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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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Was the ancestor bird pollinated when red flowers evolved?
Look at pollinators
Bee to bird poll.
Adaptation supported
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Alternative result
Bee to bird poll.
Not an adaptation
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A third possibility
Bee to bird poll.
Consistent with adaptation
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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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Dinosaur Rhodopsin
• Chang et al. (MBE 2002)
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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. 47:582-588)
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Stability to gain:loss weights
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What gain:loss 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 gain:loss bias?
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Wing loss and re-evolution?• Whiting et al.
(Nature 2003)
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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->1) and rate of
losses (1->0) that maximizes the likelihood of the data given a sample tree (and branch lengths)
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Transition rate matrix
0 1
0 1-q1 q1
1 q2 1-q2
From
To
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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 01 0 0 0 1 1 0
00
00
0
00
00
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How much of the likelihood contributed by each state at
each node
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How much of the likelihood contributed by each state at
each node
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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?
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Ree and Donoghue, 1999
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The likelihood method
• Provides a method for using the data to evaluate gain:loss bias
• Takes account of branch lengths• Still sensitive to taxon sampling
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1 1 01 0 0 0 1 1 0
Suppose this taxon contains 5000 species
Suggests that the rate of losses is low
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1 1 01 0 0 0 1 1 0
Suppose this taxon contains 5000 species
Suggests that the rate of gains is low
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After equalizing the number of species of each type
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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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Causes of non-independence
• Developmental “connectedness”• Adaptation (Correlated evolution has been
claimed to be the best evidence for evolution by natural selection)
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Non-phylogenetic (“tip”) method
• Count species• Do a chi-square test
Green eyes Blue eyes
Pale fur 2 100
Dark fur 150 2
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Hypothetical tree
Eyes g b g g b bFur d d p p d p
150 100
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Proposed solutions for discrete characters
• Do a chi-square test of changes rather than tip-states (various approaches) - Ridley; Sillen-Tullberg
• Use a Monte Carlo approach to ask if changes of the dependent variable are biased relative to expectations from changes placed on the tree at random - W. Maddison
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Non-phylogenetic (“tip”) method
Fleshy Dry
One 10 34
Many 23 62
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Maddison test
FleshyBranches
DryBranches
One->Many 3 7
Many.>One 6 2
Probability that this pattern or a more extreme pattern could arise without fruit type affecting seed number is ca. 8%.
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Problems with the Maddison test
• Requires one to define dependent and independent characters
• Does not take account of branch-length• Very sensitive to inclusion/exclusion of
species
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Maximum likelihood approach(Pagel and Milligan)
0,0 0,1 1,0 1,1
0,0 q12 q13 0
0,1 q21 0 q24
1,0 q31 0 q34
1,1 0 q42 q43
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Procedure
• Estimate the set of rates in the q-matrix that maximize the likelihood of the data and calculate that likelihood
• Constrain the matrix so that it represents independence (q12 = q34; q13 = q24; q21 = q43; q31 = q42) and repeat the calculation
• Use a likelihood ratio test to evaluate significance
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Issues to consider
• Rejection of independence does not tell you what kind of non-independence you have
• You need reasonable branch lengths• Sampling matters (if perhaps less than
parsimony)