Path dependence and the validation of agent‐based spatial models of land use

Abstract

In this paper, we identify two distinct notions of accuracy of land-use models and highlight a tension between them. A model can have predictive accuracy: its predicted land-use pattern can be highly correlated with the actual land-use pattern. A model can also have process accuracy: the process by which locations or land-use patterns are determined can be consistent with real world processes. To balance these two potentially conflicting motivations, we introduce the concept of the invariant region, i.e., the area where land-use type is almost certain, and thus path independent; and the variant region, i.e., the area where land use depends on a particular series of events, and is thus path dependent. We demonstrate our methods using an agent-based land-use model and using multitemporal land-use data collected for Washtenaw County, Michigan, USA. The results indicate that, using the methods we describe, researchers can improve their ability to communicate how well their model performs, the situations or instances in which it does not perform well, and the cases in which it is relatively unlikely to predict well because of either path dependence or stochastic uncertainty.

A highly detailed land-use vector map for Madrid region based on photo-interpretation

“…MLU can also be used as a basis for dynamic models of urban LULC change such as cellular automata models (Barredo, Demicheli, Lavalle, Kasanko, & McCormick, 2004;Batty, Xie, & Sun, 1999;White & Engelen, 1993), or agent-based models (Brown, Page, Riolo, Zellner, & Rand, 2005;Veldkamp & Verburg, 2004). Future work is likely to include the incorporation of LULC information for new neighboring regions that are usually considered to fall under the influence of the Madrid metropolitan region, such as Toledo, Segovia and Guadalajara.…”

An agent-based approach to model land-use change at a regional scale

“…These methods can be used to verify the internal properties of the simulation processes itself. Also, if consistent high-resolution data for 2 years are available, validation may be possible by comparing the simulated results to past or current land use patterns (Brown et al 2005;Pontius et al 2008). Another challenge is linked to the interactions between agents and their social networks.…”

Population growth and its spatial distribution as factors in the deforestation of Nang Rong, Thailand

“…We also assess the sensitivity of the simulations to assumptions about the spatial extent of the village settlement effect. Other approaches to assess model performance are under development (Manson, 2003) including the study of pattern invariant areas in simulations (Brown et al, 2005), and emergent patterns and the creation of development fronts through the actions of individuals or some set of base actors on the landscape (Malanson et al, 2006). There are many approaches being used to consider model performance, although there is no unifying protocol yet established.…”

“…Fundamental to assessing model performance is determining the general goals of the modeling activity -prediction or explanation (Brown et al, 2005). If prediction is the intent, then the ability of the model to replicate some measure of reality may be an appropriate evaluation metric.…”

“…Explanation is our goal, not prediction (Brown et al, 2005). CA approaches have been used to investigate land cover change in a variety of settings, both urban (e.g., Batty et al, 1999;Webster and Wu, 1999;White and Engelen, 1993;White et al, 1997) and rural (e.g., Mas et al, 2004;Messina and Walsh, 2001;Silveira et al, 2002;Walsh et al, 2006).…”