Post on 28-Mar-2015
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Gradient Analysis Approach to Ordination
Models of Species Response to Gradients
Models of Species Response
There are (at least) two models:-
• Linear - species increase or decrease along the environmental gradient
• Unimodal - species rise to a peak somewhere along the environmental gradient and then fall again
A Theoretical Model
Environmental Gradient
Abundance
80706050403020100
100
80
60
40
20
0
Linear
-0.4 +0.4
+0.0
+7.0
Unimodal
-2.5 +3.5
+0.0
+250.0
Alpha and Beta Diversity
alpha diversity is the diversity of a community (either measured in terms of a diversity index or species richness)
beta diversity (also known as ‘species turnover’ or ‘differentiation diversity’) is the rate of change in species composition from one community to another along gradients; gamma diversity is the diversity of a region or a landscape.
A Short Coenocline
-0.5 +0.7
+0.0
+8.0
Ach m il
Agr s to
Air pra
Jun a rt
Pot pa l
Ra n fla
A Long Coenocline
Inferring Gradients from Species (or Attribute) Data
Indirect Gradient Analysis
• Environmental gradients are inferred from species data alone
• Three methods: Principal Component Analysis - linear model Correspondence Analysis - unimodal model Detrended CA - modified unimodal model
PCA - linear model
Weight (g)
Head a
nd B
ill L
ength
(m
m)
1300120011001000900800700
140
130
120
110
100
Sexfemalemale
PCA for the Herring Gull Data
PCA - linear model
Axis 1
Axi
s 2
43210-1-2-3-4-5
1.0
0.5
0.0
-0.5
-1.0
-1.5
Sexfemalemale
PCA for the Herring Gull Data
Terschelling Dune Data
PCA gradient - site plot
PCA 1
PCA
2
2.01.51.00.50.0-0.5-1.0-1.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
Managmentbiodynamichobbynaturestandard
PCA Plot for Dune Species Data
PCA gradient - site/species biplot
Axis 1
Axi
s 2
210-1-2
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
Ach mil
Agr sto
Alo gen
Ant odo
Bel perBro hor
Ele pal
Ely rep
Jun art
J un buf
Leo aut
Lol per
Pla lan
Poa pra
Poa tri
Ran flaRum ace
Sag pro
Tri rep
Bra rut
Biplot for Dune Species Data
Reciprocal Averaging
Site A B C D E F Species
Prunus serotina 6 3 4 6 5 1 Tilia americana 2 0 7 0 6 6 Acer saccharum 0 0 8 0 4 9 Quercus velutina 0 8 0 8 0 0 Juglans nigra 3 2 3 0 6 0
Reciprocal Averaging
Site A B C D E F Species ScoreSpecies Iteration 1
Prunus serotina 6 3 4 6 5 1 1.00 Tilia americana 2 0 7 0 6 6 0.63 Acer saccharum 0 0 8 0 4 9 0.63 Quercus velutina 0 8 0 8 0 0 0.18 Juglans nigra 3 2 3 0 6 0 0.00
Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99 Site Score
Reciprocal Averaging
Site A B C D E F Species ScoreSpecies Iteration 1 2
Prunus serotina 6 3 4 6 5 1 1.00 0.68 Tilia americana 2 0 7 0 6 6 0.63 0.84 Acer saccharum 0 0 8 0 4 9 0.63 0.87 Quercus velutina 0 8 0 8 0 0 0.18 0.30 Juglans nigra 3 2 3 0 6 0 0.00 0.67
Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99 Site 2 0.65 0.00 0.88 0.05 0.78 1.00 Score
Reciprocal Averaging
Site A B C D E F Species ScoreSpecies Iteration 1 2 3
Prunus serotina 6 3 4 6 5 1 1.00 0.68 0.50 Tilia americana 2 0 7 0 6 6 0.63 0.84 0.86 Acer saccharum 0 0 8 0 4 9 0.63 0.87 0.91 Quercus velutina 0 8 0 8 0 0 0.18 0.30 0.02 Juglans nigra 3 2 3 0 6 0 0.00 0.67 0.66
Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99 Site 2 0.65 0.00 0.88 0.05 0.78 1.00 Score 3 0.60 0.01 0.87 0.00 0.78 1.00
Reciprocal Averaging
Site A B C D E F Species ScoreSpecies Iteration 1 2 3 9
Prunus serotina 6 3 4 6 5 1 1.00 0.68 0.50 0.48Tilia americana 2 0 7 0 6 6 0.63 0.84 0.86 0.85Acer saccharum 0 0 8 0 4 9 0.63 0.87 0.91 0.91Quercus velutina 0 8 0 8 0 0 0.18 0.30 0.02 0.00Juglans nigra 3 2 3 0 6 0 0.00 0.67 0.66 0.65
Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99 Site 2 0.65 0.00 0.88 0.05 0.78 1.00 Score 3 0.60 0.01 0.87 0.00 0.78 1.00 9 0.59 0.01 0.87 0.00 0.78 1.00
Reordered Sites and Species
Site A C E B D F Species Species Score
Quercus velutina 8 8 0 0 0 0 0.004Prunus serotina 6 3 6 5 4 1 0.477Juglans nigra 0 2 3 6 3 0 0.647Tilia americana 0 0 2 6 7 6 0.845Acer saccharum 0 0 0 4 8 9 0.909
Site Score 0.000 0.008 0.589 0.778 0.872 1.000
Lake Nasser Invertebrates
CA - unimodal model
-2 0 2 4
-4-3
-2-1
01
23
CA1
CA
2 ++
+
+
++ +
+
+ +Protozoa
Rotifera
Cladocera
Copepoda
InsectaTurbellaria
Tardigrada
Annelida Nematoda
Arches - Artifact or Feature?
The Arch Effect
• What is it?
• Why does it happen?
• What should we do about it?
From Alexandria to Suez
CA - with arch effect (species)
-3.0 +4.5
-3.5
+4.5
HAL SAL
ECH SERASP MIC
THY HIR
HAM ELEACH SANLAU SPIZYG DEC
CRO AEG
ART JUD
VER OFF
LAS HIR
LYC SHA
OCH BAC
PUL UND
IPH MUC
ZYG COC
LAU NUD
PAN TUR
KIC AEG
LYG RAE
AST GRA
ART MON
FAR AEG
ECH SPI
SAL LAN
ATR CAR
MOL CIL
EUP RET
CON LAN
ANA ART
PIT TOR
FAG ARA
SAL AEGZIL SPI
PER TOM
CAL COM
STI LAN
GYP CAP
AST SPI
HYO MUT
CLE DRO
RUT TUB
HEL ARA
SPH AUC
CA - with arch effect (sites)
-3.0 +4.5
-3.5
+4.5
ALEX 07
ALEX 05
ALEX 06ALEX 08
CSRA 23
CSRA 16CSRA 17
CSRA 22CSRA 20CSRA 21
CSRA 12
ALEX 03
ALEX 02
CSRA 13
CSRA 15
ALEX 04
CSRA 11
CSRA 14
CSRA 18CSRA 19
ALEX 01
CSRA 30CSRA 32
CSRA 24CSRA 31
CSRA 25ALEX 10ALEX 09
CSRA 33
CSRA 35
CSRA 26
CSRA 29CSRA 34
CSRA 27CSRA 28
Long Gradients
A B C D
Gradient End Compression
CA - with arch effect (species)
-3.0 +4.5
-3.5
+4.5
HAL SAL
ECH SERASP MIC
THY HIR
HAM ELEACH SANLAU SPIZYG DEC
CRO AEG
ART JUD
VER OFF
LAS HIR
LYC SHA
OCH BAC
PUL UND
IPH MUC
ZYG COC
LAU NUD
PAN TUR
KIC AEG
LYG RAE
AST GRA
ART MON
FAR AEG
ECH SPI
SAL LAN
ATR CAR
MOL CIL
EUP RET
CON LAN
ANA ART
PIT TOR
FAG ARA
SAL AEGZIL SPI
PER TOM
CAL COM
STI LAN
GYP CAP
AST SPI
HYO MUT
CLE DRO
RUT TUB
HEL ARA
SPH AUC
Detrending by Segments
-3.0 +4.5
-3.5
+4.5
HAL SAL
ECH SERASP MIC
THY HIR
HAM ELEACH SANLAU SPIZYG DEC
CRO AEG
ART JUD
VER OFF
LAS HIR
LYC SHA
OCH BAC
PUL UND
IPH MUC
ZYG COC
LAU NUD
PAN TUR
KIC AEG
LYG RAE
AST GRA
ART MON
FAR AEG
ECH SPI
SAL LAN
ATR CAR
MOL CIL
EUP RET
CON LAN
ANA ART
PIT TOR
FAG ARA
SAL AEGZIL SPI
PER TOM
CAL COM
STI LAN
GYP CAP
AST SPI
HYO MUT
CLE DRO
RUT TUB
HEL ARA
SPH AUC
DCA - modified unimodal
-1.0 +5.5
-1.5
+4.5
CSRA 23
CSRA 16
CSRA 17
CSRA 22
CSRA 12
CSRA 21CSRA 20
CSRA 13
CSRA 15
CSRA 11CSRA 14
CSRA 18CSRA 19
CSRA 29
CSRA 26
CSRA 34
CSRA 27CSRA 28
CSRA 35CSRA 33
ALEX 09
CSRA 25CSRA 31
ALEX 10
CSRA 24
CSRA 32CSRA 30
ALEX 01
ALEX 04ALEX 02ALEX 03
ALEX 08ALEX 05ALEX 06ALEX 07
HAM ELEACH SANLAU SPIZYG DECCRO AEG.ART JUD
VER OFF.
