CALCULATION OF MEAN ELLENBERG
INDICATOR VALUES
EIV-reaction 1 2 3
Mycelis muralis 6 1 0 0
Moehringia trinervia 7 0 1 1
Mercurialis perennis 7 1 0 1
Lathyrus vernus 4 0 1 0
Myosotis sylvatica 7 1 1 0
Milium effusum 5 0 0 1
Melica nutans 3 1 1 0
Melampyrum pratense 2 0 1 1
Myosotis ramosissima 1 1 1 0
Lychnis viscaria 2 0 0 1
Melittis melissophyllum 3 0 1 0
CALCULATION OF MEAN ELLENBERG
INDICATOR VALUES
EIV-reaction 1 2 3
Mycelis muralis 6 1 0 0
Moehringia trinervia 7 0 1 1
Mercurialis perennis 7 1 0 1
Lathyrus vernus 4 0 1 0
Myosotis sylvatica 7 1 1 0
Milium effusum 5 0 0 1
Melica nutans 3 1 1 0
Melampyrum pratense 2 0 1 1
Myosotis ramosissima 1 1 1 0
Lychnis viscaria 2 0 0 1
Melittis melissophyllum 3 0 1 0
4.8
mean
CALCULATION OF MEAN ELLENBERG
INDICATOR VALUES
EIV-reaction 1 2 3
Mycelis muralis 6 1 0 0
Moehringia trinervia 7 0 1 1
Mercurialis perennis 7 1 0 1
Lathyrus vernus 4 0 1 0
Myosotis sylvatica 7 1 1 0
Milium effusum 5 0 0 1
Melica nutans 3 1 1 0
Melampyrum pratense 2 0 1 1
Myosotis ramosissima 1 1 1 0
Lychnis viscaria 2 0 0 1
Melittis melissophyllum 3 0 1 0
mean EIV: 4.8 3.9 4.6
CALCULATION OF MEAN ELLENBERG
INDICATOR VALUES
EIV-reaction 1 2 3 4
Mycelis muralis 6 1 0 0 0
Moehringia trinervia 7 0 1 1 1
Mercurialis perennis 7 1 0 1 1
Lathyrus vernus 4 0 1 0 0
Myosotis sylvatica 7 1 1 0 0
Milium effusum 5 0 0 1 1
Melica nutans 3 1 1 0 0
Melampyrum pratense 2 0 1 1 1
Myosotis ramosissima 1 1 1 0 0
Lychnis viscaria 2 0 0 1 1
Melittis melissophyllum 3 0 1 0 0
mean EIV: 4.8 3.9 4.6 4.6
mean EIV inherits information about
compositional similarity between plots
CALCULATION OF MEAN RANDOMIZED
ELLENBERG INDICATOR VALUES
EIV-reaction 1 2 3 4
Mycelis muralis 6 1 0 0 0
Moehringia trinervia 7 0 1 1 1
Mercurialis perennis 7 1 0 1 1
Lathyrus vernus 4 0 1 0 0
Myosotis sylvatica 7 1 1 0 0
Milium effusum 5 0 0 1 1
Melica nutans 3 1 1 0 0
Melampyrum pratense 2 0 1 1 1
Myosotis ramosissima 1 1 1 0 0
Lychnis viscaria 2 0 0 1 1
Melittis melissophyllum 3 0 1 0 0
CALCULATION OF MEAN RANDOMIZED
ELLENBERG INDICATOR VALUES
EIV-reaction 1 2 3 4
Mycelis muralis 7 1 0 0 0
Moehringia trinervia 5 0 1 1 1
Mercurialis perennis 4 1 0 1 1
Lathyrus vernus 2 0 1 0 0
Myosotis sylvatica 3 1 1 0 0
Milium effusum 2 0 0 1 1
Melica nutans 7 1 1 0 0
Melampyrum pratense 3 0 1 1 1
Myosotis ramosissima 7 1 1 0 0
Lychnis viscaria 6 0 0 1 1
Melittis melissophyllum 1 0 1 0 0
