Parsimony

One intuitive score for a phylogenetic tree is the number of changes along edges. The approach of minimizing this score is called parsimony. The logic is the basic philosophy of Okham's razor - finding the simplest explanation that works. Let us mark the vertices of a tree by V(T), and its edges by E(T). Denote the value of the jth character of vertex $v \in V(T)$ by v_j.  

That is - the total number of times the value of some character changes along some edge.

Example 9.2   Figure 9.1 shows an optimal parsimony phylogeny for 5 species with a single character. The parsimony score of this tree is 1 - with the change being either from T to C or vice-versa. Note that this tree can be unrooted, yielding the tree in figure 9.2. The unrooted tree has the same parsimony score as the rooted one. In fact, no matter how we choose to root it, the score will remain the same. Figure 9.3 illustrates a more complex parsimony tree, in which the species have 6 characters each.

  

Figure 9.1: A most parsimonious 5-species phylogeny for a single DNA site. The bars mark the two possible edges along which there can be a mutation.

  

Figure 9.2: The unrooted counterpart of the phylogeny in figure 9.1. Notice that there is now no ambiguity about the placement of the mutation.

  

Figure 9.3: A most parsimonious 5-species phylogeny for 6 characters, reconstructed from the data in table 9.1. The numbers by the mutation bars indicate the changed character.

 

Table 9.1: 6 DNA site values for 5 species. This data was used to infer the phylogeny in figure 9.3.

	1	2	3	4	5	6
Aardvark	C	A	G	G	T	A
Bison	C	A	G	A	C	A
Chimp	C	G	G	G	T	A
Dog	T	G	C	A	C	T
Elephant	T	G	C	G	T	A

 

There are two levels of problems in parsimony, duly named small parsimony and large parsimony.