Models of complex systems are built and used to gain understanding of target system properties and dynamics and to mediate between linked theories and observations. Models are particularly useful for earth systems including ecological processes, which have complex properties such as feedbacks, path-dependence, downward causation and tipping points that are not meaningful from the perspective of classic linear causal relationships. In composing such models, how do modellers carve nature at its joints, that is, decompose their complex, multilevel systems into processes, interactions, components and their organization? Two examples illustrate two strategies. The first is to limit the range of spatiotemporal scales by parameterising the smaller-scale processes and by imposing the larger-scale processes in the initial and boundary conditions. The second is to separate physical, biological and other levels. This allows control on the causes, processes, their interactions and organization in order to explore, explain and predict their effects.