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The +I+G Models

The +I+G Models. …an aside. Modelling Rate Variation. Not every site in a sequence evolves at the same rate. Assign sites to rate categories. Gamma distribution (+G model) 1 Rate categories come from a discrete approximation of the Gamma probability distribution

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The +I+G Models

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  1. The +I+G Models …an aside

  2. Modelling Rate Variation Not every site in a sequence evolves at the same rate

  3. Assign sites to rate categories Gamma distribution (+G model) 1 • Rate categories come from a discrete approximation of the Gamma probability distribution Invariant sites (+I model) 2 • Rates are either “No Change” or “Some Change” 1: Yang (1993) 2: Hasegawa, Kishinoand Yano (1987)

  4. Using both +I and +G Done by Guet al. in 1995 • Estimate a proportion, p0 , of invariable sites • Fit the remaining sites to a gamma distribution

  5. Criticism “This model is somewhat pathological as the gamma distribution with α ≤ 1 already allows for sites with very low rates; […] adding a proportion of invariable sites creates a strong correlation between p0 and α, making it impossible to estimate both parameters reliably” Ziheng Yang, Computational Molecular Evolution (2006)

  6. Identifiability Sullivan et al. (1999)

  7. Theoretical Justification PROOF! (2001)

  8. Theoretical Justification DISPROOF! (2001) (2008)

  9. Theoretical Justification PROOF! (again) (2001) (2011)

  10. Theoretical Justification PROOF! (again) (2001) (2011) • +I+G is proved to work under a continuous Gamma distribution • All implementations use discrete approximations to the Gamma • It is not clear if +I+G is identifiable under the approximation

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