  We consider the reconciliation problem, in which the task is to find a
mapping of a gene tree into a species tree, so as to maximize the likelihood of
such fitting, given the available data. We describe a model for the evolution
of the species tree, a subfunctionalisation model for the evolution of the gene
tree, and provide an algorithm to compute the likelihood of the reconciliation.
We derive our results using the theory of matrix-analytic methods and describe
efficient algorithms for the computation of a range of useful metrics. We
illustrate the theory with examples and provide the physical interpretations of
the discussed quantities, with a focus on the practical applications of the
theory to incomplete data.
