Population Dynamics and Fourier Series Analysis of Toona ciliata of Qizimeishan Nature Reserve

Yixian CHEN,Yingnan CAO,Min ZHANG,Xinzhi LI,Yang WANG

Hubei Vocational College of Economical Engineering,Wuhan 430200,China

Population Dynamics and Fourier Series Analysis of Toona ciliata of Qizimeishan Nature Reserve

Yixian CHEN,Yingnan CAO,Min ZHANG,Xinzhi LI,Yang WANG*

Hubei Vocational College of Economical Engineering,Wuhan 430200,China

To investigate the population dynamics of Toona ciliata in Qizimeishan Nature Reserve,the age classes and population quantity of Toona ciliata in Qizimeishan were analyzed by transforming diameter classes into corresponding age classes.A static life table was prepared.Moreover,the curves of survival rate,mortality rate and killing powder were drawn so as to perform spectral analysis for Toona ciliata in Qizimeishan Nature Reserve.The results showed that the Vpi and Vpi′of the Toona ciliata population were 32.32%and 4.039%,respectively,indicating that Toona ciliata is a stable growth-oriented population with high risk sensitivity.The survival rate curve was approximately fitted to the Deevey II type,so the individuals in each age class had an equivalent mortality rate in overall.The qxand Kxall reached peaks simultaneously at 1,4 and 6 age classes,indicating great effects of physiological properties,environmental sieves and human disturbances on Toona ciliata population at various growth stages.The spectral analysis showed that the fundamental wave A1was 0.752 8,while A3showed an obvious minor cycle deviating from A1.It suggests that there is a periodicity,with minor cycles of multi-harmonic superposition,in natural regeneration of Toona ciliata population.

Toona ciliata;Population dynamics;Spectral analysis

P opulation dynamics refers to the variation in size and quantity of certain population within certain temporal and spatial scales.It is the result of interaction between individual viability and environment,and has become one of the hotspots of plant ecology research[1].Life table can predict the possibilities of survival and reproduction of a species under certain conditions,and can help to understand the existing state of a population and analyze its structure in the past and disturbed state,thereby predicting future population dynamics[2].

Fourierspectralanalysis is a mathematical tool for exploring the fluctuation of natural population distribution and periodicity of population regeneration.The dynamics in natural population regeneration can be reflected by fluctuation of plant quantity at different growth stage[3-4].Wu et al. consider that the natural regeneration of Pinus koraiensis is fluctuantly periodic,and this is a stable feature of Pinus koraiensis.Fluctuation can be observed in all of the vegetation, and spectral analysis can reveal the period fluctuation of variation in pop ulation quantity[5].Therefore,the dynamic study and spectral analysis of plant population play an important role in research on life processes of population,especially of endangered dominant population.

Toona ciliata (Meliaceae)is a large deciduous tree,and is known as“Chinese mahogany”.It has been listed as a national second-class protected wild plant[6].Toona ciliata is scattered in Enshi,Hubei.However, due to overexploitation,changes in natural environment and slow naturalregeneration,the distribution of Toona ciliata is gradually shrinking.In this study,the growth status and dynamic law of Toona ciliata population in Qizimeishan Nature Reserve were studied through field trip so as to provide a theoretical basis for the protection and management of Toona ciliata population.

Overview on Survey Spot

The survey spot is located in the Qizimeishan National Nature Reserve (109°38′30″-109°47′00″E,29°39′30″-30°05′15″N),which is located in the Yien County in Wuling mountainous area of western Hubei Province.Qizimeishan Nature Reserve covers an area of 34 550 hm2,and is composed of Qizimeishan,Qinjiada Mountain and Badagong Mountain.The rock stratum is mainly composed of quartz sand, shale and sandy layer[7].The soil type varied with the increase in altitude. The area,with altitude below 1 500 m, has a subtropical monsoon climate, and is mainly composed of yellowbrown soil.In the subalpine zone with altitude ranging from 800 to 1 200 m, the annual average temperature is 13.7℃;the frost-free period lasts for 263 d;the annual precipitation is 1 635.3 m[8];the annual sunshine duration is 1 212.4 h.The vegetation in Qizimeishan Nature Reserve is mainly composed of evergreen and deciduous mixed broad-leaved forest,and the nature reserve has the typical vegetation type in subtropical mountains[9].

