model can accurately describe the dynamic changes in forest ecosystems by analyzing the growth patterns of natural forests. This is particularly important for Qinghai, a region with a fragile ecological environment and abundant natural forest resources. The natural forests in Qinghai play a crucial role in maintaining regional ecological balance and biodiversity. They also significantly contribute to ecological services such as windbreak, sand fixation, water conservation, and climate regulation. Therefore, this study aims to establish a climate-sensitive transition matrix growth model to predict the growth of natural forests in Qinghai Province. It will forecast changes in forest species composition, stand basal area, and stand density under different climate scenarios. This provides a foundational basis for the future management of natural forests in Qinghai Province.

2. Materials and Methods

2.1. Study Area

Qinghai, located in northwest China, lies between the geographical coordinates of 89°35′–103°04′ E and 31°36′–39°19′ N. It experiences a plateau continental climate characterized by cold and dry winters, short and cool summers, long hours of sunshine, and intense solar radiation. The annual average temperature ranges from −5.1 °C to 9.0 °C, while the average annual precipitation varies from 15 mm to 750 mm, gradually decreasing from southeast to northwest. The region features diverse and complex terrain, with the general topography sloping from high elevations in the northwest to lower elevations in the southeast. The eastern part of Qinghai is predominantly mountainous, whereas the western part consists of plateaus and basins. The area is rich in rivers and lakes, with an average elevation exceeding 3000 m above sea level [8].

2.2. Data Sources

The research data are derived from the 8th and 9th Chinese National Forest Inventory (CNFI) data of Qinghai Province. The survey plots are distributed within 4 km × 4 km grids, each measuring 0.067 hectares (Chinese unit of area equivalent to 1 Mu). During the survey, basic information such as plot coordinates, dominant tree species, slope, aspect, etc., was recorded. Each sample tree was individually measured and marked with a tree tag number to facilitate subsequent re-surveys. A total of 327 natural forest plots were selected for this study. The data were randomly split into 227 plots for model establishment and 100 plots for model validation (Figure 1). The selected plots have not been subjected to artificial logging or natural disturbances like pests and diseases.

This study categorizes Qinghai Province’s natural forests into four tree species: Qinghai spruce (Picea crassifolia Kom.), White birch (Betula platyphylla Sukaczev), Cupressus (Cupressus funebris Endl.), and other species. The “other species” category comprises several species, each contributing less than 5% of the total.

The establishment of the transition matrix growth model in this study selected variables that may influence the growth of natural forests in Qinghai Province, including mean annual temperature (MAT), mean annual precipitation (MAP), species diversity (S_d), size diversity (D_c), Slope (SLcos), diameter at breast height (DBH), stand basal area (Ba), and number of trees per hectare (N). The climate data were obtained from the Asia-Pacific database within the Climate AP (v2.30) software, providing the annual mean temperature and annual mean precipitation for each study site.

The formulas for calculating S_d and D_c are as follows:

$${\mathrm{S}}_{\mathrm{d}}=-\sum _{\mathrm{i}=1}^{\mathrm{m}}{\displaystyle \frac{{\mathrm{B}\mathrm{a}}_{\mathrm{i}}}{\mathrm{B}\mathrm{a}}}\mathrm{l}\mathrm{n}\left({\displaystyle \frac{{\mathrm{B}\mathrm{a}}_{\mathrm{i}}}{\mathrm{B}\mathrm{a}}}\right)$$

(1)

$${\mathrm{D}}_{\mathrm{c}}=-\sum _{\mathrm{j}=1}^{\mathrm{n}}{\displaystyle \frac{{\mathrm{B}\mathrm{a}}_{\mathrm{j}}}{\mathrm{B}\mathrm{a}}}\mathrm{l}\mathrm{n}\left({\displaystyle \frac{{\mathrm{B}\mathrm{a}}_{\mathrm{j}}}{\mathrm{B}\mathrm{a}}}\right)$$

(2)

Ba_i and Ba_j represent the breast height cross-sectional area for species i and diameter class j. Ba is the total breast height cross-sectional area of the plot. m represents the number of species, and n represents the number of diameter class.

Detailed descriptions of each parameter’s performance are provided in

Table 1. Plot summary statistics.

