1. Multivariate Ordination Techniques
* Used where clear hierarchical structure is lacking or greatly obscured
- especially where there is much overlapping variation.
Types of Multivariate Analyses
* principal components analysis
* principal coordinates analysis
* discriminate function analysis
* canonical variates analayis
* non-metric multidimensional scaling
* factor analysis
* correspondence analysis
* multidimensional scaling

2. In systematics used
a.) for initial evaluation of OTU’s
- how many taxa might there be?
b.) as a rigorous method for quantifying morphological differences
- the best means of dealing with morphometric data (e.g.,
to study character evolution
c.) as an identification tool for closely related taxa (employed in
expert systems)
d.) hybrid analysis

3. Principal Components Analysis
* Goal: to find groups (entities) that might not be otherwise apparent.
* PCA attempts to maximize or explain the greatest amount of variation in the fewest # of summary components
* Reduces a set of many complex variables into a few linear axes that allows visual inspection of data for structure by producing a few "summary variables" or "components"

4. Discriminate Function, Canonical Variates Analysis, and MANOVA (=linear discriminate analyses)
* Goal: produce new canonical variables which maximize distance (variance) between previously defined groups and minimizes within group distance (variance)
* All OTU's (individuals/taxa) classified prior to study
* DF designed to deal with two groups
* Canonical Variates Analysis an MANOVA deal with multiple groups
* most commonly used multivariate techniques in systematics

5. Classification Matters
Classification is a two part process:
Step 1: Inference of evolutionary relationships
Step 2: Building a classification
* ET argues that synapomorphy and plesiomorphy and autopomorphy
together, are informative (contain information)
* To an ET relative degree of plesiomorphy and autopomorphy matter
They often ask “Isn’t overall similarity (plesiomorphy) evolutionarily and
ecologically meaningful?”
“Don’t long branches (with much anagenetic evolution) merit special
taxonomic status”
Perhaps clade has moved into a new adaptive zone and are no longer like
their ancestors
* Consequence: if such is allowed (recognition of symplesiomorphic and
autapomorphic groups) leads to formal recognition of paraphyletic taxa)
* Clade vs grade issue

6. “It is no longer legitimate to express relationships in terms of genealogy. The amount of genetic similarity now becomes the dominant consideration for the biologist. When an evolutionary taxonomist speaks of the relationship of various taxa, he/she is quite right in thinking in terms of genetic similarity, rather than in terms of genealogy.”
Ernst Mayr 1969

7. ...However, a number of evolutionary processes may result in a discordance between genealogy and the kind of similarity traditionally relied on by taxonomists. For instance, sister groups may diverge at very different rates. The possibility of conflict between genealogical splitting and evolutionary divergence was known to Darwin, and he recommended that it be taken into consideration in the ranking of taxa, stating that “the amount of difference in the several branches or groups, though allied in the same degree in blood to their common progenitor may differ greatly, being due to the different degrees of modification which they have undergone, and this is expressed by the forms being ranked under different genera, families, sections or orders” (1859:420).

8. Information Content of Evolutionary Trees
(a) common ancestry (branching sequence) [cladistics]
(b) degree of divergence (horizontal axis) (xb-xa) [phenetics]
(c) geologic time (vertical axis) (yb-ya) [chronistics]
(d) rate of divergence (slope) (xb-xa/yb-ya) [patristics]