The recently developed Domain-Gene-Species (DGS) reconciliation framework, which jointly models the evolution of a domain family inside one or more gene families and the evolution of those gene families inside a species tree, represents one of the most powerful computational techniques for reconstructing detailed histories of domain and gene family evolution in eukaryotic species. However, the DGS reconciliation framework allows for the reconciliation of only a single domain tree (representing a single domain family present in one or more gene families from the species under consideration) at a time, i.e., each domain tree is reconciled separately without consideration of any other domain families that might be present in the gene trees under consideration. However, this can lead to conflicting gene-species reconciliations for gene trees containing multiple domain families. In this work, we address this problem by extending the DGS reconciliation model to simultaneously reconcile a set of domain trees, a set of gene trees, and a species tree. The new model, which we call the multi-DGS (mDGS) reconciliation model, produces a consistent joint reconciliation showing the evolution of each domain tree in its corresponding gene trees and the evolution of each gene tree inside the species tree. We formalize the mDGS reconciliation framework and define the associated computational problem, provide a heuristic algorithm for estimating optimal mDGS reconciliations (both the DGS and mDGS reconciliation problems are NP-hard), and apply our algorithm to a large dataset of over 3800 domain trees and over 7100 gene trees from 12 fly species. Our analysis of this dataset reveals interesting underlying patterns of co-occurrence of domains and genes, demonstrates the importance of mDGS reconciliation, and shows that the proposed heuristic is effective at estimating optimal mDGS reconciliations.
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