Cespitose Population Structure and Dynamics of Rare Fraxinus sogdiana in the Yili River Valley, China

Abstract

Fraxinus sogdiana Bunge is a class II key protected plant in China, known as the “living fossil of broad-leaved trees”. It is commonly found in multi-stemmed cespitose forms created by the sprouting of its root systems and stumps. We sampled plots in the east and west of the Kashi River in the Xinjiang Yili F. sogdiana National Nature Reserve. We investigated the cespitose F. sogdiana by using population ecology methods in order to provide scientific information for the conservation and sustainable development of the species as well as for the management of the reserve. We chose diameter class structure instead of age class structure to establish a population static life table, draw population survival and mortality curves, calculate a population dynamic index, and use spectral analysis to explore the fluctuation cycle of the population. The results show that age classes II–IV, comprising 74.72%, 91.53%, and 81.77% of the two cespitose populations in the east and west of the Kashi River and the total population, respectively, showed that the populations had a growing age structure. Still, there were very few individuals in age class I. The survival curves tended to be the Deevey–II type, with peak mortality occurring at age class IX in the east of the Kashi River and age class V in the west of the Kashi River. The dynamic index of populations changed the V_pi in the east and west of the Kashi River and the total population were greater than 0, indicating they were growing-type populations, and the V′_pi of the east of the Kashi River population was closer to 0, meaning that this population was relatively more resilient to external disturbances. Spectral analysis revealed that the periodic fluctuation of the population was mainly controlled by the biological characteristics of the population. Additionally, the east of the Kashi River population and the total population exhibited obvious multi-harmonic small periodic fluctuations. We suggest that the habitat of the cespitose F. sogdiana populations should be protected and improved to strengthen the nurturing management of individuals of age classes I and II for maintaining the natural renewal and development of the population.

1. Introduction

Plants that form multi-stemmed cespitose growth forms by using dormant or adventitious buds on their root systems and stumps to produce sprouting stems are called cespitose plants [1,2]. Morphologically, cespitose plants consist of a clump of trees, of all the individuals from the same seed germination or later-stage connected by roots. After a disturbance, cespitose plants can produce sprouting stems through their existing root systems and residual stumps, rapidly replenishing aboveground biomass loss, renewing in situ, and reclaiming spatial resources to maintain their intrinsic ecological niches [3,4]. Even in the absence of a disturbance, cespitose plants enhance carbon accumulation and sexual reproductive output through newly sprouted stems, ultimately increasing tree fitness [5,6]. Most woody broad-leaved species in forests enhance cespitose growth, and studying cespitose plants has notable implications for understanding population persistence mechanisms, community assembly processes, and ecosystem stability [7,8].

Population structure and dynamics are important attributes of populations and are core contents in population ecology research [9,10]. Population structure refers to the distribution and allocation of individuals of different sizes within a population, reflecting the dynamics and changing trends of the population [11,12]. Population dynamics refer to the changing patterns of a population size over time and space, which can reveal the relationships between a population and its environment [13,14]. Population statistics are an effective method for studying population structure and dynamics. In population statistics, the static life table is considered the core, and the population age composition, survival rate, and mortality rate are counted [9,14]. Then, a comprehensive analysis is made by combining quantitative, spectral analyses of population dynamics [15,16]. This method reflects the survival status of the population, the disturbed situation, and the suitability of individuals to the environment. The development trend and natural regeneration dynamics of the population are also revealed by this method [17,18]. The population age structure and dynamics of cespitose plants have been studied, such as Nitraria tangutorum Bobrov [19], Salix psammophila [20], and Juglans regia L. [21]. Still, few studies have been conducted on the dynamic changes in cespitose plant populations in the Fraxinus genus. These studies focused on the growth characteristics and regeneration patterns of the species [22,23]. In the population sense, the cespitose growth pattern facilitates prolonged plant survival, expands population competitiveness, and further influences population range and dynamic characteristics [1,7]. Therefore, studying the structure and dynamics of cespitose plant populations is of great significance for the protection and ecological restoration of rare plant populations and communities [14,24].

Fraxinus sogdiana is a deciduous tree belonging to the Fraxinus genus in the Oleaceae plant family. The species is a class II key protected wild plant in China [25,26]. This species is a remnant of Tertiary temperate deciduous broadleaf forests, is regarded as the “living fossil of broadleaf trees”, and is only distributed in patches in Xinjiang Yili Fraxinus sogdiana National Nature Reserve in Central Asia [25,26]. The root system and stumps of F. sogdiana produce sprouting stems, forming cespitose F. sogdiana with multi-stemmed growth forms, and its populations are clusters distributed in the nature reserve. F. Sogdiana, which is of considerable scientific value in studying the origin and evolution of the species of the Fraxinus genus [26,27]. The species plays an important role in conservating soil and water, regulating climate, protecting biodiversity, as well as maintaining ecological balance in the Yili River Valley [25,26,27]. Currently, there are limited studies on F. sogdiana, including its seed flora [28], phenotypic plasticity and biomass allocation of compound leaf components [25,27], regulation of branch growth [26], and identification of diseases [29]. However, research on its population structure, especially the structure and dynamics of the cespitose population, has not been reported. This study considered cespitose F. sogdiana in the Xinjiang Yili F. sogdiana National Nature Reserve as the research object. We analyzed the age structure and survival status of the cespitose F. sogdiana population. For this, we used the population statistics method, predicted the future development trend and fluctuation period of the population, and provided scientific references for the conservation of this species and the management of the Xinjiang Yili F. sogdiana National Nature Reserve.

