NETWORK MODELS FOR SEQUENCE EVOLUTION

We introduce a general class of models for sequence evolution that inc ludes network phylogenies. Networks, a generalization of strictly tree -like phylogenies, are proposed to model situations where multiple lin eages contribute to the observed sequences. An algorithm to compute th e probability distribution of binary character-state configurations is presented and statistical inference for this model is developed in a likelihood framework. A stepwise procedure based on likelihood ratios is used to explore the space of models. Starting with a star phylogeny , new splits (nontrivial bipartitions of the sequence set) are success ively added to the model until no significant change in the likelihood is observed. A novel feature of our approach is that the new splits a re not necessarily constrained to be consistent with a treelike mode o f evolution. The fraction of invariable sites is estimated by maximum likelihood simultaneously with other model parameters and is essential to obtain a good fit to the data. The effect of finite sequence lengt h on the inference methods is discussed. Finally, we provide an illust rative example using aligned VP1 genes from the foot and mouth disease viruses (FMDV). The different serotypes of the FMDV exhibit a range o f treelike and network evolutionary relationships.