1. Community Ecology Conceptual Issues –Community integrity (Clements v Gleason) Individualistic responses versus super-organism –Community change St ate-transition models Gap models Assembly rules –Description, scenario development, prediction –Is there such a thing as a community?

2. Community Ecology Practical Issues –Phytosociology, the releve, and classification –Gradient analysis and continuous variation –Direct vs indirect gradient analysis –The math of ordination Linear vs curvilinear responses –Cluster analysis –PCA, DCA, Discriminant Function Analysis

3. Simple Linear Regression All of the error is assumed to be in the response variable (Y), which is also the DEPENDENT variable……. Predicting Y from X

4. Type II regression

5. Principal Components Analysis First Principal Component This is mathematically a type II regression

7. Conceptual Issues –What is a community (Clements v Gleason) Individualistic responses versus super-organism The mythical environmental gradient DOWN Community as super-organism (Clements) Abundance UP Comm. A B C

8. Conceptual Issues –Community integrity (Clements v Gleason) Individualistic responses versus super-organism The mythical environmental gradient UP DOWN INDIVIDUALISTIC RESPONSES (Gleason) Abundance

9. Community change Succession State-transition models Gap models Assembly rules Initial Floristic Composition Relay Floristics Time Early Abundance Late Comm. A B C

10. Community change Succession State-transition models Gap models Assembly rules Initial Floristic Composition Relay Floristics The idea is that all species enter early on, but dominate at different points along the way Early Abundance

11. Community change Succession State-transition models Gap models Assembly rules Facilitation Tolerance Inhibition Methods: Chronosequence, Toposequence Initial Floristic Composition Relay Floristics

12. Toposequence Succession State-transition models Gap models Assembly rules

13. Community change Succession State-transition models Gap models Assembly rules Methods: Large census to predict recruits under canopy trees A B C D E F ABCDEFABCDEF Yup, it is that matrix thing again. Next Generation Current.45.35.15.10.03.02.45.35.15.10.03.02.03.10.15.35.45

14. Community change Succession State-transition models Gap models Assembly rules Methods: Large census to predict recruits under canopy trees with physiological measures of the plants, intensive computer simulation

15. Community change Succession State-transition models Gap models Assembly rules Paul Keddy: centrifugal succession

16. Phytosociology, the releve, and classification We perceive the world as a patchy place. Sample each type of patch.

17. Phytosociology, the releve, and classification These samples are releve’s. In each one you record cover values In each patch you record all species observed

18. TWINSPAN: Two Way Indicator Species Analysis: Groups plots and species by similarity of where they occur. Facilitates classification into discrete community types

19. Gradient analysis An obvious gradient is a mountainside, but vegetation may be responding to less obvious gradients (eg, soil nutrition). A DIRECT gradient analysis is where you know the underlying gradient. An INDIRECT gradient analysis is used when you recognize that you might not. Indirect gradient analysis is typically used because even though you see one gradient (eg, elevation) it may be underlain by some other gradients.

20. Gradient analysis is well suited for detecting continuous variation Vegetation of Lassen and Yosemite. 1995. Bulletin of the Torrey Botanical Society.

21. Gradient analysis is also well suited for comparing sites Vegetation of Lassen and Yosemite. 1995. Bulletin of the Torrey Botanical Society.

22. Linking Twinspan clasification with Gradient Analysis Vegetation of Lassen and Yosemite. 1995. Bulletin of the Torrey Botanical Society.

23. Cluster analysis

24. Cluster analysis: many varieties Nearest neighbor Group centroids Furthest neighbor

25. No “RIGHT” answer Nearest neighbor Group centroids Furthest neighbor

26. PCA, DCA, DFA,CCA Principal Components Analysis Detrended Correspondence Analysis Discriminant Function Analysis Canonical Correspondence Analysis A B C D E F G H

27. PCA, DCA, DFA,CCA Principal Components Analysis: “The horseshoe effect” A and H are similar by virtue of lacking the species in C – G, and get placed close in the ordination A B C D E F G H A H D

28. PCA, DCA, DFA,CCA Detrended Correspondence Analysis: Removes the “The horseshoe effect” A H D A H Used by PLANT ECOLOGISTS who assume a curvilinear response to the environment

29. PCA, DCA, DFA,CCA Discriminant Function Analysis: Isn’t concerned with explaining variance, but correctly distinguishing known groups. A measure of accuracy can be derived. The model can then be used to classify unknown cases

30. CCA

32. Multiple regression Y = Constant + a 1 X 1 + a 2 X 2 + a 3 X 3

33. Multiple regression

34. Canonical Correlation b 1 Y 1 + b 2 Y 2 +b 3 Y 3 = Constant + a 1 X 1 + a 2 X 2 + a 3 X 3 Gets pretty tough to visualize, But it is the same principle