2. Materials and Methods

2.1. Study Area

The Xinjiang Yili Fraxinus sogdiana National Nature Reserve is located in the eastern part of Yining County, Xinjiang (43°42′08″–43°50′47″ N, 81°49′42″–82°10′37″ E), where the Kashi River flows into the mouth of the Yili River, with a total area of about 9229 hm² [25,27]. The reserve has a typical temperate continental climate, with an annual mean temperature of 8.5 °C, an accumulated temperature of ≥10 °C of 3684 °C, and a mean temperature of −10.0 °C in January, the coldest month [26,27]. The mean temperature in the reserve was 26.5 °C in July, the hottest month, with the most extreme low temperature being −39.2 °C and the highest temperature being 40.0 °C [25,26]. The average number of annual sunshine hours was 2800 h, the annual precipitation was 330 mm, the annual evapotranspiration was 1300–1700 mm, the relative humidity was 60%–70%, and the frost-free period was 162 days [26]. The soil types found within the reserve were chestnut soil and sierozem, with deep layers and a pH level of 8.0 [25,27]. F. sogdiana was mainly distributed in riverine lowlands and open deciduous forests at an altitude of 500–820 m. Its associated tree species primarily include Ulmus pumila L., Populus talassica Kom., Morus alba L., Tamarix ramosissima Ledeb., and Betula tianschanica Rupr.. Its associated understory shrubs primarily include Berberis heteropoda Schrenk., Spiraea chamaedryfolia L., Ephedra przewalskii Stapf, Caragana halodendron Dum. Cours., and Rosa berberifolia Pall. Finally, its associated herbaceous plants primarily include Glycyrrhiza uralensis Fisch., Aster altaicus Willd., Artemisia absinthium L., Inula britannica L., and Plantago major L. [25,26,27].

2.2. Research Methods

2.2.1. Sample Plot Setting and Survey

F. sogdiana can sprout seedlings from the same root system or the same stump and develop into 2–12 cespitose plants. The same root system or the same stump with two trunks are defined as two cespitose plants, three trunks are defined as three cespitose plants, and so on. Ten 20 m × 20 m quadrats were set in two different habitats, the east and west of the Kashi River, after a comprehensive survey of Xinjiang Yili F. sogdiana National Nature Reserve in September 2023. Each quadrat was divided into 16 small quadrats of 5 m × 5 m using the adjacent grid method [30], and the number of groups of all F. sogdiana in each quadrat was recorded (the number of cespitose plants developing from the same root system or the same stump is one group). The number of plants in each group, the diameter at breast height (DBH; base diameter for seedlings), the tree height (plant height for seedlings), and the crown width of each plant were obtained, and the habitat conditions of the entire sample site were considered (

Table 1. Vegetation characteristics of the cespitose F. sogdiana population in the Xinjiang Yili F. sogdiana National Nature Reserve.

Population Habitat	East of the Kashi River	West of the Kashi River
Vegetation coverage (%)	87.26 ± 6.82	77.31 ± 13.49
Crown density (%)	91.02 ± 7.37	78.97 ± 18.51
Population DBH (cm)	24.96 ± 18.05	17.53 ± 8.43
Population height (m)	11.69 ± 4.43	10.87 ± 5.73
Population crown width (m)	4.92 ± 1.95	3.65 ± 1.82
Soil moisture content (%)	24.86 ± 1.40	11.62 ± 1.67
Soil organic matter content (g∙kg−1)	34.91 ± 1.64	23.53 ± 1.33
Dominant species	Fraxinus sogdiana, Morus alba, Ulmus pumila	Fraxinus sogdiana, Ulmus pumila, Populus talassica

). Among these, the DBH was obtained by measuring the circumference of tree trunks at 1.3 m above the ground in the field using a steel tape measure and then converting it using the formula d = C/π, with d being the diameter of tree trunks, which represents the DBH, and C being the circumference of tree trunks. The DBH was mainly applicable to young-age, middle-age, mature-age, and old-age arbors. The basal diameter was obtained by measuring the diameter of the plant at 0.1 m above the ground using vernier calipers in the field, which was mainly applicable to arbor seedlings and shrubs. Tree height was measured using a laser rangefinder (Deli DL331050L, Deli, Ningbo, China), and seedling height was measured using a steel tape measure. Crown width is the average of the vertical projection widths of the crown of the F. sogdiana trees growing in the two directions of east–west and north–south, measured with a tape measure.

2.2.2. Division of Population Age Structure

The dynamic change attributes of the F. sogdiana population were studied by replacing time with the diameter at breast height (DBH) structure instead of the age class structure [31]. This study was conducted based on the fact that the diameter and age classes of the same tree species have the same response law to the same environment [15]. The population of cespitose F. sogdiana in the east of the Kashi River was divided into 13 age classes according to its growth and development in the natural reserve, combined with its biological characteristics and growth law, and the population in the west of the Kashi River was divided into six age classes (

Table 2. Classification of DBH classes of cespitose F. sogdiana population.