		MAT (°C)	MAP (mm)	DBH	Sd	Dc	SLcos	Ba (m2/ha)	N (Trees/ha)
Model Development (227 Plots)	Max	5.02	786.00	76.40	1.03	2.40	37.00	65.72	2400
	Min	−2.80	308.60	5.00	0.00	0.00	−43.00	1.92	465
	Mean	1.52	535.31	14.75	0.28	1.68	−1.73	26.89	1255
	SD	1.40	86.77	9.40	0.31	0.44	22.31	15.14	525
Model Validation (100 Plots)	Max	5.98	835.20	90.80	1.34	2.37	45.00	83.03	3120
	Min	−2.40	296.00	5.00	0.00	0.00	−43.00	1.58	465
	Mean	1.70	550.98	15.23	0.19	1.66	−3.18	26.59	1190
	SD	1.42	95.72	9.92	0.30	0.39	21.88	15.65	544

.

2.3. Model Structure

In this study, stepwise regression was used to select independent variables to ensure optimal model performance. The variance inflation factor (VIF) was used to check for multicollinearity in the tree growth, regeneration, and mortality. Generally, a VIF value of less than 5 indicates the absence of multicollinearity issues. All the selected independent variables in this study had VIF values below 5, indicating no multicollinearity among these variables [39].

The transition matrix growth model formula is generally expressed as follows:

$${\mathrm{y}}_{\mathrm{t}+1}={\mathrm{G}}_{\mathrm{t}}\left({\mathrm{y}}_{\mathrm{t}}-{\mathrm{h}}_{\mathrm{t}}\right)+{\mathrm{R}}_{\mathrm{t}}+{\mathsf{ϵ}}_{\mathrm{t}}$$

(3)

In the formula, y_t = [y_ijt] represents the number of surviving trees of species i (i = 1, 2, 3, ..., sp) and diameter class j (j = 1, 2, 3, ..., dc) at time t. h_t = [h_ijt] represents the number of trees of species i and diameter class j that are harvested at time t; if there is no harvesting at time t, it is recorded as 0. R_t represents the number of trees growing into the smallest diameter class during the time interval, and ϵt represents the random error.

The expressions for G and R are as follows:

$$\begin{gathered} \mathrm{G}=\left[\begin{array}{cccc}{\mathrm{G}}_1& & & \\ & {\mathrm{G}}_2& & \\ & & \ddots & \\ & & & {\mathrm{G}}_{\mathrm{m}}\end{array}\right],\mathrm{G}\mathrm{i}=\left[\begin{array}{ccccc}{\mathsf{\alpha }}_{\mathrm{i}1}& & & & \\ {\mathrm{b}}_{\mathrm{i}1}& {\mathsf{\alpha }}_{\mathrm{i}2}& & & \\ & \ddots & \ddots & & \\ & & {\mathrm{b}}_{\mathrm{i},\mathrm{n}-2}& {\mathsf{\alpha }}_{\mathrm{i},\mathrm{n}-1}& \\ & & & {\mathrm{b}}_{\mathrm{i},\mathrm{n}-1}& {\mathsf{\alpha }}_{\mathrm{i}\mathrm{n}}\end{array}\right] \\ \mathrm{R}=\left[\begin{array}{c}{\mathrm{R}}_1\\ {\mathrm{R}}_2\\ \text{⋮}\\ {\mathrm{R}}_{\mathrm{m}}\end{array}\right],{\mathrm{R}}_{\mathrm{i}}=\left[\begin{array}{c}{\mathrm{R}}_{\mathrm{i}}\\ 0\\ ⋮\\ 0\end{array}\right] \end{gathered}$$

(4)

The variable α_ij represents the probability that trees of species i and diameter class j will remain in the same diameter class from time t to t + 1. The variable b_ij represents the probability that trees of species i and diameter class j will grow into the next diameter class j + 1 from time t to t + 1. The relationship between α_ij and b_ij can be expressed as follows:

$${\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}=1-{\mathrm{b}}_{\mathrm{i}\mathrm{j}}-{\mathrm{m}}_{\mathrm{i}\mathrm{j}}$$

(5)

In the formula, the parameter m_ij represents the mortality rate. The parameter b_ij is obtained by dividing the growth increment(g_ij) by the diameter class width (5 cm in this study).

