Ant colony optimisation is a constructive metaheuristic that successively builds solutions from problem-specific components. A parameterised model known as pheromone--an analogue of the trail pheromones used by real ants--is used to learn which components should be combined to produce good solutions. In the majority of the algorithm's applications a single parameter from the model is used to influence the selection of a single component to add to a solution. Such a model can be described as first order. Higher order models describe relationships between several components in a solution, and may arise either by contriving a model that describes subsets of components from a first order model or because the characteristics of solutions modelled naturally relate subsets of components. This paper introduces a simple framework to describe the application of higher order models as a tool to understanding common features of existing applications. The framework also serves