MO640 - Exercises - SCJ Distances and Medians, Feijao and Meidanis 2011

Exercises marked with (*) require further reading/search beyond the suggested texts.

1. Solve the small phylogeny problem under SCJ for the genomes and topology below.

five genomes phylogeny

Answer:

First, write down each genome as an adjacency set, and create a color code for each adjacency used:

genomes as adjacency sets; color code for adjacencies

Adjacencies XhZt and ZhYt have the same pattern in all genomes. Therefore, Fitch's algorithm will run on the same data for both adjacencies. Below is the result of this algorithm on these data:

Fitch's algorithm on XhZt and ZhYt

Fitch's algorithm for adjacency for YhXt:

Fitch's algorithm on YhXt

Fitch's algorithm for adjacency for XhYt:

Fitch's algorithm on XhYt

Fitch's algorithm for adjacency for ZhZt:

Fitch's algorithm on ZhZt

Final result (a most parsimonious SCJ tree) with all ancestors.

a most parsimonious SCJ tree

Computation of SCJ total branch length (TBL) in the most parsimonious tree. For each node except the root, the distance to its parent is computed, and all these distances are summed up. Notice that in our tree all internal nodes ended up with the same ancestral genome, so the distance to parent is zero for the internal nodes. Below one can find this computation for the leaves. The TBL is 7.

computation of total branch length


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© 2015 Joao Meidanis