The growth increment g_ij is calculated using the following formula:

$$\log \left({\mathrm{g}}_{\mathrm{ij}}+1\right)={\mathsf{\gamma }}_{\mathrm{i}1}+{\mathsf{\gamma }}_{\mathrm{i}2}\mathrm{DBH}+{\mathsf{\gamma }}_{\mathrm{i}3}{\mathrm{S}}_{\mathrm{d}}+{\mathsf{\gamma }}_{\mathrm{i}4}{\mathrm{D}}_{\mathrm{c}}+{\mathsf{\gamma }}_{\mathrm{i}5}\mathrm{Ba}+{\mathsf{\gamma }}_{\mathrm{i}6}\mathrm{SLcos}+{\mathsf{\gamma }}_{\mathrm{i}7}\mathrm{MAT}+{\mathsf{\gamma }}_{\mathrm{i}8}\mathrm{MAP}+{\mathsf{\mu }}_{\mathrm{ij}}$$

(6)

In the formula, DBH represents the diameter at the breast height of trees, S_d represents species diversity. D_c represents diameter class diversity. SLcos represents slope × cos(aspect) [40], γ denotes parameters, and μ_ij represents the error term.

Since the number of tree recruitment is always greater than or equal to zero, a Tobit model was used in the calculation [41].

$$\mathrm{R}=\mathsf{\Omega }\left({\displaystyle \frac{{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}}{{\mathsf{\sigma }}_{\mathrm{i}}}}\right){\mathsf{\beta }}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\sigma }}_{\mathrm{i}}\mathsf{\omega }\left({\displaystyle \frac{{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}}{{\mathsf{\sigma }}_{\mathrm{i}}}}\right)$$

(7)

$${\mathsf{\beta }}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}={\mathsf{\beta }}_{\mathrm{i}1}+{\mathsf{\beta }}_{\mathrm{i}2}{\mathrm{N}}_{\mathrm{i}}+{\mathsf{\beta }}_{\mathrm{i}3}\mathrm{Ba}+{\mathsf{\beta }}_{\mathrm{i}4}{\mathrm{S}}_{\mathrm{d}}+{\mathsf{\beta }}_{\mathrm{i}5}{\mathrm{D}}_{\mathrm{c}}+{\mathsf{\beta }}_{\mathrm{i}6}\mathrm{SLcos}+{\mathsf{\beta }}_{\mathrm{i}7}\mathrm{MAT}+{\mathsf{\beta }}_{\mathrm{i}8}\mathrm{MAP}+{\mathrm{v}}_{\mathrm{i}}$$

(8)

In the formula, N_i represents the number of trees per hectare for species i. Ω and ω are the standard normal cumulative distribution and density functions. σ_i is the standard deviation of the residual v_i obtained in the parameter estimation β.

The mortality distribution of the stand follows a binomial distribution. Hence, the mortality rate m_ij is calculated using a Probit model [42].

$${\mathrm{m}}_{\mathrm{ij}}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{ij}}}{\mathrm{T}}}={\displaystyle \frac{1}{\mathrm{T}}}\mathsf{\Omega }({\mathsf{\delta }}_{\mathrm{i}1}+{\mathsf{\delta }}_{\mathrm{i}2}\mathrm{DBH}+{{\mathsf{\delta }}_{\mathrm{i}3}\mathrm{B}\mathrm{a}+\mathsf{\delta }}_{\mathrm{i}4}{\mathrm{H}}_1+{\mathsf{\delta }}_{\mathrm{i}5}{\mathrm{H}}_2+{\mathsf{\delta }}_{\mathrm{i}6}\mathrm{SLcos}+{\mathsf{\delta }}_{\mathrm{i}7}\mathrm{MAT}+{\mathsf{\delta }}_{\mathrm{i}8}\mathrm{MAP}+{\mathsf{\xi }}_{\mathrm{ij}})$$

(9)

In the equation, M_ij represents the probability of trees of species i and diameter class j dying within time T, where δ_i is a parameter and ξ_ij is the error term.

2.4. Model Evaluation and Validation

Using the 9th National Forest Inventory data of Qinghai Province, the accuracy of the model was assessed. The goodness-of-fit of these three models was first compared using Akaike information criterion (AIC) and Bayesian information criterion (BIC). The root mean square error (RMSE) and mean absolute error (MAE), as evaluation metrics, were calculated to evaluate the mode accuracy. RMSE reflects the square root of the average squared deviation between model predictions and actual observations, measuring the standard deviation of prediction errors. Meanwhile, MAE provides the average absolute difference between model predictions and actual values. The model was developed and validated using R version 4.5.1, package censReg [43].

