Relative rate clarification

[Tim McInerney]

Hi all,

I'm just seeking a clarification on how relative rates are calculated? More specifically, what are relative to?

For example, in my output I get this:

Category  Relative_rate  Proportion

  0         0              0.7933

  1         0.6464         0.05166

  2         2.282          0.05166

  3         4.825          0.05166

  4         11.6           0.05166

Relative rates are computed as MEAN of the portion of the Gamma distribution falling in the category.

I understand that the relative rate of category 4 is calculated as the mean relative rate of all sites that fall in that category, but I do not understand what it is relative to.

Sorry if this is an obvious question, but I haven't been able to find an answer.

Thank you in advance,

Tim

[Bui Quang Minh]

Dear Tim, 

this is a good question. The “relative” means that the Gamma rates are rescaled such that the weighted sum of rates is 1 (see below), so that the branch lengths of the tree are interpreted as the number of substitutions per site. More specifically, the +I+G4 model effectively means that one has five rate categories:

Category  Rate   Proportion

   0             0            p_inv

   1             r_1         (1-p_inv)/4

   2             r_2         (1-p_inv)/4

   3             r_3         (1-p_inv)/4

   4             r_4         (1-p_inv)/4

where p_inv is the proportion of invariable sites. The rates r_i are first inferred from the Gamma distribution, and then rescaled s.t. the following weighted sum is 1:

sum_i (r_i * (1-p_inv)/4) = 1

Does this answer your question?

Minh

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Bui Quang Minh

Center for Integrative Bioinformatics Vienna (CIBIV)

Campus Vienna Biocenter 5, VBC5, Ebene 1

A-1030 Vienna, Austria

Phone: ++43 1 4277 74326

Email: minh.bui (AT) univie.ac.at