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Parsimony method  
Parsimony is the simplest method for ancestral sequence
reconstruction. It is based on the following principle: the
ancestral sequences (posed in nodes of a phylogenetic tree)
should be such that the minimal required number of character
replacements on the branches of the tree is less than for any
other choice of sequences. Example 1. Suppose we have the following tree and a position which contains the following letters in the contemporary sequences:
In this case the minimal number of replacements is two and there is only one way to reconstruct the letters in all three ancestral nodes so that this minimal number would be realised:
Example 2:
In this case the minimal number of replacements is also 2, but there are several ways of character reconstruction:
Notice that the node 2 is considered to contain the character A by all variants. Thus, the result of parsimonious reconstruction is following:
Algorithm The following is done independently for every alignment position.
This algorithm consists of three parts.
Second, we define a preliminary character for every node. The preliminary character is *, if the set of the node contains more than 1 element; otherwise the preliminary character is the only element of the set. Third, we define an output character for every node. If the preliminary character of the node is some letter (not the asterisk *), then its output character is also this letter. If the preliminary character of the node is *, but the output character of its immediate ancestor is some letter (say, X), and its set of possible characters contains X, then the output character of the node is also X. If the preliminary character of the node is X, but the above conditions are not satisfied, then the output character is *. According to this rule, the output characters could be determined recursively, from the root to leaves.
Additionally, the program prints the output characters in two possible manners: in uppercase (that means very probable reconstruction) if the output characters off all immediate ancestors of the node coincide with this letter; or in lowercase (less probable reconstruction) if there are asterisks among the preliminary characters of the immediate characters. Note that these preliminary asterisks can be replaced (on the third stage of algorithm), but the character remains small. 

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