DIRECT ORDINATION

What kind of biological questions can we answer?

How can we do it in CANOCO 4.5?

Our questions are often about the effects of something on something else….

• How important is climate for plants?• What are the effects of pesticides on

arthropods in the soil?• What happens to cultural landscapes when

the land-use changes? • Do different fish species have different

planctonic diets? • What is the effect of small-scale

disturbances for the vegetation?

Answering questions with ordination

• Indirect ordination: – Find the structure in the species data– Relate to explanatory variables

• Direct ordination:– Analyse compositional responses along

envionmental gradients– … or differences among places or treatments,

or…. – Statistical testing!!!

Answering questions with ordination

Response model

Linear Unimodal

Indirect PCA CA, DCA

Direct RDA CCA (DCCA)

What are predictor variables?

Pinus Tsuga

Site 1 3 10

Site 2 5 1

Site 3 0 2

Site 4 4 8

Site 5 3 5

....... .... ....

Response data predictor data

Altit. pH

Site 1 354 4.5

Site 2 67 5.2

Site 3 779 4.6

Site 4 7 4.9

Site 5 98 5.1

....... .... ....

Possible kinds of predictor variables for ordination

• Quantitative (sensu lato)– pH, temperature, altitude, distance…– Classes, ranks,

• Binomial (Presence-absence, dummies)– Treatment vs. Control, sites,

Constrained CA = CCA• species scores are weighted averages of site

scores – the weights are related to how common the species are in

the sites

• site scores are weighted averages of species scores– the weights are (again) related to how commmon the species are in

the sites

• site scores are linear combinations of the environmental variables

ITERATIVE METHOD!

Constrained CA = CCA

• Axes are ’synthetical’ gradients that maximise the dispersion of the species– E.g. 1,5*pH + 7*Altitude

• WARNING: If we have many environmental variables – relative to species or sites, then the constraint is not very strong!– We want to avoid putting too many environmental

variables into constrained ordinations!

Interpretation

• Species, sample, and environmental variables can be presented in ordinaion diagrams

• These diagrams tell us something about the relationship of species and samples with the environment

• Interpretation differs between ordination diagrams from linear methods (RDA) and unimodal methods (CCA)!

RDA

pH

RDA

pH

CCA

Decreasing probability of occurrence

pH

CCA

pH

Partial ordination• CANOCO offers the possibility to control for – or remove - variation explained by one (set of) variables prior to the ordination

– Remove variation among experimental block in an experiment – Investigate wether there is any effect of altitude after temperature has been controlled for– Investigate wether two (groups of) variables explain the same or different fraction of floristic variance

• Partial RDA, partial CCA

Statistical testing in CANOCO

• Choose a test statistic that expresses the strenght of the species – environmental relationship (e.g F-ratio, correlation,…)– Calculate it for your data (F0)– Compare your value to a reference distribution

under the null hypothesis of no effect– Calculate the probability that F0 or larger values

occur in the reference distribution

• CANOCO uses your data to create a reference distribution for the test

Monte Carlo permutation test

Statistical testing – permutation tests

Pinus Tsuga

Site 1 3 10

Site 2 5 1

Site 3 0 2

Site 4 4 8

Site 5 3 5

....... .... ....

Response data predictor data

Altit. pH

Site 1 354 4.5

Site 2 67 5.2

Site 3 779 4.6

Site 4 7 4.9

Site 5 98 5.1

....... .... ....

The ’real’ species – environment relation

Calculate F0

Statistical testing – permutation tests

Pinus Tsuga

Site 1 3 10

Site 2 5 1

Site 3 0 2

Site 4 4 8

Site 5 3 5

....... .... ....

Response data predictor data

Altit. pH

Site 1 354 4.5

Site 2 67 5.2

Site 3 779 4.6

Site 4 7 4.9

Site 5 98 5.1

....... .... ....

Permutation # 1

Calculate F

Statistical testing – permutation tests

Pinus Tsuga

Site 1 3 10

Site 2 5 1

Site 3 0 2

Site 4 4 8

Site 5 3 5

....... .... ....

Response data predictor data

Altit. pH

Site 1 354 4.5

Site 2 67 5.2

Site 3 779 4.6

Site 4 7 4.9

Site 5 98 5.1

....... .... ....

Permutation # 2

Calculate F

Statistical testing in CANOCO

• Repeat this a largish number of times – (499, 999,…)

• The Monte Carlo significance level is the rank order position of F0 among all F’s / number of permutations +1

Monte Carlo permutation test

Answering questions with direct ordination

• How much of the variation in the species data can my variables explain?– Full CCA/RDA with forward selection & testing

• What is the most important variable here? – Forward selection

• Is e.g. temperature significant?– CCA/RDA of single variable & testing of axis 1

Answering questions with direct ordination

• Which variables are important here? – CCA/RDA of all variables one at a time &

testing of axis 1.– Variance partitioning (VP) with testing of

the unique contributions of each variable.

• How does the effect of a treatment change through time?– Principal response curves (PRC)

Statistical testing in CANOCO

• Choose a test statistic that expresses the strenght of the species – environmental relationship (e.g F-ratio, correlation,…)– Calculate it for your data (F0)– Compare your value to a reference distribution

under the null hypothesis of no effect– Calculate the probability that F0 or larger values

occur in the reference distribution

• CANOCO uses your data to create a reference distribution for the test

Monte Carlo permutation test