Familiar summaries of evolution by natural selection hold that one requirement for evolutionary change of this kind is heredity. Parents must resemble their offspring; like must beget like. In many organisms, however, that is not how things seem to work. Many life cycles feature long and complex chains in which like begets unlike, before they return to their starting point. Ferns and jellyfish are interesting examples. These phenomena show how strongly our familiar descriptions of evolution have been guided by a vertebrate-centric view of life. After describing the problem I'll offer a solution, in which the familiar notion of reproduction is generalized. Simple and familiar forms of reproduction are one among many modes of cyclical production, a mode distinguished by a particular placement of features including the sexual fusion of lineages, multiplication, and "bottlenecks" or narrowings of structure. Genetic "replication," rather than being treated as fundamental, should be handled within the same framework. I'll also say a word or two about applications to cultural evolution.