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Botanical Sciences

On-line version ISSN 2007-4476Print version ISSN 2007-4298

Bot. sci vol.98 n.1 México Jan./Mar. 2020  Epub June 20, 2020 


Population structure and quantitative characteristics of Tetracentron sinense (Trochodendraceae) in Leigong Mountain Nature Reserve, China

Estructura poblacional y características Tetracentron sinense cuantitativas de (Trochodendraceae) en la Reserva Natural de la Montaña Leigog, China

Huan Zhang1  2 

Fan Duan1  2 

Yang Li1  2 

Qinqin Wang1  2 

Xueheng Lu1  2 

Xiaohong Gan1  2  *

Zhenguo Xie3 

Junfeng Tang1 

1Key laboratory of southwest China wildlife resources conservation (Ministry of Education), Nanchong, China.

2Institute of Plant Adaptation and Utilization in Southwest Mountain, China West Normal University, Nanchong, China.

3Leigong Mountain National Nature Reserve Administration Bureau, Leishan county, Guizhou Province, China.



Knowledge of plant population structure facilitates conservation, management, and utilization of endangered plants.

Research question:

What is the current status of the natural populations of Tetracentron sinense in Leigong Mountain Nature Reserve (LMNR) and what future population development trends can be predicted?

Studied species:

Tetracentron sinense.

Study site and period of research:

T. sinense populations in LMNR in China in 2018.


The population structure and quantity dynamics of four typical patches were studied using static life tables, survival curves, survival analyses, and time series analyses.


The age structures of the T. sinense populations were spindle-shaped, with few seedlings and saplings, and Deevey type II and III survival curves. The mortality rate (q x ) of each patch increased quickly, and then plateaued, finally increasing again. Survival rate (S x ) showed a contrary trend to q x . Trends in cumulative mortality rate (F (i) ), killing power (K x ), mortality density (f (ti) ), and hazard rate (λ (ti) ) with increasing age class were similar: increasing at a younger age, gradually stabilizing in middle age, and then increasing slightly in older age. The number of individuals in these T. sinense populations was predicted to decrease sharply in future, with younger individuals being seriously deficient. The results showed that the natural populations of T. sinense in the LMNR were relatively stable but were in an early stage of decline.


The lack of younger individuals might reflect a bottleneck for regeneration of T. sinense populations, leading to a decline in population size.

Key words: Population structure; static life table; survival analysis; time series analysis



El conocimiento de la estructura poblacional de una planta facilita su conservación, manejo y utilización.

Pregunta de investigación:

¿Cuál es el estado actual de las poblaciones naturales de Tetracentron sinense en la Reserva Natural de la Montaña Leigong (LMNR) y qué tendencias futuras de desarrollo de la población se pueden predecir?

Especies estudiadas:

Tetracentron sinense.

Sitio y período de investigación:

Poblaciones en LMNR, China, 2018.


Se usaron tablas de vida estáticas, curvas de supervivencia, análisis de supervivencia y análisis de series de tiempo para el análisis de la estructura poblacional y dinámica de parches.


Las estructuras de edad de las poblaciones de T. sinense mostraron forma de huso, con pocas plántulas y juveniles. Curvas de supervivencia Deevey tipo II y III. La tasa de mortalidad (q x ) de cada parche aumentó rápidamente, para estabilizarse y finalmente aumentar nuevamente. La tasa de supervivencia (S x ) mostró una tendencia contraria a q x . Las tendencias en las tasas de mortalidad acumulada (F (i) ), mortalidad (K x ), densidad de mortalidad (f (ti) ), y tasa de riesgo (λ (ti) ) fueron similares con el aumento de la clase de edad. Las poblaciones naturales de T. sinense en el LMNR eran relativamente estables, aunque en etapa temprana de disminución. El número de individuos en poblaciones de T. sinense disminuirá drásticamente en el futuro, donde los más jóvenes mostrarán serias deficiencias.


La ausencia de individuos más jóvenes podría reflejar un cuello de botella para la regeneración de las poblaciones de T. sinense, lo que lleva a una disminución en el tamaño de la población.

Palabras clave: Análisis de series de tiempo; análisis de supervivencia; estructura de población; tabla de vida estática

Tetracentron sinense Oliver, the only species in the Trochodendraceae family (Fu & Bartholomew 2001), mainly distribute in southwestern and central China (Doweld 1998, Fu & Bartholomew 2001, Zhang et al. 2019). Its fossils appeared in the Eocene, indicating that this is a relict species, making it important for the study of ancient flora and phylogeny in angiosperms. Its importance in ornamental (Zhang et al. 2019), medicinal (Wang et al. 2006), and furniture products, has resulted in excessive deforestation of T. sinense. Thus, the populations are scattered in distribution, and their natural regeneration is very poor (Wang et al. 2006, Gan et al. 2013). As such, it is currently listed in CITES Appendix III (Convention on International Trade in Endangered Species of Wild Fauna and Flora,, and as a national second-grade protected plant in China (Fu 1992). To date, the conservation and management of the germplasm resources for T. sinense have attracted the most attention. Over the past 10 years, the community ecology (Tian et al. 2018), sporogenesis and gametophyte development (Gan et al. 2012), pollination ecology (Gan et al. 2013), seed and seedling ecology (Luo et al. 2010, Cao et al. 2012, Tang et al. 2013, Han et al. 2015, Li et al. 2015), and genetic diversity (Li et al. 2016, Han et al. 2017, Li et al. 2018) of T. sinense have been studied, with the aim of improving the conservation of its germplasm resources. Generally, the natural regeneration in plants is a complex process including some important links of life history, such as the production, diffusion and germination of seed, seedling settlement and sapling formation. Among them, the obstacles that occur in any link will lead to the failure of regeneration (Herrera 1991). To date, there are no relevant reports on the current situation of T. sinense natural population, and which link in its life history has the obstacle that causes it poor regeneration is unclear.

