With one partition, the process will build a rate matrix for the observed data such as this:

===

Number of site patterns: 470

SUBSTITUTION PROCESS --------------------

Model of substitution: GTR+I+G4+F

Rate parameter R:

A-C: 5.3776

A-G: 8.6588

A-T: 2.4670

C-G: 0.2153

C-T: 19.8536

G-T: 1.0000

State frequencies: (empirical counts from alignment) pi(A) = 0.2702 pi(C) = 0.2855 pi(G) = 0.1658 pi(T) = 0.2785

Rate matrix Q:

A -0.6971 0.2926 0.2735 0.1309

C 0.2769 -1.338 0.006801 1.054

G 0.4458 0.01172 -0.5106 0.05308

T 0.127 1.08 0.03159 -1.239

====

With 3 partitions, one for each codon position in a protein-coding gene, for example, there will be 3 different rate matrices, such as:

=== Codon site 1 ===

Number of site patterns: 104

SUBSTITUTION PROCESS --------------------

Model of substitution: GTR+I+G4+F

Rate parameter R:

A-C: 1.6947

A-G: 3.4995

A-T: 0.8215

C-G: 0.3912

C-T: 7.4781

G-T: 1.0000

State frequencies: (empirical counts from alignment) pi(A) = 0.2624 pi(C) = 0.2205 pi(G) = 0.2887 pi(T) = 0.2284

Rate matrix Q:

A -0.8931 0.2123 0.5741 0.1066

C. 0.2527 -1.288. 0.06418 0.9707

G 0.5218 0.04902 -0.7007 0.1298

T 0.1225 0.937. 0.1641 -1.224

====

===== Codon site 2 ===

Number of site patterns: 32

SUBSTITUTION PROCESS --------------------

Model of substitution: GTR+I+G4+F

Rate parameter R:

A-C: 16.7755

A-G: 14.2403

A-T: 6.0705

C-G: 18.9927

C-T: 31.6964

G-T: 1.0000

State frequencies: (empirical counts from alignment) pi(A) = 0.1825 pi(C) = 0.2629 pi(G) = 0.151 pi(T) = 0.4035

Rate matrix Q:

A -0.7738 0.3787 0.1847 0.2104

C 0.263 -1.608 0.2463 1.098

G 0.2232 0.4288 -0.6867 0.03465

T 0.09516 0.7156 0.01297 -0.8237

====

===== Codon site 3 ===

Number of site patterns: 386

SUBSTITUTION PROCESS --------------------

Model of substitution: GTR+I+G4+F

Rate parameter R:

A-C: 0.0001

A-G: 26.0200

A-T: 0.2049

C-G: 0.0001

C-T: 9.7400

G-T: 1.0000

State frequencies: (empirical counts from alignment) pi(A) = 0.3656 pi(C) = 0.3733 pi(G) = 0.05754 pi(T) = 0.2036

Rate matrix Q:

A -0.5853 1.42e-05 0.5694 0.01587

C 1.39e-05 -0.7543 2.188e-06 0.7543

G 3.618 1.42e-05 -3.695 0.07745

T 0.02849 1.383 0.02188 -1.433

====

You can see for example that codon position 3 is very poor in G (5%) while positions 1 and 2 have 29% and 15% respectively, and that C-G mutations are rare in codon position 3 vs very common in codon position 2.

These things have a larger impact on branch lengths than tree topology, but in the end the changes in branch lengths can affect the topology as well.

My example data was Vertebrate mitochondrial COI gene including fish, chicken, alligator, whale, primate and bovine. This is a very bad data set because the gene is small and the distances are far too great for accurate phylogenetic reconstruction with so little data. I only used it here to illustrate how differently the 3 partitions are observed to evolve.

Thank you Brian!

Partition affected the substitution probability which made the difference.

Then, if the substitution parameter is constant (e.g. Juke-Cantor), the branch length and the tree topology must be exactly the same?

Did I understand it correctly?

Yes, under the Jukes-Cantor model it is assumed that base frequencies are equal at 25% each and that all base substitutions are equally probable, so there is no point in partitioning the data if you will use that model on all partitions.

One of the interesting thing to learn about phylogenetic analyses, is that even if the models and methods do not exactly fit the true evolution of the sequences, mainly because they can't take selection pressures into account, the results can still tell us a lot about the history. For example we can often "see" different selection pressures on different codons in the gene (amino acids in the protein). Or we can observe that the transition:transversion rate ratio is different in one genus of bacteria than in another.

Quite often researchers get so interested in "the tree" that they forget to look at other aspects of the data.

Brian

Thank you for the reply!!!

I have another question!

I am studying evolution of Cerambyicds, the longhorned beetles.

I used some famous genes like COI, CAD, Wng, 18s, 28s and others.

When aligning rRNA sequences (e.g. 16s, 18s, 28s...),

I found that the sequences are

divided into Ultraconserved and Ultravariable regions.

for example,

UC / UV / UC / UV ...

aatttatcccc/tatcctct - -/aattaaccc/tctatcc.....

aatttatcccc/at- caat - -/aattaaccc/atatcct.....

aatttatcccc/cact-caat/aattaaccc/tt- aagt.....

Generally we have partitioned sequence by genes and codon positions.

If this be the case, I think I need some different approaches.

How can I deal with this data?

I know this won't make a dramatic change, but just curious:-)

In my experience, many regions that are difficult to align end up having more noise than signal for phylogenetic purposes. Leaving them in the alignment for analysis, or removing them altogether changes branch lengths but not topology. Building a tree with just the difficult regions alone is usually just a mess. Giving them a different partition, with different weighting for the mutation matrix will not make as much difference as removing them entirely.

It can be interesting and informative to see what the observed mutation matrix is for those regions (based on a tree made from all data) compared to the matrix for other regions. For example what is the tranistion:transversion ratio in rRNA genes, protein-coding genes, variable regions, conserved regions? Interesting from the aspect of molecular biology, not interesting in terms of beetle populations etc...