CALCULATION OF MEAN RANDOMIZED
ELLENBERG INDICATOR VALUES
EIV-reaction 1 2 3 4
Mycelis muralis 7 1 0 0 0
Moehringia trinervia 7 0 1 1 1
Mercurialis perennis 5 1 0 1 1
Lathyrus vernus 3 0 1 0 0
Myosotis sylvatica 2 1 1 0 0
Milium effusum 6 0 0 1 1
Melica nutans 2 1 1 0 0
Melampyrum pratense 7 0 1 1 1
Myosotis ramosissima 4 1 1 0 0
Lychnis viscaria 3 0 0 1 1
Melittis melissophyllum 1 0 1 0 0
CALCULATION OF MEAN RANDOMIZED
ELLENBERG INDICATOR VALUES
EIV-reaction 1 2 3 4
Mycelis muralis 6 1 0 0 0
Moehringia trinervia 4 0 1 1 1
Mercurialis perennis 3 1 0 1 1
Lathyrus vernus 3 0 1 0 0
Myosotis sylvatica 5 1 1 0 0
Milium effusum 7 0 0 1 1
Melica nutans 7 1 1 0 0
Melampyrum pratense 1 0 1 1 1
Myosotis ramosissima 7 1 1 0 0
Lychnis viscaria 2 0 0 1 1
Melittis melissophyllum 2 0 1 0 0
CALCULATION OF MEAN RANDOMIZED
ELLENBERG INDICATOR VALUES
EIV-reaction 1 2 3 4
Mycelis muralis 6 1 0 0 0
Moehringia trinervia 4 0 1 1 1
Mercurialis perennis 3 1 0 1 1
Lathyrus vernus 3 0 1 0 0
Myosotis sylvatica 5 1 1 0 0
Milium effusum 7 0 0 1 1
Melica nutans 7 1 1 0 0
Melampyrum pratense 1 0 1 1 1
Myosotis ramosissima 7 1 1 0 0
Lychnis viscaria 2 0 0 1 1
Melittis melissophyllum 2 0 1 0 0
Mean RANDOMIZED EIV: 5.6 4.1 3.4 3.4
EIV-reaction 1 2 3
Mycelis muralis 6 1 0 0
Moehringia trinervia 7 0 1 1
Mercurialis perennis 7 1 0 1
Lathyrus vernus 4 0 1 0
Myosotis sylvatica 7 1 1 0
Milium effusum 5 0 0 1
Melica nutans 3 1 1 0
Melampyrum pratense 2 0 1 1
Myosotis ramosissima 1 1 1 0
Lychnis viscaria 2 0 0 1
Melittis melissophyllum 3 0 1 0
Mean EIV: 4.8 3.9 4.6
EIV-reaction 1 2 3
Mycelis muralis 6 1 0 0
Moehringia trinervia 4 0 1 1
Mercurialis perennis 3 1 0 1
Lathyrus vernus 3 0 1 0
Myosotis sylvatica 5 1 1 0
Milium effusum 7 0 0 1
Melica nutans 7 1 1 0
Melampyrum pratense 1 0 1 1
Myosotis ramosissima 7 1 1 0
Lychnis viscaria 2 0 0 1
Melittis melissophyllum 2 0 1 0
Mean RANDOMIZED EIV: 5.6 4.1 3.4
EIV-reaction 1 2 3
Mycelis muralis 6 1 0 0
Moehringia trinervia 7 0 1 1
Mercurialis perennis 7 1 0 1
Lathyrus vernus 4 0 1 0
Myosotis sylvatica 7 1 1 0
Milium effusum 5 0 0 1
Melica nutans 3 1 1 0
Melampyrum pratense 2 0 1 1
Myosotis ramosissima 1 1 1 0
Lychnis viscaria 2 0 0 1
Melittis melissophyllum 3 0 1 0
Random variable: 4.6 4.8 3.9
THREE TYPES OF VARIABLES:
DATA USED FOR ANALYSES
Dataset 1
94 vegetation plots
forest vegetation in Vltava river
valley
measured soil pH
