text: user10330: I am trying to calculate the substitution probabilities for amino acids (i.e. the probability of one amino acid given another). In theory, you should be able to derive them from a log-likelihood matrix (also called log-odds), such as Blosum62.
  Does anyone know how to calculate probabilities from log-likelihoods or have a good modern source for a substitution probability matrix?
  
  user2108: UPDATE2
  @chubs wants to compare different clades. This is possible within recent releases of ConSurf:
  
  It is additionally quite possible to use ConSurf's default outputs to get per-position conservation scores that can be used for post-processing in any fashion, as well as prefab scripts that can be used with PyMol to make custom visualization:
  
  For all cases, ConSurf creates the following outputs:
  
  The sequence and MSA colored by ConSurf conservation scores.
  
  A text file that summarizes for each position the normalized score calculated, the assigned grade (1-through-9), the reliability estimation (for the Bayesian method) and the amino acids/nucleotides observed in the respective MSA column.
  
  The sequences selected for the MSA and the MSA constructed (unless those files were uploaded by the user).
  
  A file with the frequency of each amino acid/nucleotide observed in each column of the MSA.
  
  The evolutionary tree, which was calculated by the server or uploaded by the user, together with the MSA are shown using the WASABI platform (Veidenberg et al., 2015).  Moreover, using WASABI, a user can select a subtree containing a fraction of the homologous sequences and conduct a follow-up ConSurf analysis with these selected sequences. To refine a ConSurf analysis to a selected subtree, a user can choose any internal node on the phylogenetic tree and open a WASABI menu by using a right mouse click. Selecting the option 'run ConSurf on subtree' will issue a new window with the new ConSurf run for the selected subtree sequences (see example in Figure 3).
  
  
  
  UPDATE
  It seems that what @chubs really wants to do is map protein conservation onto a structure. There are various tools for doing this (here, here). ConSurf is the older and more established tool, using evolutionary conservation to rule out trivial apparent associations due to phylogenetic non-independence.
  here is the  somewhat related 3DPatch workflow, which uses profile HMM information as a measure of conservation:
  
  Here is the output that they get:
  
  Likewise ConSurf gets similar looking outputs:
  
  ORIGINAL ANSWER
  I think that more information is needed here to answer this question properly (what is your data? what is your ultimate goal? what are the things you've already tried?), but we can say a few things right away.
  I would strongly suggest looking into substitution models, which are literally substitution probability matrices. Note that these are probabilities per unit time, which is to say that they are calibrated to e.g. evolutionary rates along a specific phylogenetic tree. I would therefore strongly suggest incorporating a phylogenetic model of some kind.
  If you have e.g. a multiple sequence alignment, you can estimate a phylogenetic tree by one of the many tree estimation methods, which will give you a substitution probability matrix "for free" as this estimation is taken care of in the process of tree estimation. These will again be substitution probabilities per unit time; you will honestly not be able to get rid of the time-dependence here, as that's how evolution works.
  I am a little behind the times, but some tools you might look into for tree estimation are PhyML and FastTree. If you only have sequences and haven't aligned them yet, you can use a tool like MUSCLE, ClustalO, or MAFFT.
  BLOSUM and related models are derived from specific slices of protein sequence identity (evolutionary history) calibrated to certain scopes, it's unlikely that they are appropriate to your case, unless your data fits inside those rather narrow slices.
  
