R軟件與生物多態(tài)性分析

1、1會計學(xué)R軟件與生物多態(tài)性分析軟件與生物多態(tài)性分析Common data formats:(1) Presence/absence data, i.e., 0-1 data(2) Abundance data: number of individuals of each species(3) Cover/biomass data. Cover/biomass are measurements often used in plant ecology. Biomass is occasionally used in insect, marine ecology etc.But (2) and (3

2、) can be converted into presence/absence dataThere are many field methods for collecting the above data. Some common ones include:1. Quadrat sampling/transect line2. Trapping (light, pitfall, suction): Mainly used to collect insects. The common form is abundance data. Trapping data cannot be easily

3、linked to sampling area because we do not know the area base where the insects come from.3. Sighting/hearing (for surveying birds, mammals): Collecting presence/absence data, not accurate for abundance (count).4. Capture-remark methods: Birds, mammals, fishes.A basic data form spcode abund1 ACACME 1

4、2 ADE1TR 233 AEGIPA 44 ALCHCO 375 ALLOPS 106 ALSEBL 2317 AMAICO 18 ANACEX 49 ANDIIN 910 ANNOSP 411 APEIME 4712 APEITI 413 ASPICR 1014 AST1ST 4215 AST2GR 1316 BEILPE 7717 BROSAL 4818 CALOLO 1419 CASEAC 320 CASEAR 15Species diversity consists of two fundamental components: abundance and richness.Suppo

5、se x = (x1, x2, , xS) is a sample of abundance of a community, where S is the number of species.1. Abundance: the number of individuals of a species in a given area. The total number of abundance is N = x1 + x2 + +xS = sum(xi)2. Richness: the number of species in a given area which is S.These two co

6、mponents are not independent of each other, they are related. Most diversity indices are quantitative combinations of abundance and richness in such a way that richness is weighted by relative abundance of each species.Diversity indices3. The Shannon index, H Diversity indicesSiiippH1)ln(4. The Simp

7、son index, D2ipDThe Shannon and Simpson indices are the two most widely used in the literature. The Shannon weighs towards rare species , while the Simpson weighs towards the abundant species.5. The Margalefs index6. The Menhinicks index7. The McIntosh index, D8. The Berger-Parker index, d9. Brillou

8、in index, HBNSDMgln1NSDMnNNnNDi2NNdmaxNnNHiB!ln!lnDiversity indicesRelationship among the indicesMany indices are not independent but related. Hill demonstrates their relationship.where Da is the a-th order of diversity, pi is the proportional abundance of the n-th species. It follows that D0 = numb

9、er of speciesD1 = exponential Shannon indexD2 = the Simpson indexD = the Berger-Parker indexProof: the Shannon index at a - 1 (use lHpital rule):aasaaapppD1121.Hill, M.O. 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54:427-431.1.)log(.)log()log(exp1).log(exp2122112

10、1asaasasaaasaaapppppppppapppD1HeD Evaluation and choice of diversity indicesTwo criteria of “good” indices:High discriminating power: The ability to detect subtle (not unduly) differences between samples. This is an important criterion because one of the major applications of diversity measures is t

11、o gauge the effects of environmental changes (pollution or other disturbances) on communities.Independent of sample size: This criterion is most commonly used to judge whether an index is satisfactory or not. A good index must be relatively independent (no indices are truly independent of sample siz

12、e) of sample size so that one can make sure that the index estimated from relatively small samples will represent the true community.There is little concensus on which indices are “good” (let alone “best”). In general, indices can be divided into two types:Type 1- Indices weighted towards species ri

13、chness (or rarity): Richness, the Margalef, the Menhinicks, the Shannon index, the Brillouin, logseries a a index, and the lognormal l l.Type 2 Indices weighted towards species dominance/evenness (or abundance of species): the Simpson, the McIntosh D, and the Berger-Parker indices.Quadrat PlotX coor

14、dinateY coordinate020406080100020406080100#spp.area=function(data,sides)result=list()nrow=length(sides)for (i in 1:nrow)resulti=spp.area.onetime(data,sidesi)fullresult=matrix(nrow=0,ncol=5)for(i in 1:length(result)fullresult=rbind(fullresult,resulti)colnames(fullresult)=c(area,ind,spp,shannon,simpso

15、n)fullresult=data.frame(fullresult)par(mfrow=c(2,2)plot(fullresult$area,fullresult$spp,col=red)lines(fullresult$area,fullresult$spp,col=green)plot(fullresult$area,fullresult$ind,col=blue)lines(fullresult$area,fullresult$ind,col=green)plot(fullresult$area,fullresult$shannon,col=black)lines(fullresult

16、$area,fullresult$shannon,col=black)plot(fullresult$area,fullresult$simpson,col=black)lines(fullresult$area,fullresult$simpson,col=black)return(fullresult)A grid systemsample.side=function(data,side,plotdim) x=y=seq(0,plotdim1-side,by=side)n=length(seq(0,plotdim1-side,by=side)x1=rep(x,each=n)y1=rep(y

17、,n)loc=data.frame(x1,y1)no.ind=numeric()no.spp=numeric()for (i in 1:n2)randsample=subset(data,data$gx=loci,$x1&data$gx=loci,$y1&data$gy(loci,$y1+side)no.indi=length(randsample$sp)no.sppi=length(unique(randsample$sp)return(data.frame(x=x1,y=y1,ind=no.ind,sp=no.spp)55101020205050100100250250Gi

18、ven a geostatistical model, Z(s), its variogram g(h) is formally defined aswhere f(s, u) is the joint probability density function of Z(s) and Z(u).For an intrinsic random field, the variogram can be estimated using the method of moments estimator, as follows:where h is the distance separating sampl

19、e locations si and si+h, N(h) is the number of distinct data pairs. In some circumstances, it may be desirable to consider direction in addition to distance. In isotropic case, h should be written as a scalar h, representing magnitude.us)u, s ()u() s (21)u() s (var21)h(2ddfZZZZg2)(1)()()(21)( hhsshh

20、NiiizzNgVariogramThe main goal of a variogram analysis is to construct a variogram that best estimates the autocorrelation structure of the underlying stochastic process. A typical variogram can be described using three parameters:Nugget effect represents micro-scale variation or measurement error.

21、It is estimated from the empirical variogram at h = 0.Range is the distance at which the variogramreaches the plateau, i.e., the distance (if any)at which data are no longer correlated.Sill is the variance of the random field V(Z),disregarding the spatial structure. It is theplateau where the variog

22、ram reaches at therange, g(range).hg(h)02468100.00.40.81.2range h = 5nugget = 0.2sill = 1.0)( hgVariogramlibrary(vegan) ; varpartSampling species areaNumber of speciesSpecies-area curveThe generalized species-area model asossasfdads)()(32gazcas )ln(azcszacbsLogarithmic modelPower modelLogistic model

23、A special case of the logistic model (z = 1):The derivative describes the rate of change in the number of species with one unit of change in area. An important point to make: models change with the change of scale.cabas1Michaelis-MentenHe, F. and Legendre, P. 1996. On species-area relationships. Ame

24、rican Naturalist 148(4): 719-737cdf.obsi=length(abundabund 1 (use lHpital rule):aasaaapppD1121.Hill, M.O. 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54:427-431.1.)log(.)log()log(exp1).log(exp21221121asaasasaaasaaapppppppppapppD1HeD Given a geostatistical model, Z

25、(s), its variogram g(h) is formally defined aswhere f(s, u) is the joint probability density function of Z(s) and Z(u).For an intrinsic random field, the variogram can be estimated using the method of moments estimator, as follows:where h is the distance separating sample locations si and si+h, N(h) is the number of distinct data pairs. In some circumstances, it may be desirable to consider direction in addition to distance. In isotropic case, h should be written as a scalar h, representing magnitude.us)u, s ()u() s (21)