Description & Analysis of community composition

The individualistic hypothesis

• Henry Gleason

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

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)

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.

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

Transformed valuesA. 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

Direct Gradient AnalysisR.H. Whittaker – Smoky Mountains

Great Smoky Mts

• Topographic-moisture and elevation

R.H. Whittaker 1956

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.

Origins of Indirect Gradient Analysis

J.T. Curtis – Southern Wisconsin

Importance values

Composite indices (e.g. Wisconsin Importance Value) 

Species # BA Freq R.Den R.Dom R.Freq Sum /300Acer 40 0.7 10 50.0 23.3 40.0 113.3

.378Quercus 20 1.5 8 25.0 50.0 32.0 107.0 .356Prunus 10 0.5 5 12.5 16.7 20.0 49.2 .164Torreya 10 0.3 2 12.5 10.0 08.0 30.5 .102Total 80 3.0 25 100.0 100.0 100.0 300.0

1.000 Assume 0.1 ha

BA=30 m2/ha; Density = 800 trees/ha

Curtis’ methods• Leading dominants from 95 upland forest stands

Pioneer to climax (including mesophytism)• Weighted average species positions

Bur oak 1.0Black oak 2.5White oak 3.5Red oak 5.5Basswood 7.5Beech 9.5Sugar Maple 10.0

Wisconsin Continuum Index

 

Species R.Den R.Dom R.Freq Sum Ad.V. CIAcer saccarum 50.0 23.3 40.0 113.3 101133Quercus rubra 25.0 50.0 32.0 107.0 5 535Ulmus rubra 12.5 16.7 20.0 49.2

7 344Quercus alba 12.5 10.0 08.0 30.5

3 92 100.0 100.0 100.0 300.0 2104 

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

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.

Bray Curtis ordination

• Data matrix• Standardized and relativized• Similarity matrix

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.

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.

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).

ApplicationsDirect 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

Steps common to most methods

• Field data • Data matrix• Data quality control• Data transformation• Distance measure• Magic • Relate to environment with correlations,

or visualizations

Distance measures

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

Modern methods

• Detrended correspondence analysis

• Multidimensional scaling

Environmental interpretation?

An example:Southern Wisconsin forests

Another example:Duke Forest•Environmental vectors•Progressive fragmentation

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

Numerical Classification

Approaches to Numerical Classification

• Hierarchical vs non-hierarchical?• Divisive vs agglomerative?• Monothetic vs polythetic?• Qualitative vs quantitative?• Emphasis on abundant species?

Issues• Distance measure• Linkage rules • Scaling rules• Stopping rules• Group quality

chaining, interpretability