DBH (cm)

≤5

5–15

15–25

25–35

35–45

45–55

55–65

65–75

75–85

85–95

95–105

105–115

>115

Age class

I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

XIII

). Such classes referred to the classification method of arbor population diameter classes proposed by Yi et al. (2015) [32]. At the same time, the cespitose F. sogdiana population was divided into five age stages: seedling stage (age class I), young-age stage (age class II), middle-age stage (age class III–IV), mature-age stage (age class V–VI) and old-age stage (age class VII–XIII).

2.2.3. Compilation of Population Static Life Table and Fitting of the Survival Curve

Three assumptions needed to be met to develop a static life table: (1) the population quantity is static, (2) the age combination of the population is stable, and (3) the migration of individuals in the population is balanced, with no difference between migration in and out. The presence of negative mortality rates in the survey data was inconsistent with the three assumptions, so the original survey data were processed using a smoothing technique, which led to the development of static life tables [9,17]. The calculation formula is as follows:

$$l_x=a_x/a_0\times 1000$$

(1)

$$d_x=l_x-l_{x+1}$$

(2)

$$q_x=d_x/l_x\times 100\%$$

(3)

$$L_x=(l_x/l_{x+1})/2$$

(4)

$$T_x={\displaystyle \sum _x^{\infty }{L}_x}$$

(5)

$$e_x=T_x/l_x$$

(6)

$$K_x=\ln l_x-\ln l_{x+1}$$

(7)

$$S_x=l_{x+1}/l_x$$

(8)

where x is the age class, a_x is the survival number in the uniform sliding correction x age class, a₀ is the initial value of a_x, l_x is the standardized survival number of x age class, d_x is the number of standardized deaths in the interval from x to x + 1 age class, q_x is the mortality rate in the interval from x to x + 1 age class, L_x is the number of individuals surviving from x to x + 1, T_x is the total number of individuals from x age class to age elder than x, e_x is the average life expectancy of individuals entering the x age class, K_x is the population Vanish rate, and S_x is the population survival rate.

Deevey Jr (1947) [33] classified survival curves into three basic types. Type I is a convex curve, where the vast majority of populations belonging to Type I survive to the age of the species and have a low early mortality rate. Still, when they reach a certain physiological age, they are almost all dead within a short period. Type II is diagonal, and populations belonging to type II have essentially the same mortality rate of individuals at all ages. Type III is a concave curve, and populations belonging to type III have a high rate of mortality of their individuals in the early stages of life but a lower rate of mortality once they live to a certain age.

The population survival curve is drawn with the age class as the abscissa and normalized survival logarithm lnl_x as an ordinate. The exponential and power function models fit the survival curves of Deevey–II and Deevey–III, respectively. The fitting effect of the model is considered according to the determination coefficient R² and F test values [34], and the description equations are as follows:

$$N_x=N_0{e}^{-bx}$$

(9)

$$N_x=N_0{x}^{-b}$$

(10)

where N_x is the survival number of x age class after uniform sliding, N₀ is the actual survival number, and b is the mortality rate.

2.2.4. Dynamic Quantitative Analysis

Population dynamic quantitative analysis was used to quantitatively describe the population dynamic of cespitose F. sogdiana [35], and the calculation formula was as follows:

$$V_n={\displaystyle \frac{S_n-S_{n+1}}{\max (S_n,S_{n+1})}}\times 100\%$$

(11)

$$V_{pi}={\displaystyle \frac{1}{{\displaystyle \sum _{n=1}^{k-1}{S}_n}}}\times {\displaystyle \sum _{n=1}^{k-1}(S_n\times V_n)}$$

(12)

$$V_{pi}^{\prime }={\displaystyle \frac{{\displaystyle \sum _{n=1}^{k-1}(S_n\times V_n)}}{k\times \min (S_1,S_2\cdots S_k){\displaystyle \sum _{n=1}^{k-1}{S}_n}}}$$

(13)

$$P_{\max }={\displaystyle \frac{1}{k\times \min (S_1,S_2\cdots S_k)}}$$

(14)

where V_n represents the dynamic change in the number of individuals between two adjacent age classes in the population, V_pi and V′_pi respectively represent the dynamic indexes of the change in the number of the whole population structure when external interference is ignored and future external interference is considered, P_max is the maximum probability of the population, taking risks under external environmental interference, S_n and S_n+1 are the number of individuals in the n and n + 1 age classes, respectively, and K is the number of age classes. When V_n, V_pi, and V′_pi take positive, negative, and zero values, they reflect the structural dynamic relationship between the growth, decline, and stability of the number of individuals in two adjacent age classes in the population (or the whole population).