Plant population structure is the most basic characteristic of a population. It can reflect population dynamics and development trends, in addition to the correlation between a population and its environment, including its actual location within that environment (Chapman & Reiss 2001, Xie et al. 2014). Knowledge of plant population structure can illuminate the past and future trends of a population, and then elucidate the weak links in life history correlated to poor regeneration, which is of relevant for conservation, management, and utilization of endangered plants (Harper 1977). Life tables and survival curves are important tools for the evaluation of population dynamics as they show the actual numbers of surviving individuals, deaths, and survivorship trends for all age classes in the population. Life tables are also used to explain changes in population size (Smith & Keyfitz 1947, Skoglund & Verwijst 1989, Armesto et al. 1992). Survival curves can elucidate the trends in population changes directly and quickly (Zhang & Zu 1999, Wu et al. 2000, Bi et al. 2001). The four survival functions (survival rate, cumulative mortality, mortality density, and hazard rate) can more accurately explain current population structure and the development parameters of a given population when combined with life tables (Harcombe 1987, Zhang et al. 2008). Time series analysis, an important method in population statistics, is usually used to forecast population dynamic trends in the future (Xie et al. 2014). Therefore, life tables and time series analyses based on the quantitative characteristics of an endangered plant population, are of practical importance for the effective conservation and management of endangered plants (Wu et al. 2000, Phama et al. 2014).

In this paper, the population structure and derived metrics of four typical T. sinense patches in the Leigong Mountain Nature Reserve (LMNR) were studied. The aims of the study were: (1) analyze the current status of T. sinense populations in the LMNR, and to reveal the weak links in life history correlated to poor regeneration; (2) predict future development trends of natural T. sinense populations in the LMNR; (3) put forward some strategies for the conservation and management of these endangered plants.

Materials and methods

Study area. The LMNR, located in the central part of Qiandongnan, Guizhou Province, China, is made up of steep slopes, which lead into narrow valleys and small waterfalls. It spans the four counties of Leishan, Taijiang, Jianhe, and Rongjiang, and is a watershed between the Yangtze River and the Pearl River (26° 20' 25″-26° 25' 00″ N, 108° 12' 00″-108° 20' 00″ E, 2,178 m asl). LMNR is characterized by a typical subtropical humid climate, with abundant rainfall and less daylight time (Chen et al.2012). The mean annual temperature is about 10 °C; July is the hottest month, with an average temperature of less than 25 °C. The soil is an acidic mountain yellow soil. The mountain forests are structurally and floristically heterogeneous (Tang et al. 2007, Tang & Ohsawa 2009), with a distinctive vertical distribution of vegetation. The flora is mainly divided into evergreen broad-leaved forests at lower elevations (below 1,350 m asl), evergreen and deciduous broad-leaved mixed forests at middle altitudes (1,350-2,100 m asl), and deciduous broad-leaved forests at higher altitudes (over 2,100 m asl). The T. sinense populations in the LMNR were mainly scattered throughout evergreen and deciduous broad-leaved mixed forests. We investigated the distribution of T. sinense throughout the China and found that the distributions of the population of T. sinense were patchy. In LMNR, we found that there were four patches which were the most typical, and they could well represent the distributions of the natural population of T. sinense. Therefore, the four representative patches were chosen as experimental plots rather than artificial plots (population 1: 7 ha; population 2: 1.905 ha; population 3: 7.4 ha; population 4: 7.02 ha).

Age structure. In order to minimize the damage to T. sinense, 19 individuals with intact growth and different diameter grades were randomly selected in these four patches and their cores were taken to determine their ages. Then the relationship between the age and the DBH of the T. sinense were modeled to obtain the fitting curve (Wang et al. 1995, Harper 1977, Zhang et al. 2007). According to the fitting curve, the age of all individuals in the four populations were calculated (Hett et al. 1976). According to the life history characteristics of T. sinense and the methods of Brodie et al. (1995) and Guedje et al. (2003), these populations were grouped into 11 age classes. Pre-reproductive and juvenile trees were classified as seedlings and saplings (I, 0~20 ages), or juveniles (II, 20~40 ages; III, 40~60 ages; IV, 60~80 ages; V, 80~100 ages; VI, 100~120 ages; VII, 120~140 ages). Adult trees were grouped into four age classes (VIII, 140~160 ages; IX, 160~180 ages; X, 180~200 ages; XI, 200~220 ages). The number of T. sinense in each age class was counted, and then the age structure of the populations was analyzed.

Population dynamics analysis. The dynamic change in number of individuals between adjacent age classes (V n ) was analyzed according to the method of Chen (1998), using the following formula:

Vn=SnSn+1max(Sn,Sn+1)×100% (1)

where S n and S n+1 are the number of individuals in the n th age class and the next age class, respectively. Max (... ...) represents the maximum value in parentheses; V n ∈ [-1, 1] When V n > 0, this means the number of individuals is increasing in a dynamic relationship between adjacent age classes; when V n < 0, this means there is a decline in the dynamic relationship; when V n = 0, the dynamic relationship is stable.

The quantity dynamic index (V pi ) of the age structure of these populations was obtained by weighting the number of individuals (S n ) of each age class by V n . Because there is no V n for the maximum age class (K), the K value was excluded (Chen 1998):

Vpi=1n=1k1Snn=1k1(SnVn) (2)

Because the external environmental effect on the population age structure is not considered in equation (2), the quantity dynamic index of population age structure (V pi ) should be corrected accordingly, that is:

Vpi'=n=1k1SnVnkminS1,S2,S3,...,Skn=1k1Sn (3)

where min (... ...) means the minimum value of the sequence in parentheses, and K is the age class.

Establishment of a static life table. Given that T. sinense is, a long-life cycles tree species, a static life table was established. Static life tables capture discrete periods of the dynamic process of aging where multiple estimate the number of surviving individuals (x) (Jiang 1992, Zhou et al. 1992), based on the following formulas (Silvertown 1982, Jiang 1992). According to the assumptions underlying static life tables, the age combination is stable, and the proportion of each age class remains constant (Jiang 1992). Then the data of the four populations in LMNR were corrected by smoothing technique (Proctor 1980, Brodie et al. 1995, Molles 2002).

T=xnax (4)

ax¯=Tn (5)

where T: the sum of all the individuals in each group; n: the number of age classes in each group; ax: individuals of each groups in the x age class; ax¯ : the means of each group, which were considered to be the mid-value. Based on the differences between the maximum and minimum values of number surviving in the two groups and the difference between the means of the two groups, the number of individuals in each age class was corrected by one unit of smoothing (Jiang 1992).

lx=AxA1×1000 (6)

dx=lxlx+1 (7)

qx=dxlx×100% (8)

Lx=(lx+lx+1)2 (9)

Tx=xLx (10)

ex=Txlx (11)

Kx=lnlxlnlx+1 (12)

Sx=lx+1lx (13)

where x: the age class; a x : number of surviving individuals in age class x; A x : number of surviving individuals in age class x after smoothing; A 1 : number of surviving individuals in the I age class after smoothing; l x : standardized number of surviving individuals at the beginning of age class x (generally converted to 1,000); d x : standardized number of individuals dying between age classes x and x+1; q x : mortality rate between age classes x and x+1; L x : number of surviving individuals between age classes x and x+1; T x : total number of individuals from age class x; e x : life expectancy at age class x; K x : killing power; S x : survival rate (Silvertown 1982, Jiang 1992).

