TWINSPAN

Lecture graphics

To this point, we have discussed only euclidean distance as a measure of similarity

Another measure of similarity is chord distances

Chord distance is still a linear measure of distance, but a spatial transformation is imposed

Points falling short of chord are stretched, those beyond chord are shrunk

Distance between entities is measured along the arc (geodesic distance) or across arc, on straight line

Disadvantages:

1. use of chord distance implicitly assumes species are independent

2. in practice, using Ward's method w/ chord distance causes "chaining"

For these reasons, chord distances are not widely used

TWINSPAN (Two Way INdicator SPecies ANalysis)

Unlike the other clustering methods we have discussed, TWINSPAN is a divisive method

TWINSPAN algorithm

1. Samples are ordinated w/ RA

2. A crude dichotomy is formed: the RA centroid is used as a dividing line between two groups (negative and positive)

3. The dichotomy is refined by a process comparable to iterative character weighting

4. Dichotomies are ordered so that similar clusters are near each other

   
   
   
   
   
   
   
   

   Assuming higher groups have already been ordered, ordering of lower groups proceeds by taking into accound similarity of nearby clusters

   In the absence of ordering, arrangement of groups 1-8 is arbitrary (i.e., hierarchical structure only indicates that 1 should be next to 2, 3 next to 4, etc.)

   Ordering places 2 next to 3 if 2 is more similar to B than 1 and 4 is more similar to C than 3

   For this reason, it is said that the dichotomy is determined by relatively large groups, so that it depends on general relations more than on accidental observations

5. Species are classified

   In light of quadrat classification: based on fidelity to particular sites (clusters of quadrats)

6. Structured table is made from both classifications

Presentation of cluster analysis results

Species-by-site (i.e., species-by-quadrat) table used by TWINSPAN

Additional information is usually given for sites (quadrats)--e.g., environmental variables

Rarely used w/ large data sets because table is very large and patterns are not readily discernible

Dendogram

Combined w/ ordination (clusters or communities shown on ordination diagram)

Interpretation of cluster analysis results

Calculate descriptive statistics at each dichotomy

Perform discriminant analysis at each dichotomy to quickly identify environmental variables which are "most different" between clusters

Statistical tests of significance may be used to determine whether environmental variables are "different" on each side of a dichotomy

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