2.2.5. Spectral Analysis Methods

Spectral analysis can reveal the natural regeneration process of the cespitose F. sogdiana population, which is the expansion of the Fourier series [36], written in sine wave form as follows:

$$N_t=A_0+{\displaystyle \sum _{t=1}^n{A}_k}\sin ({\omega }_{k}t+{\theta }_k)$$

(15)

where N_t is the size of the population at time t; A₀ is the average value of periodic changes, which determines the baseline of the population fluctuation; A_k is the amplitude of each harmonic (k = 1, 2, 3,⋯, p; p = n/2, which is the total number of harmonics), and the difference in its value reflects the magnitude of the action in each period; and ω_k and θ_k are the frequency and phase angle of each harmonic, respectively [37].The parameters in the sine wave form of spectral analysis can be estimated using the following formula:

$$A_0={\displaystyle \frac{1}{n}}{\displaystyle \sum _{t=1}^n{X}_t}$$

(16)

$$A_k^2=a_k^2+b_k^2$$

(17)

$${\omega }_k={\displaystyle \frac{2\pi k}{t}}$$

(18)

$${\theta }_k=arctg\left(\left.{\displaystyle \frac{a_k^2}{b_k^2}}\right)\right.$$

(19)

$$a_k={\displaystyle \frac{2}{n}}{\displaystyle \sum _{t=1}^n{X}_t\cos \frac{2\pi k(t-1)}{n}}$$

(20)

$$b_k={\displaystyle \frac{2}{n}}{\displaystyle \sum _{t=1}^n{X}_t}\sin {\displaystyle \frac{2\pi k(t-1)}{n}}$$

(21)

where a_k and b_k are parameter estimates; X_t is the number of individuals in the sequence at age t, corresponding to the value in the A_x column of the static life table. However, according to the actual situation, considering that the number of plants in each age class is quite different, X_t is logarithmized before the calculation of spectral analysis, and X_t is replaced by ln(X_t + 1). The amplitude (A_k) of each waveform is calculated for each case using the formulae in the spectral analysis, A₁ for the fundamental, and A₂–A_k for the harmonics. The period of each harmonic is 1/2, 1/3, …, 1/p of the fundamental period, respectively [38].

3. Results

3.1. Situation of F. sogdiana Population Cespitose

A total of 548 groups of 1717 cespitose F. sogdiana populations were investigated in the 20 study quadrat, including 334 groups of 997 plants in the east of the Kashi River and 214 groups of 720 plants in the west of the Kashi River (Figure 1). The number of cespitoses and the number of plants in the east of the Kashi River were larger than that in the west of the Kashi River, which indicated that it was easy for the microhabitat of the east of the Kashi River to be covered by cespitose F. sogdiana. The same root system or stump of F. sogdiana could grow and develop 2–12 cespitose plants. The populations in the east and west of the Kashi River had two cespitose plants in the largest proportion (55.09% and 46.26%), followed by three (20.66% and 17.29%) and four cespitose plants (11.08% and 12.62%). There were few 5–12 cespitose plants, and there were no 11 cespitose plants. Overall, cespitose F. sogdiana mainly comprised 2–4 cespitose plants, totaling 82.66%. This result may be the survival strategy chosen by F. sogdiana to cope with competition for survival and environmental disturbances.

3.2. Population Age Structure

The age structure of cespitose F. sogdiana populations was plotted with age class as the horizontal coordinate and the number of cespitose plants as the vertical coordinate (Figure 2). The number of surviving plants in age class I of the two populations in the east and west of the Kashi River and the total population accounted for only 3.51%, 5.42%, and 4.31%, respectively. The number of surviving plants was mainly concentrated in the age classes II–IV, which accounted for 74.72%, 91.53%, and 81.77%, respectively. After, the age class IV accounted for 21.77%, 3.06%, and 13.92% of surviving plants, respectively. The age structures of the two populations in the east and west of the Kashi River and the total population were similar. All populations were irregular pyramids, and all had growth-type age structures. The number of plants in age class I was low, revealing that individuals in age class I of the cespitose F. sogdiana populations could hardly develop from seedlings and young trees to middle-aged trees and then complete the whole life cycle through the strong environmental sieve.

3.3. Population Static Life Table, Survival Curve, and Mortality Curve

3.3.1. Static Life Table

The static life table showed that the standardized survival number of the two populations in the east and west of the Kashi River and the total population decreased gradually with increasing age class (

Table 3. Static life table of cespitose F. sogdiana population.

