K K K

Taxon A Taxon 8

For each network, likelihoods are evaluated on a site-by-site basis. The probabilities (Pef) of all possible combinations of character states at the internal nodes are calculated for each site (i.e., each character) using a specified model of molecular evolution and estimated branch lengths (see below). The likelihood of the site is the sum total of all the probabilities for all the possible combinations of character states at the internal nodes of the network (Felsenstein 1981b; Swofford et al. 1996; Huelsenbeck and Crandall 1997). In the four-taxon case, there are two internal nodes and therefore 16 possible combinations of character states and 16

probabilities for each site (when gaps are not considered) (Eq. 4). It is clear that some of these combinations, or scenarios, are more plausible than others given the data at the leaves. However, every combination of states at the internal nodes is theoretically possible and each is therefore given a probability (O Figure 5.7).

O Figure 5.7

Illustration of the possible character states at the internal nodes for the four-taxon, four-character statement

O Figure 5.7

Illustration of the possible character states at the internal nodes for the four-taxon, four-character statement

The overall likelihood of the network or tree is calculated as the product of the site likelihoods (Lsiten) because each site is assumed to evolve independently of one another (Eq. 5).

Ltr! — Leite! X Leite?. X Leitet X • • • X L,

Theoretically, this procedure is repeated for each possible unrooted network, although there are "pruning" algorithms that do not require every tree to be considered thereby improving computational efficiency in large data sets (Felsenstein 1981b; Swofford et al. 1996). The network with the highest overall likelihood is the maximum likelihood result, and the preferred phylogenetic hypothesis. It is the network topology that maximizes the likelihood function for the data given the specified model (Felsenstein 1973). It is possible that the network represents only a local maximum, or that it is one of a larger number of equally likely networks. It is important to remember that the likelihood of a network is

NOT L = P(H|D), which is the probability of the hypothesis. The network is converted into a tree by rooting it with an outgroup or a molecular clock (Swofford et al. 1996; Felsenstein 2004).

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