$$\mathrm{logL}\left(\mathsf{\theta }\right)=\sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{logf}({\mathrm{y}}_{\mathrm{i}}\left|\mathsf{\theta }\right)$$

(10)

$$\mathrm{AIC}=2\mathrm{k}-2\mathrm{logL}$$

(11)

$$\mathrm{BIC}=\log \left(\mathrm{n}\right)\text{·}\mathrm{k}-2\mathrm{logL}$$

(12)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{\mathrm{m}}}\sum _{\mathrm{n}=1}^{\mathrm{m}}{({\mathrm{y}}_{\mathrm{n}}-{\widehat{\mathrm{y}}}_{\mathrm{n}})}^2}$$

(13)

$$\mathrm{MAE}={\displaystyle \frac{1}{\mathrm{m}}}\sum _{\mathrm{n}=1}^{\mathrm{m}}|{\mathrm{y}}_{\mathrm{n}}-{\widehat{\mathrm{y}}}_{\mathrm{n}}|$$

(14)

ŷ_n represents the predicted value, y_n represents the actual measured value, and m denotes the number of samples, where k is the number of estimated parameters in the model, n is the sample size, and logL is the log-likelihood value. Lower values of AIC and BIC indicate better model performance, with AIC favoring predictive accuracy and BIC being more conservative by applying a stronger penalty for model complexity.

2.5. Growth Prediction

Using the established transition matrix growth model, we selected representative sample plots for growth simulation. During the simulation process, we predicted the growth status of the forest over the next 50 years under different climate scenarios (RCP 2.6, RCP 4.5, RCP 8.5), explicitly analyzing changes in stand volume and stand density. The three climate scenarios used in this study—RCP 8.5, RCP 4.5, and RCP 2.6—are derived from the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report. These scenarios represent high, medium, and low levels of future carbon dioxide emissions, respectively [44]. Using the ClimateAP (v2.30) software, we projected the average annual temperature and precipitation in Qinghai Province over the next 50 years under each scenario [45]. These projections were then used to estimate forest growth and development under future climate conditions. These simulations and analyses provide a better understanding of the dynamic trends of forests at different time stages, providing important insights for sustainable forest management and informed decision-making. These results will help us formulate more effective forest management strategies to ensure the health and stable development of forest ecosystems.

3. Results

3.1. Model Parameters and Validation

The growth model shows a significant positive correlation with diameter at breast height (DBH) and size diversity (D_c), and a significant negative correlation with species diversity (S_d) and basal area (Ba) for most species groups, except for White birch. For all species except White birch, tree growth is significantly positively correlated with mean annual temperature (MAT) and mean annual precipitation (MAP) (

Table 2. Statistical results of the parameters of the growth mode.

	Qinghai Spruce	White Birch	Cupressus	Others
Intercept	3.938 × 10−2	5.435 × 10−1 ***	3.558 × 10−1 ***	5.347 × 10−1 ***
DBH	7.968 × 10−3 ***	1.171 × 10−2 ***	1.346 × 10−3 ***	6.90 × 10−3 ***
SLcos 1	8.961 × 10−4 **	−6.989 × 10−4 ***	3.419 × 10−4 ***	2.813 × 10−3 ***
Sd	1.488 × 10−1 ***	−8.197 × 10−2 ***	−5.896 × 10−2 ***	−1.971 × 10−1 ***
Dc	3.150 × 10−1 ***	9.960 × 10−2 ***	4.878 × 10−2 ***	1.264 × 10−2
MAT	6.075 × 10−2 ***	−1.619 × 10−2 ***	1.565 × 10−2 ***	1.069 × 10−2 *
MAP	2.128 × 10−4 ***	−3.358 × 10−4 ***	8.679 × 10−4 ***	4.484 × 10−4 ***
Ba	−9.965 × 10−3 ***	−5.432 × 10−3 ***	−1.314 × 10−3 ***	−7.811 × 10−3 ***
R2 2	0.44	0.29	0.22	0.30
AIC 3	371.33	91.30	−4610.09	270.41
BIC 4	424.52	148.48	−4561.69	322.71
LogLik 5	−64.56	−865.59	2314.05	−75.15

Note: Significance levels: * p < 0.10; ** p < 0.05; *** p < 0.01; ¹ SLcos = Slope × cos(Aspect); ² R²: Nagelkerke’s pseudo R-squared; ³ AIC: Akaike information criterion; ⁴ BIC: Bayesian information criterion; ⁵ LogLink: log-likelihood value.

