The problem:

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Terminology

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Biological Assumptions

Character Homology

Bifurcating descent

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Estimation Principles

Distance relationships

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Nested character-states

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Likelihood

Suppose we see “AAAT”, what is the probability of drawing a base “A”?

Markov chain model of character evolution

Transition probability is specified from node to node

The character evolution model is determined by the form of the constraints on the transition matrix

The model is specified by the branching order of the tree, the initial state at the common ancestor, and a transition matrix for each branch

Given the model, the probability of any character pattern at the tips of the tree can be computed

For t number of taxa and n-state characters there are nt number of character patterns at the tips of the tree

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Algorithmic Structure

Optimization

Combinatorial Optimization

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Number of possible unrooted binary trees with n-taxa

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Solutions

Exhaustive search

Branch-and-bound search

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Divide-and-conquer

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Dynamic Programming

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Heuristics

Greedy search

Stochastic search

Simulated annealing

Super-duper clever search

Heuristic solutions are dependent on ...

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Neighbor relations of trees

NNI configuration

TBR Configuration

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Statistical Properties

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Accuracy is some measurement of the dispersal of the estimator distribution around the “true” value

“?????”???We need a way of measuring deviation between trees

Partition metric

Consensus

Majority-rule consensus

Consensus tree can be used to define a deviation measure

Tree neighbor relations can be used to define deviation

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Power and Error

Power, Error, and Accuracy are not necessarily related to each other

Confidence Limits

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Bootstrap resampling as a means of generating replicate samples (step 2)

Majority-rule consensus trees can be used to select confidence sets (step 4)

Misc. confidence limites