Comparative methods: Using trees to study evolution

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Comparative methods Using trees to study
evolution
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Some uses for phylogenies

• Character evolution
• Ancestral states
• Trends and biases
• Correlations among characters
• Molecular evolution
• Evidence of selection
• Key innovations
• Diversification rate

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Why reconstruct character evolution?

• Can evaluate homology

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How do we know that bat and bird wings are not
homologous?
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Why reconstruct character evolution?

• Can evaluate homology
• Can determine character-state polarity

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Why reconstruct character evolution?

• Can evaluate homology
• Can determine character-state polarity
• Can evaluate the selective regime when a
  character evolved

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Map on selective regime
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Now look at character evolution
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Now look at character evolution
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Why reconstruct character evolution?

• Can evaluate homology
• Can determine character-state polarity
• Can evaluate the selective regime when a
  character evolved
• Can recreate ancestral genes/proteins

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Character optimization using parsimony

• Pick the reconstruction that minimizes the cost
• What do you do if more than one most-parsimonious
  reconstruction
• ACCTRAN/DELTRAN
• Consider all
• What character-state weights should you use?

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Cost-change graph(Ree and Donoghue 1998 Syst.
Biol. 47582-588)
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Stability to gainloss weights
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What gainloss weight to use?

• If you believe gains are more common (hence
  weighted less) you will find more gains (and vice
  versa)
• So how can you use a tree to establish if there
  is a gainloss bias?

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A likelihood approach

• Developed (in parallel) by Mark Pagel and Brent
  Milligan in 1994
• Continuous time Markov model
• Select the rate of gains (0-gt1) and rate of
  losses (1-gt0) that maximizes the likelihood of
  the data given a sample tree (and branch lengths)

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Transition rate matrix
To
From
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Logic

• Calculate the likelihood of the data for a given
  value of q1 and q2
• Modify q1 and q2 to find a pair of values that
  maximizes the probability of the data

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Probabilities summed across all possible
ancestral states
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
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Are gain and loss rates different?

• Likelihood ratio test
• Model 1 gains and losses free to vary
  independently
• Model 2 gains and losses equal
• How many degrees of freedom?
• .but invalid due to tree like structure

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Montecarlo approach

• Estimate parameters under model 2
• Use those parameters to simulate evolution up the
  tree
• Take the simulated data and calculate the LR of
  model 1 vs. model 2
• If lt5 of the simulations have a LR greater or
  equal to that observed then Model 1 is favored

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Method can be adapted to determine the
probability of an ancestral state

• For example, look at the contribution to the
  overall likelihood contributed by state 0 or
  state 1 at a node of interest
• Can be used as a statistical test of homology

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The likelihood method

• Provides a method for using the data to evaluate
  gainloss bias
• Takes account of branch lengths
• Sensitive to taxon sampling

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1
1
0
1
0
0
0
1
1
0
Suggests that the rate of losses is low
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1
1
0
1
0
0
0
1
1
0
Suggests that the rate of gains is low
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Correlated evolution

• Look at pairs of traits (where one trait can be
  an environment)
• Body size and range size
• Warning coloration and gregariousness
• Fleshy fruit and dioecy
• Do these traits evolve non-independently?

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Non-phylogenetic (tip) method

• Count species
• Do a chi-square test
• But non-independence is a huge issue