Worked example 1 illustrates the
use of Diversity.R functions
to perform simple Correspondence Analysis (CA) and Non Symetric CA (NSCA), as well as their
constrained and/or partial relatives with respect to Instrumental
Variables, CAIV
and NSCAIV (Couteron
et al. 2003). It is based on analyses of CFI
data set, from a 12 240-ha
rainforest plot called Counami Forest Inventory (CFI) in French Guiana.
1
- CFI data set
Oncethe library diversity
has been installed
and loaded:
CFI$tab is an abundance matrix of 59 tree species in 411 plots ; CFI$topo is a vector of 12
eco-topographical codes assigned to plots ; CFI$xy is a matrix of
geographical co-ordinates of plots ; CFI$dbh is a matrix of the
frequency distribution of trees within plots into 14 diameter classes.
nsca<-nsca.simpson(CFI$tab,test=F)
#Select the number of axes: 3 plot(nsca) par(mfrow=c(1,2)) s.value(CFI$xy,nsca$l1[,1]) s.value(CFI$xy,nsca$l1[,2])
3 - Constrained ordinations
with respect to topography and stand structure
3.1 - CAIV and
NSCAIV with respect to topography
ca.topo<-ca.richness(CFI$tab~CFI$topo)#Select
the number of axes:
2 sum(ca.topo$eig)/sum(ca$eig)
#[1]
0.0652135 summary(ca.topo) #class: summary.dudiv #metric: Richness #call: ca.richness.formula(formula =
CFI$tab ~ CFI$topo) #total diversity: 58 #explained diversity: 0.363 #ratio of explained diversity:
0.00626 #Pr(>ratio): 0.001 based on 999
replicates
nsca.topo<-nsca.simpson(CFI$tab~CFI$topo)
#Select
the number of axes:
2 sum(nsca.topo$eig)/sum(nsca$eig)
#[1] 0.1107594 summary(nsca.topo) #class: summary.dudiv #metric: Simpson #call: nsca.simpson.formula(formula
= CFI$tab ~ CFI$topo) #total diversity: 0.89 #explained diversity: 0.0129 #ratio of explained diversity:
0.0145 #Pr(>ratio): 0.001 based on 999
replicates
3.2 - CAIV and
NSCAIV with respect to stand structure ca.dbh<-ca.richness(CFI$tab~CFI$dbh)#Select
the number of axes:
2 sum(ca.dbh$eig)/sum(ca$eig)
#[1] 0.04908191 summary(ca.dbh) #class:
summary.dudiv #metric:
Richness #call:
ca.richness.formula(formula = CFI$tab ~ CFI$dbh) #total
diversity: 58 #explained
diversity: 0.273 #ratio of
explained diversity: 0.00471 #Pr(>ratio):
0.003 based on 999 replicates nsca.dbh<-pcaiv(nsca,CFI$dbh,scannf=F)
#Select
the number of axes:
2 sum(nsca.dbh$eig)/sum(nsca$eig)
#[1] 0.07496595 summary(nsca.topo) #class: summary.dudiv #metric: Simpson #call: nsca.simpson.formula(formula
= CFI$tab ~ CFI$topo) #total diversity: 0.89 #explained diversity: 0.0129 #ratio of explained diversity:
0.0145 #Pr(>ratio): 0.001 based on 999
replicates
3.3 - CAIV
and NSCAIV with respect to both topography and stand structure
ca.topoPdbh<-ca.richness(CFI$tab~CFI$topo+CFI$dbh)#Select the number of axes: 3 sum(ca.topoPdbh$eig)/sum(ca$eig)
#[1] 0.1083041 summary(ca.topoPdbh)
#class: summary.dudiv
#metric: Richness
#call: ca.richness.formula(formula = CFI$tab ~ CFI$topo + CFI$dbh)
#total diversity: 58
#explained diversity: 0.603
#ratio of explained diversity: 0.0104
