Cladistic methods

Parsimony

Parsimony allows the use of all known evolutionary information in tree building

(In contrast, distance methods compress all of the individual differences between pairs of sequences into a single number)

The most parsimonious tree is the one that requires the fewest evolutionary changes for all sequences to derive from a common ancestor.

This is easiest to explain by example:

Consider four sequences: ATCG, TTCG, ATCC, and TCCG.

• Imagine a tree that branches once at the first position, thus grouping ATCG and ATCC on one branch, and TTCG and TCCG on the other branch.
  
  
• Then each branch sub-divides into two sub-branches for a total of 3 nodes in the tree (Fig. 1).
  
  
• Counting backward from the bottom, each sequence is separated from the root by two nodes, so the sum of the changes is equal to 8.
  
  
• This is a more parsimonious tree than one that first divides ATCC on its own branch, then splits off ATCG, and finally divides TTCG from TCCG (Fig.2).
  
  
• This tree also has three nodes, but when all of the distances back to the root are summed, the total is equal to 9.

         Fig. 1	                  Fig. 2

B. Maximum Likelihood

Certainly, for this given model of evolution, no other method will perform as well nor provide you with as much information about the tree.

Unfortunately, this is computationally difficult to do and hence, the model of evolution must be a simple one. Even with simple models of evolutionary change the computational task is enormous and this is thus the slowest of all methods.

• Let all sites be selectively neutral and let them spontaneously mutate at a constant rate per gamete per generation.
  
  
• Let the mutation rates to and from each nucleotide be equal.
  
  
• Generations are assumed to be discrete and the evolution of each site is assumed to be independent of all other sites.

(This may seem like a lot of assumptions but in reality most other methods will not work very well without them either).

Given a particular tree, each branch point (node) is calculated individually for each base in the sequence, starting at the top and working down to the root.

First, calculate the most probable ancestor for each neighboring pair of sequences joined by a branch of the tree.

Then the sequences at these nodes are used to calculate the most probable ancestral sequences at the next higher level of branch points, and this is continued until an single most probable ancestral sequence is computed at the "root" of the tree.