1. Description & Analysis of community composition

2. The individualistic hypothesis Henry Gleason

3. Why vegetation composition? Pattern recognition Parameter estimation Inventory & site assessment Classification development Monitoring

4. Three types of data tables 1. Table of observation x species showing importance values (e.g., Site #3 was 50% Pond Pine, 25% Live oak, and 25 % Coastal Juniper). 2. Table of observations x site attributes (e.g., at Site 3 the soil contained 100 ppm Calcium and 1,000 ppm Sodium). 3. Table of species x traits (e.g., Pond pine is an evergreen conifer tree with serotinous cones)

5. Importance values No correct answer, pick for study at hand For this discussion, thinking only of species composition. Density and Percent cover are typical measures.

6. Importance values Frequency: % of sample units (quadrats) Will vary with unit size and pattern of dispersal Density: Individuals or stems per unit area Difficult for some groups like grasses, shrubs, clonal herbs Cover: Biomass or production (or yield): Dimension analysis, gas exchange, harvest – difficult. Dominance: Influence on other species Basal area (m2/ha*4.356 = ft2/ac)

7. Transformed values A. Increase comparability Centering (Y* = Y - Ybar) Standardizing by variance (Y* = [Y - Ybar]/s) Standardizing by range (Better between sites comparisons) Standardize (relativize) by plot totals B. Increase linearity or interpretability Cover/abundance to percent log transformation

8. Direct Gradient Analysis R.H. Whittaker – Smoky Mountains

10. Great Smoky Mts Topographic-moisture and elevation R.H. Whittaker 1956

11. Whittaker’s methods Plot species distributions along a gradient, find modes, assign values. Calculate weighted average stand positions: curve smoothing. Problems: –Need to know what the critical factors are at start. –Factor selection and gradient construction are highly subjective. Results from Whittaker –Hypothesis of bell curves formulated and supported. –Hypothesis of independent distributions supported. –Method for examining pattern and framing other hypotheses.

13. Origins of Indirect Gradient Analysis J.T. Curtis – Southern Wisconsin

15. Importance values Composite indices (e.g. Wisconsin Importance Value) Species # BA Freq R.Den R.Dom R.Freq Sum /300 Acer 40 0.7 10 50.0 23.3 40.0 113.3.378 Quercus 20 1.5 8 25.0 50.0 32.0 107.0.356 Prunus 10 0.5 5 12.5 16.7 20.0 49.2.164 Torreya 10 0.3 2 12.5 10.0 08.0 30.5.102 Total 80 3.0 25 100.0 100.0 100.0 300.0 1.000 Assume 0.1 ha  BA=30 m 2 /ha; Density = 800 trees/ha

16. Curtis’ methods Leading dominants from 95 upland forest stands Pioneer to climax (including mesophytism) Weighted average species positions Bur oak1.0 Black oak 2.5 White oak 3.5 Red oak5.5 Basswood 7.5 Beech 9.5 Sugar Maple 10.0

17. Wisconsin Continuum Index Species R.Den R.Dom R.Freq Sum Ad.V.CI Acer saccarum 50.0 23.3 40.0 113.3 101133 Quercus rubra25.0 50.0 32.0 107.0 5535 Ulmus rubra 12.5 16.7 20.0 49.2 7344 Quercus alba 12.5 10.0 08.0 30.5 392 100.0 100.0 100.0 300.0 2104

18. The Wisconsin forest continuum Curtis sought arrangement of forest samples from southern Wisconsin to provide a framework for subsequent work. Use the Gleasonian assumptions; but not a test of Gleason

19. Types of gradient analysis Direct gradient analysis – Relationship of vegetation to environment shown directly since environmental variation used to show variation in vegetation. Indirect gradient analysis -- Patterns of community variation displayed. Environmental variation introduced after analysis to aid interpretation of environmental factors and gradients.

20. Bray Curtis ordination Data matrix Standardized and relativized Similarity matrix

23. Similarity measures The traditional Wisconsin measure is 2w/a+b. This is called “coefficient of community” if used with presence –absence data, or percent similarity if used with relativized importance values. W = amount in common (minimum of pair), a = total for one of pair, b = total for other of pair. If used with relativized data, this simplifies to the sum of the minimums. This can be converted to a distance matrix by subtracting from 100.

25. The Bray-Curtis ordination We now select two very different stands to serve as endpoints. Note that the lowest similarity in the matrix is 3.7 between 6 and 8, so these two are selected as endpoints. The distribution of a point on the axis defined by 6 and 8 can be determined by calculating the distance from that point to each of 6 and 8, and then drawing circles where the radius is the distance. The location where the circles intersect is the designated location. Beals pointed out that this can be calculated as X = (L2+D12+D22)/2L where L is the distance between the two endpoints.

26. A second axis Next select two very different points near the center of the first axis to define the second axis. One approach commonly used is to assume good end points would have large differences from both of the first two endpoints, which means that the circles meet high above the first axis, which can be calculated as e = SQRT(D12-X2) Guidelines: Middle of first axis, Close to each other, Most dissimilar of pairs, High e values (1 vs 12; 4 vs 10).

29. Applications Direct Gradient Analysis Conceptual framework for ecosystem & community ecology. Stress gradients. Environmental impact & global change. Disturbance overlays & prediction Environmental prediction and weighted averages Geographic comparisons & patterns Rare plant distributions and introductions

30. Steps common to most methods Field data Data matrix Data quality control Data transformation Distance measure Magic Relate to environment with correlations, or visualizations

31. Distance measures Sorenson = 1 - [2(A ∩ B)/(A+B)] Jaccard = 1 – [(A ∩ B)/(A+B)] Euclidean = √ Σ(A-B)**2 Manhattan = Σ|A-B|

32. Modern methods Detrended correspondence analysis Multidimensional scaling

33. Environmental interpretation?

34. An example: Southern Wisconsin forests

37. Another example: Duke Forest Environmental vectors Progressive fragmentation

38. Community Classification “ Classification attempts to identify discrete, repeatable classes of relatively homogeneous communities or associations about which reliable statements can be made. Classification assumes either that natural groupings (communities) do occur, or that it is reasonable to separate a continuum of variation in composition and/or structure into a series of arbitrary classes.” after Kimmins 1997

39. Numerical Classification

42. Approaches to Numerical Classification Hierarchical vs non-hierarchical? Divisive vs agglomerative? Monothetic vs polythetic? Qualitative vs quantitative? Emphasis on abundant species?

43. Issues Distance measure Linkage rules Scaling rules Stopping rules Group quality chaining, interpretability