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Understanding the I+G Models: Rate Variation in Site Evolution

The I+G models explore how not every site in a sequence evolves at the same rate. Using a discrete approximation of the Gamma probability distribution, sites are categorized into rate classifications. The Invariant sites (I model) determine whether rates indicate "No Change" or "Some Change", with methods proposed by Yang (1993) and Hasegawa et al. (1987). While the models estimate a proportion of invariable sites and fit the remaining sites to a Gamma distribution, criticism arises from the correlation between parameters, raising identifiability questions under discrete approximations.

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Understanding the I+G Models: Rate Variation in Site Evolution

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Presentation Transcript

  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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