第5章生态多样性及其测度

1、 参考书：E.C.Pielou 1975,Ecological Diversity 文献 Anne E.magurran 1988 Ecological Diversity and its measurement 李典谟 1987， 生态的多样性度量 生态学杂志 ，6（4):49-52 马克平 第十章 生物群落多样性的测度方法 中国科学院生物多样性委员会主编 “生物多样性研究的原理与方法” 1994There are three reasons why ecologists are interested in ecological diversity and its measurement.F

2、irst, despite changing fashions and preoccupations, diversity remained a central theme in ecology. The well documented patterns of spatial and temporal variation in diversity which intrigued the early investigators of the natural world continue to stimulate the minds of ecologists today.Second, meas

3、ures of diversity are frequently seen as indicators of the wellbeing of ecological systems.Thirdly, considerable debate surrounds the measurement of diversity. Diversity may appear to be a straightforward concept which can be quickly and painlessly measured. There is however a simple explanation why

4、 diversity is so hard to define. That is because diversity consists of not one but two components. These are first the variety and secondly the relative abundance of species. （1）种数多少 （2）各种之间相对丰富度首先是由Fisher提出， Williams引用 （ Fisher et al 1943)01r01 Fisher (k+r)1=() () ; ( )r! (k) 111() ; (n+1)=n!1rkzuk

5、ppzue duPppp指数设一个种有r个个体的概率服从负二项分布000001, (1)(k+r) (1)(k+r)1r! (k) 1 (1) r!(1) , ( )1 (1) ( )lim; =lim!1 ln 1rrkkrrrkkkrrkkrrppxpxxpcxpxxccrkxrxpxcrrxrx rrp在讨论多样性时， 无意义。设x=1+p令与 无关=ln(1)1 ()rrxrxxrr rr具有 个个体的种的频数n =s=s对数级数rr=1r=1rr=1r=1 =n=ln(1) r n=1 S,N, rrxSxrr xxNrxxFisher 所有种数所有个体数于是通过抽样， 由是多样性指

6、数先决条件， 具有r个个体的种的频率是服从对数级数分布即（）式-1p =; x=ln(1-x)1+p-11 =1ln(1)ln()1+pV p=1msp为什么 是多样性指数在负二项分布中所以，分布越均匀，V越小， p也越小，ln(1+p)越小，越大 大量的研究表明（magurran,1988):是一个很好的多样性指数，即使对数级数模型不是最好的理论分布的时候也是如此。Magurran，A.E.1988. Ecological Diversity and Its Measurement. New Jersey:Princeton University Press 2.多样性的信息度量A1p1A2

7、P2AjPjAsPsSj11 p=1(,.), ,. )2(2)L(s)=HsSH ppi123s12s总体分为 类，找到一个函数，有下面几个性质1（1）对于给定s,当p = 时s1 11L(s)=H(有最大值，越均匀多样性越高s ss（ ） H(p ,p ,p ,.p ,0,.0) =H(p ,p ,.p ) 一致性条件保证了对两个种间数量分布均匀的总体，种数越多，多样性越高1 11111( , ,. ,0)H(,.,)L(s+1)s sss+1s+1 s+1 (3) A分类 B分类A1p1AjPjAsPsB1 q1Bk qkBt qt A1B111AjAjBkjkAs Bt sk独立时，

8、kkjkjjkjjp qp q独立时，不独立时，11,12,. H(AB)=H()st,.123( )()( ), jjjjjjH BH qqqp H BjAj为在A 类内，在B分类之下的多样性令H (B)=A分类里在B分类之下的平均多样性AA3 H(AB)=H(A)+H (B)H(AB)=H(A)+H(B)H(AB) H(A) H (B) 12s ii条件如A,B独立，表明，多样性像方差一样，具有可加性总体全部多样性则是总体中不同属多样性考虑到每一属中种的多样性，然后再对属在总体中的比例加权得到的属中种的平均多样性数学上证明H(pp .p )=-plogp 的形式niii=1niii=1ss

9、iiii1sii13 (1)Simpson(1949)N (N-1) N (N-1)N (N-1) N (N-1)PIE=probability of interspecific encounterN (N-N)N (N-1-N+1 =)N (N-1)NN-1NN-1N-1 =()N N-1N-1i其他多样性指数指数两次连续抽样属于同一种的概率D=1-sii1sii1NN-1(1-)NN-1N N-1 =1-N N-1Dnnijiji=1j=1ijijij(2) & Ehrlich(1971)N(Nx ) D=N(N-1) x =0 x =1 12iix =i01iHendrickso

10、na其中，i=j时，ij时，此时（ ）和（ ）同等b)H&E 引入生态位概念种生态位j种生态位- 种生态位j种生态位种生态位j种生态位介于 和 ，表 种和j种生态位不相似的程度12123(1967), N=)1 1. 11NN, 0 McIntoshNDD 1，2ss2i1+2si=1s2iii=112s（ ）一个几个种的样本可以用n维空间中的点（NN .N )表示，其和原点距离U=(NN N +.+N =常数a) 当s上升，U下降; b) 均匀性上升，U下降当N =1 U=(N这时多样性最高， 应为当N = ，N =0，.N =0U= N-N- ND 多样性最低 Umax11maxm