Habitat	Age Class	Ax	ax	lx	lnlx	dx	qx	Lx	Tx	ex	Kx	Sx
East of the Kashi River	I	35	430	1000	6.908	184	0.184	908	2900	2.900	0.203	0.816
	II	311	351	816	6.705	184	0.225	724	1992	2.440	0.255	0.775
	III	272	272	633	6.450	256	0.404	505	1267	2.004	0.518	0.596
	IV	162	162	377	5.932	153	0.407	300	763	2.025	0.523	0.593
	V	96	96	223	5.408	119	0.531	164	463	2.073	0.758	0.469
	VI	45	45	105	4.651	14	0.133	98	299	2.856	0.143	0.867
	VII	39	39	91	4.508	19	0.205	81	201	2.218	0.230	0.795
	VIII	12	31	72	4.278	19	0.258	63	120	1.661	0.298	0.742
	IX	14	23	53	3.979	42	0.783	33	57	1.065	1.526	0.217
	X	5	5	12	2.453	2	0.200	10	24	2.100	0.223	0.800
	XI	1	4	9	2.230	2	0.250	8	14	1.500	0.288	0.750
	XII	3	3	7	1.943	2	0.333	6	6	0.833	0.405	0.667
	XIII	2	2	5	1.537	–	–	–	–	–	–	–
West of the Kashi River	I	39	450	1000	6.908	182	0.182	909	2221	2.221	0.201	0.818
	II	263	368	818	6.707	182	0.223	727	1312	1.605	0.252	0.777
	III	286	286	636	6.454	391	0.615	440	586	0.921	0.956	0.385
	IV	110	110	244	5.499	198	0.809	146	170	0.695	1.656	0.191
	V	21	21	47	3.843	44	0.952	24	24	0.524	3.045	0.048
	VI	1	1	2	0.799	–	–	–	–	–	–	–
Total population	I	74	880	1000	6.908	183	0.183	909	2566	2.566	0.202	0.817
	II	574	719	817	6.706	183	0.224	726	1657	2.029	0.254	0.776
	III	558	558	634	6.452	325	0.513	472	932	1.470	0.719	0.487
	IV	272	272	309	5.734	176	0.570	221	460	1.489	0.844	0.430
	V	117	117	133	4.890	81	0.607	93	239	1.799	0.934	0.393
	VI	46	46	52	3.956	8	0.152	48	147	2.804	0.165	0.848
	VII	39	39	44	3.791	9	0.205	40	98	2.218	0.230	0.795
	VIII	12	31	35	3.562	9	0.258	31	59	1.661	0.298	0.742
	IX	14	23	26	3.263	20	0.783	16	28	1.065	1.526	0.217
	X	5	5	6	1.737	1	0.200	5	12	2.100	0.223	0.800
	XI	1	4	5	1.514	1	0.250	4	7	1.500	0.288	0.750
	XII	3	3	3	1.226	1	0.333	3	3	0.833	0.405	0.667
	XIII	2	2	2	0.821	–	–	–	–	–	–	–

Note: A_x, Actual survival number; a_x, Correction value; l_x, Standardized number of surviving individuals of age class x; d_x, Standardized number of death individuals from age class x to x + 1; q_x, Mortality rate from age class x to x + 1; L_x, Survival individuals from age class x to x + 1; T_x, Total individuals from age class x and age elder than x; e_x, Life expectancy; K_x, Vanish rate; S_x, Survival rate.

). Individuals in the east and west of the Kashi River populations showed the highest life expectancy in age class I, which followed their biological characteristics. The maximum life expectancy was greater for the population in the east of the Kashi River (2.900) than in the west (2.221). This result indicated that the east of the Kashi River cespitose F. sogdiana population was more adaptable to the environment. The highest life expectancy value (2.804) was found in age class IV of the total population, indicating that the individuals of the cespitose F. sogdiana population in this age class had the highest quality of survival.

3.3.2. Survival Curve

As shown in Figure 3, the survival curves of the two populations in the east and west of the Kashi River and the total population may be of Deevey–II or Deevey–III types. The mathematical test models of the survival curve showed (

Table 4. Test of survival curve types of cespitose F. sogdiana population.

Habitat	Equation	R2	F	p	Type
East of the Kashi River	Nx = 9.481e−0.125x	0.923	132.010	0.000	Deevey–II
	Nx = 10.354x−0.556	0.703	26.019	0.000
West of the Kashi River	Nx = 14.628e−0.361x	0.652	7.510	0.052	Deevey–II
	Nx = 10.460x−0.845	0.450	3.267	0.145
Total population	Nx = 10.815e−0.173x	0.922	129.619	0.000	Deevey–II
	Nx = 12.191x−0.769	0.700	25.636	0.000

Note: N_x, The correction value of actual survival number in age class x.

) that the R² and F values of the exponential function models of the two populations in the east and west of the Kashi River and the total population were larger than those of the power function model. The p values of the exponential function model were small, indicating that the survival curve of cespitose F. sogdiana populations tended to be the Deevey–II type.

3.3.3. Mortality Curve

The mortality rate curve of the east of the Kashi River population and the total population had the same trend (Figure 4). The peak mortality occurred in age class IX (0.783 and 0.783), and the second peak mortality occurred in age class V (0.531 and 0.607). The mortality rate curve of the west of the Kashi River population showed an increasing trend. It reached the maximum mortality rate at age class V (0.952). This indicates that the age class and frequency of environmental screening experienced by the cespitose F. sogdiana population in different habitats differed. Still, they all suffered more intense environmental screening in age class V.

3.4. Population Dynamic Quantitative Analysis

As can be seen in

Table 5. Dynamic change index of cespitose F. sogdiana population.

Dynamic Index Class	Dynamic Index Value (%)
	East of the Kashi River	West of the Kashi River	Total Population
V1	−88.75	−85.17	−87.11
V2	12.54	−8.04	2.79
V3	40.44	61.54	51.25
V4	40.74	80.91	56.99
V5	53.13	95.24	60.68
V6	13.33	–	15.22
V7	69.23	–	69.23
V8	−14.29	–	−14.29
V9	64.29	–	64.29
V10	80.00	–	80.00
V11	−66.67	–	−66.67
V12	33.33	–	33.33
Vpi	28.04	32.03	29.65
V′pi	2.16	5.34	2.28
Pmax	7.69	16.67	7.69

Note: V₁–V₁₂, Dynamic index of number between adjacent age classes in population; V_pi, Number dynamic index of population; V′_pi, Number dynamic index of population when there is external interference; P_max, Maximum probability of random disturbance risk.

