The ability to model land use change as an emergent property of the interaction between individual farm-agents — through space and time — provides a basis for simulating and evaluating the impacts of changes in agricultural policy on landscape quality via changes in farm-agent behaviour. This is done by incorporating into the model mathematical functions that relate changes in land use to environmental variables. The functions used to measure changes in mosaic and biodiversity are described below.
The more diverse and heterogeneous a landscape, the more complex its mosaic, and hence the more it can potentially contribute to amenity, recreational, cultural and knowledge values. Hence, mosaic complexity can be taken as a general indicator of landscape value. Changes in the landscape mosaic were measured using Shannon’s Diversity Index (SDI):
where H denotes mosaic diversity, I is the set of different land uses, i e I, and pt is the share of the total land area covered by the ith land use (i.e. pi =VЪ ai where ai is the
area of land use i). It can be shown that, for any given number of land uses, there is a maximum possible diversity, Hmax = ln I, which occurs when all land uses are present in
equal area, i.e. pt = 1/1 for all i. According to this indicator, mosaic value increases if the area of a relatively scarce land use (i.e. pt < 1/1) increases or a relatively common land-use (i.e. pt > 1/1) decreases (and vice versa). This is consistent with our
understanding that humans prefer a mosaic landscape (as observed in some reference year) compared to a more homogenous landscape.