original_text: 10330: <p>I am trying to calculate the substitution probabilities for amino acids (i.e. the probability of one amino acid given another). In theory, you should be able to derive them from a log-likelihood matrix (also called log-odds), such as Blosum62.</p>
  <p>Does anyone know how to calculate probabilities from log-likelihoods or have a good modern source for a substitution probability matrix?</p>
   2108: <p><strong>UPDATE2</strong></p>
  <p>@chubs wants to compare different clades. This is possible within recent releases of ConSurf:</p>
  <p><a href="https://i.stack.imgur.com/xyu0W.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/xyu0W.png" alt="consurf table 1" /></a></p>
  <p>It is additionally quite possible to use ConSurf's <a href="https://consurf.tau.ac.il/overview.php#_Toc311131301" rel="nofollow noreferrer">default outputs</a> to get per-position conservation scores that can be used for post-processing in any fashion, as well as prefab scripts that can be used with PyMol to make custom visualization:</p>
  <blockquote>
  <p>For all cases, ConSurf creates the following outputs:</p>
  <ol>
  <li><p>The sequence and MSA colored by ConSurf conservation scores.</p>
  </li>
  <li><p>A text file that summarizes for each position the normalized score calculated, the assigned grade (1-through-9), the reliability estimation (for the Bayesian method) and the amino acids/nucleotides observed in the respective MSA column.</p>
  </li>
  <li><p>The sequences selected for the MSA and the MSA constructed (unless those files were uploaded by the user).</p>
  </li>
  <li><p>A file with the frequency of each amino acid/nucleotide observed in each column of the MSA.</p>
  </li>
  <li><p>The evolutionary tree, which was calculated by the server or uploaded by the user, together with the MSA are shown using the WASABI platform (Veidenberg et al., 2015).  Moreover, using WASABI, a user can select a subtree containing a fraction of the homologous sequences and conduct a follow-up ConSurf analysis with these selected sequences. To refine a ConSurf analysis to a selected subtree, a user can choose any internal node on the phylogenetic tree and open a WASABI menu by using a right mouse click. Selecting the option 'run ConSurf on subtree' will issue a new window with the new ConSurf run for the selected subtree sequences (see example in Figure 3).</p>
  </li>
  </ol>
  </blockquote>
  <p><strong>UPDATE</strong></p>
  <p>It seems that what @chubs really wants to do is map protein conservation onto a structure. There are various tools for doing this (<a href="https://academic.oup.com/bioinformatics/article/35/2/332/5040318" rel="nofollow noreferrer">here</a>, <a href="https://academic.oup.com/nar/article/44/W1/W344/2499373" rel="nofollow noreferrer">here</a>). ConSurf is the older and more established tool, using evolutionary conservation to rule out trivial apparent associations due to phylogenetic non-independence.</p>
  <p>here is the  somewhat related 3DPatch workflow, which uses profile HMM information as a measure of conservation:</p>
  <p><a href="https://i.stack.imgur.com/fDWGY.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/fDWGY.png" alt="3Dpatch workflow" /></a></p>
  <p>Here is the output that they get:</p>
  <p><a href="https://i.stack.imgur.com/eAUSL.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/eAUSL.png" alt="3dpatch figure" /></a></p>
  <p>Likewise ConSurf gets similar looking outputs:</p>
  <p><a href="https://i.stack.imgur.com/EyfY6.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EyfY6.png" alt="consurf figure" /></a></p>
  <p><strong>ORIGINAL ANSWER</strong></p>
  <p>I think that more information is needed here to answer this question properly (what is your data? what is your ultimate goal? what are the things you've already tried?), but we can say a few things right away.</p>
  <p>I would strongly suggest looking into <a href="https://en.wikipedia.org/wiki/Substitution_model#The_mathematics_of_substitution_models" rel="nofollow noreferrer">substitution models</a>, which are literally substitution probability matrices. Note that these are probabilities <em>per unit time</em>, which is to say that they are calibrated to e.g. evolutionary rates along a specific phylogenetic tree. I would therefore strongly suggest incorporating a phylogenetic model of some kind.</p>
  <p>If you have e.g. a multiple sequence alignment, you can estimate a phylogenetic tree by one of the many tree estimation methods, which will give you a substitution probability matrix &quot;for free&quot; as this estimation is taken care of in the process of tree estimation. These will again be substitution probabilities per unit time; you will honestly not be able to get rid of the time-dependence here, as that's how evolution works.</p>
  <p>I am a little behind the times, but some tools you might look into for tree estimation are <a href="http://www.atgc-montpellier.fr/phyml/" rel="nofollow noreferrer">PhyML</a> and <a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0009490" rel="nofollow noreferrer">FastTree</a>. If you only have sequences and haven't aligned them yet, you can use a tool like MUSCLE, ClustalO, or MAFFT.</p>
  <p>BLOSUM and related models are derived from specific slices of protein sequence identity (evolutionary history) calibrated to certain scopes, it's unlikely that they are appropriate to your case, unless your data fits inside those rather narrow slices.</p>
  