LAS HIR
LYC SHA
OCH BAC
PUL UND
IPH MUC.
ZYG COC
LAU NUD
PAN TUR
KIC AEG
LYG RAE
AST GRA
FAR AEG
ECH SPI
ATR CAREUP RETPIT TOR
FAG ARA
SAL AEG
ZIL SPI
CAL COM
STI LAN
AST SPI
HYO MUTCLE DRO
RUT TUB
HEL ARA
GYP CAPPER TOM
ANA ART
CON LAN
MOL CIL
SAL LAN.
ART MON
HAL SALECH SER.
THY HIR
ASP MIC
SPH AUC
Making Effective Use of Environmental Variables
Direct Gradient Analysis
• Environmental gradients are constructed from the relationship between species environmental variables
• Three methods: Redundancy Analysis - linear model Canonical (or Constrained) Correspondence
Analysis - unimodal model Detrended CCA - modified unimodal model
CCA - site/species joint plot
-1.0 +1.0
-1.0
+1.0
MaEs10
AlEd6AlEd5
ZaEs20
KrEs14
KrWs12
MrWd3MrWd2
TuW23TuW24TuW22
IbEd16
MrWs4
MaEd9
IbEs15
MaW11
AlEs7AlEs8
IbWd18
MrEd1
Annelida
Protozoa
Turbellaria
Tardigrada
Nematoda
Cladocera
Insecta
Ostracoda
Copepoda
Rotifera
CCA - species/environment biplot
-1.0 +1.0
-1.0
+1.0
TDSMg
lgNO2
EC
DO
NO3
Ca
pH
WD
PO4TH
lgTSS
Annelida
Protozoa
Turbellaria
Tardigrada
Nematoda
Cladocera
Insecta
Ostracoda
Copepoda
Rotifera
Removing the Effect of Nuisance Variables
Partial Analyses
• Remove the effect of covariates variables that we can measure but which are of
no interest e.g. block effects, start values, etc.
• Carry out the gradient analysis on what is left of the variation after removing the effect of the covariates.
Testing Significance in Ordination
Randomisation Tests
Lake Species Richness Area Fertilised
1 32 2.0 yes
2 29 0.9 yes
3 35 3.1 yes
4 36 3.0 yes
5 41 1.0 no
6 62 2.0 no
7 88 4.0 no
8 77 3.5 no
Randomisation Tests
0.5950 0.0894 0.0259 0.0047 0.2879 0.1839 0.0493 0.0166 0.1810 0.0001 0.0028 0.0838 0.0016 0.4809 0.0072 0.0094 0.0084 0.0315 0.0807 0.1322 0.1649 0.0068 0.4786 0.0842 0.0066 0.3674 0.1496 0.0501 0.0434 0.0544 0.0643 0.0107 0.0101 0.3152 0.0015 0.3450 0.0004 0.1151 0.0125 0.0635
Randomisation Example
Model: cca(formula = dune ~ Moisture + A1 + Management, data = dune.env)
Df Chisq F N.Perm Pr(>F)
Model 7 1.1392 2.0007 200 < 0.005 ***
Residual 12 0.9761
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05