11、ax411-( log )log(1966)-(log)loglogsisiiiHsssPielouppHRHsHR HRs（ ）种间均匀性测量 提出均匀测量为即多样性由种数和均匀性两部分构成21122222maxmax)()iNNnNNnnnNNnDNNNUDNUNNRNNDNNnnNNnni=1i=1对于McIntosh指数，我们也可以给出一个均匀性的量度假定总个数N和种数n是固定的则最大的多样性指数是n个种，N每个种有个个体 U=(n Note on biological diversity ,evenness and homogeneity measures T.O.Kvalseth

12、et al 1991 OIKOS 62：（1）一个可以接受的多样性的测度至少应具备：（1）合理地简单，便于计算和理解（2）从生物学、统计学或者数学上有适当的基础（3）包含种数和均匀性两个概念（4） 有一个直观合理的解释（5）具有所希望的特性221112Odds measures of diversity 1- (1) Simpdon index() (Ludwig and reynold, 1988 Magarran 1988,2 411() OddsisiDpDppiDssss多样性的机会测度两次连续抽样不属于同一种的概率很多科学家用 第八章第 ，章）当时， 很难找到统计学意义定义-1/(1

13、- ), for a random event whose probability is p0.60.6/0.41.51.51-(1- ) 1 (1-(1- OpppoppOddspOp：As a formal definition,the odds are given by 设对一事件 成功的机会和失败的机会之比为假如，是事件的概率，那么对应该事件的机会是-1211-1)1 Odds measures of diversity ()1 pppODpi对应于（ ）两次连续抽样不属于同一种的机会max Berger-Parker index of species dominance(Bergen

14、 and Parker,1970)P difined as the proportion of the most abundant species.May(1975)指出这个指数作为一个单参数描述的种群分布来说是非常好的，被许多人用来度量多样性（Magurran,1988) 缺乏统计学的意义-1-1-1-1-14max 5min1(1)2121(1)max 4max min5 -1 -1 ()112 ()1 -1 lim()-1iiiDPDPNPSNPODNPDPPNPD 一个随机抽取的个体不属于最富集种的机会更为一般当-11(1) min lim ()iPP21-log1logexp(-lo

15、g)-1(2) Heip(1974)21()-1(3)(1981)3exp(-log)-134(1991)4-1 eeiiiiiiippEsppEspAlataloEppEODkvalsethEs均匀性测度(1) Pielou(1977)提出： 提出：上述两种都和样本大小有关，因此是无用的提出：不受样本大小的影响（ ）提出： 标准21()1iODp化的机会度量 Kemoton(1979)noted that different diversity indices often produced inconsistent orderings of communities. He did howev

16、er conclude that this inconsistency is rarer in field data than analyses using artificial and unrealistic data suggest. The discussion above supports this finding provided that indices from within either the species richness group or the dominance/evenness group are chosen.Discriminant ability Sensi

17、tivity to sample size Richness or evenness dominance Calculation Widely sued?(log series) Good lowrichnesssimpleYes(log normal)Good moderaterichnesscomplexnoQ(statistic)Good lowrichnesscomplexnoS(species richness)Good HighrichnesssimpleYesMargalef indexGood HighrichnesssimplenoShannon indexmoderatem

18、oderaterichnessintermediateYesBrillouin indexmoderatemoderaterichnesscomplexno McIntosh U indexGood moderaterichnessintermediatenoSimpson indexmoderatelowdominanceintermediateYesBerger-Parker indexpoorlowdominancesimplenoShannon evennesspoormoderateevennesssimplenoBrillouin evennesspoormoderateevenn

19、esscomplexnoMcIntosh D indexpoormoderatedominancesimplenoTable: A summary of the performance and characteristics of a range of diversity statisticsIndex calculated for light-trap catches The advent of modern computers has opened up a series of new statistical techniques that are of great importance

20、to ecologists because they release us from two restrictive assumptions of parametric statistics:(1) the normal frequency distribution,and (2) must have good theoretical properties, so that confidence limits can be derived mathematically. Step 1. Recombine the original data: We do this by omitting on

21、e of the n replicates from the jackknife sample. Step 2. Calculate pseudovalues of the parameter of interest for each recombining of the data: Step 3. Estimate the mean and standard error of the parameter of interest from the resulting pseudovalues.(1). .iTiTnSnSwherePseudovalue for jackknife estima

22、teinOriginal sample sizeSOriginal statistical estimateSStatisticale estimate when original valuei has beendiscarded from sampleisamp.(1,2,3,., )le numbern( (1)(14 13)/(11360 11359) (153 152)/(11360 11359)( (1)0.20161/4.96iisn nDN NDD5.2454.9644.89Excluded section1VJiVPi 14.895.24 25.293.64 34.935.08

23、 45.522.72 54.636.28 VPi的平均数是4.59,它是河中鱼的最好的估计量. SEVP=SDVPi/n Summary The large number of diversity statistics available means that it may be difficult to select the most appropriate methods of measuring diversity. When applied to realistic data sets these diversity indices can be divided into two ca

24、tegories. On one hand there are the indices which reflect the species richness element of diversity while on the other hand there are measures which express the degree of dominance(evenness)on the data. As a general observation,indices in the first category are better at discriminating between samples but are more affected by sample size than the dominance/evenness set of diversity measures. For reasons of standardization it would be prudent if ecologists would concentrate on one or a few indices. The log series index , the Berger-Parker domi