, the dynamic index V_pi and V′_pi values were greater for the west of the Kashi River population (32.03% and 5.34%) than for the total population (29.65% and 2.28%) and the east of the Kashi River population (28.04% and 2.16%). This indicated that the population structure of cespitose F. sogdiana was a growth-type and that the growth potential of the population in the west of the Kashi River population was greater than that of the east of the Kashi River population. Still, the east of the Kashi River population was relatively more resistant to external disturbances. The maximum probability P_max of the risk of random disturbance for the two populations in the east and west of the Kashi River and the total population were 7.69%, 16.67%, and 7.69%, respectively. This result indicates that the cespitose F. sogdiana population was more sensitive to external random disturbances. Still, the west of the Kashi River population was weaker in resisting the disturbance and had less stability when disturbed by external disturbances.

3.5. Spectral Analysis

The age class of the east of the Kashi River population and total population was 13, which rose to 14 by interpolation for comparative analysis. The total wave sequence k was 7. The age class of the west of the Kashi River population was 6, and the total wave sequence k was 3. The spectral analysis results showed (

Table 6. Periodic fluctuation of cespitose F. sogdiana population.

Habitat	A0	A1	A2	A3	A4	A5	A6	A7
East of the Kashi River	3.259	2.103	0.835	0.292	0.226	0.367	0.138	0.140
West of the Kashi River	3.903	2.283	0.732	0.487	–	–	–	–
Total population	3.474	2.378	1.013	0.329	0.194	0.384	0.211	0.213

Note: A₀, Mean value of cyclical variation; A₁, Fundamental amplitude; A₂–A₇, Amplitude of each harmonic.

) that the amplitude values of the two populations and the total population were the greatest for the basal wave A₁. This indicated that the quantity dynamic change in the cespitose F. sogdiana population was controlled by the biological characteristics of the whole life cycle and had an obvious macrocycle. From the change in the harmonic amplitude A_k, the growth dynamic of the east of the Kashi River population and the total population showed apparent small-period fluctuations, both of which were harmonic A₅, and indicated 1/5th of the fundamental period. According to the wave sequence k = n/2, it is known that A₁ corresponded to the age classes I and II of the time series, A₂ corresponded to the age classes III and IV, and so on, and A₅ corresponded to the age classes IX and X. Combined with the static life table, the result showed that the east of the Kashi River population and total population declined in survival in age class IX, with peak mortality. Therefore, the small-period fluctuation was age class IX, corresponding to the spatial sequence 75–85 cm. This small-period fluctuation may be related to the physiological characteristics of cespitose F. sogdiana. The west of the Kashi River population did not show small-period fluctuations because the age class was not large enough, considering the study data.

4. Discussion

4.1. Strategies for Maintaining and Renewing the F. sogdiana Population

Field investigations show that cespitose F. sogdiana can be formed in two ways. One is that the root system of F. sogdiana produces sprouting seedlings, which form multiple trunks in the process of growth and development. The other is that the stumps of mature F. sogdiana trees sprout seedlings at the base of the stumps and grow and develop into young trees or even mature trees. Some studies have shown that the phenomenon of cespitose in woody plants is affected by various factors, such as habitat, disturbance, and resource level [39,40]. Cespitose in F. sogdiana is presumed to result from the combined effects of soil resource conditions, pests and diseases, intraspecific competition, and environmental disturbances. The soil type of the reserve is mainly sandy loam. The high sand content in the soil profile makes it difficult to maintain soil moisture and nutrients for a long period [27]. When the water and nutrients that the root system of F. sogdiana draws from the soil do not satisfy the growth needs of its seedlings, this leads to the death of new shoots of F. sogdiana and the sprouting of dormant or indeterminate shoots in the following year. This is similar to the cause of cespitose in J. regia reported by Wei et al. (2023) [21]. Additionally, F. sogdiana in the reserve is affected by diseases and pests, such as Septoria lycopersici and Agrilus planipennis, and disturbances, such as grazing (cattle, sheep, and horses) and fruit picking, occur occasionally. These diseases, pests, and disturbances can easily cause the trunks of young and middle-aged F. sogdiana trees to wither and break, promoting the development of dormant buds or adventitious buds on the stumps of F. sogdiana trees [26]. Most of the F. sogdiana distribution sites in the reserve are pure forests with strong intraspecific competition. Cespitose is a survival strategy for F. sogdiana to maintain population survival and development in these environments. The proportion of 2–4 cespitose F. sogdiana plants in the total number of cespitose plants was higher than 80.00%. Such a proportion resulted from the competition for resources and the different degrees of biotic and abiotic disturbances in the long-term evolution of F. sogdiana. Generally speaking, cespitose plants have the effect of a “persistent ecological niche”, helping trees to reduce the biomass loss caused by disturbances and accelerating the succession of plant communities [39]. Therefore, the cespitose F. sogdiana population plays an important role in maintaining the stability and renewal of the F. sogdiana community and population.

4.2. Age Structure and Distributional Variability of Cespitose F. sogdiana Population

The age structure of plant populations is affected by a combination of their biological characteristics and environmental factors. It reflects the advantages and disadvantages of the environmental conditions in which the populations are located and future renewal strategies [41,42]. The east and west of the Kashi River cespitose F. sogdiana populations showed a growth-type age structure. Still, the total number of plants in the east of the Kashi River population was 16.13% higher than in the west of the Kashi River population. There was large variability in the age-class distribution of the two populations, which manifested as a severe lack of old individuals in the west of the Kashi River population. This result suggests that the distribution of the cespitose F. sogdiana population results from its long-term interactions and adaptations to the environment [37]. The field investigation found that there is more low–lying land in the east of the Kashi River, and most tree canopies were well developed. There, herbaceous plants are relatively abundant, with a cover of nearly 90.00%. The luxuriant branches and leaves intercept precipitation, shade light, and provide much organic matter after withering. Herbaceous plants have a strong ability to nourish water, resulting in the understory being more humid. Therefore, the soil in this area has high moisture and organic matter content, and the plants grow vigorously. In the west of the Kashi River, there is waterlogging from irrigation. Some plants had fallen over, and the trees were tall but had small crowns. This results in weaker soil moisture and organic matter content and weaker tree growth than in the east of the Kashi River. Therefore, soil moisture and organic matter content may be the main limiting factors contributing to the growth and development of cespitose F. sogdiana. This was similar to the results of Dang et al. (2010) [41] on Abies fargesii Franch. Additionally, there are resource allocation trade-offs and coordination among growth, reproduction, and defense functions during plant development. An increase in inputs for one process will inevitably come at the cost of a decrease in inputs for another [43]. The absence of old individuals in the west of the Kashi River population may imply an important resource allocation strategy for this population.

The seedling stage is the most important and sensitive period in plant growth [44], and the insufficient number of seedling individuals and high mortality rate are the most important causes of plant endangerment [45]. The seedling plants of the cespitose F. sogdiana population in the east and west of the Kashi River were very few, accounting for only 3.51% and 5.42% of the total plants, respectively. This may be due to the low competitive ability of the cespitose F. sogdiana population in the seedling stage and its weak ability to resist environmental disturbances [24]. The field investigation found that F. sogdiana seedlings were small in size and light in mass and preferred a warm and humid environment. Although the habitats were different, most F. sogdiana seedling individuals gathered and distributed in the lowlands beside the Kashi River and under the forest windows with sufficient light, as well as around the large trees of other trees (such as U. pumila and P. talassica). The effects of self-thinning and fierce intraspecific competition lead to a large number of deaths of the seedling individuals. At the same time, the cespitose of F. sogdiana had a difficult time occurring, and the seedling individuals growing on the forest floor were affected by the large crown density and animal trampling and feeding, making it difficult for them to survive. In summary, the seedling stage of cespitose F. sogdiana is the “bottleneck” period for the renewal and development of this population [46].

4.3. Dynamics and Development Trend of Cespitose F. sogdiana Population

The static life table and survival curves of plant populations can reflect the survival status of populations and their adaptation to the environment [47,48]. The static life table showed that the life expectancy of the cespitose F. sogdiana population in the east and west of the Kashi River fluctuated. The highest life expectancy was found in individuals of age class I. This result was attributed to the fact that cespitose F. sogdiana underwent strong environmental screening and eliminated more individuals at this stage. Therefore, the surviving plants were more vigorous. The physiologically vigorous period of the cespitose F. sogdiana population differed among habitats. The high life expectancy of the east of the Kashi River population indicated that the duration of the physiologically vigorous period of individuals in this population was long, and survival was strong. The demand of individuals for space and resources increased, and intraspecific and interspecific competition intensified with the growth of cespitose F. sogdiana. The crowding and self-thinning effects were enhanced, resulting in a higher mortality rate for individuals in the population [9]. Hence, the populations in the east and west of the Kashi River occurred at the sub-peak and peak mortality in age class V. The total population showed the highest life expectancy at age class VI, suggesting that the two populations had elevated survival quality, and physiological activities became vigorous after passing the developmental bottleneck at age class V [38].

However, the peak mortality in the east of the Kashi River population occurred in age class IX. This result is because, as cespitose F. sogdiana entered the old age stage, competition for resources such as space, light, and water decreased. The survival of individuals was weakened, progressively causing senescence and death [49,50]. Generally speaking, mature and old individuals occupy more space resources within the plant population. Consequently, the death of a few individuals will have a certain impact on the dynamic development of the population. Still, from the perspective of the development of the entire cespitose F. sogdiana population, the death of a few mature and old individuals creates a space for the survival of seedlings and young individuals. Additionally, the occurrence of trunk root sprouting or stump sprouting can provide a better survival environment for the population to renew and develop, thus forming a benign systematic cycle [21].

The survival curves show that the east and west of the Kashi River cespitose F. sogdiana populations belonged to the Deevey–II type, indicating that the number of surviving individuals in the two populations decreases with age, and the mortality rates at different age stages are basically the same. They are stable populations, which are basically the same as the rare tree species J. regia cespitose population distributed in the Yili River Valley [21]. However, there were differences in the trends in the survival curves of the two populations. This result reflects the characteristics of the survival process of the same population with the change in habitat [51]. This result suggests that the survival curves of the population were not intrinsic to the same kind of population or a certain stage of growth and might have been influenced by the habitat and external disturbances. The results of the dynamic index showed that the cespitose F. sogdiana populations were generally in a stable state and were a growth-type population, which was basically consistent with the research results of Liu et al. (2023) [9] on the rare tree species Taxus cuspidata Sieb. et Zucc. population. However, the ability and stability of the west of the Kashi River population were weaker than that of the east of the Kashi River population. This result might be due to the relatively poor soil conditions (moisture and organic matter content) in the west of the Kashi River (Table 1). In contrast, the east of the Kashi River had good soil moisture conditions and rich soil humus, which could provide better nutritional conditions for the growth of cespitose F. sogdiana (Table 1).

