IAE
Two 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 to 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 size) of sample size so that one can make sure that the index estimated from relatively small samples will represent the true community.
a a a Da p1 p2 ... ps


1 1 a
where Da is the a-th order of diversity, pi is the proportional abundance of the n-th species. It follows that D0 = number of species
Institute of Applied Ecology, CAS
IAE
A basic data form
spcode abund 1 ACACME 1 2 ADE1TR 23 3 AEGIPA 4 4 ALCHCO 37 5 ALLOPS 10 6 ALSEBL 231 7 AMAICO 1 8 ANACEX 4 9 ANDIIN 9 10 ANNOSP 4 11 APEIME 47 12 APEITI 4 13 ASPICR 10 14 AST1ST 42 15 AST2GR 13 16 BEILPE 77 17 BROSAL 48 18 CALOLO 14 19 CASEAC 3 20 CASEAR 15 ……
IAE
用R语言进行生物多样性分析
王绪高 中国科学院沈阳应用生态所
Institute of Applied Ecology, CAS
IAE
Diversity
Which one is more diverse?
Institute of Applied Ecology, CAS
IAE Common data formats:
There are many field methods for collecting the above data. Some common ones
include: 1. Quadrat sampling/transect line
2. Trapping (light, pitfall, suction): Mainly used to collect insects. The common form is abundance data. Trapping data cannot be easily 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.
Institute of Applied Ecology, CAS
IAE
Diversity indices
5. The Margalef’s index
DMg
S 1 ln N
6. The Menhinick’s index
DMn
S N
7. The McIntosh index, D
D
N N
Institute of Applied Ecology, CAS
IAE
Sample
Quadrat Plot
100 Y coordinate 0
0
Single sampling ~ square
sample.ran.squ=function(data, side, plotdim=c(1000,500)) { xlo=runif(1,min=0,max=plotdim[1]-side) ylo=runif(1,min=0,max=plotdim[2]-side) xhi=xlo+side yhi=ylo+side randsample=subset(data, gx>=xlo&gx<xhi&gy>=ylo&gy<yhi) no.ind=length(randsample$sp) no.spp=length(unique(randsample$sp)) return(c(side^2/1e4,no.ind,no.spp))
n
N
2 i
8. The Berger-Parker index, d
d
N m ax N
9. Brillouin index, HB
HB
ln N ! ln ni ! N
Institute of Applied Ecology, CAS
IAE
Relationship among the indices Many indices are not independent but related. Hill demonstrates their relationship.
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)
H ' pi ln( pi )
i 1
4. The Simpson index, D
D pi2
The 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.
20
40
60
80
20
40
60
80
100
X c oordinate
}
Institute of Applied Ecology, CAS
IAE
Sample
Single sampling ~ rectangular
sample.ran.rect=function(data, side.x, side.y, plotdim=c(1000,500)) { xlo=runif(1,min=0,max=plotdim[1]-side.x) ylo=runif(1,min=0,max=plotdim[2]-side.y) xhi=xlo+side.x yhi=ylo+side.y randsample=subset(data, gx>=xlo&gx<xhi&gy>=ylo&gy<yhi) no.ind=length(randsample$sp) no.spp=length(unique(randsample$sp)) return(c(side.x*side.y/1e4,no.ind,no.spp)) }
•
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 richness (or rarity): Richness, the Margalef, the Menhinick’s, the Shannon index, the Brillouin, logseries a index, and the lognormal l. Type 2 – Indices weighted towards species dominance/evenness (or abundance of species): the Simpson, the McIntosh D, and the Berger-Parker indices.
(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) can be converted into presence/absence data