Dataset 2
1000 vegetation plots
forest vegetation
randomly selected from Czech
National Phytosociological
Database
INFORMATION ABOUT COMPOSITIONAL
SIMILARITY AMONG PLOTS INHERITED INTO
measured pH calculated mean EIV for soil
reaction
r , P - results of Mantel’s test of correlation between two dissimilarity matrices
plot 1 plot 2 plot 3 plot 4
plot 2 0.33
plot 3 0.34 0.37
plot 4 0.35 0.22 0.42
plot 5 0.84 0.84 0.76 0.82
plot dissimilarity
Δ measured pH
plot 1
5.10
plot 2
4.09
plot 3
4.10
plot 4
4.15
plot 2 4.09 1.01
plot 3 4.10 1.00 0.01
plot 4 4.15 0.95 0.06 0.05
plot 5 5.35 0.25 1.26 1.25 1.20
Bray-Curtis
distance
INFORMATION ABOUT COMPOSITIONAL
SIMILARITY AMONG PLOTS INHERITED INTO
measured pH calculated mean EIV for soil
reaction
r , P - results of Mantel’s test of correlation between two dissimilarity matrices
INFORMATION ABOUT COMPOSITIONAL
SIMILARITY AMONG PLOTS INHERITED INTO
mean randomized EIV for soil
reaction random variable
r , P - results of Mantel’s test of correlation between two dissimilarity matrices
EIVS AS EXPLANATORY VARIABLES IN CCA
vegetation
Ecological
knowledge
(Ellenberg)
explanatory
variable dependent
variable
Circularity of
reasoning
Species
composition
Calculated
mean EIV
COMPARISON OF MEASURED PH AND
CALCULATED EIV FOR SOIL REACTION
++
+
+
++
++
+
+
+
+
+
+
+
+
+
+++
+
+
+
+
+
+
+
+
+
++
+
+
+
+
+
+
++
+
+
+
+
+
+
+
+ ++++
+
+
+++
++
++
+
+
+
+
+
+
+
++
+
+
+
+ +
+
+
+
+
+
++
+
+
+
+
+
+
+
++
+
++
+
2
3
4
5
6
7
3.5 4.0 4.5 5.0
Measured soil pH
Me
an
Elle
nb
erg
re
actio
n
Data: dataset 1 – river valley
CCA: COMPARISON OF MEASURED PH AND
CALCULATED EIV FOR SOIL REACTION
0
1
2
3
4
5
real pH Ellenberg reaction
Exp
lain
ed
va
ria
bili
ty [
%]
CCA: COMPARISON OF MEASURED PH AND
CALCULATED EIV FOR SOIL REACTION
0
1
2
3
4
5
real pH Ellenberg reaction
Exp
lain
ed
va
ria
bili
ty [
%]
1.1
%
CCA: COMPARISON OF MEASURED PH AND
CALCULATED EIV FOR SOIL REACTION
2.0
%
2.0
%
0
1
2
3
4
5
real pH Ellenberg reaction
Exp
lain
ed
va
ria
bili
ty [
%]
EIVS CORRELATED WITH DCA SCORES
vegetation
Circularity of
reasoning
correlation
Species
composition
sample scores
on DCA axis
Calculated
mean EIV
Ecological
knowledge
(Ellenberg)
MEAN EIVS CORRELATED WITH DCA SCORES
-2 -1 0 1 2
-2
-1
0
1
2
DCA1
DC
A2
Light Temp
Cont Moist
Nutr
React
DCA1 DCA2
Light +++ +++
Temp ++ +++
Cont ++ +++
Moist - - - n.s.
Nutr - - - n.s.
React - - - n.s.