The fluctuation of the distribution of plants in each age class of the population in spectral analysis can show the dynamics of the natural regeneration of this population [30]. From the results of the spectral analysis, the natural regeneration process of the cespitose F. sogdiana population was significantly affected by fundamental wave A₁. The period length of the fundamental wave was determined by the fluctuating characteristics of the population, indicating that the biological characteristics of the species had a considerable influence on the regeneration of the population [37]. However, the maximum diameter at breast height (DBH = 137.1 cm) time-series length of the investigated cespitose F. sogdiana population was not long enough to show a significant intrinsic fluctuation cycle length, but its existence is certain. However, the east of the Kashi River population and the total population also showed fluctuations of small cycles within the large cycle. All fluctuations were more pronounced in the age class IX, because the cespitose F. sogdiana had already entered the physiological decline period at that stage, and the mortality rate of the population increased, causing fluctuations in population size. Additionally, this small-period fluctuation can contribute to the natural thinning and quantitative regulation of the cespitose F. sogdiana population, which is conducive to maintaining population stability [36].

4.4. Conservation Countermeasures for Cespitose F. sogdiana Population

Based on the above research results, the following problems existed in the cespitose F. sogdiana population. First, there were few seedling individuals, and developing from seedling and young to mature individuals is challenging. Second, in the east of the Kashi River population, old individuals were clearly aging and dying, while the west of the Kashi Rive population severely lacked old individuals. Therefore, some conservation measures were recommended. The first recommendation was the adoption of appropriate anthropogenic disturbances to the cespitose F. sogdiana forests with high crown density, such as the inter-felling and selective felling of understory shrubs, artificial seedling thinning, and the timely cleaning of “diseased and withered” individuals. Such measures could enable seedlings and young individuals to obtain more living space and light resources [18]. The second recommendation is that during the field survey, we noted experimental areas in the periphery of the F. sogdiana main forest area where live seedling breeding occurred. We suggest increasing the scale of the study on how to improve the survival rate of live seedlings to promote the cespitose occurrence of F. sogdiana. The third recommendation regards the current establishment of the Xinjiang Yili F. sogdiana National Nature Reserve. This reserve played a significant role in protecting the animal and plant resources of the region. However, anthropogenic disturbances in the nature reserve (such as collecting fruits, traveling, and grazing), coupled with irrigation and drainage in the forest area, are not timely, and there are severe pests and diseases.

Additionally, part of the woodland west of the Kashi River was severely waterlogged, resulting in cespitose F. sogdiana and other arbor species falling more often. It is recommended that the reserve strengthen its management efforts to prevent human damage, adopt site-specific management methods, and formulate scientific and effective improvement measures for the cespitose F. sogdiana population. Such actions are especially important for the west of the Kashi River population to promote the sustained and healthy development of the cespitose F. sogdiana population.

4.5. Discussion on the Dynamic Analysis Method of Cespitose F. sogdiana Population

Currently, the static life table is the basic method for studying long-lived woody plant populations [10,41]. The population dynamics quantitative analysis and spectral analysis can further characterize changes in population dynamics and the natural renewal process [9,36]. Adopting the above three research tools, combined with the comprehensive analysis of the actual distribution status of populations during field surveys, can obtain a relatively reliable law of population dynamics change, providing a scientific basis for forest management and the protection of rare tree species. However, it is undeniable that there are certain limitations in the static life table, which assumes that the population density of cespitose F. sogdiana is constant, the age structure is independent of time, and the birth and death rates are constant. Still, in the actual environment, the existence of pests, diseases, and human interference in Xinjiang Yili Fraxinus sogdiana National Nature Reserve may lead to an increase in the mortality rate of individuals of a certain age and a dynamic change in the age structure of the population. In addition, interannual variations in environmental conditions (such as precipitation, temperature, and light) may have a greater impact on the population dynamics of cespitose F. sogdiana. Therefore, based on the results of this study, the further introduction of environmental variables, combined with the long-term dynamic monitoring of the population of cespitose F. sogdiana, will help in better understanding the structure and dynamic characteristics of this population and provide a more scientific basis for the conservation of this species.

5. Conclusions

The static life table showed that the cespitose F. sogdiana in the east and west of the Kashi River and the total population exhibited growth-type age structures. However, there were very few individuals in age class I. The survival curves followed the Deevey–II type, with extremely high mortality rates of individuals of age class V. The quantitative analysis of population dynamics revealed that the east of the Kashi River population was relatively more resistant to external disturbances. Spectral analysis indicated that the periodic fluctuation of the cespitose F. sogdiana population was mainly controlled by biological characteristics. Additionally, the east of the Kashi River population and total population showed distinct small-scale periodic fluctuations. We recommend strengthening the nurturing of seedlings and young individuals, improving the habitat of the west of the Kashi River population, avoiding excessive anthropogenic disturbances, and strengthening the prevention and control of pests and diseases in order to realize the conservation and long-term survival of the cespitose F. sogdiana population.