A Likelihood Approach to Estimating Phylogeny from Discrete Morphological Character Data

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A Likelihood Approach to Estimating Phylogeny
from Discrete Morphological Character Data

• by Paul O. Lewis, Systematic Biology,
  50(6)913-925, 2001.

Presented by Alex Phan
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Phylogenetic Systematics

• Definition A branch of Systematic Biology that
  deals with the reconstruction and study of the
  patterns of evolutionary relationships in the
  tree of life, which includes living and extinct
  taxa
• Based on cladistics, a method of hypothesizing
  relationships based on shared, derived characters
  (synapomorphies)
• Assumptions related by descent, bifurcation,
  characters change over time

www.ucmp.berkeley.edu www.evolution.berkeley.edu
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Some Definitions

• Character heritable trait
• 1. Determine which characters to use
• 2. Determine the polarity of each character
• Apomorphic the changed state of the character
  (derived)
• Plesiomorphic the original state of the
  character (primitive)
• Synapomorphic the shared, derived state of the
  character
• Homoplasious homologous character due to shared
  function
• Autapomorphic a character unique to a taxon
• Taxa are traditionally defined using
  synapomorphic characters

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A quick example

• A human, a jellyfish, and a starfish.
• Characters lives in water, has radial symmetry,
  is an invertebrate

J
S
H
S
H
J
wrong
right
Animals
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The Utility of Morphological Data

• Lack of molecular data
• Resolves relationships between extinct and living
  taxa and relationships among extinct taxa
• Provides congruence with molecular data
• Detection of error

John Wiens The Role of Morphological Data in
Phylogeny, Systematic Biology 53(4) 653-661,
2004.
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Alternatives to MP for Morphological DataWhy?

• Maximum parsimony cannot estimate evolutionary
  parameters time-independent
• Convergent evolution, reversals, multiple
  changes, unusual topologies are problematic
  with MP
• MP tends to have biased branch lengths
• Basically, when conditions are complex, MP
  performance deteriorates

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A Basic Likelihood Model Mk

• M stands for Markov, k refers to the number
  of states, or characters
• This is a generalized Jukes-Cantor model
• (Neyman Model)
• Maximum average likelihood

MavgL
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Maximum Likelihood Definition
ML method selects the tree (T) that maximizes
the likelihood function for the data (Dc)
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Nuisance Parameters

• Definition information needed to fully define
  P(DT)
• Examples edge length( ), transition/transversion
  bias (substitution matrix parameters),
  parameters that describe how rates vary across
  sites
• Two flavors
• 1. Structural (e.g. edge length)
• 2. Incidental arises from
• (1) speculation about a state (missing data)
• (2) process varies from site to site

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Mk ModelLooks Familiar
Transitional Probabilities
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Mk Conditions

• No character is assumed plesiomorphic or
  apomorphic beforehand
• A character can change state at any instant in
  time (dt) along a particular branch
• The probability of a change is equal for all dt
• Only 1 change per dt
• Probabilities of a state changes are independent
  of different dt
• Reversible character(i) lt-gt character(j)

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Two Objections Posed, Another Implied

• Evolution gradual vs. episodic
• Mk model predicts the number of changes will
  increase over time -gt gradual?
• However, this is an average and does not
  predetermine evolutionary mechanism.
• State symmetry biologically sound?
• All characters have the same rate?!

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The Problem of Constant Characters

• A constant character is a character of which the
  same state is shared by every taxon in the tree
• Problems (1) constant characters not usually not
  recorded and (2) which/how many constant
  characters -gt acquisition bias -gt over-estimation
  of branch lengths -gt bias in tree selection

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Correcting for Acquisition Bias

• Instead of previous, normal likelihood, compute
  the conditional likelihood that only variable
  characters are present

Mkv Model
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Mk v. Mkv

• Characters generated until 200 variable
  characters reached
• Mean SD of 1000 replicates

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Parsimony v. Mkv Brachonidae
Alomya outty
Alomya inny
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Parsimony v. Mkv An Example
W
Y
W
X
2
2
Y
W
3
7
2
2
2
4
6
5
1
1
2
1
Z
Y
Z
X
Z
X
Maximum Parsimony
Mkv
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Mkv Conclusions

• All characters are used
• Autapomorphic states are now informative
• Can reconstruct ancestral states
• Utilize likelihood ratio tests to test
  evolutionary hypotheses
• Adopt Bayesian methods for unequal tree weights
  P(TD)
• Combined-data phylogeny (morphology molecular)