Cladogram construction Thanks to Leandro Gaetano

Construction Methods requiring a priori polarization of the characters: Hennig argumentation Wagner Tree Methods that do not require a priori polarization of the characters: Exacts Heuristics

Hennig argumentation Character based

Most parsimonious solution: one homoplasy (-10) Two homoplasies (-2 and 3)

Construction (Kluge y Farris, 1969; Farris, 1970) Analyse one taxon each time following a determined order (= sequence addition = stepwise addition) Taxon are added in a position that minimize number of steps of the three Wagner Tree Taxon based

Example, Wagner Tree For this method we need a previous polarization In relation to the outgroup 1. Taxon C is united to the outgroup Addition order will be in a growing order of apomorphies Construction

Wagner tree 2. Add next taxon (B) (the one following in less steps differences) in the only possible place and establish hypothetical character states in the ancestor

Construction Wagner Tree 3. Addition of A, that can be done in different three places I will add A where less steps are introduced in the tree

Construction 4. A is placed as sister taxon of B (that produce only one step) and define the ancestor between A and B. Then we have to compare with ABC to redefine the ancestor of the three taxa Wagner Tree

5. We can continue with D or E. Arbitrarily we continue with D 6. Position basal to ABC introduce less steps. Then we redefine the ancestors Wagner Tree Construction

Wagner Tree Final tree: One branch collapse because the ancestors are the same Construction

Wagner tree: PROBLEMS Tree topologies obtained are dependant on the order of addition of the taxa. Obtained trees are not necessarily the most parsimonious Not always are obtained ALL the most parsimonious trees Construction

Exact Method Guarantied finding the shortest trees Two methods: exhaustive search and branch and bound It work with unrooted trees (do not require a priori polarization) and at the end of the search root the cladogram using the outgroup Construction

Exhaustive search All possible trees are obtained Construction

Exhaustive search: problem n = nº de taxa Construction

Branch and Bound For 20 to 30 taxa Do not examine ALL the trees, but equally find the shortest Construction

1. Search of a Wagner tree. The length of that tree will be referent in next search L=10 2. Two of the taxa are connected to the outgroup in the only possible way (as network) Branch and Bound Construction

3. C is added. That can do it in three different positions (to B, to A or with the outgroup). The position in which the three is shorter is chosen Branch and Bound Construction All trees longer than 10 steps (number of steps of the initial Wagner tree) are discarded.

4. D is placed in all possible positions and optimizations is done to obtain the shortest tree Branch and Bound Construction

5. Rooting the most parsimonious tress Advantage: 10 trees instead of 15 were analysed Branch and Bound Construction

Heuristic methods  Trial and error  Do not necessarily find the shortest trees  Used when data-matrices have above of taxa Construction

Heuristic methods 2 stages (which are repeated n times: replicas) 1. Production of a Wagner tree Construction 2. This preliminary tree is subjected to a series of arrangements named branch swapping (basically branch of the tree are cut and placed in other position of the tree). There are three types of rearranges: NNI, SPR, TBR Rearrangements are by chance Examination of how these movements of branch affect the length of the tree

Heuristic methods: synthesis 1) Random addition sequence of the taxa (RAS) 2) Explore all possible rearrangement on obtained trees (branch swapping) 3) Shortest trees are saved, remaining are discarded. If a new tree is shorter that the currently saved, then the latter are erased form the memory and the shorter new is saved 4) Rearrangement of shortest tree(s) until new shortest trees are found 5) Repetition of anterior steps N times keeping in the memory only shortest trees. Construction

From Andersen (2001)

From Lipscomb (1998)