The invention relates to a tire having a rubber tread comprised of cap/base construction where the tread cap layer provides the running surface of the tread and the tread base layer underlies the tread cap layer and thereby provides a transition between the tread cap layer and the tire carcass. For this invention, the tread cap layer is comprised of a plurality of individual circumferential load-bearing zones of rubber compositions, which exhibit graduated physical properties, and which extend from the outer running surface of the tread cap layer radially inward to said tread base layer. In one aspect, the zoned rubber tread cap layer and rubber tread base layer are co-extruded together to form a unit as an integral tread rubber composite.