NAME

       pbsScoreMatrix - Generate log-odds score matrices for use in alignment of

DESCRIPTION

       Generate  log-odds  score matrices for use in alignment of probabilistic biological sequences (PBSs).  By
       default, generates a matrix for every branch of the tree (as defined in tree.mod), but can also  generate
       a  matrix  for  a  given  branch  length (see --branch-length).  For a code size of N, an N x N matrix is
       generated by default; --half-pbs will produce an N x 4 matrix, and --no-pbs will produce a 4 x  4  matrix
       (assuming a four-character nucleotide alphabet).

       Two  sequences  are assumed to have evolved from a common ancestor by a reversible continuous-time Markov
       substitution process, and to be separated by a branch of length t.  The conditional probability of a base
       j in one sequence given a base i in the other, P(j | i, t) is given by element (i, j) of the matrix

              P(t) = exp(Qt)

       where  Q  is  the  rate  matrix  defining  the  substitution  process,  and  element  (i,  j) of Q is the
       instantaneous rate at which base i changes to base j.

       Let S_t(i, j) be a log odds score for the alignment of two bases, i and j, based on P(t):

              S_t(i, j) = log P(i, j | t) / (pi(i) * pi(j))

              = log P(j | i, t) pi(i) / (pi(i) * pi(j))

              = log P(j | i, t) / pi(j)                         (1)

       where pi(x) is the "equilibrium" or "background" probability of base x.  Because of  reversibility,  S(i,
       j)  =  S(j,  i),  and the S(i, j) form a symmetric 4 x 4 matrix.  This is the matrix that is generated by
       pbsScoreMatrix with the --no-pbs option.  If each "letter" in  each  sequence  represents  a  probability
       distribution over bases, as in a PBS, then the score for two letters k and l can be shown to be

              S'_t(k, l) = log sum_i sum_j p_k(i) p_l(j) exp S_t(i, j) (2)

       where  the  two  sums are over the four bases, p_k(i) is the probability of base i under the distribution
       for k, and p_l(j) is the probability of base j under the distribution for l.

       Notice that (2) reduces to (1) when p_k(i) = p_l(j) = 1 for some i and j and for  all  other  i'  and  j'
       p_k(i')  =  p_l(j') = 0 (i.e., when all of the probability mass is on a single base in both distributions
       and the PBS reduces to an ordinary nucleotide sequence).  The special case of p_l(j) = 1 only is also  of
       interest when aligning a PBS and a nucleotide sequence:

              S''_t(k, j) = log sum_i p_k(i) exp S_t(i, j) (3)

       This is the matrix generated by pbsScoreMatrix with the --half-pbs option.  Note: all logs are base 2.

EXAMPLE

       Generate  an  N x N matrix for every branch of the tree, using a code file "code" (generated by pbsTrain)
       and a tree model file "mytree.mod" (generated by phyloFit):

              pbsScoreMatrix mytree.mod code > matrices.dat

       Generate an N x N matrix for a branch length of 0.2 expected substitutions per site.

              pbsScoreMatrix --branch-length 0.2 mytree.mod code > matrix.dat

       Generate an N x 4 matrix:

              pbsScoreMatrix --branch-length 0.2 --half-pbs mytree.mod code > matrix.dat

       Generate a 4 x 4 matrix:

              pbsScoreMatrix --branch-length 0.2 --no-pbs code mytree.mod > matrix.dat

       (In this case, a code file is not needed.)

OPTIONS

       --branch-length, -t <length>

              Output a matrix for a branch of the specified length, rather than a matrix for every branch of the
              tree.  The given length must be non-negative and in units of expected substitutions per site.

       --half-pbs, -H

              Output an N x 4 matrix, as described above.

       --no-pbs, -N Output a 4 x 4 matrix, as described above.  With this option, a code file is not needed.

       --help, -h

              Show this help message.