Tab.: significance of
Pearson’s correlation
coefficient
MEAN EIVS CORRELATED WITH DCA SCORES
sample scores on DCA axis
mean E
IV
information
about
compositional
similarity
MEAN RANDOMIZED EIV CORRELATED
WITH DCA SCORES
Mean randomized EIV
inherits information about compositional similarity among plots
carry no ecological information
more than 50% are significantly (p < 0.05) correlated with the first DCA axis!
mean EIV
mean randomized EIV
random variable
0
10
20
30
40
50
60
DCA1 DCA2 DCA3 DCA4
Sig
nific
ant corr
ela
tions [%
]
REGRESSION OF SPECIES RICHNESS ON MEAN
EIVS
10
20
30
40
50
2 3 4 5 6
Nu
mb
er
of
sp
ecie
s
Mean EIV for soil reaction
R2 = 0.30
p < 0.001
information
about
compositional
similarity
REGRESSION OF SPECIES RICHNESS ON MEAN
EIVS
10
20
30
40
50
2 3 4 5 6
Nu
mb
er
of
sp
ecie
s
Mean EIV for soil reaction
R2 = 0.30
p < 0.001
mean EIV
mean randomized EIV
random variable
Almost 40% of
significant
regressions !
0
10
20
30
40
50
Species richness
Sig
nific
ant re
gre
ssio
ns [%
]
Dependent variable: species richness
Explanatory variables: mean EIV
measured variables
USE OF MEAN EIVS IN REGRESSION AND
CLASSIFICATION TREES
Moist <> 5.82266
React <> 4.19643
14.4 7 obs
1 Nutr <> 5.02273
SOILDPT <> 1.325
RALTRIV <> 0.6
29.7 6 obs
2
24 6 obs
339.6 5 obs
4
pH.H <> 4.265
ASPSSW <> 80
RELPOS <> 0.5
21.7 7 obs
5
26.1 7 obs
6
sute <> 0.5
22.6 5 obs
7
17.7 6 obs
8
28.1 9 obs
9
Moist <> 6.54378
35.7 6 obs
10
41.3 7 obs
11
REGRESSION TREES – VARIABILITY EXPLAINED
BY MEAN RANDOMIZED EIV
0
5
10
15
20
Expla
ined v
ariabili
ty [%
]
mean randomized EIV
1 2
random variable
1 2
SUMMARY
mean Ellenberg indicator values inherits information about
compositional similarity among plots
use in CCA (as explanatory variables)
circularity of reasoning
unrealistically high explained variability
use in DCA (correlation with DCA axis)
circularity of reasoning less obvious, but still present
unrealistically high correlation coefficients
~ 50 % probability of significant result even in case of no
ecological meaning
SUMMARY
correlation with species richness
unrealistically high correlation coefficients and higher probability
of significant results
use in regression trees
when mixing mean EIVs with measured variables, mean EIVs will
perform as better predictors
unrealistically high explained variability
randomized values
mean randomized EIV
REGRESSION OF MEAN EIV WITH 1ST AXIS OF DCA MODIFIED MONTE-CARLO PERMUTATION TEST
R2
De
nsity
0
10
20
30
40
50
60
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
0
10
20
30
40
50
60
0.112
0.166
R2 threshold
for p < 0.05
Monte-Carlo distribution of R2
0
20
40
60
80
100
Temp Cont Light Moist Nutr React
Sig
nific
an
t re
su
lts [
%]
REGRESSION OF MEAN EIV WITH 1ST AXIS OF DCA MODIFIED MONTE-CARLO PERMUTATION TEST
mean EIV
mean randomized EIV
Data: dataset 2 – 100 plots
randomly selected from database
CONCLUSIONS
for any analysis with mean EIV: be careful with testing the
significance of relationship
for DCA: do not test the significance of correlation between mean
EIV and plot scores on DCA axes - or use modified Monte-Carlo test
for correlation with species richness or other vegetation-derived
variable: expect unrealistically high correlation coefficient and higher
probability of getting significant result
for regression and classification trees: do not mix mean EIV with
measured variables, if dependent variable is derived from species
composition (species richness, classification)