Although Toona ciliata is also scattered in the connection section between western Qizimeishan Nature Reserve and Shadaogou Town and some of them have a diameter at breast height(DBH)more than 100 cm,there is no complete population of Toona ciliata there,which makes it difficult to perform sampling and researches.The survey spot is located in the Hejiawan of Houhe Village, Changtan Town(109°41′30″E,30°02′34″N),where the most intact and largest Toona ciliata population was discovered.In the survey spot,Toona ciliata is the dominant species,and it is distributed in a mountain trench with yellow-brown soil and abundant sunshine.Due to serious human disturbance,the species richness is extremely low.The arbor cultivars(S=7) include mainly Trachycarpus fortunei H.and Cerasus pseudocerasus,and the shrub and vine cultivars include mainly Alangium platanifolium,Hydrangea villosa Rehd and Stachyurus chinensis.In the survey spot,herb and fern cultivars are rich,including Goniophlebium niponicum,Saxifraga aculeate and Impatiens tubulosa.

Methods

Survey method

The Toona ciliata discovered in the Qizimeishan Nature Reserve is the largest and relatively intact population discovered in Yien County.The survey spot had an area of 400 m2(40 m×10 m),and it covered all the Toona ciliata population.In the survey spot,total 16 plots (5 m×5 m)were arranged.In each of the plots,the toon plants were surveyed one by one.For the plants with diameter at breast height less than 2.5 cm,the ground diameter and height of each plant were measured; for the plants with diameter at breast height more than 2.5 cm,the height, diameteratbreastheight,crown breadth,heightunderbranch and branching angle were measured.The environmental factors were recorded. Under the forest,the arbor,shrub, herb and vine plants were all surveyed one by one(Table 1).

Classification of age classes and dynamic analysis

To maintain the ecological integrity of the nature reserve,the data about Toona ciliata population were analyzed as described by Dai et al.[10],and the fitting between diameter at breast height and age class was performed as described by Long et al.[11].Based on the analysis of average diameter at breast height and growth process of Toona ciliata,the population dynamics were analyzed by replacing age class structure by tree class structure[12-13]. Every four years were classified as one age class,and the Toona ciliata population was classified into 8 age classes,including I(DBH≤2.5 cm), II(2.5 cm≤DBH≤7.5 cm),III(7.5 cm≤DBH≤12.5 cm),IV(12.5 cm≤DBH≤17.5cm),V(17.5cm≤DBH≤22.5 cm),VI(22.5 cm≤DBH≤27.5 cm),VII(27.5 cm≤DBH≤32.5 cm) and VIII(DBH≥32.5 cm).

The dynamic index (V)of each age class was deduced using the mathematical model of Chen,and the population dynamics of Toona ciliata were quantitatively described[14].The positive values of Vn,Vpi and Vpi′represented increased individual quantity in the population or adjacent age class;the negative values of Vn,Vpi and Vpi′represented decreased individual quantity in the population or adjacent age class;when the Vn,Vpi and Vpi′values were zero,the individual quantity in the population or adjacent age class was stable.

Preparation of static life table

The static life table of the Toona ciliata population was prepared.Within a specific time,the life table contains the following parameters:x represents the age class;axrepresents the existing individual number at the x class;lxrepresents the standardized survived individual number at the x class at the initial time (usually converted to 1 000);dxrepresents the standardized dead individual number during the interval from x class to (x+1)class;qx represents the mortality rate during the interval from x class to (x+1)class;Lxrepresents the survived individual number during the interval from x class to (x+1)class;Txrepresents the total individual number at the x class;Exrepresents the individual life expect or average expected life among the individuals at the x class at the initial time; Kxrepresents the killing power[12,15-16].

Spectral analysis of population

Spectral analysis is Fourier series expansion.Its sine wave form is as follows:

Wherein,A0represents the average periodic variation;Akrepresents the amplitude of each harmonic;ωkrepresents the harmonic ratio;θkrepresents the phase angle;Ntrepresents the population size at the t time.The individualnumbersatvariousage classes were treated as a time series t, and xtrepresents the number of individuals at t age class.The previously classified age classes were treated as an age class series.n represents the total length of the series;P(=2/n)represents the total number of harmonics. T represents the fundamental period ofa sine wave.It is the longest period of the time series t,and is also total length of the data.It has been known that T is equivalent to n (T=n).The various parameters in the Fourier series expansion can be estimated by following formulas[3-4]:

Results and Analysis

Structureand dynamicsofage classes

Total 16 plots were arranged in the survey spot,and in the survey spot,there were total 41 plants.With age class as the abscissa and survived individual number at each age class as the ordinate,the distribution diagram of Toona ciliata population at various age classes was drawn.As shown in Fig.1,there were 15 survived plants at age class I,accounting for 36.59%of the total surveyed plants; there were less plants at age classes IV,V and VI,while the survived plants at age class V were least,accounting for only 2.44%.The survived plants at age class VII accounted for 12.20%of the total plants.Fig.1 directly showed the sizes of Toona ciliata populations at various age classes.

The dynamics in Toona ciliata populations at various age classes were quantitatively analyzed.The dynamic indexes of individual numbers at age classes I,II,III and IV were 40.00%,55.56%,50.00%and 50.00% respectively, indicating that there were positive growths in population sizes at the classes above.However, the dynamic indexes ofindividual numbers at age classes V,VI and VII were-50.00%,-33.33%and-40.00% respectively,indicating that there were negative growths in population sizes at the classes above.These results were consistent with Fig.1.The dynamic index of the whole population (Vpi)was 32.32%,indicating that the whole Toona ciliata population was growth-oriented[17].The Vpi′value of the whole population was 4.039%(＞0),indicating that the population remained stable.The P value of the population was 0.125,indicating that the population had a high risk resistance capacity.

Static life table and survival curve

The age structure,static life table and population dynamics prediction are all based on actual data,and they can reflect the basic properties of the population,and the results are in line with the natural dynamic laws of the population[5,20].In the preparation of life table,the dxvalues of age classes V and VI were negative,and this was inconsistent with the original mathematicalhypothesis.Therefore,in the preparation of life tables,many scholars adopted the smooth out technology that was ever adopted by Lowe in his research on red deer population[12]. This study also adopted the technology.The Toona ciliata population was smoothed,thus the axvalues were converted into a′xvalues.And then, the life table was prepared.

Table 1 Environmental characteristics of survey spot

Table 2 Static life table of Toona ciliata population in Qizimeishan Nature Reserve

Table 3 Periodic fluctuation of Toona ciliata population

The static life table and survival curve reflect the trends of population dynamics in overall[15].As shown in Table 2,the qxvalue was largest at age classes I and IV,indicating that the size of young toon population was largest;while the qxvalue at age class VII was zero,and this was consistent with the appearance of Kxat age class VII.Exvalue was highest at age class II.Moreover,the Exvalues at age classes I,II,III,IV and V were higher than those at age classes VI and VII.It suggested that the viability was higher at seedling and early adult stages,and then,the population viability was strong.The Kxvalue was highest at age classes I(0.492)and IV(0.336), and correspondingly,the killing power was also highest.At age class VII,the killing power turned zero,indicating that the population dynamics turned stable.

Survival curve reflects the survival of the individual in the population at different age class,and it describes the mortality rate at certain age class with the survived plant number[18].As shown in Fig.2,in the intervals between age classes I and II and VI and VII,the mortality rate was highest and the young seedlings were most,indicating that the growth and development of the population was gradually restricted by environment sieves.After the two high mortality rates,the Toona ciliata population became relatively stable,and this was due to the physiological properties of Toona ciliata.The entire development process,except the young seedling stage,of Toona ciliata all required high intensity sunlight.Therefore,during the development of the population,the middle age classes were inevitably missing.The survival curve the Toona ciliata population was fitted to theDeeveyII type[19].

Analysis on mortality rate and killing power

The mortality curve (qx)reflects the dynamic changes in the population mortality.The killing power curve(Kx) reflects the lethal force or killing power at each age class.Fig.3 showed that the mortality curve and killing power curve of Toona ciliata population were basically consistent.The mortality and killing power of Toona ciliata population all declined in the intervals between age classes I and II and VI and VII.At age class I,the mortality was highest,and till the age class IV,the mortality reached the second peak.It suggested that at that time,the environment had a high screening intensity,and this was mainly reflected from the aspects of light factor and competition within and between species,as well as human disturbance.Correspondingly,the Kxalso reached the peaks at age classes I,IV and VI.The population was relatively stable at age classes II and V.During those intervals,the mortality and killing power were also relatively low.The high qxand Kxvalues at age class I might be caused by physiological properties of Toona ciliata;while the high qxand Kxvalues at age classes IV and VI indicated that the population scale was related to the restrictions by tree age, soil,space,water and other ecological factors,as well as human disturbance.

Spectral analysis of Toona ciliata population

Wu considered that the regularity in time interval among the generations was the reflection of periodic natural regeneration of Pinus koraiensis population[3].Dominant species have some commonalities.In this study,the dynamics in Toona ciliata population was investigated through studying its survived plant number at different age class.The spectral analysis adopted the differentials (total 8 classes)used by static life table and the unsmoothed data.The total wave sequence (K=N/2)was 4.The amplitude(Ak,k=1,2,…,P)of each wave was calculated by spectral analysis formula(Table 3).As shown in Table 3,A1was the fundamental wave,and A2,A3and A4were various harmonics. The differences in Akvalues reflected the differences in effects of various periods.The fundamental wave (A1= 0.752 8)was inherent in the population,and it reflected the fluctuation characteristic of the population.Besides the effect of fundamental wave, the size of Toona ciliata population was also showed significant small periodic fluctuations.The A3value was 0.035 2,indicating a significant small period,which occurred at the DBH of 13 (8×5/3)cm,also the age class IV. This was consistent with the high mortality and killing power at age class IV described in the static life table.

The fluctuation period of Toona ciliata population was restricted by surveyed area and tree age,so the entire life period could not be reflected completely.However,the spectral analysis showed that there was periodicity in natural regeneration of Toona ciliata population.The period was not single period,and it was characterized by multi-harmonic superposition.The period of small fluctuation was about 12-16 years(A3),and it was the theoretical minimum period.The formation mechanism still needed further study. This kind of fluctuation was consistent with the description by the static life table.The small-period fluctuation ensured the maintenance and continuing of self-stability of a population[5].

Conclusions and Discussion

Toona ciliata is a light-demanding plant,so it is mainly distributed in sunny slopes or places with good lighting conditions near the river.The developmentofToona ciliata plantsis greatly affected by environmental factors.When the Toona ciliata plants grow to the age class IV,they are often lack of light.Thus they cannot maintain their carbon balance,and will die before they enter the subject layer.The static life table showed that the survival rate of Toona ciliata population in the Qizimeishan Nature Reserve was fitted to the Deevey II type, and they had the same mortality at various growth stages.

The mortality and survival rate of population are the results of interactionsbetween internalchangesin population and extreme environmental conditions[20].The Toona ciliata population in the Qizimeishan Nature Reserve was distributed in the connection zone between naturalforestand farmland,which was probably due to severe human disturbance and great effects of environmental factors on population structure.The reason for two types of survival curves of Toona ciliata from different germplasm sources is complex and still needs further study.

The mortality and killing power curves all showed three peaks,indicating that some of the Toona ciliata plants obtained a gap opportunity during theirdevelopmentfrom young seedlings to young trees.The second peak was caused by crown closure and increased competition within and among species.The second peak might be due to age and other physiological factors.

Fluctuation occurs in all vegetation,and periodic fluctuation can be a mechanism to maintain the stability of a population.The spectral analysis can be used to describe this mechanism[4].Due to the constraint in surveyed resource,the population environment,physiological characteristics and human disturbance all can affect the length of the period.It is undoubted that there is periodicity in the natural regeneration of Toona ciliata population.The period is not a single period.Instead,it is characterized by multi-harmonic superposition.The period of the small fluctuation is about 12-16 years (A3),indicating that the periodic fluctuation in the natural regeneration of Toona ciliata population is closely related to the growth dynamics.In the same period,the aggregated distribution of Toona ciliata increases the competition within species or inhibits the lighting environment,and then the high mortality at the age class IV makes some room for the remaining plants,promoting the growth of dominant individuals.On the other hand, the growth of individuals in the same period may be affected by the former and latter periods,but this still needs further study.

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Responsible proofreader:Xiaoyan WU

珍稀植物红椿种群动态与傅里叶级数分析

陈益娴，操英南，张敏，李新枝，汪洋*
（湖北生态工程职业技术学院，湖北武汉430200）

为研究七姊妹山红椿种群动态，将林木径级代表年龄结构，分析了龄级与种群数量动态，编制静态生命表，绘制并分析了存活曲线、死亡率曲线和种群损失度曲线，对种群进行谱分析。结果表明：红椿种群Vpi=32.32%，Vpi′=4.039%，属于增长型稳定种群，风险敏感度较高。存活曲线接近DeeveyⅡ型，各龄级个体具有大体相等的死亡率。qx与Kx均在1、4、6级出现高峰，说明不同阶段红椿生理特性、环境筛与人为干扰因素对种群影响较大。波谱分析基波A1=0.752 8，A3反应明显出小周期，表明红椿种群天然更新存在周期性，且有小周期的多谐波叠加。

红椿；种群动态；谱分析

湖北省科技厅公益性科研项目（40 2012DBA40001）。

陈益娴（1986-），男，湖北武穴人，助理工程师，研究方向：林业技术与栽培，E-mail：511514067@qq.com。*通讯作者，副教授，E-mail：walter202628@163.com。

2015-07-03

修回日期 2015-08-07

Supported by Special Scientific Research Fund of Public Welfare Profession of Department of Science and Technology of Hubei Province(40 2012DBA40001).

*Corresponding author.E-mail:walter202628@163.com

Received:July 3,2015 Accepted:August 7,2015