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Multiple Substitution Matrices along a Phylogeny (Read 2321 times)

Miguel Lacerda

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Multiple Substitution Matrices along a Phylogeny
Oct 19^th, 2008 at 2:46pm

Hi Sergei,

Would you mind taking a look at the attached code please? I have set up a model with two rate matrices; the first is called SubsMatrixM1 and applies to branches leading to leaf nodes, whilst the other is called SubsMatrixM2 and applies to branches leading to ancestral nodes. In this code, I have two parameters which I am estimating, w0 and p0 which should be around 0.1 and 0.5 respectively when SubsMatrixM1 = SubsMatrixM2 (I simulated the attached data as such).

In the attached code, I have made SubsMatrixM1 and SubsMatrixM2 identical (or at least I think I have!!) which is the same as just having one substitution process along all branches. The problem is that setting up my models as:

Model M1 = (SubsMatrixM1, EFV, 1);
Model M2 = (SubsMatrixM2, EFV, 1);

gives me incorrect values for the parameters I am estimating, whereas:

Model M1 = (SubsMatrixM1, EFV, 1);
Model M2 = (SubsMatrixM1, EFV, 1);
/* both use SubsMatrixM1 */

OR:

Model M1 = (SubsMatrixM2, EFV, 1);
Model M2 = (SubsMatrixM2, EFV, 1);
/* both use SubsMatrixM2 */

give me the same and correct values for the parameters! How is this possible?

Thanks so much for your help!

Miguel

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Sergei

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Re: Multiple Substitution Matrices along a Phylogeny
Reply #1 - Oct 20^th, 2008 at 5:11pm

Dear Miguel,

Because you have two independent category variables in your models (omegaM1 and omegaM2), even when you constrain their hyper-parameters to be the same, the model will still be different from a single model scenario. This is because omegaM1 and omegaM2 will both be integrated out in the mixed model, hence you will have NINE (not 3) rate categories, with a 3x3 joint distribution. You want omegaM1 and omegaM2 to be perfectly correlated. For that, you need to define omegaM2 conditionally on omegaM1, as follows:

Code:

categFreqMatrixM2 = {{1,0,0}{0,1,0}{0,0,1}};
categRateMatrixM2 = {{w0, 1, w2}};

category omegaM2 = (3, categFreqMatrixM2, MEAN, omegaM1, categRateMatrixM2, 0, 1e25);

The frequency matrix is now a covariance matrix (i.e. the k-th row is the conditional distribution of omegaM2 given that omegaM1 has taken on it's k-th value) and the construction of omegaM2 now uses omegaM1 in place of its density argument to specify that omagaM2 conditionally depends on omegaM1.

Cheers,
Sergei

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Division of Infectious Diseases
Division of Biomedical Informatics
School of Medicine
University of California San Diego

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Miguel Lacerda YaBB Newbies Offline Feed your monkey! Posts: 36 Natl Univ of Ireland, Galway Gender:	Re: Multiple Substitution Matrices along a Phylogeny Reply #2 - Oct 21^st, 2008 at 1:49am Oh, that makes sense! Thanks a lot for your help, Miguel
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