Statistical modelling of homologous sequences through profile HMM disregards the phylogenetic links between those. Here we present models harnessing an efficient combination of horizontal and vertical features, simultaneously figuring sequences as chains of aminoacids and products of an evolutionary process. Such models belong to the phylo-HMM family introduced in the '90s (e.g. Mitchison & Durbin). Focusing on the detection of remote homologues in databases, we develop a framework for an exhaustive derivation of phylo-HMM parameters basing on the phylogeny. The models we build are ancestral re-construction HMM, output by a process of phylogenetic inference of conserved positions, Match and Insert emission probabilities, and transition probabilities. Finally, we propose new models of evolution for transitions between states of the HMM and for insert lengths. The training framework we describe has been implemented and tried on testbenches of homologous sequences. It brings improved likelihoods and a better discriminative power on detecting remote homologues in large databases of proteins sequences
