Notes 20100624 CS 798 Picking a Tree out of many possible Phylogenies

From SnOwy - Ed's Wiki Notebook

Contents 1 Majority rule supertree 2 Parsimony 3 Rooted family of trees 4 Paleontology 5 Fossil Strata 6 Stratolikelihood

Majority rule supertree

• find all splits found within > k/2 trees
• this is a voting system
• the tree that agrees with the majority of trees on a pass of the algorithm
• what if we chose the wrong k trees in the first place?
• remember there are several scenarios to picking trees in the first place
  1. Bayesian world
     • sampling from the posterior
  2. k-different experiments, each experiment is on a different gene pretend mutual independence...
  3. Multiple optima
     • we manage to have several modes
• majority rule still makes sense
  • we are saying that the split that occurs most often is the most likely
• giving one vote for every sample isn't that silly: it's one point from the sample distribution
• this is kind of weird too: similar to putting everyone's votes on a ballot, then throwing out all the ballots but one

Parsimony

• three possible optima which look like...

(1)                 |
           +--------+--------+
           |                 |
     +-----+----+            |
     |          |            |
  +--+--+       |            |
  |     |       |            |
+-+-+   |       |            |
|   |   |       |            |
A   B   C   subtree(D)   subtree(E)

(2) vs a vote where ((((A, C), B), subtree(D)), subtree(E))

(3) vs a vote where ((((A, C), subtree(D)), B), subtree(E))

• we basically have two trees which agree that A~B~C should be be together (1 and 2) and one that's radically different
• but think about what we're doing-- we basically are saying we don't know which of (1, 2) or (3) is better, so we give (1, 2) an additional vote
  • is this sane?
  • what does this mean informationally-- does it have an informational meaning?
• other options strict concensus tree: only keep splits that occur in 100% of samples
• assume that the algorithm uniformly samples at random from all optimal trees
  • we still bias the result based on the combinatorial structure of the multiple optima
• summary trees end up being useful for visualization etc., i.e. don't count on it to represent reality

Rooted family of trees

• tripartition
• naturally: the ancestor of three taxa is further back than the ancestor of two taxa
• ((A, B), C)
• Adam's concensus: find all tripartitions not incompatible with any of the trees
  • topology only (no edge lengths)
• i.e. find all the tripartitions that ARE COMPATIBLE with all trees
  • the result is a collection of tripartitions which can be used to build a tree
• tripartitions evaluated for each tripartition in each tree
• is unlikely to create the majority rule tree nor the strict concensus tree

Paleontology

• how do we incorporate n-living species and m-fossils
• we must now switch to a different kind of data
• we can get some DNA out of fossils, not a lot
• we have morphology -- morphological characters
• feathers, claws, bone structures (ratios, linear dimensions, curve parameters etc.!), limbs, most likely colour (given microscopic structures)
• usually bitvector elements
• how do we build this into a tree?
• fossils are not necessarily ancestors of modern taxa
• most fossils are not direct ancestors of currently extant species-- many are aunts, uncles, cousins etc.,
• example: hominids -- how close must the edge lengths be to the trunk of the tree for us to categorize a given species as our ancestor?

Fossil Strata

• should be dense
• a stratum is a period of time
• a given stratum should contain fossils corresponding to the species that exists before and after it
• a stratum that misses a lineage is rare
• parsimony tries to find the topology to minimize forced mutations
  • we can add one additional item to this with fossils
  • we sprinkle the fossil characters into a phylogenetic tree of modern species
  • our objective function pays for all the physical mutations to sanely insert a fossil into a tree
  • we'll also pay whenever we expected a fossil but didn't find one
• this method is very sensitive to the number of fossils that have been found
• stratocladistics == geological parsimony

Stratolikelihood

• depositing a fossil happens in some probabilistic process
  • Poisson process
• expect to see k-lambda fossils
• likelihood is the continuous interpretation of parsimony...
• we need a model of fossil deposition and a model of evolution
• including fossils that contain molecular biosequence
• ancient molecular sequence
  • HIV