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Background  Co-evolution is the process in which two (or more) sets of orthologs exhibit a similar or correlative pattern of evolution. Co-evolution is a powerful way to learn about the functional interdependencies between sets of genes and cellular functions and to predict physical interactions. More generally, it can be used for answering fundamental questions about the evolution of biological systems.  Orthologs that exhibit a strong signal of co-evolution in a certain part of the evolutionary tree may show a mild signal of co-evolution in other branches of the tree. The major reasons for this phenomenon are noise in the biological input, genes that gain or lose functions, and the fact that some measures of co-evolution relate to rare events such as positive selection. Previous publications in the field dealt with the problem of finding sets of genes that co-evolved along an entire underlying phylogenetic tree, without considering the fact that often co-evolution is local.    Results  In this work, we describe a new set of biological problems that are related to finding patterns of  local  co-evolution. We discuss their computational complexity and design algorithms for solving them. These algorithms outperform other bi-clustering methods as they are designed specifically for solving the set of problems mentioned above.  We use our approach to trace the co-evolution of fungal, eukaryotic, and mammalian genes at high resolution across the different parts of the corresponding phylogenetic trees. Specifically, we discover regions in the fungi tree that are enriched with positive evolution. We show that metabolic genes exhibit a remarkable level of co-evolution and different patterns of co-evolution in various biological datasets.  In addition, we find that protein complexes that are related to gene expression exhibit non-homogenous levels of co-evolution across different parts of the  fungi  evolutionary line. In the case of mammalian evolution, signaling pathways that are related to  neurotransmission  exhibit a relatively higher level of co-evolution along the  primate  subtree.    Conclusions  We show that finding local patterns of co-evolution is a computationally challenging task and we offer novel algorithms that allow us to solve this problem, thus opening a new approach for analyzing the evolution of biological systems.

Discovering local patterns of co - evolution: computational aspects and biological examples