direct ordination what kind of biological questions can we answer? how can we do it in canoco 4.5?
TRANSCRIPT
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DIRECT ORDINATION
What kind of biological questions can we answer?
How can we do it in CANOCO 4.5?
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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?
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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!!!
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Answering questions with ordination
Response model
Linear Unimodal
Indirect PCA CA, DCA
Direct RDA CCA (DCCA)
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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
....... .... ....
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Possible kinds of predictor variables for ordination
• Quantitative (sensu lato)– pH, temperature, altitude, distance…– Classes, ranks,
• Binomial (Presence-absence, dummies)– Treatment vs. Control, sites,
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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!
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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!
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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)!
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RDA
pH
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RDA
pH
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CCA
Decreasing probability of occurrence
pH
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CCA
pH
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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
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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
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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
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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
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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
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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
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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
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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)
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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