Survival curve. Taking the ln lx of the number of survivors as the vertical coordinate and each age class as the horizontal coordinate, the static life table was used as a basis for the survival curve, which was fitted using SPSS 23.0 software and was modeled by R language (R Core Team 1995). OriginPro 8.0 software was used to draw the mortality rate (q x ) and killing power (K x ) curves (Feng 1983).

According to Hett & Loucks (1976), three kinds of mathematical models (linear equation, exponential equation, and power function equation) can be used to test of the best fit of the survival curve on T. sinense data (Deevey 1947). These were:

Deevey type I: Nx=N0+bx (14)

Deevey type II: Nx=N0ebx (15)

Deevey type III: Nx=N0xb (16)

where x is age class, N x is the natural logarithm of the standardized number of surviving individuals in age class x, N x = lnl x ; N 0 and b were directly obtained by fitting the mathematical model.

Survival analysis. To better analyze the age structure of the T. sinense populations in each patch of LMNR and further clarify the survival rules for the populations, this study introduced four functions. The survival functions are functions relating to any age class, which are more intuitive than the survival curve, so survival analysis has a greater practical applied value in the analysis of population life tables compared to survival curves (Yang et al. 1991, Guo 2009). The four functions (population survival rate function S (i) , cumulative mortality function F (i) , mortality density function f (ti) , and hazard rate function λ (ti) were calculated as follows:

S(i)=S1S2S3......Si (17)

Fi=1S(i) (18)

f(ti)=Si1Sihi (19)

λ(ti)=2(1Si)[hi(1+Si)] (20)

where i is age class; S i is the survival rate in age class i; S i = S x as in equation (2); and h i is the width of the age class.

Time series analysis. Time series analysis is often used to predict dynamic changes in population size (Xiao et al. 2004, Zhang et al. 2017). In this paper, the moving average method was applied to the analysis:

Mt(1)=1nk=tn+1tXk (21)

where n is the time being predicted (age class period in the study); M (1) t is the population size in age class t after n age class periods in the future, and the population size of the current k age class of X k . The population quantity dynamics in the next 2, 4, 6, 8, and 10 age class time periods were predicted.


Age structure of T. sinense populations. The fitting results showed that the relationship between the ages and DBH was well fitted by the linear regression (R 2 = 0.826, P < 0.01). Therefore, in 95 % prediction range, the family had better fitting observation value. The ages of T. sinense in four populations were calculated by the formula (y = 3.15 × x + 21.68) (Figure 1). Then the structures of age were analyzed according to the ages.

Figure 1 The relationship between DBH and Age 

The age structures of the T. sinense populations in the LMNR were all close to the pyramid type, although their age structures were all incomplete. The maximum number of individuals in each population was observed in the II or III age class, there were relatively no seedlings and saplings existed in these populations except for Population 2 (Figure 2).

Figure 2 Age structure of T. sinense in the four populations 

Quantitative dynamic analysis of the T. sinense populations. There were significant fluctuations among different age classes in these populations, with a decreasing trend between some age classes. The most obvious negative trends appeared between adjacent age classes. The dynamic indices of each population in I age class were the negative value. As the age class increased, the indexes fluctuated between positive, zero and negative (Table 1). The maximum V pi appeared in Population 1, indicating the highest stability, but its value was only 50 %. Although the population dynamic indexes of the four populations were positive, the values were very small. Even though the numbers of medium and young age class individuals in the populations were greater than those of adult individuals, the number of seedlings and saplings was much less, and the fluctuations within populations were very large (Table 2). To some extent, the four populations are all at risk.

Table 1 Dynamic index (%) between adjacent age classes in the four populations of T. sinense 

Pop.1 -100 6.67 100 0 0 0 0 0 -100 100 -
Pop.2 -95.24 -4.55 90.91 50 100 -100 100 -100 100 -100 -
Pop.3 -100 -31.25 93.75 -66.67 100 -100 50 100 0 0 -
Pop.4 -100 36.84 91.67 0 -50 100 0 0 0 -100 -

Table 2 Dynamic index (%) of each population 

Population V pi V pi
Pop.1 50 4.55
Pop.2 46.18 4.20
Pop.3 46.75 4.25
Pop.4 25.92 2.36

Static life tables and survival curves. As age class increased, l x decreased, the trend of l x in population 2 was more apparently. While a higher individual e x was apparent in the I, II age classes. In the X and XI age classes, e x became minimal. The d x of populations were decreased sharp in their younger age class, excepted population 1. Its d x was more stable in I to VII ages classes (Table 3).

