MVA 3 CCA 2021 Handout

EM1 Canonical Corresp Analysis

1

REG 31806 (2021)

MVA 3. Canonical Correspondence Analysis

Analysis of

communities

Today’s topics:

1. Interpreting ordination diagrams

2. Testing the significance of ordination axis

3. Testing effect of envir vars

4. Extracting & illustrating the effect of one or two (or three) env vars on axis 1 and 2

5. Env vars should co-determine ordination

CCA

4

reas

on

s to

use

CC

A

First axis

Sec

on

d a

xis

Wageningen 5o E, 52o N

Seattle 122o W, 48o N

Rio de Janeiro 43o W, 23o S

Melbourne 145o E, 38o S

Nutr

Moist

Moist 1 2 4 8 Nutr 2 3 4 2

values = plot ordination

scores (Q) on axis 1

Q -1.1 -0.2 0.6 1.2

Correlate Q values with Moist, Nutr:

Q and Moist: r = 0.9122

Q and Nutr: r = 0.4004

First ordination axis

Nutr

Moist

Moist 1 2 4 8 Nutr 2 3 4 2

0.91220.4004

Second ordination axis

values = plot ordination

scores (Q) on axis 2

Q 0.3 -0.5 -0.25 1.1

Correlate Q values with Moist, Nutr:

Q and Moist: r = 0.4036

Q and Nutr: r = -0.7481

Nutr

Moist

Moist 1 2 4 8 Nutr 2 3 4 2 0.4036

-0.7481

1 2

3 4

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2

Plotted “on top” of thebiplot; no influence on

ordination results

Triplot of species + samples + environmental variables

Moist

Nutr

Moist 1 2 4 8 Nutr 2 3 4 2

Plotted “on top” of the biplot; no influence on

ordination results


Moist

Nutr

Moist 1 2 4 8 Nutr 2 3 4 2


ordination results


Moist

Nutr

Moist 1 2 4 8 Nutr 2 3 4 2


ordination results


Moist

Nutr

Moist 1 2 4 8 Nutr 2 3 4 2

Today’s topics:






CCA

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CC

A

Today’s topics:


2. Testing the significance of our ordination axis

H0: Our ordination axis explains the same amount of variance as a random ordination axis

CACCA

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9 10

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3

Random table.......

Biplot of species + samples

Ordination on Random table Ordination on

Random dataOrdination on Observed data

Today’s topics:



3. Testing effect of envir vars:

H0: random ‘association’ between ordination scores and envir vars

CACCA

Moist

Water table

r (correlation coefficient)

Axis1 Axis2

Moisture 0.78 0.32

Water table 0.16 0.24

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4

Moist

Nutr

%sand

Water table

r (correlation coefficient)

Axis1 Axis2

Moisture 0.78 0.32

Water table 0.16 0.24

+ many more Env Vars...

Meaning....? Significant?

Better than random ‘association’ ?

Today’s topics:





CACCA

Eutrophication of ground water: more nutrients

Lowering ground water level: easy access for farmers

Nutr

Water table

Management actions:

-increasing the water table

-adding nutrients

How does the speciescomposition change when water table goes up? And when nutrientsare added?

Today’s topics:


2. Testing significance of ordination axis



5. Env vars should co-determine ordination.

CACCA

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5

Ordination of :

1. Species

2. Plots

3. Environmental variables

IF the environmental variables determine the species composition,

THEN the CCA result should be (almost) identical to the CA result

Polar Ordination → CA → CCA

PO : calculate ordination for plots, species separately;

later, correlate envir. vars with ordination axes

CA: plots + species in one calculation (Reciprocal Averaging);

later, correlate envir. vars with ordination axes

CCA: plots + species + environmental vars in one calculation;

(1) envir. vars influence ordination values of plots and species

(2) this reveals the explanatory power of the envir. variables

That is the idea

Next: how it is done

Canonical CA is also based on Reciprocal Averaging

but

it includes additional steps: it directly includes the

environmental variables

Which MVA technique to apply?

Species’ response to gradient in the environment

Unimodal ‘Linear’

Use Envir. Vars

RedundancyAnalysis (RDA)

PrincipalComponents

Analysis (PCA)

Env gradient < 3 s.d.Env gradient > 4 s.d

Use Envir. Vars

Directly = explanatory

Afterwards = supplementary

Polar Ordination;(Detrended)

CorrespondenceAnalysis (D)CA

CanonicalCorrespondenceAnalysis (CCA)

Indirect ordination: Environmental variables are afterwards plotted “on top” of the sites & species ordination diagram as supplementary variables. Polar Ordination, CA, PCA.

