User:R. Eric Collins/MBL/Codon

Bielawski

Codon models

• "a model is an INTENTIONAL simplification..." Daniel L. Hartl

1. parameter estimation
2. hypothesis testing
3. site identification

• t is mean # of substitutions per CODON site
  • t=3 indicates saturation

• assumptions/simplifications about molecular evolution:
  • codon frequencies unbiased (1/61 usage)
  • all point mutations equally likely (transition/transition bias)
  • single/multiple mutations at one point

• models
  • Nei and Gojobori 1986 should be avoided at all cost
  • others should be used with caution BASED ON KNOWING YOUR DATA
  • Goldman-Yang (GY)
  • proportional to target codon
  • Muse-Gaut (MG)
    • proportional to target nucleotide
    • no effect of context: (mammals yes, drosophila no...)

• likelihood
  • of the data at a site: sum over each codon: product of equilibrium frequency, likelihood of transition from each codon to observed codons
  • of entire alignment: product of likelihoods at each site
  • in some examples: If we average over the tree, we do NOT detect positive selection;

• Problem: averaging over a pair has very low power if the questions are about “when” or “where”!
  • Solution: Phylogenetic estimation of selection pressure
    • variable ω over branches (when?)
    • variable ω over sites (where?)
    • variable ω over branches and sites (when and where?)

• branch models (time)
  • episodic large-scale changes
  • site-wise: if have hundreds of sequences, can use this

• • M1a + M2a (plus LRT) is very robust
    • best model FOR WHAT? 'best' model overall may not be the best for my purposes
    • M1a doesn't allow positive selection
    • M2a does allow for positive selection
    • so LRT between them can demonstrate positive selection
    • for most well-behaved datasets, empirical codon bias (pi) can be used
    • M2a is not best explanation but has better LRT properties because more robust to changes in assumptions

• • M7 + M8
    • M7 uses beta distribution (0..1) that explains 'boring' stuff
    • M8 uses beta distribution (0..1) plus omega (>1) to account for positive selection
    • M8 is 'best' model but is more sensitive to changes in assumptions

• • chi-squared & boundary problem
    • the LRT does not follow the χ2 distribution
    • no other mixture distribution works well
    • too costly to do parametric bootstrapping/simulations for each LRT
    • so using chi-square anyway (naively), how bad could it be?
    • even still, the LRT is conservative AND powerful
    • there's a window of sequence divergence where these will work, outside of those (short branches/very long branches) it may not

• examples
  • need to know data, but how many possible types of "data" are there?
    • how many ways are there for a protein family to evolve?
  • GFP
    • color variation, purifying selection due to antagonistic host interactions
  • proteorhodopsin
  • Listeria
    • looking at variations in omega along the tree, isolating groups/clusters of genes/networks under selection

average of tree average of sites variation in sites and tree