A Hierarchical Organization of Landscape Models

Due to the spatial scale at which most empirical landscape studies are performed, replica-tion is rarely feasible, and experimenters may require artiicial replication through the use of landscape models that are synthetically generated. In our view, a landscape is a heterogeneous region on the surface of the earth, and a landscape model is a simpliied representation (e.g. as a digital map) of a landscape of interest. A generator of landscape models is a procedure for producing landscape models. Artiicial generation of landscape models is becoming increasingly prevalent in landscape ecology and is useful for a variety of purposes, including comparison with real data, testing general theoretical hypotheses, and providing input to simulation models. However, the number of generators of landscapes models is increasing and there is no framework within which generators can be analyzed, compared and organized. In this paper, we propose a hierarchical framework that uniies landscape models within a formal organizational system. A landscape model that is artiicially generated using a simple random process is called a neutral model. Generators of neutral models produce instances of landscape models with two patch types, and constrain the patterns generated by specifying the proportion of the model covered by each patch type. We develop a generalization of neutral models, where landscape models are generated according to a set of constraints on possible patterns. A set of constraints is a landscape model prototype. Diierent landscape model prototypes can be compared according to the number and type of restrictions, where a prototype is considered \less neutral" or \more restricted" than another if the former has a superset of the constraints of the latter. This relation produces a hierarchy that captures gradients of neutrality among prototypes. The hierarchy thus formalizes, in a mathematically elegant manner, a multi-dimensional transition from neutral models that impose few restrictions on pattern generation to predictive models that impose a variety of more ecologically motivated constraints on the generation of landscape models. In a more practical context, this hierarchy may be used to guide the development of landscape model generators, to aid selection of appropriate existing generators, and to assist in the analysis of models derived from real landscapes through the use of landscape model prototypes.