According to an aspect of the invention, a curable rubber composition is provided which includes a high molecular weight diene elastomer; optionally, a carbon black composition; a silica composition; and a farnesene polymer comprising farnesene monomers. The farnesene polymer is modified with at least one silane group, has a number average molecular weight of 1,000 g/mol to 100,000 g/mol, and has a glass transition temperature of equal to or less than −50° C. According to another aspect of the invention, a method for producing a rubber composition for use in a tire is provided. The method includes forming a composition by mixing a farnesene polymer modified with at least one silane group, a silica composition, a high molecular weight diene elastomer, and optionally a carbon black composition, the farnesene polymer comprising farnesene monomers; and curing the composition.