Table 3 Life table of LMNR populations 

Population Age-class Age a x A x l x ln lx d x q x L x T x e x K x S x
Pop.1 I 0~20 0 8 1000 6.91 125 0.13 937.5 4375 4.38 0.13 0.88
II 20~40 15 7 875 6.77 125 0.14 812.5 3437.50 3.93 0.15 0.86
III 40~60 14 6 750 6.62 125 0.17 687.5 2625 3.50 0.18 0.83
IV 60~80 0 5 625 6.44 125 0.20 562.5 1937.5 3.10 0.22 0.80
V 80~100 0 4 500 6.21 125 0.25 437.5 1375 2.75 0.29 0.75
VI 100~120 0 3 375 5.93 125 0.33 312.5 937.5 2.50 0.41 0.67
VII 120~140 0 2 250 5.52 125 0.50 187.5 625 2.50 0.69 0.50
VIII 140~160 0 1 125 4.83 0 0 125 437.50 3.50 0 1
IX 160~180 0 1 125 4.83 0 0 125 312.50 2.50 0 1
X 180~200 1 1 125 4.83 0 0 125 187.50 1.50 0 1
XI 200~220 1 1 125 4.83 125 1 62.5 62.5 0.50 4.83 0
Pop.2 I 0~20 1 21 1000 6.91 428.57 0.43 785.71 2976.19 2.98 0.56 0.57
II 20~40 21 12 571.43 6.35 47.62 0.08 547.62 2190.48 3.83 0.09 0.92
III 40~60 22 11 523.81 6.26 95.24 0.18 476.19 1642.86 3.14 0.20 0.82
IV 60~80 2 9 428.57 6.06 95.24 0.22 380.95 1166.67 2.72 0.25 0.78
V 80~100 1 7 333.33 5.81 95.24 0.29 285.71 785.71 2.36 0.0.34 0.71
VI 100~120 0 5 238.10 5.47 95.24 0.40 190.48 500 2.10 0.51 0.60
VII 120~140 2 3 142.86 4.96 47.62 0.33 119.05 309.52 2.17 0.41 0.67
VIII 140~160 0 2 95.24 4.56 47.62 0.50 71.43 190.48 2 0.69 0.50
IX 160~180 1 1 47.62 3.86 0 0 47.62 119.05 2.50 0 1
X 180~200 0 1 47.62 3.86 0 0 47.62 71.43 1.50 0 1
XI 200~220 1 1 47.62 3.86 47.62 1 23.81 23.81 0.50 3.86 0
Pop.3 I 0~20 0 14 1000 6.91 357.14 0.36 821.43 2428.57 2.43 0.44 0.64
II 20~40 11 9 642.86 6.47 357.14 0.56 464.29 1607.14 2.50 081 0.44
III 40~60 16 4 285.71 5.65 0 0 285.71 1142.86 4 0 1
IV 60~80 1 4 285.71 5.65 71.43 0.25 250 857.14 3 0.29 0.75
V 80~100 3 3 241.29 5.37 71.43 0.33 178.57 607.14 2.83 0.41 0.67
VI 100~120 0 2 142.86 4.96 71.43 0.50 107.14 428.57 3 0.69 0.50
VII 120~140 2 1 71.43 4.27 0 0 71.43 321.43 4.50 0 1
VIII 140~160 1 1 71.43 4.27 0 0 71.43 250 3.50 0 1
IX 160~180 0 1 71.43 4.27 0 0 71.43 178.57 2.50 0 1
X 180~200 0 1 71.43 4.27 0 0 71.43 107.14 1.50 0 1
XI 200~220 0 1 71.43 4.27 71.43 1 35.71 35.71 0.50 4.27 0
Pop.4 I 0~20 0 11 1000 6.91 363.64 0.36 818.18 2863.64 2.86 0.45 0.64
II 20~40 19 7 636.36 6.46 272.73 0.43 500 2045.45 3.21 0.56 0.57
III 40~60 12 4 363.64 5.90 90.91 0.25 318.18 1545.45 4.25 0.29 0.75
IV 60~80 1 3 272.73 5.61 0 0 272.73 1227.27 4.50 0 1
V 80~100 1 3 272.73 5.61 0 0 272.73 954.54 3.50 0 1
VI 100~120 2 3 272.73 5.61 90.91 0.33 227.27 618.82 2.27 0.41 0.67
VII 120~140 0 2 181.82 5.20 90.91 0.50 136.36 454.54 2.20 0.69 0.50
VIII 140~160 0 1 90.91 4.51 0 0 90.91 318.18 3.50 0 1
IX 160~180 0 1 90.91 4.51 0 0 90.91 227.27 2.50 0 1
X 180~200 0 1 90.91 4.51 0 1 90.91 136.36 1.50 0 1
XI 200~220 2 1 90.91 4.51 90.91 1 45.45 45.45 0.50 4.51 0

DBH: diameter at breast height; a x : individual number of age class x; A x : the revised data of ax; l x : the standardized number of surviving individuals of age class x; lnl x : the natural logarithm of lx; d x : the standardized number of death individuals from age class x to age class x+1; q x : mortality from age class x to age class x+1; L x : the number of surviving individuals from age class x to age class x+1; T x : the total individual number of age class x and age classes older than x; e x : life expectancy of individuals in the age class x; K x : killing power; S x : survival rate.

The l x of T. sinense decreased rapidly in the I to VIII (Populations 1 and 2) or I to III (Populations 3 and 4) age classes, but more slowly in the IV or VII age classes, and then remained at a relatively low level thereafter (Figure 3). By modeling and comparing the survival curves of four populations, it was found that the fluctuating trend of the four populations was generally the same, and the P value = 0.6, which proved that there was no significant difference among the four populations (Figure 4).

Figure 3 Survival curve of the T. sinense populations 

Figure 4 Survival distributions of the T. sinense populations 

Based on the change trend of the survival curve in the four populations, these survival curves all tended to the Deevey-II and Deevey-III types. The model simulation showed that the R 2 and F values from equation (13) were both greater than those from equation (14) did (Table 4), indicating that the survival curves of the T. sinense populations1, 2,4 were a Deevey-II type, but population 3 were a Deevey-III typ.

Table 4 Test models fitted to the survival curve of the T. sinense population 

Population Equation R2 F Type
Pop.1 Nx = 7.44e-0.04x 0.931 120.609 Deevey-II
Nx = 7.63x-0.18 0.797 35.314 Deevey-III
Pop.2 Nx = 7.59e-0.06x 0.952 178.981 Deevey-II
Nx = 7.83x-0.26 0.798 35.566 Deevey-III
Pop.3 Nx = 6.89e-0.05x 0.895 76.858 Deevey-II
Nx = 7.32x-0.23 0.923 108.170 Deevey-III
Pop.4 Nx = 6.97e-0.04x 0.926 117.879 Deevey-II
Nx = 7.27x-0.19 0.895 76.926 Deevey-III

Mortality rates and killing power curves. The variation patterns of q x and K x were similar (Figure 5). In Populations 1 and 2, there was a peak value in the VII age class; in Populations 3 and 4, the peak values appeared in the II and VI or II and VII age classes, respectively. When came to IX and X age classes, the values of two in all populations were stable. By the X and XI age classes, the q x and K x had dramatically increased.

Figure 5 Mortality (q x ) and killing power (K x ) curve of the T. sinense populations 

Survival analysis. The survival function values were obtained according to the static life tables (Table 5). In the four populations, the S (i) declined monotonically with increasing age class, while the F (i) increased monotonically, showing a complementary trend. In the four Populations, the S (i) and the F (i) both changed noticeably during the I, II age classes, and then more gradually; while all the Populations in LMNR, a halcyon change trend appeared after the VII age class (Figure 6). The S (i) of the four populations generally continued to decline throughout the survival process until the individuals died.

