The Compleat Cladist: Chapter Five

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The Compleat CladistChapter Five
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Tree Length (s)

• Total number of steps

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Consistency Index (ci)

• How a transformation series or entire data matrix
  fits a particular tree topology
• Little or no homoplasy ? high consistency index
• Maximum ci is 1.0 (no homoplasy)
• Lots of homoplasy ? low ci

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Consistency Index (ci)

• ci m / s
• ratio of minimum amount of changes (steps) it
  might show (m) and the amount of change (steps)
  it does show on a particular topology (s)

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ci m / s 1 / 1 1.0
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ci m / s 1 / 2 0.5
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But character 1 in (a) is an autapomorphy,
whereas in (b) it is a synapomorphy. How do we
reflect this difference?
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Rescaled Consistency Index (rc)

• This tales into account any synapomorphic value
  of characters
• rc is the product of the ci and the retention
  index (ri)
• rc ci x r

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Retention Index (ri)

• The retention index measures the fraction of
  apparent synapomorphy to actual synapomorphy
• ri (g - s) / (g - m)
• g how many steps a character would need under
  the worst possible scenario, a polytomy

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g 2
g 1
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(a) ri g s / g m 1 1 / 1 1 0.0
(b) ri g s / g m 2 1 / 2 1 1.0
Therefore rc ri x ci
(a) rc 0 x 1.0 0 (b) rc 1.0 x 1.0 1.0
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From Table 5.1 in CC
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g 3
ci m / s 1 / 1 1.0 ri g s / g m 3
1 / 3 1 2 / 2 1.0 rc ri x ci 1.0 x
1.0 1.0
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g 3
ci m / s 1 / 2 0.5 ri g s / g m 3
2 / 3 1 1 / 2 0.5 rc ri x ci 0.5 x
0.5 0.25
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g 2
ci m / s 1 / 2 0.5 ri g s / g m 2
2 / 2 1 0 / 1 0 rc ri x ci 0.5 x 0 0
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Ensemble Indices (CI, RI, RC)

• Used to examine the entire data matrix on a
  particular tree topology

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CI M / S 8 / 11 0.727 RI G - S / G - M
18 - 11 / 18 - 8 7 / 10 0.700 RC CI x RI
0.727 x 0.700 0.509
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Consensus Techniques

• How to represent difference but equally
  parsimonious topologies
• There are two common types of strict consensus
• Strict Consensus
• Majority Rule Consensus
• You do not need to know Adams consensus for the
  quiz

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Strict Consensus

• Only contains those monophyletic groups that are
  common to all competing trees

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1. Draw a Venn diagram for each tree.
2. Combine the Venn diagrams.
3. Erase all intersecting ellipses.
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4. Translate Venn diagram into a tree.
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Majority Rules Consensus

• Contains monophyletic groups that occur in a
  majority of the competing trees.

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If there is an even result
A polytomy results.