Simpleminded molecular homology

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Simple-minded molecular homology
Evolutionary sense of the word
Two nucleotides in different DNA sequences are
homologous if and only if the two sequences
acquired that state directly from their common
ancestor
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Molecular homology

• Two proteins in two different organisms may be
  encoded by the same gene
• I.e., the genes are direct descendants of a gene
  in the MRCA. They are homologous.
• The two genes may share many aa in common and
  have similar function
• But, if functionality has been acquired
  independently, then functionality is not
  homologous

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Classes of molecular homology

• For many, still, similarity homology (read
  Reeck et al 1987). Isology?
• Most genes are evolutionarily related extant
  genomes were derived by duplication,
  modification, and recombination of a small number
  (one?) of original replicators
• Most genes are at some level homologous?
• Need to constrain the term to make it useful

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Different processes of divergence result in
different classes of homology

• Speciation the divergence of lineages of
  organisms
• Gene duplication the divergence of lineages of
  genes within an organismal lineage
• Horizontal gene transfer the divergence of
  lineages of genes by transfer across different
  organismal lineages

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Each of these processes is of interest to
molecular evolutionary biologists

• Each process results in genes that trace back to
  a single genealogical precursor
• But, all three processes are not studied
  simultaneously, so we need to make distinctions
  when only one of these processes is of interest
• Walter Fitch (1970) and Gray and Fitch (1983)
  proposed the following terms...

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Molecular homology

• Orthologous genes diverged as a result of a
  speciation event
• Paralogous genes diverged as a result of a gene
  duplication event
• Xenologous genes diverged as a result of lateral
  gene transfer

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Evolution of globin genes in vertebrates

• All genes can be traced back to common ancestor,
  so they are all homologous (at some level)
• Duplication event gave rise to the a- and b-
  hemoglobin gene families
• All tetrapods have both types of globin genes

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To reconstruct organismal phylogeny we need to
compare orthologous genes
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Concerted evolution

• Above arguments assume that duplicated genes will
  evolve independently following the duplication
  event
• But many duplicated genes will continue to
  interact
• Observation
• multiple copies of many repeated gene families
  are very similar within an individual and within
  a species
• But they were quite different among closely
  related species

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Concerted evolution

• If duplicated genes evolved independently, expect
  greater within species than between species
  divergence (among duplicated genes). Left bottom

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Concerted evolution

• Under concerted evolution, expect greater between
  species than within species divergence (among
  duplicated genes). Right bottom

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Six kinds of nucleotide substitution
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Substitutions in mt COII gene among bovids
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The need to correct observed sequence differences
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Possible substitutions among four nucleotides
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Rate 3a
K 2(3at)
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Temporal change in the probability of having a
certain nucleotide, say A, at a given nucleotide
site
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Using two parameters transitions and
transversions
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Temporal change in the probability of having a
certain nucleotide, say A, at a given nucleotide
site
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Jukes-Cantor one parameter model
Kimuras 2 parameter model
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Jukes-Cantor is a special case of Kimuras
model(they are nested models)
JC
K2P
When alfa beta these two are the same
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Felsenstein 1981s model

• Base composition may cause some substitutions to
  be more frequent than others
• If a sequence contains very few Gs, then we would
  not expect to see many changes involving that
  nucleotide
• This model allows the frequencies of the four
  nucleotides to be different
• Jukes Cantor is a special case of this model too,
  when all nucleotides have the same frequency

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Felsenstein 1981
pi is the frequency of the ith base averaged over
the sequences being compared
If pApCpGpT then F81 JC
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Hasegawa, Kishino, Yano 1985

• This model merges the K2P and F81 models
• Allows TS and TV to occur at different rates
• Allows base frequencies to vary
• JC, K2P, and F81 call be considered special cases
  of this model (they are nested)

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HKY85
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General time-reversible model
6 parameters in substitution matrix
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Any Model
Substitution probability matrix
Base composition vector
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More models
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Real DataObserved and expected changes

• Comparison of human and chimp mtDNA sequences
  (307/1333 sites are different)
• K2P assigns P0.22, Q0.011
• HKY85 assigns A0.37, T0.18, C0.40, G0.05
• Parameter-rich models more closely approximate
  the observed pattern

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How to choose a model

• More parameters, more realism, but
• Each time we add a parameter, we must estimate
  the value for the parameter using the data
• The more parameters we add, the greater
  uncertainty in our estimates (sampling error
  increases)
• Fewer parameters inaccurate estimates
• Many parameters low precision

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Likelihood

• Given observed data and an hypothesis, how can we
  decide if the hypothesis is an adequate
  explanation?
• Probability of observing the data given a
  particular model. LPr(DH)
• As we have seen, different models may make the
  observed data more or less probable

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Likelihood

• Distinguish between
• Pr (getting observed data)
• Pr (the underlying model being correct)
• Sobers example Loud noise and gremlins playing
  bowling.
• Likelihoods for different models can be compared
  if the models are nested (LRT 2x difference
  between log-L is Chi-square distributed)

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lnL-2064.8
lnL-2691.8
lnL-2424.8
lnL-2075.4
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Good question

• Why is the likelihood of the observed data not
  L1?
• Likelihood is the probablity of observing the
  data given the model (LPr (DH)
• If we could calculate this value for all possible
  data sets, the sum would be one
• Since we are only concerned with the Pr of one of
  those data sets (the observed data), then L lt1

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More Assumptions

• All nucleotide sites change independently
• The substitution rate is constant over time and
  in different lineages
• The base composition is at equilibrium
• The conditional probabilities of nucleotide
  substitutions are the same for all sites, and do
  not change over time
• Most of these are not true in many cases

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Independence
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Base composition
LogDet transformation recovers additive distances
between sequences even when base composition is
variable
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Rate variation among sites

• Equal rates among sites simplifies the math, but
  at a cost to biological realism
• Figure shows different rates of substitution in
  different parts of the genome of mammals

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Invariant sites (I)

• If some sites are constrained to vary by
  selection
• Sequences that evolve fast may show less
  divergence than sequences that are slower

A 0.5 rate, 20I B 2 rate, 50 I
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Gamma distribution
Allow more than just two categories (zero and
non-zero rates)
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How to chose a model? Modeltest
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How to choose parameters for your model?

• Alternative 1 estimate from data directly as
  each tree is being evaluated (time consuming)
• Alternative 2 find a reasonable tree and
  estimate parameters based on that tree (Modeltest
  will do this for you)
• Alternative 3 iterate on ML trees obtained with
  parameters estimated in step 2, until nothing
  changes