Interpretation. Because the primary goal of Hy-Phy is to provide flexible modeling of the nucleotide substitution process, Hy-Phy includes a more general parameterization scheme than most phylogeny estiamtion programs. Perhaps the most important difference for the user to recognize is the difference between local and global parameters. A local parameter is one that is specific for a single branch on a tree. In contrast, a global parameter is shared by all branches. To illustrate, consider the output generated by the batch file localglobal.bf when run using (demo.seq): Original HKY85 Analysis Log Likelihood = -579.03975528721; Tree myTree=((a{a=0.106343,b=0.024239},b{a=0.000000,b=0.007742}) Node1{a=0.118759,b=0.041943},c{a=0.085374,b=0.022151}, og{a=0.246895,b=0.050413}); Local HKY85 Analysis Log Likelihood = -579.039980005965; Tree myTree=((a{R=4.350942,b=0.024447},b{R=0.000000,b=0.007724}) Node1{R=2.835357,b=0.041878},c{R=3.828977,b=0.022304}, og{R=4.876743,b=0.050627}); Global HKY85 Analysis Log Likelihood = -579.621469358837; Shared Parameters: V=3.772178 Tree myTree=((a{b=0.024878},b{b=0.004718}) Node1{b=0.035926},c{b=0.020933}, og{b=0.060754}); In localglobal.bf we have moved beyond the default settings of Hy-Phy, and the details of the batch file will be discussed below. For now, concentrate on the results. localglobal.bf performs three analyses of the data in demo.seq, all using the HKY85 model of sequence evolution. The first, labeled ``Original HKY85 Analysis'', is the same analysis that was performed in the previous example (models.bf). Note that the output format is different. Rather than report the branch lengths for each branch in the tree, the individual parameter estimates are shown. Note that each branch has an associated value of a and b. These parameters control the relative frequencies of transitions and transversions in the HKY85 model. This output reveals that the original analysis was an example of a local analysis. In the context of this batch file, there was a local value of the transition-transversion ratio for each branch in the tree. The second analysis in localglobal.bf repeats the original analysis, but uses a different formulation of the HKY85 model (see below). Note that the likelihood values differ only slightly between the ``Original HKY85 Analysis'' and the ``Local HKY Analysis''. The differences are the results of approximation error in the numerical optimization process. The parameter lists for the two analyses are also different. Except for approximation error, the values of b in the two analyses are the same. On inspection, one notices that the values of a in the first analysis are equal to the products of b and R in the second analysis. The second analysis is simply a reparametrization of the first one, making explicit use of the transition-transversion ratio, R. The third analysis performed in localglobal.bf is an example of a global analysis. In contrast to the previous two analyses (which you should now understand were really replicates of a single analysis), the ``Global HKY85 Analysis'' invokes a global transition-transversion ratio, V. In other words, all branches share the same value of V. This fact is evident in the output for the ``Global HKY85 Analysis''. Note that the tree list contains only values of b for each branch. The estimated global value of V is shown under the heading of Shared Parameters. The local and global analyses use different numbers of parameters. The local analysis uses a transition and transversion rate for each of the 5 branches, along with 3 base frequencies, for a total of 13 parameters. The global analysis includes a transversion rate for each branch, 3 base frequencies, and a single transition-transversion rate, for a total of 9 parameters. The global analysis is a special case of the local analysis; therefore, the log-likelihood value for the global analysis (-579.62) is lower than that of the local anaysis (-579.03). The fact that the addition of 4 parameters results in such a small difference in model fit suggests that the data harbor little support for the hypothesis that the transition-transversion rate varies among these lineages.
Sergei L. Kosakovsky Pond and Spencer V. Muse, 1997-2002