#Pr(>ratio): 0.001 based on 999 replicates
Fig. 6 in Couteron
et al. (2003) is obtained from: par(mfrow=c(2,2)) s.class(ca.topoPdbh$l1[,1:2],CFI$topo,cell=0)
s.corcircle(ca.topoPdbh$cor[13:26,],2,3)
scatterutil.eigen(ca.topoPdbh$eig/sum(ca.topoPdbh$eig))
nsca.topoPdbh<-nsca.simpson(CFI$tab~CFI$topo+CFI$dbh)
#Select the number of axes:
2 sum(nsca.topoPdbh$eig)/sum(nsca$eig)
#[1] 0.1847913 summary(nsca.topoPdbh)
#class: summary.dudiv
#metric: Simpson
#call: nsca.simpson.formula(formula = CFI$tab ~ CFI$topo + CFI$dbh)
#total diversity: 0.89
#explained diversity: 0.0216
#ratio of explained diversity: 0.0242
#Pr(>ratio): 0.001 based on 999 replicates Fig. 7 in Couteron
et al. (2003) is obtained from:
3.4 - Partial CAIV and
NSCAIV with respect to topography once stand structure has been
factored out
ca.topoSdbh<-ca.richness(CFI$tab~CFI$topo+Condition(CFI$dbh))
#Select the number of axes: 2 sum(ca.topoSdbh$eig)/sum(ca$eig)
#[1] 0.05519235 summary(ca.topoSdbh)
#class: summary.dudiv
#metric: Richness
#call: ca.richness.formula(formula = CFI$tab ~ CFI$topo +
Condition(CFI$dbh))
#total diversity: 58
#explained diversity: 0.307
#ratio of explained diversity: 0.0053
#Pr(>ratio): 0.001 based on 999 replicates
nsca.topoSdbh<-nsca.simpson(CFI$tab~CFI$topo+Condition(CFI$dbh))
#Select the number of axes:
2 sum(nsca.topoSdbh$eig)/sum(nsca$eig)
#[1] 0.1024110 summary(nsca.topoSdbh) #class: summary.dudiv #metric: Simpson #call: nsca.simpson.formula(formula
= CFI$tab ~ CFI$topo + Condition(CFI$dbh)) #total diversity: 0.89 #explained diversity: 0.0119 #ratio of explained diversity:
0.0134 #Pr(>ratio): 0.001 based on 999
replicates
3.5 -
Partial CAIV and NSCAIV with respect to stand structure once topography
has been factored out
ca.dbhStopo<-ca.richness(CFI$tab~CFI$dbh+Condition(CFI$topo))
#Select the number of axes:
2 sum(ca.dbhStopo$eig)/sum(ca$eig)
#[1] 0.04085322 summary(ca.dbhStopo)
#class: summary.dudiv
#metric: Richness
#call: ca.richness.formula(formula = CFI$tab ~ CFI$dbh +
Condition(CFI$topo))
#total diversity: 58
#explained diversity: 0.228
#ratio of explained diversity: 0.00392
#Pr(>ratio): 0.009 based on 999 replicates nsca.dbhStopo<-nsca.simpson(CFI$tab~CFI$dbh+Condition(CFI$topo))#Select
the number of axes:
2 sum(nsca.dbhStopo$eig)/sum(nsca$eig)
#[1] 0.07071023 summary(nsca.dbhStopo) #class:
summary.dudiv #metric:
Simpson #call:
nsca.simpson.formula(formula = CFI$tab ~ CFI$dbh + Condition(CFI$topo)) #total
diversity: 0.89 #explained
diversity: 0.00825 #ratio of
explained diversity: 0.00927 #Pr(>ratio):
0.001 based on 999 replicates
3.6 -
Residual CAIV and NSCAIV once topography and stand structure have been
factored out ca.res<-ca.richness(CFI$tab~Condition(CFI$topo+CFI$dbh),test=F)
#Select the number of axes:
3 sum(ca.res$eig)/sum(ca$eig)
#[1] 0.891696
nsca.res<-nsca.simpson(CFI$tab~Condition(CFI$topo+CFI$dbh),test=F)#Select the number of axes:
2 sum(nsca.res$eig)/sum(nsca$eig)
#[1] 0.8152087 Fig. 8 in Couteron
et al. (2003) is obtained from:
