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.