).

The mortality is significantly negatively correlated with DBH and significantly positively correlated with Ba. S_d and D_c are positively correlated with tree mortality for most species (

Table 3. Statistical results of the parameters of the mortality model.

	Qinghai Spruce	White Birch	Cupressus	Others
Intercept	−1.479 × 100 ***	−2.78 × 100 ***	−2.085 × 100 ***	−2.682 × 100 ***
DBH	−2.635 × 10−2 ***	−3.052 × 10−2 ***	−1.579 × 10−2 ***	−3.043 × 10−2 ***
SLcos	3.371 × 10−3	−7.136 × 10−3 ***	−3.587 × 10−3 ***	6.382 × 10−4
Sd	1.063 × 10−1	−4.770 × 10−1 ***	5.846 × 10−1 ***	1.827 × 10−1
Dc	−3.186 × 10−1	5.963 × 10−1 ***	−7.463 × 10−3	2.505 × 10−1
MAT	8.475 × 10−2 *	6.262 × 10−2 **	1.580 × 10−3	8.940 × 10−2
MAP	−1.269 × 10−3	7.612 × 10−4 **	4.533 × 10−4	−1.181 × 10−3
Ba	2.833 × 10−2 ***	1.669 × 10−2 *	1.092 × 10−3	1.001 × 10−2 ***
R2	0.28	0.27	0.24	0.19
AIC	707.51	3032.59	1841.78	553.91
BIC	756.74	3085.98	1897.76	602.33
LogLik	−345.76	−1508.29	−912.89	−268.96

Note: Significance levels: * p < 0.10; ** p < 0.05; *** p < 0.01.

). MAT and MAP show a significant positive correlation with White birch mortality and no significant correlation with other species.

During the field investigation, it was observed that Cupressus exhibits poor natural regeneration capacity. Moreover, most site conditions in Qinghai Province are not conducive to Cupressus regeneration. As a result, natural regeneration of Cupressus in the region is extremely limited. Due to the insufficient data, it was not feasible to develop a recruitment model for Cupressus in this study. The number of trees per hectare (N) correlates significantly positively with recruitment for all species and significantly negatively with Ba. S_d and D_c correlate negatively with recruitment for most species, while MAT and MAP show a significant positive correlation (

Table 4. Statistical results on the parameters of the recruitment model.

	Qinghai Spruce	White birch	Others
Intercept	−4.511 × 102 ***	2.28 × 102 ***	−8.62 × 101 ***
N 1	2.41 × 10−1 ***	8.03 × 10−2 ***	1.14 × 10−2 ***
SLcos	2.77 × 100 ***	1.32 × 100 ***	2.13 × 10−1 **
Sd	−4.85 × 10−1	−4.73 × 101 ***	7.54 × 101 ***
Dc	2.42 × 102 ***	−2.19 × 101 **	−2.74 × 101 ***
MAT	8.00 × 100 ***	−3.70 × 101 ***	1.11 × 101 ***
MAP	2.17 × 10−1 ***	7.29 × 10−2 **	3.37 × 10−1 ***
Ba	−9.15 × 100 ***	−4.88 × 100 ***	−5.64 × 100 ***
LogSigma 2	4.97 × 100 ***	4.97 × 100 ***	4.74 × 100 ***
R2	0.42	0.33	0.19
AIC	28,369.25	30,196.09	41,308.93
BIC	28,424.63	30,250.56	41,369.01
LogLik	−14,175.62	−15,089.05	−20,645.47

Note: Significance levels: ** p < 0.05; *** p < 0.01; ¹ N: number of plots with recruitment, the total number of plots; ² logSigma: log of the standard deviation of residuals.

).

The fitted parameters of the climate-sensitive transition matrix growth model were validated against independent data from natural forests in Qinghai Province. The results showed RMSE = 1.53 m²/ha, MAE = 1.46 m²/ha, and a relatively high coefficient of determination (R²). These metrics indicate that the model can provide reasonable predictions of growth trends in natural secondary forests. However, given the relatively small plot size and potential sampling bias, the results should be interpreted with caution.

