1. DIRECT ORDINATION What kind of biological questions can we answer? How can we do it in CANOCO 4.5?

2. 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?

3. 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!!!

4. Answering questions with ordination Response model LinearUnimodal IndirectPCACA, DCA DirectRDACCA (DCCA)

5. What are predictor variables? PinusTsuga Site 1310 Site 251 Site 302 Site 448 Site 535........... Response data predictor data Altit.pH Site 13544.5 Site 2675.2 Site 37794.6 Site 474.9 Site 5985.1...........

6. Possible kinds of predictor variables for ordination Quantitative (sensu lato) –pH, temperature, altitude, distance… –Classes, ranks, Binomial (Presence-absence, dummies) –Treatment vs. Control, sites,

7. 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!

8. 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!

9. 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)!

10. RDA pH

11. RDA pH

12. CCA Decreasing probability of occurrence pH

13. CCA pH

14. 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

15. 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 (F 0 ) –Compare your value to a reference distribution under the null hypothesis of no effect –Calculate the probability that F 0 or larger values occur in the reference distribution CANOCO uses your data to create a reference distribution for the test Monte Carlo permutation test

16. Statistical testing – permutation tests PinusTsuga Site 1310 Site 251 Site 302 Site 448 Site 535........... Response data predictor data Altit.pH Site 13544.5 Site 2675.2 Site 37794.6 Site 474.9 Site 5985.1........... The ’real’ species – environment relation Calculate F 0

17. Statistical testing – permutation tests PinusTsuga Site 1310 Site 251 Site 302 Site 448 Site 535........... Response data predictor data Altit.pH Site 13544.5 Site 2675.2 Site 37794.6 Site 474.9 Site 5985.1........... Permutation # 1 Calculate F

18. Statistical testing – permutation tests PinusTsuga Site 1310 Site 251 Site 302 Site 448 Site 535........... Response data predictor data Altit.pH Site 13544.5 Site 2675.2 Site 37794.6 Site 474.9 Site 5985.1........... Permutation # 2 Calculate F

19. Statistical testing in CANOCO Repeat this a largish number of times –(499, 999,…) The Monte Carlo significance level is the rank order position of F 0 among all F’s / number of permutations +1 Monte Carlo permutation test

20. 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

21. 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)

22. 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 (F 0 ) –Compare your value to a reference distribution under the null hypothesis of no effect –Calculate the probability that F 0 or larger values occur in the reference distribution CANOCO uses your data to create a reference distribution for the test Monte Carlo permutation test