Minimal sets in monotone and concave skew-product semiflows I: A general theory

The long-term dynamics of a general monotone and concave skew-product semiflow is analyzed, paying special attention to the region delimited from below by the graph of a semicontinuous subequilibrium or by a minimal set admitting a flow extension. Different possibilities arise depending on the existence and number or absence of minimal sets strongly above the initially fixed one, as well as on the coexistence or not of bounded and unbounded semiorbits on the region. Previous results are unified and extended, and significative differences with the sublinear case are established. Some scenarios which are impossible in the autonomous or periodic cases may occur in this setting.