Measuring Emergent Properties of Agent-Based Landcover/Landuse Models using Spatial Metrics

Agent-based modeling is emerging as a promising new tool for constructing spatially detailed models of land use. Agent-based models offer several advantages over previously used techniques, since they are well suited for modeling complex phenomenon. Several important sources of complexity influence land-use decisions -- for example, spatial heterogeneity, spatial interdependencies, increasing returns to spatial scale, and scale-dependent nesting. The often nebulous concept of "emergence" is a key feature of complex systems. In order to evaluate the success of agent-based models of land use, therefore, the emergent properties of such a system must be identified. The aspatial aggregate distribution of economic activity has been traditionally identified as an emergent property in agent-based models. We argue that landscape pattern is also a key emergent property of agent-based models of land use, and therefore, pattern measurement should be emphasized when evaluating the success of such models. Traditional goodness of fit measures of land-use models have focused on either aggregate landscape composition (the aspatial distribution of land uses between classes) or on the correct estimation of land-use locations. A reasonable estimate of composition should be a minimum hurdle for any model of land use, since composition has important implications for both economic activity and ecological function. Important information regarding both the ecological and economic function of landscapes is also contained in measures of landscape pattern. Therefore, a means for assessing landscape pattern outcomes is a critical for evaluating model success. We argue that assessment based on correct estimation of land-use locations should be de-emphasized due to both the difficulty in estimating actual locations and the low information value of location. Two landscapes may be identical in terms of composition, but differ completely in terms of landscape function. Alternatively, two landscapes may have completely different land-use locations but be identical in terms of both composition and function. Therefore, an assessment of model fit based on composition and location only may provide an incomplete and misleading picture of the empirical success of a land-use model. Further, this strategy may fail to reveal emergent relationships between spatial complexity and landscape function that are expressed in landscape pattern outcomes. Landscape-based spatial metrics have long been used by ecologists to characterize ecological function. For example, core area and edge density measures are used to characterize the ability of landscapes to support populations that require undisturbed habitat. Connectivity measures are used to measure the ability of a species to migrate between habitat areas. A variety of economic forces potentially impact spatial patterns of land use. Their impacts can also be measured using spatial metrics. Agglomeration economies and some forms of spatial competition may lead to clustering of similar land uses, while monopolistic competition can lead to spatial dispersal of land use. Both forces are potentially measured through nearest neighbor metrics and through evenness indices, which reflect spatial concentration of land area. Transportation costs, measured through network analysis, play an important role in determining patterns of economic activity. Positive or negative spatial spillovers may potentially impact the probability of finding contiguous parcels in a similar land use. These impacts can be assessed through landscape statistics related to parcel juxtaposition, edge density, and parcel compactness. We present a series of examples to illustrate our arguments. These examples are generated by an agent-based model of land-owner decision making, where agents allocate their land to the use that generates highest land rents. The model outputs both pattern metrics and economic welfare measures. A first example illustrates two simulated urban landscapes which are identical in terms of land-use composition but radically different in economic function. One landscape exhibits compact development patterns and spatial segregation of incompatible land uses, reflecting an efficiently functioning city. The second urban landscape exhibits sprawling and fragmented patterns of development, reflecting relative inefficiency in terms of transportation networks and impacts of spatial externalities. A second example demonstrates the pitfalls of validating based on location. A simple stochastic model is shown to produce two distributions of agricultural activity identical in terms of composition and landscape metrics, but disparate in terms of location. In this case, assessment based on land-use location would reject a theoretical model that correctly estimates composition, function, and economic efficiency.