Gradient Analysis Approach to Ordination. Models of Species Response to Gradients.

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