In the models of tree growth, mortality, and recruitment developed in this study, we applied appropriate variable importance analysis methods tailored to linear and generalized linear models to systematically assess the independent contribution of each predictor. For the growth model, we used the LMG method (Lindeman, Merenda, and Gold), which decomposes the total R² by averaging each variable’s marginal contribution across all possible orderings of entry into the model, thereby providing a robust estimate of independent explanatory power. For the mortality model, we employed dominance analysis, which evaluates variable importance across general, conditional, and complete dominance frameworks. For the recruitment model, standardized regression coefficients derived from the censored regression were used to infer relative contributions.

The results consistently revealed that Ba and DBH were the most influential variables across all models, with independent contributions substantially greater than those of topographic or climatic factors.

3.2. Growth Simulation

However, during the climate data projection process, we found that the variations in temperature and precipitation among the three climate scenarios were relatively small, making it difficult to discern any substantial changes. Using the established transition matrix growth model, we selected actual forest plots to simulate growth over the next 50 years under different climate scenarios. By comparing changes in stand volume, and the number of trees per hectare, the number of trees per hectare showed a decreasing trend throughout the simulation (from 2235 to 855), particularly for White birch (from 1740 to 90), which exhibited a continuous decline. Qinghai spruce showed an initial increase followed by a decrease, while other species groups showed a consistent yearly increase (Figure 2). There were no significant differences in tree numbers across the three climate scenarios.

Regarding changes in stand volume, the volume increased annually throughout the simulation (from 76.96 to 798.02). White birch and Cupressus showed an increasing trend in the first 30 years of the prediction period, after which their volume remained stable without significant increases or decreases. Qinghai spruce followed a similar pattern, with an increasing trend in the first 35 years and a slight decrease. In contrast, other species groups consistently increased throughout the simulation period, ending with the largest share of volume (Figure 3). Similarly to tree number changes, different climate scenarios did not result in significant differences in stand volume.

4. Discussion

4.1. Model Parameters and Validation Results

According to the result, the diameter at breast height (DBH) is significantly positively correlated with tree growth (Table 2) and significantly negatively correlated with tree mortality (Table 3). Du found similar results in a transfer matrix growth modeling study of oak species in Shanxi Province and attributed the phenomenon to the theory of ecological niche competition [45]. Wang came to the same conclusion in his study of Masson pine in Hunan Province, attributing it to the greater competitive ability of larger-diameter trees for light, water, and soil nutrients, leading to faster growth rates [46]. In addition, Zhou also mentioned that after a long period of competition, with the growth and succession of the forest, the larger diameter trees have a stronger resistance to survival [47].

Species diversity (S_d) is significantly negatively correlated with tree growth of most tree species (Table 2), likely due to increased competition among species during growth, which slows tree growth. In a study of beech forests in New Zealand, Coomes found that competition for light and nutrients during the early stages of a forest’s seedling life can lead to a slowdown in forest growth [48]. However, Forrester pointed out that the relationship between species diversity and productivity can be either promotive or inhibitory depending on the species and the succession stage, mainly depending on whether the competition between species is benign [49]. This is the same as our findings that even though forest growth and species diversity were significantly negatively correlated in most species groups, Qinghai spruce showed a significant positive correlation. Species diversity shows different responses among various species, potentially related to different species responses to changes in species diversity.

Searle study on Canadian and American forests noted that increased species diversity can increase tree mortality, with higher species diversity leading to higher tree mortality rates [50]. Conversely, Edgar and Burke, in a study of northeastern Minnesota, found that an increase in tree species diversity resulted in the growth of the stand being slowed down [51]. Therefore, the response of tree mortality to species diversity varies by region and species. Our results found that tree species diversity was significantly negatively correlated with White birch and significantly positively correlated with Cupressus mortality (Table 3). Although it has been shown that an increase in species diversity may promote forest growth to certain extent [52], especially in the case of White birch, which is a pioneer species and is more adaptable to the environment [53], an increase in species diversity may lead to an increase in the competition for nutrients between species, which may result in the death of Cupressus [54]. Furthermore, results indicate species diversity (S_d) positively correlates with forests recruitment (Table 4). Young reported similar results, attributing this to the niche complementarity principle, where differences in species growth lead to complementarity and niche differentiation, thereby increasing recruitment in species-rich forests [55]. Vencurik came to the same conclusion in his study of the European yew, and attributed it to the principle of interspecific complementarity [56].

