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Maximum parsimony. Kai Müller. P hylogenetic trees. Cladogram Branch lenghts without meaning Slanted / rectangular Network/ unrooted Parenthetical notation ( Newick ). P hylogenetic trees. Phylogram. Chronogram. character changes. time. an ultrametric tree.

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p hylogenetic trees
Phylogenetic trees
  • Cladogram
    • Branchlenghtswithoutmeaning
    • Slanted/rectangular
    • Network/unrooted
  • Parentheticalnotation(Newick)
p hylogenetic trees1
Phylogenetic trees

Phylogram

Chronogram

character changes

time

an ultrametric tree

free rotation around all nodes
Free rotation around all nodes

a phylogram

the same phylogram

=

how many trees are there

A

B

C

A

D

B

D

A

B

A

D

B

C

C

C

E

D

A

B

D

E

A

B

D

A

E

B

D

E

A

B

D

A

E

B

C

C

C

C

C

How many trees are there?
  • for n taxa, there arepossible rooted trees
too many

A

B

C

A

C

B

C

A

B

C

A

B

Too many!
  • for n taxa, there arepossible rooted trees
types of characters
Typesofcharacters
  • Morphological
  • Molecular
    • DNA sequences
    • Aminoacidsequences
    • Presence of genes in Genome
    • Genomicrearrangements
    • Presence ofintrons
    • Single substitutions (SNP, RFLP, AFLP etc.)
different types of sequence homology1
Different types of sequence homology
  • Imagineweareunawareofthegeneduplicationand sample onlyalpha-chick,alpha-frog, beta-mouse:

!=

true organismal relationships

erroneously inferred by a mixture of paralogous & orthologous sequences

maximum parsimony1
Maximum parsimony
  • parsimony principle
    • most parsimonious explanation should be preferred to others
    • Ockham‘s razor
    • parsimony analysis ~= cladistics
    • the oldest phyl. reconstr. method
    • still widely used because
      • principle/optimality criterion easy to grasp
      • quick
      • without convincing alternatives for morphological data
parsimony informative characters1
Parsimony-informative characters
  • >= 2 states, >= 2 ofwhichoccur in >=2 taxa
character conflict
Character conflict
  • character state distributions of different characters do not all support the same topology
  • example for the following tree:
character conflict example2
Character conflict: example
  • suggested topology No 1: 10 steps
character conflict example3
Character conflict: example
  • suggested topology No 2: 9 steps
the shortest tree
The shortest tree
  • length of tree = #steps = #character state transitions
  • out of the two trees tried, 9 is the best score
  • trying all other out of the 15 possible trees shows: there are more that require 9, but non with fewer steps
consensus trees
Consensus trees
  • strict
  • loose (semi-strict)
  • majority rule
  • Adams

.

.

.

  • supertrees
consensus trees1
Consensus trees

strict/semistrict

50% Majority-rule

Adams

types of parsimony
Types of parsimony
  • different types of parsimony
    • Wagner parsimony
      • binary or ordered multistate characters
      • i.e, states are on a scale and changes occur via intermediate steps only
      • free reversibel, 01 = 10
    • Fitch parsimony
      • binary or unordered multistate characters
      • not on a scale, no intermediate steps required: cost(02)= cost(01)
      • free reversibel
    • Dollo parsimony
      • polarity: ancestral/primitive vs. derived states defined a priori
      • derived states may occur only once on a tree, but can undergo >1 reversals
    • Generalized parsimony
      • cost (step) matrices define state transition costs
weighted parsimony
Weighted parsimony
  • differential weight given to each character
  • relative importance of upweighted characters grows
  • other tree length results:
  • different trees may be preferred now
  • successive weighting
  • problematic
    • risk of circularity
calculating tree length
Calculatingtreelength
  • initialize L=0; root arbitrarily (root taxon);
  • postorder traversal: assign each node i a state set Siand adjust L:
    • the set for terminal nodes contains the state of this leaf
    • cycle through all internal nodes k for which Sk has not yet been defined, unlike for its child nodes m and n; if
    • if k is parent node to root node, stop; if state at root node not in current Sk,
calculating tree length1
Calculatingtreelength

1

tax1T

tax2 G

tax3 T

tax4 A

tax5 A

1)

+ 1

Example:

tax6 A

L:

calculating tree length2
Calculatingtreelength

1

tax1T

tax2 G

tax3 T

tax4 A

tax5 A

1)

+ 1

Example:

2

tax6 A

L:

2)

+ 0

calculating tree length3
Calculatingtreelength

1

3

tax1T

tax2 G

tax3 T

tax4 A

tax5 A

1)

+ 1

3)

+ 0

Example:

2

tax6 A

L:

2)

+ 0

calculating tree length4
Calculatingtreelength

4

1

3

tax1T

tax2 G

tax3 T

tax4 A

tax5 A

1)

+ 1

= 2

3)

+ 0

4)

+ 1

Example:

2

tax6 A

L:

2)

+ 0

tree searching exhaustive search
Tree searching: exhaustive search
  • branch addition algorithm
branch and bound
Branch and bound
  • Lmin=L(random tree)
  • „search tree“ as in branch addition
    • at each level, if L < Lmin go back one level to try another path
    • if at last level, Lmin=L and go back to first level unless all paths have been tried already
heuristic searches
Heuristicsearches

best

  • stepwise addition
    • as branch addition, but on each level only the path that follows the shortest tree at this level is searched
branch swapping
Branchswapping

NNI: nearest neighbour interchanges

SPR: subtree pruning and regrafting

TBR: tree bisection and reconnection

tree inference with many terminals
Tree inference with many terminals
  • general problem of getting trapped in local optima
  • searches under parsimony: parsimony ratchet
  • searches under likelihood: estimation of
    • substitution model parameters
    • branch lengths
    • topology
parsimony ratchet
Parsimonyratchet
  • generate start tree
  • TBR on this and the original matrix
  • perturbe characters by randomly upweighting 5-25%. TBR on best tree found under 2). Go to 2) [200+ times]
  • once more TBR on current best tree & original matrix
  • get best trees from those collected in steps 2) and 4)
bootstrapping
Bootstrapping
  • estimates properties of an estimator (such as its variance) by constructing a number of resamples of the observed dataset (and of equal size to the observed dataset), each of which is obtained by random sampling with replacement from the original dataset
bootstrapping1
Bootstrapping
  • variants
    • FWR (Frequencies within replicates)
    • SC (strict consensus)
bremer support decay
Bremer support / decay
  • Bremer support (decay analysis) is the number of extra steps needed to "collapse" a branch.
  • searches under reverse constraints: keep trees only that do NOT contain a given node
  • Takes longer than bootstrapping: parsimony ratchet beneficial (~20 iterations)