We develop the concepts of ontogenesis and phylogenesis in the context of discrete dynamical systems, in particular, iterated interval maps. The topological dynamics of a continuous interval is characterised by the kneading invariant. Using symbolic dynamics, we show how to define and study systematic changes in this type of systems. Moreover, the study of a particular type of interactions between a large number of discrete dynamical systems with common characteristics - a population - gives us the possibility of studying how these population characteristics evolve with time.