Provided that the phylogenetic relationships among OTUs are already resolved, my question is what methods are available to optimise with high efficiency the branches lenghts. The observed data would be a protein or DNA sequence alignment.
Thanks in advance.
I guess your best option is to browse Jo felsenstein's webpage: http://evolution.genetics.washington.edu/phylip/software.html
It depends on what you are interested in, but for the estimation of branch lengths you need a proper program for phylogenetic tree inference and a set of aligned sequences. Branch lengths are proportional to the number of mutations incorporated in each of the sequences and these are calculated (with or without correction) from a multiple sequence alignment. A good programs for sequence alignment is ClustalX, which also calculates distances, percentage identities and simple trees, and for the creation of a phylogenetic tree PhyML, MrBayes and BEAST. If you want some basic information I suggest that you brows my 18-year old web site on protein evolution . If you want to know more about the subject I recommend browse the book “The Phylogenetic Handbook”, Lemey, Salemi and Vandamme, eds, Cambridge press. In the case you would need some help with a dataset you may always contact me at [email protected]
Most phylogenetic reconstruction programs allow you to fix the topology in order to optimise the other parameters (branch lengths & model parameters; these other parameters can also be fixed). Maximum likelihood is probably your best choice. If you want speed I would recommend RAxML. I also like Phyml.
Before running RAxML / Phyml you may want to determine first which is the best-fit model of evolution. For this, I recommend ModelTest. If you are going to skip this computationally demanding step, I would recommend you to just choose the model GTR+G.
In addition to the ML programs RAxML and PhyML, there is IQ-Tree (Nguyen et al., MBE, 2015, http://dx.doi.org/10.1093/molbev/msu300). It implements all common models ranging from DNA and protein to codon models, but also several recently published complex models. Furthermore, it allows to do modeltesting to figure out the best-fit model for your data within the program, hence, not requiring additional software. IQ-Tree also offers a web-interface at http://iqtree.cibiv.univie.ac.at/ which allows to perform all these analyses (modeltest and tree-reconstruction or branch length estimation for a given tree topology online.
A comment to Federico's comment about modelest - the modeltest is very efficiently implemented in IQ-Tree and is, hence, typically running much faster in there compared to the modeltest software.
Thanks for your answers guys. Your suggestions have been both interesting and appropriate. However, my interest was mainly in the detailed methods to estimate branches lengths with fixed phylogenies from the mathematical perspective because I once read (I can't remember where) that branches lengths can be optimized by the Newton's method (which makes sense since the likelihood function is continuous and differentiable). However I didn't want to deal with that by myself and though that maybe there are other analythic methods around beyond the Maximum-Likelihood or Bayesian phylogenetic estimation with constraints.
I know, I should have explained that since the beginning. :)
Yes that's right, but you don't have a phylogeny. That's your problem.
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