Production method for copolymer, copolymer, rubber composition, and tire

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It is an object of the disclosure to provide a production method for a copolymer in which a copolymer with a high content of cis-1, 4 bonds of a conjugated diene portion can be obtained at a high yield even when a cyclic olefin compound is used as a monomer. In order to achieve the object, the present disclosure includes a step of polymerizing a conjugated diene compound and a cyclic olefin compound in the presence of a catalyst composition containing a rare-earth element compound represented by the following formula (I), at least one compound selected from the group consisting of an ionic compound and a halogen compound, a compound represented by the following formula (II), and a coordination compound that can be a ligand : [in-line-formulae]M-(AQ1)(AQ2)(AQ3)  (I)[/in-line-formulae][in-line-formulae]YR1aR2bR3c  (II).[/in-line-formulae]