Table 5 Functional values of survival analysis of T. sinense population in LMNR 

Population Age-class S (i) F (i) f (ti) λ (ti) Population Age-class S (i) F (i) f (ti) λ (ti)
Pop.1 I 0.88 0.13 0.044 0.007 Pop.3 I 0.64 0.36 0.032 0.022
II 0.75 0.25 0.006 0.014 II 0.29 0.72 0.018 0.056
III 0.63 0.375 0.006 0.023 III 0.29 0.72 0 0.056
IV 0.50 0.50 0.006 0.033 IV 0.21 0.79 0.004 0.065
V 0.38 0.63 0.006 0.045 V 0.14 0.86 0.004 0.075
VI 0.25 0.75 0.006 0.06 VI 0.07 0.93 0.004 0.087
VII 0.13 0.88 0.006 0.078 VII 0.07 0.93 0 0.087
VIII 0.13 0.88 0 0.078 VIII 0.07 0.93 0 0.087
IX 0.13 0.88 0 0.078 IX 0.07 0.93 0 0.087
X 0.13 0.88 0 0.078 X 0.07 0.93 0 0.087
XI 0 1 0.006 0.1 XI 0 1 0.004 0.1
Pop.2 I 0.57 0.43 0.029 0.027 Pop.4 I 0.64 0.36 0.032 0.022
II 0.52 0.48 0.002 0.031 II 0.36 0.64 0.014 0.047
III 0.43 0.57 0.005 0.040 III 0.27 0.73 0.005 0.057
IV 0.33 0.67 0.005 0.050 IV 0.27 0.73 0 0.057
V 0.24 0.76 0.005 0.062 V 0.27 0.73 0 0.057
VI 0.14 0.86 0.005 0.075 VI 0.181 0.82 0.005 0.069
VII 0.01 0.91 0.002 0.083 VII 0.09 0.91 0 0.083
VIII 0.05 0.95 0.002 0.091 VIII 0.09 0.91 0. 0.083
IX 0.05 0.95 0 0.091 IX 0.09 0.91 0 0.083
X 0.05 0.95 0 0.091 X 0.09 0.91 0 0.083
XI 0 1 0.002 0.10 XI 0 1 0.005 0.1

S (i) : The population survival rate; F (i) : Cumulative mortality rate; f (ti) : Mortality density rate; λ (ti) : Hazard rate.

Figure 6 Survival rate S (i) and cumulative mortality F (i) curve of the T. sinense populations. 

In the four populations, the changing trend of f (ti) was similar to that of λ (ti) , as both peaked in the II and IX age classes. The changing in population 4 was softer (Figure 7).

Figure 7 Mortality density f (ti) and hazard rate λ (ti) curve of the T. sinense population 

Time series analysis. The number of individuals in T. sinense populations in the LMNR is predicted to decline over time. When the 2-age class for new plants was reached, the numbers of surviving individuals in the younger age classes (III and IV age classes) in four Populations were predicted to decrease significantly; conversely, the number of individuals in the middle age classes all numbers of individuals remained relatively stable. When the 4-age class time for new plants was reached, the number of individuals showed a decreasing trend with increasing age class, which was similar to the change law of mortality curve. In the future, the number of individuals decreased sharply over time. When it was time for new plants to reach the 10-age class, the number of individuals predicted to survive in the four populations was no more than ten (Table 6).

Table 6 Time series analysis of age structure of T. sinense 

Population Age-class ax M2 M4 M6 M8 M10 Population Age-class ax M2 M4 M6 M8 M10
Pop.1 I 0 Pop.3 I 0
II 15 7.5 II 11 5.5
III 14 14.5 III 16 13.5
IV 0 7 7.25 IV 1 8.5 7
V 0 0 7.25 V 3 2 7.75
VI 0 0 3.5 4.83 VI 0 1.5 5 5.17
VII 0 0 0 4.83 VII 2 1 1.5 5.5
VIII 0 0 0 2.33 3.625 VIII 1 1.5 1.5 3.83 12.25
IX 0 0 0 0 3.625 IX 0 0.5 0.75 1.17 4.25
X 1 0.5 0.25 0.167 1.875 3 X 0 0 0.75 1 2.875 3.4
XI 1 1 0.5 0.33 0.25 3.1 XI 0 0 0.25 0.5 0.875 3.4
total 31 30.5 18.75 12.487 9.375 6.1 total 34 34 24.5 17.17 20.25 6.8
Pop.2 I 1 Pop.4 I 0
II 21 11 II 19 9.5
III 22 21.5 III 12 15.5
IV 2 12 11.5 IV 1 6.5 8
V 1 1.5 11.5 V 1 1 8.25
VI 0 0.5 6.25 7.83 VI 2 1.5 4 5.83
VII 0 1 1.25 8 VII 0 1 1 5.83
VIII 1 1 0.75 4.67 6.125 VIII 0 0 0.75 2.67 4.375
IX 0 0.5 0.75 1 6.125 IX 0 0 0.5 0.67 4.375
X 0 0.5 0.75 0.667 3.5 5 X 0 0 0 0.5 2 3.5
XI 1 0.5 0.25 0.667 0.875 5 XI 2 1 0.5 0.67 0.75 3.7
total 51 50 33 22.834 16.625 10 total 37 36 23 16.17 11.5 7.2


The population dynamics and changes in population structure of T. sinense are the result of its biological characteristics and interaction with the environment (Grubb 1977). Population structure in plants can be divided into three types, i.e., increasing, stable, and declining (Guo 2009). Relict and endangered plants with long lifespans tend to be of the declining type (Zhang et al. 2004, Zhang et al. 2008). The reasons for population decline in endangered plants are mainly attributed to two factors: poor regenerative ability and adaptation (including poor seed set and low germination), and anthropogenic factors (over-exploitation, over-grazing, forest floor denudation) (Gupta & Chadha 1995, Jasrai & Wala 2001). In our study, there was a significant positive correlation between age and DBH, the ages can be well fitted by the DBH in LMNR (Hett et al. 1976). The age structures of the T. sinense populations in the LMNR were all close to the pyramid type, with the survival curve approximating a Deevey-II type and Deevey-III type; in the four populations of LMNR, their survival was similar. The population dynamic indexes of these populations (V pi ) were all greater than zero. However, the dynamic index between adjacent age classes was negative, especially for the I age class. Furthermore, the seedling and sapling individuals were usually lacking that was consistent with those of Davidia involucrata (Liu et al. 2012). These results indicated that most of the T. sinense populations investigated in the LMNR were relatively stable, but some of they were in early recession (Deevey 1947).

