Comparative methods: Using trees to study evolution

Some uses for phylogenies

• Character evolution– Ancestral states– Trends and biases– Correlations among characters

• Molecular evolution– Evidence of selection

• “Key innovations”– Diversification rate

Why reconstruct character evolution?

• Can evaluate homology

How do we know that bat and bird wings are not homologous?

Why reconstruct character evolution?

• Can evaluate homology• Can determine character-state polarity

Why reconstruct character evolution?

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

character evolved

Was the ancestor bird pollinated when red flowers evolved?

Look at pollinators

Bee to bird poll.

Adaptation supported

Alternative result

Bee to bird poll.

Not an adaptation

A third possibility

Bee to bird poll.

Consistent with adaptation

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

Dinosaur Rhodopsin

• Chang et al. (MBE 2002)

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?

Cost-change graph(Ree and Donoghue 1998: Syst. Biol. 47:582-588)

Stability to gain:loss weights

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?

Wing loss and re-evolution?• Whiting et al.

(Nature 2003)

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)

Transition rate matrix

0 1

0 1-q1 q1

1 q2 1-q2

From

To

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

Probabilities summed across all possible ancestral states

1 1 01 0 0 0 1 1 0

00

00

0

00

00

How much of the likelihood contributed by each state at

each node

How much of the likelihood contributed by each state at

each node

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?

Ree and Donoghue, 1999

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

1 1 01 0 0 0 1 1 0

Suppose this taxon contains 5000 species

Suggests that the rate of losses is low

1 1 01 0 0 0 1 1 0

Suppose this taxon contains 5000 species

Suggests that the rate of gains is low

After equalizing the number of species of each type

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?

Causes of non-independence

• Developmental “connectedness”• Adaptation (Correlated evolution has been

claimed to be the best evidence for evolution by natural selection)

Non-phylogenetic (“tip”) method

• Count species• Do a chi-square test

Green eyes Blue eyes

Pale fur 2 100

Dark fur 150 2

Hypothetical tree

Eyes g b g g b bFur d d p p d p

150 100

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

Non-phylogenetic (“tip”) method

Fleshy Dry

One 10 34

Many 23 62

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%.

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

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

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

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)