Landscapes change as episodic natural events such as climatic extremes, earthquakes, and volcanic eruptions create and destroy landforms, and this change can be modeled statistically as a renewal process. Events, or attacks on the landscape, result in erosion and deposition, which cumulatively create or destroy parts of it, leaving an array of landscape components of different origins, sizes, ages, and states of preservation. At steady state or equilibrium, the average number of components in the population is a constant, and destructions balance renewals. Probability distributions can be derived for the ages and life spans in such a population. The model is applied to geomorphic systems involving steady-state and unsteady component creation and loss and uses; examples are landslides and a continuous sedimentary sequence. In addition to conceptual benefit to mechanistic descriptions of landscape evolution, the model allows the quantitative measure of the tempo of geomorphic activity and an accounting of the destruction of evidence with time.