The mortality rate and killing power curve can be seen to reflect the quantity dynamic change of T. sinense populations. The two curves for these populations showed that two peaks appeared in the II and IX age classes, or the VII age class. The peak in the II age class suggested that the juveniles in T. sinense populations were vulnerable to pests and diseases and adverse environments due to lower competitive ability (Han et al. 2015, Li et al. 2018); these harsh environmental conditions would result in the greater mortality rate of juveniles, this characteristic was common with Abies fanjingshanensis, the rare and endangered plant endemic to Guizhou (Li et al. 2011). In addition, the rapid growth of saplings into juveniles would gradually increase inter- and intra-species competition for limited environmental resources (such as light and mineral nutrition) in the T. sinense community (Tian et al. 2018). This phenomenon might explain the higher mortality rate of juveniles.

Previous studies have showed that a sufficient number of younger individuals are a prerequisite for the successful regeneration of a tree population (Pala et al. 2012, Dutta & Devi 2013), especially for endangered species (Xie & Chen 1999, Guo 2009). Therefore, the deficiency of seedlings, saplings and the greater mortality rate of juveniles may cause a bottleneck in the regeneration and recovery of these natural T. sinense populations, which might eventually result in population decline (Cao et al. 2012). Therefore, the apparently relatively stable population of T. sinense might already be in the early stages of decline, similar to that reported for Emmenopterys henryi (Kang et al. 2007) and Aloe peglerae (Phama et al. 2014).

The survival curve showed that the l x of T. sinense decreased rapidly in the I ~ VIII (Populations 1 and 2) or I ~ III (Populations 3 and 4) age classes, but more slowly in the IV or VII age classes, and then remained at a relatively low level. The S (i) and the F (i) both changed noticeably during the I, II age classes, and then more gradually. The changing trend of f (ti) was similar to that of λ (ti) , as both peaked in the II and IX age classes. These findings suggested that the T. sinense population slumped during the early stage, and then remained stable during the middle stage, before a decline in the final stage. However, the dynamic trend detected for T. sinense differed from that obtained for Pinus taiwanensis (Bi et al. 2001) and Taxus yunnanensis (Su et al. 2005). The lower fitness of seeds and seedlings leads to a deficiency in the number of seedlings (Gan et al. 2013, Han et al. 2015, Li et al. 2018). The juvenile trees of T. sinense that survive this natural environmental screening process will have stronger resistance and competitive ability, leading to a decline (Li et al. 2015, Cao et al. 2012). As a result, the population size might remain relatively stable in its middle stages. By the time T. sinense individuals enter the older ages, they are in a physiological senescence phase (Silvertown et al. 2001, Xiao et al. 2004, Zhang et al. 2008). Therefore, the population decline in its final stages might be attributed to the physiological senescence of T. sinense individuals (Han et al. 2015, Li et al. 2018).

Time series analysis showed that, over the next 10 age class times, the number of individuals in the T. sinense populations would decrease sharply, and the number of adult individuals would gradually increase, while the number of younger individuals was increasingly insufficient, seriously affecting the survival and development of the T. sinense populations. It can be inferred that as time goes by, there will be fewer and fewer individuals of the T. sinense population in LMNR (Li et al. 2015).

In general, in order to adapt to the abominable environment (the flowering period coincides with the rain period), most of them were inbred, which leaded to the low germination rate of seeds in the field. The survival rate of seedlings was affected by the environment in which they lived (including the associated species and the litter thickness) (Cao et al. 2012, Tian et al. 2018). In the natural population of T. sinense, the niche of associated species was larger, the natural regeneration of T. sinense population was poor, and there was a danger that it would be replaced by its associated tree species (such as Crecidiphyllum japonicum, Acer pictum subsp. mono) (Li 2015, Tian et al. 2018). Therefore, the populations of T. sinense in LMNR will gradually decline if the current problem is not resolved.

In order to effectively protect the endangered plants T. sinense, some management strategies should be carried out. First, some of the more competitive tree species should be thinned to reduce interspecific competition and provide a better habitat for the growth of juveniles of T. sinense. In addition, improved conditions for the germination of T. sinense seeds and seedling establishment should be created to accelerate the natural regeneration of the population.


The age structure of T. sinense populations in the LMNR were all close to the pyramid type, with few seedlings and saplings, indicating that the population was in the early stages of decline. The population size of T. sinense slumped during the early age classes, and then remained relatively stable in the middle, followed by a decline in the final stages. The lack of seedlings or saplings in the populations might reflect a bottleneck in the regeneration of the T. sinense populations that were studied here. Through the investigation of T. sinense population in the LMNR, we have confirmed that it is in a dangerous situation. Based on our study, we have suggested several strategies to conserve and manage the T. sinense population.


We thank all students who help to collecting and analyzing data: Yang Chen, Wenying Li. Funding was provided by The Applied Basic Research Project of Sichuan Province, China (No.2017JY0164), Meritocracy Research Funds of China West Normal University (No.17YC325), The manuscript was supported by The fourth General Survey of the Resources of traditional Chinese Medicines in China (No.2018PC001) and the Fundamental Research Funds of China West Normal University (No. 18B026).

Literature cited

Armesto JJ, Casassa I, Dollenz O. 1992. Age structure and dynamics of Patagonian beech forests in Torres del Paine National Park, Chile. Vegetation 98: 13-22. [ Links ]

Bi XL, Hong W, Wu CZ, Yan SJ. 2001. Analysis on the life table of Castanopsis eyrei population in Wuyi Mountain. Journal of Tropical and Subtropical Botany 9: 243-247. DOI: [ Links ]

Brodie C, Howle G, Fortin MJ. 1995. Development of a Populus balsamifera clone in subarctic Québec reconstructed from spatial analyses. Journal of Ecology 83: 309-320. DOI: [ Links ]

Cao LL, Gan XH, Song HE. 2012. Effects of different geographical provenances and matrix on seed germination and seedling initial growth of Tetracentron sinense. Guihaia 32: 656-662. DOI: [ Links ]

Chapman JL, Reiss MJ. 2001. Ecology: Principles and Application,. Cambridge: Cambridge University Press, 23-48. ISBN-10: 0521588022; ISBN-13: 978-0521588027 [ Links ]