Diameter class diversity (D_c) positively correlates with stand growth and mortality. Consistent with the present work, Liang found that size diversity strongly correlates with tree growth in studies on American Douglas fir and western hemlock [57]. The positive correlation between size diversity and forest mortality was observed, and similar results were obtained in a study of Douglas-fir–western hemlock forest in the Pacific Northwest of the United States by Liang, he suggesting that increased size diversity promotes tree mortality due to asymmetric competition, where size differences lead to varying competitive abilities for nutrients, increasing tree mortality [58]. Lei and Tan found that diameter class diversity significantly positively correlates with tree growth and recruitment [59,60]. Many studies also indicate that size diversity promotes forests recruitment, attributed to niche competition theory [61,62]. However, our study found that only Qinghai spruce D_c positively correlates with forest recruitment, while other species groups show a significant negative correlation. Liang similarly found that size diversity negatively correlates with recruitment in monocultures [57]. Young, on the other hand, suggested that the reduction in size diversity reduces competition between ecological niches for light and nutrients, which in turn promotes seedling growth and allows for more recruitment to the forest [55].

Basal area (Ba) is negatively correlated with tree growth and recruitment. The research of Rozendaal similarly concluded that increased basal area gradually reduces forest growth in Amazonia and tropical Africa [63]. Kaber also noted a negative correlation between basal area and forest recruitment, it is attributed to the fact that an increase in basal area represents an increase in forest competition for above and below-ground nutrients, which further leads to a decrease in the forest recruitment [64]. Additionally, our study found that basal area significantly positively correlates with tree mortality. Chen obtained similar results, attributing this to increased competition intensity among trees as basal area increases, leading to higher mortality [65].

Mean annual temperature (MAT) and mean annual precipitation (MAP) showed positive correlations with the growth, mortality, and recruitment of most species, with particularly strong correlations for growth and recruitment. Many studies on climate and forest growth have found that temperature promotes tree growth [66,67]. Moreover, Liu concluded in his study of forests in the Northern Hemisphere that warming temperatures have a positive effect on the radial growth of forests in the Northern Hemisphere [68]. However, the growth model for white birch showed a negative coefficient for MAT (Table 2), which contrasts with general ecological expectations that warmer conditions promote tree growth. This may reflect the unique environment of Qinghai Province, characterized by high elevation, cold temperatures, and semi-arid conditions [8]. White birch is highly tolerant of cold and drought and may be better adapted to such settings, elevated temperatures could potentially exceed its upper tolerance limit. Similar patterns were documented in Mongolia by Gradel (2017a, 2017b), with birch growth exhibiting a negative relationship to climatic variables [69,70]. In addition, it should be noted that white birch is not a dominant tree species in Qinghai. Consequently, the sample size and distribution range of this species in our dataset were limited, which may have led to parameter estimates that do not fully align with its general ecological characteristics. For example, the negative coefficients of climatic variables observed in our model are likely to reflect localized adaptations of white birch within specific environments rather than universal growth responses of the species. Therefore, the simulation results for white birch presented in this study should be interpreted as being applicable primarily to a subset of Qinghai’s forests, and not as representative of the overall species characteristics. Future research should incorporate data from broader geographic ranges and diverse site conditions, together with species-specific physiological traits and volume equations, to more comprehensively reveal the growth response patterns of white birch.

Interestingly, although MAT also showed a positive correlation with tree mortality in our model, its parameter significance was low. While some studies suggest that rising temperatures can exacerbate drought-related tree mortality [71,72], this may not be applicable in our case. The relatively low MAT observed in Qinghai (mean maximum of 5.98 °C and minimum of −2.80 °C) does not appear to induce drought stress in the sampled plots. Therefore, temperature may not be the primary driver of tree mortality in this region.

Similarly, MAP positively correlates with stand growth and mortality, which is consistent with existing research. Sarris and Trouet found that increased precipitation promotes tree growth to some extent [73,74]. Our results suggest that increased precipitation leads to higher mortality of White birch, though current studies generally indicate that increased precipitation reduces forest mortality [75,76]. Considering the characteristics of high-altitude areas, increased precipitation may cause soil saturation, leading to oxygen deficiency in tree roots, affecting respiration and nutrient absorption, and ultimately increasing mortality [77]. Additionally, our study found that temperature and precipitation promote forest regeneration. In a study of Ponderosa and lodgepole pine forests, Petrie noted that moderate increases in temperature and precipitation promoted forest recruitment and seedling growth [78]. Wang found that increased precipitation could promote forest regeneration in a study of mixed-native evergreen broad-leaved forest in Maoming City, Guangdong Province [79]. And Du et al., in their study of alpine plants, found that increased temperatures promote the growth and recruitment of forests in high elevations [80].

