On the microscale, migration, proliferation, adhesion and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation, adhesion and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions of population-level behaviour are assumed. For example, the logistic model is often used to describe population growth. In this talk I will outline some moment-dynamics models for analysing exclusion process representations of cell biology processes, and demonstrate that they can often correctly capture system behaviour in regions of parameter space where mean-field models fail.