Chen XD. 1998. Study on dynamic quantitative analysis of plant population and community structure. Acta Ecologica Sinica 18: 214-217. DOI: [ Links ]

Chen ZY, Yang N, Yao XM, Tian XM, Yang MY.2012. Life history and spatial distribution of a Taiwania flousiana population in Leigong Mountain, Guizhou Province, China. Acta Ecologica Sinica 32: 2158-2165. DOI: [ Links ]

Deevey ES. 1947. Life tables for natural populations of animals. Quarterly Review of Biology 22: 283-314. [ Links ]

Doweld AB. 1998. Carpology, seed anatomy and taxonomic relationships of Tetracentron (Tetracentraceae) and Trochodendron (Trochodendraceae). Annals of botany 82: 413-443. 10.1006/anbo.1998.0679 [ Links ]

Dutta G, Devi A. 2013. Plant diversity, population structure, and regeneration status in disturbed tropical forests in Assam, northeast India. Journal Forestry Research 24: 715-720. [ Links ]

Feng SY. 1983. Survival analysis (III). Mathematics in practice and theory 2: 70-76. [ Links ]

Fu DZ, Bartholomew B. 2001. Tetracentraceae. Flora of China 6: 125. [ Links ]

Fu LG, Jin JM. 1992. Chinese plant red book - rare and endangered plants (Volume 1). Beijing: Science Press 590-591. ISBN: 7030004841 [ Links ]

Gan X, Xie D, Cao LL. 2012. Sporogenesis and development of gametophytes in an endangered plant, Tetracentron sinense Oliv. Biological Research 45: 393. DOI: [ Links ]

Gan XH, Cao LL, Zhang X, Li HC. 2013. Floral biology, breeding system and pollination ecology of an endangered tree Tetracentron sinense, Oliv. (Trochodendraceae). Botanical Studies 54: 50. DOI: [ Links ]

Grubb PJ. 1977. The maintenance of species-richness in plant communities: the importance of the regeneration niche. Biological Reviews 52: 107-145. [ Links ]

Guedje NM, Lejoly J, Nkongmeneck BA, Jonkers WBJ. 2003. Population dynamics of Garcinia lucida (Clusiaceae) in Cameroonian Atlantic forests. Forest Ecology and Management 177: 231-241. [ Links ]

Guo LJ. 2009. Population structure and dynamics of the endangered plant Emmenopterys henryi. Journal of Wuhan Botanical Research 27: 509-514. DOI: [ Links ]

Gupta R, Chadha KL. 1995. Medicinal and aromatic plant research in India. pp. In: KL. Chadha, R. Gupta, eds. Advances in Horticulture, Medicinal and Aromatic Plants. New Delhi, India: Malhotra House, 1-43. ISBN-10: 8185048290; ISBN-13: 978-8185048291 [ Links ]

Han HY, Li S, Gan XH, Zhang XM. 2017. Phenotypic diversity in natural populations of an endangered plant Tetracentron sinense. Botanical Sciences 95: 283-294. [ Links ]

Han HY, Xu N, Li S, Li S, Zhang XM, Li X, Li MT, Gan XH. 2015. Effects of low temperature treatment on seed germination characteristics in Tetracentron sinense Oliv. Plant Diversity and Resources 37: 586-594. [ Links ]

Harcombe PA. 1987. Tree Life Tables: Simple birth, growth, and death data encapsulate life histories and ecological roles. Bioscience 37: 557-568. [ Links ]

Harper JL.1977. Population Biology of Plants. London: Academic Press. ISBN-10: 1932846247; ISBN-13: 978-1932846249 [ Links ]

Herrera J. 1991. The reproductive biology of a riparian mediteranean shrub, Nerium oleander (Apocynaceae). Botany Journal Linnean Society 106: 147-172. [ Links ]

Hett JM, Loucks OL. 1976. Age structure models of balsam fir and eastern hemlock. Journal of Ecology 64: 1029-1044. [ Links ]

Jasrai Y, Wala TB. 2001. Curculigo orchioides Gaertn. (Kali musli): an endangered medicinal herb. pp. In: I. A. Khan, A. Khanum, eds. Role of Biotechnology in Medicinal and Aromatic Plants. Vol. IV. Hyderabad, India: Ukaaz Publication, 89-95. ISBN 13: 9788190044158 [ Links ]

Jiang H. 1992. Population ecology of spruce. Beijing: China Forestry Press 55-135. ISBN: 9787503811838 [ Links ]

Kang HJ, Chen ZL, Liu P, Hao CY, Wei FM. 2007. The population structure and distribution pattern of Emmenopterys henryi in Dapanshan Natural Reserve of Zhejiang Province. Acta Ecologica Sinica 27: 0389-0396. [ Links ]

Li HC, Gan XH, Zhang ZP, Zhang CX, Song L. 2015. Effects of altitudes and the DBH of seed trees on biological characteristics of Tetracentron sinense (Tetracentraceae) Seeds. Plant Diversity & Resources 37: 177-183. DOI: [ Links ]

Li S, Gan XH, Han HY, Xu N, Hou ZY, Chen Y, Deng XJ. 2016. Leaf phenotypic traits of Tetracentron sinense, an endangered plant species. Forest Research 29: 687-697. [ Links ]

Li S, Gan X, Han HY, Zhang XM, Tian ZQ. 2018. Low within-population genetic diversity and high genetic differentiation among populations of the endangered plant Tetracentron sinense Oliver revealed by inter-simple sequence repeat analysis. Annals of Forest Science 75: 74. DOI: [ Links ]

Li XX, Wang QC, Cui GF, Yang CD. 2011. Structure and dynamic characteristics of wild populations of Endangered Abies arborescens fan jingshanensis. Acta Botanica Boreali-Occidentalia Sinica 31: 1479-1486. [ Links ]

Liu HY, Jin XL, Shen SY, Zhang RQ. 2012. Population quantitative characteristics and dynamics of rare and endangered plant Davidia involucrata in Hunan Province. Acta Ecologica Sinica 32: 7738-7746.DOI: [ Links ]

Luo JD, Gan XH, Jia XJ, Xie D, Zhang L. 2010. Biological characteristics of seeds of endangered plant Tetracentron sinense (Tetracentraceae). Acta Botanica Yunnanica 32: 204-210. DOI: [ Links ]

Molles MC. 2002. Ecology Concept and Applications. New York: McGraw-Hill pp.186-254. ISBN-10: 0071122524; ISBN-13: 978-0071122528 [ Links ]