Direct = constrained = canonical ordination: Environmental variables are directly part of (= included in) the calculation of the ordination values as explanatory variables. CCA, RDA

Directly = explanatory

Afterwards = supplementary

Today

Canonical CA aims to explain patterns or associations from species data by explanatory environmental variables

Additional steps in CCA (not shown here):

1. Regress site scores Q onto environmental variables

2. Do this for each step in the RA procedure

Reciprocal averaging











1. Regress site scores Q onto environmentalvariables


3. New, stable Q values = canonical axis

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6

CA

Moist 1 2 4 8 Nutr 2 3 4 2

Triplot

Environmentalvariables correlatedpost-hoc

Calculated after the ordination

Water table

s

CCA

Moist 1 2 4 8 Nutr 2 3 4 2

* Env Vars are calculated together with species and plots* All ordination values are different from CA because* Ordination is CONSTRAINED by Env Vars* Axes are canonical axes (= composite env vars)

Triplot

Environmentalvariables part of ordinationcalculation

Water table

s

Canonical CA ordination is on the basis of

species + plots + env vars!

Ordination is CONSTRAINED by env vars

Hence, axes are canonical axes (=composite env vars)

The eigenvalues of the canonical axes are smaller than those of the original non-canonical (CA) axes

Today’s topics:






CCA

Dune species data

Dune environmental data

Monte Carlo permutation test

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(see exercises)

Re-shuffle row data

First CCA, then 499 random permutations + 499 * CCA

Re-shuffle row data

+ another 497 reshuffles...

and calculate new eigenvalues from CCA:

L1L3L5L6L8L11L16L17L18L19



and calculate new eigenvalues from CCA:

0.655

Not significant

Today’s topics:






CCA

So, which environmental variables are strongly explanatory, and which are weak?

> Forward selection of environmental variables

Available:

P(adj) > 0.05

Hence do not include A1

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TWO EVs = TWO canonical axes

All variables: = 1.365 Forward selection: = 0.905

on

on

lyT

WO

env

vars

Today’s topics:






CCA(was 0.610 in CA)

CCA(was 0.610 in CA)

CCAWater table

Water table

Water table

Water table

Since the eigenvalue of 1st CCA axis (0.596) is nearly as large as the 1st CA axis (0.610),

The selected env vars have a strong explanatory power.

Water table and Nutrientsstrongly influence the species composition in the landscape.

Strong explanatory power:

Weak explanatory power:

Water tab+Nutrients

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Eigenvalue () for each ordination axis = the proportion of variation in the data set

explained by that axis (0 < < 1)

For CCA axis 1: = 0.227

For CCA axis 2: = 0.060

Sum = 0.287

Summary of results of a Canonical Correspondence Analysis

pH + OM**** Summary ****

Axes 1 2 3 4 Total variation

Eigenvalues : 0.227 0.060 0.486 0.000 0.774Species-environment correlations: 0.762 0.451 0.000 0.000Cumulative percentage variance

of species data : 29.4 37.1 100.0 0.0of species-environment relation: 79.1 100.0 0.0 0.0

Sum of all eigenvalues 0.774Sum of all canonical eigenvalues 0.287

(weak explanatory power)

Non-canonical

axis in CCA

CCAWater table

What happens to speciescomposition if:

1. water table is increased?

2. more nutrients are added?

Today’s topics:





5. Env vars should co-determine ordination.

CCA

Ordination of :

1. Species

2. Plots

3. Environmental variables

IF the environmental variables determine the species composition,

THEN the CCA result should be (almost) identical to the CA result

Today’s topics:






CCA

4

reas

on

s to

use

CC

A

When many environmental variablesare involved in the canonical analysis........

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EM1: CollinearityWorking with envir. variables:

Check the variance inflation factor

variance

IF inflation factor > 20THEN that env. var. is strongly correlated with other env. vars. HENCE exclude env. var. with highest value from the analysis

Trends Ecol1 Stats1 Econ1

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4 5 7 7

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8 9 8 9

7 8 7 9

Confused?

Make your own matrix

and run an analysis!

Hrs/wk l/wk Min/day g/day

StuHrs Beer TravTime Veggies

12 4 10 250

10 4 5 300

1 4 120 10

9 3 30 10

8 4 30 0

8 4 45 0

CA

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CCA

+ FW env vars

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MVA 3 CCA 2021 Handout

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