4.2. Forest Growth Prediction

Based on the forest growth predictions, the number of White birch trees per hectare gradually decreases year by year under different climate scenarios, while the Qinghai spruce shows a trend of increasing and then decreasing. In contrast, the number of Cupressus remains relatively stable throughout the simulation, and other species groups show an increasing trend (Figure 2). Regarding stand volume changes, Qinghai spruce and Cupressus gradually increase in the early prediction period and remain relatively stable later. White birch, however, does not show significant increases or decreases in stand volume throughout the growth period. In contrast, other species groups do not show significant growth in the early simulation period but exhibit noticeable increases in the later stages (Figure 3). In addition, we similarly found that the number of trees per hectare of forest and the stock volume of forest gradually decreased with climate change.

This phenomenon may be due to the limited regeneration of Qinghai spruce and Cupressus in the Qinghai region. As the simulation progresses, tree deaths exceed the number of regenerations. Qinghai spruce, the main species of natural forests in Qinghai, has strong climate adaptability and can cope with the climate changes in the region [81]. Cupressus, as a coniferous species, can maintain relatively stable growth even in arid and cold areas [82], resulting in a gradual decrease in tree numbers. White birch, as a broad-leaved species, has higher water and temperature requirements than conifers. Its growth and regeneration in Qinghai are limited, this resulted in a sustained decline in forest numbers throughout the growth simulation process. Moreover, as a pioneer species, White birch is gradually replaced by other species during forest succession [83]. Based on the changes in forest stock volume, it can be seen that the total forest stock volume has been increasing despite the gradual decrease in the number of forest trees. This apparent discrepancy can be explained by the substantial growth of surviving trees. Larger diameter classes contributed disproportionately to stand volume, which is consistent with previous studies reporting that a small number of large trees dominate forest biomass and carbon storage in natural forests [84]. The small plot size (0.067 ha) may further amplify this pattern, as the recruitment and mortality of small trees are difficult to capture, while the presence of a few large individuals can markedly increase the estimated stand volume. In particular, the number of Cupressus has shown a slight annual decline in number of trees, but the amount of stock volume has been increasing. This may be due to the fact that Cupressus, as a conifer, is more tolerant of temperature and precipitation at high altitudes, and it can maintain more stable growth and lower mortality in this case [85].

Comparing the changes in forest stock volume and tree numbers under different climate scenarios, there are no significant differences in the changes in tree volume and numbers under high (RCP 8.5), medium (RCP 4.5), and low emission scenarios (RCP 2.6), but there is a slight decreasing trend. Although there are many studies suggesting that warmer temperatures promote forest growth, especially in Qinghai spruce [81]. However, we did not observe this condition in our study. Yang et al. found in their study of the Taihang Mountains that increased temperatures led to a decrease in forest stock volume [86]. He attributed this to the increase in temperature leading to a subsequent increase in plant evapotranspiration, which in turn leads to a decrease in net primary productivity. Changes in stock volume and number of trees under the three different climate scenarios in this study were different but not significant. This may be due to the fact that differences in climate change were not significant at high elevations. Additionally, the high altitude of Qinghai means that trees do not respond strongly to slight climate changes. The main factors influencing the growth of alpine forests are likely soil, topography, and human factors [87,88].

By projecting future stand growth dynamics, we can gain a clearer understanding of forest development trends and make proactive management plans. For example, appropriate thinning can be applied to promote positive forest succession; supplementary planting of Qinghai spruce can be carried out to ensure sufficient regeneration of this species; and selective harvesting of other species can help guide the forest toward a climax community dominated by the most competitive species.

5. Conclusions

This study developed a transition matrix growth model for natural forests in Qinghai Province and predicted forest growth over the next 50 years. The results indicate that the transition matrix growth model can accurately predict future growth trends with high fitting accuracy. Although changes in tree numbers and stand volume exhibit similar trends across different climate scenarios, no significant differences in tree growth were observed. All scenarios show stable volume growth. However, these predictions should be further validated with species-specific growth rates and regional ecological characteristics. This study provides a scientific forecasting model for the growth and development of natural forests in Qinghai Province, offering valuable insights for future forest management decisions. However, the limitations of the model should be noted. Future research should incorporate nonlinear growth models and additional climatic factors, along with long-term monitoring data, to further improve the accuracy and applicability of the predictions.