Pala NA, Negi AK, Gokhale Y, Bhat JA, Todaria NE. 2012. Diversity and regeneration status of Sarkot Van Panchyat in Garhwal Himalaya, India. Journal of Forestry Research 23: 399-404. DOI: [ Links ]

Phama JO, Panagos MD, Myburgh WJ, Pfab MF. 2014. The population status of the endangered endemic plant Aloe peglerae: Area of occupancy, population structure, and past population trends. South African Journal of Botany 93: 247-251. DOI: [ Links ]

Proctor MCF, Wratten SD, Fry GLA.1980. Field and Laboratory Exercises in Ecology. London: Edward Amold. DOI: [ Links ]

R Core Team 1995. R: A language and environment for. Statistical computing. R Foundation for Statistical Computing, Vienna, Austria. [ Links ]

Silvertown JW. 1982. Introduction to plant population ecology. London: Longman. pp. 75-155. ISBN-10: 0582442656; ISBN-13: 978-0582442658 [ Links ]

Skoglund J, Verwijst T. 1989. Age structure of woody species populations in relation to seed rain, germination and establishment along the river Dalalven, Sweden. Vegetation 82: 25-34. DOI: [ Links ]

Smith DP, Keyfitz N. 1947. Life Tables for Natural Populations of Animals. Quarterly Review of Biology 22: 283. [ Links ]

Su JR, Zhang ZJ, Deng J, Chen ZY. 2005. Population structure and life table of the endangered population of Taxus yunnanensis. Forest Rasearch 18. DOI: [ Links ]

Tang CQ, Peng MC, He LY, Ohsawa M, Wang CY, Xie TH, Li WS, Li JP, Zhang HY, Li Y, Yang XM, Li GS. 2013. Population persistence of a Tertiary relict tree Tetracentron sinense on the Ailao Mountains, Yunnan, China. Journal of Plant Research 126: 651. DOI: [ Links ]

Tang CQ, Ohsawa M. 2009. Ecology of subtropical evergreen broadleaved forests of Yunnan, southwestern China as compared to those of southwestern Japan. Journal of Plant Research 122: 335-350. DOI: [ Links ]

Tang CQ, Li T, Zhu X. 2007. Structure and regeneration dynamics of three subtropical midmontane moist evergreen broadleaved forests in southwestern China, with special reference to bamboo in the forest understories. Canadian Journal of Forest Research 37: 2701-2714. DOI: [ Links ]

Tian ZQ, Li HC, Li WY, Gan XH, Zhang XM, Fan ZL. 2018. Structural characteristics and niches of dominant tree populations in Tetracentron sinense communities: Implications for conservation. Botanical Sciences 96: 157-167. DOI: [ Links ]

Wang LL, Wang GL, Huang YJ, Li J, Liu DY. 2006. Age structure and niche of the endangered Magnolia sieboldii in Huangshan Mountain. Acta Ecologica Sinica 26: 1862-1871. DOI: [ Links ]

Wang B, Li MG, Peng SL. 1995. Plant population biology. Guangzhou, China: Guangdong Higher Education Press. ISBN: 7-5361-1593-8 [ Links ]

Wu CZ, Hong W, Xie JS, Wu JL. 2000. Life table analysis of Tsuga longibracteata population. Chinese Journal of Applied Ecology 11: 333-336. DOI: [ Links ]

Xiao YA, He P, Li XG, Deng HP. 2004. Study on numeric dynamics of natural populations of the endangered species Disanthus cercidifolius var. Longipes. Acta Phytoecologica Sinica 28: 252-257. DOI: [ Links ]

Xie TT, Su PX, Zhou ZJ, Zhang HN, Li SJ. 2014. Population structure and dynamic characteristics of sand and date in the transitional zone of desert oasis. Acta Ecologica Sinica 34: 4272-4279. DOI: [ Links ]

Xie ZQ, Chen WL. 1999. The endangering causes and preserving strategies for Cathaya argyophylla, a plant endemic to China. Chinese Journal of Plant Ecology. 23: 1-7. DOI: [ Links ]

Yang FX, Wang SQ, Xu HG, Xu HG, Li BQ. 1991. Survival analysis theory and its application in life table research. Acta Ecologica Sinica 11: 153-158. DOI: [ Links ]

Zhang H, Wang D, Duan F, Li S, Gan XH. 2019. Construction strategy of core collection based on leaf phenotypic traits of Tetracentron sinense. Forest Research, 32: 166-173. DOI: [ Links ]

Zhang JD, Hull V, Ouyang ZY, He L, Connor T, Yang HB, Huang JY, Zhou SQ, Zhang ZJ, Zhou CQ, Zhang HM, Liu JG. 2017. Modeling activity patterns of wildlife using time-series analysis. Ecological and Evolution, 7: 2575-2584. DOI: [ Links ]

Zhang QY, Zhang YC, Luo P, Wang Q, Wu N. 2007. Ecological characteristics of a Sabina saltuaria population at timberline on the south-facing slope of Baima Snow Mountain, southwest China. Chinese Journal of Plant Ecology 31: 857-864. DOI: [ Links ]

Zhang WH, Wang YP, Kang YX, Liu XJ. 2004. Study on the relationship between Larix chinensis population’s structure and environment factors Acta Ecologica Sinica 24: 41-47. DOI: [ Links ]

Zhang WH, Zu YG. 1999. Study on the life table and survival curve of the endangered species of salvia chinensis and its comparison with popularly planted salvia chinensis. Chinese Journal of Plant Ecology 01: 77-87. [ Links ]

Zhang ZX, Liu P, Liu CS, Liao CC, Cai MZ, Huang BW. 2008. The structure characteristics and dominant population regeneration types of Tsuga tchekiangensis communities in the Jiulongshan National Natural Reserve of Zhejiang Province. Acta Ecologica Sinica 32: 1146-1156. DOI: [ Links ]

Zhou JL, Zheng SZ, Yang Z. 1992. Plant population ecology. Beijing: Higher Education Press. ISBN: 9787040039689 [ Links ]

Received: January 06, 2019; Accepted: December 13, 2019; Published: March 11, 2020

* Corresponding author:

Associated editor: Jordan Golubov

Authors’ contributions: HZ and FD performed the experiment and statistical analysis; XG conceived the project, designed the experiments, and conducted part of the experiment; YL conceived the project, designed the experiments, and performed the experiment partly; QW, XL and ZX performed the statictical analysis partly; JT built the model.

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