Transcript PowerPoints

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 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)
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
Direct Gradient Analysis
R.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
/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 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
1.0
Black oak
2.5
White oak
3.5
Red oak
5.5
Basswood
7.5
Beech
9.5
Sugar Maple
10.0
Wisconsin Continuum Index
Species
R.Den R.Dom R.Freq Sum
Ad.V.
CI
Acer saccarum
50.0
23.3
40.0
113.3
10
1133
Quercus rubra
25.0
50.0
32.0
107.0
5
535
Ulmus rubra
12.5
16.7
20.0
49.2
7
344
Quercus 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).
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
Steps common to most methods
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Field data
Data matrix
Data quality control
Data transformation
Distance measure
Magic
Relate to environment with correlations, or
visualizations
Distance measures
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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