Validation of agent-based land use model by Markovian model Application to forest-agriculture transitions in Madagascar

The determination of transition rules that farmers adopt to manage crop-fallow after forest clearing, is essential for deciding a sustainable strategy for forest conservation. The effect of the type of farms with respect to these transition rules in forest border may mitigate incentive measures planned by forest conservation policy. Agent-base modeling (ABM) of land use is a relevant approach to manage the dynamics of heterogeneous mosaic landscapes such as the border of the Malagasy Eastern rainforest. Transition rules between six land uses (forest, fallow, crop, grass, plantation and paddy field) are formalized at a plot level. A historical database containing transitions between the first four land use states was used to calibrate transition models for the ecological and farmer land use dynamics. Three land-use models have been built: (1) a Markov chain (stochastic), (2) a timed automaton (deterministic), (3) and an agent-based model, which introduces the farmers. The land use ABM allows to test scenarios of deforestation with both varying initial population and farm spatial organization, size or strategy. The land use ABM is first calibrated via a timed automaton, fitting time delay parameters, the duration of each land use state (fallow, crop, grass), and the number of V2CS special issue of Studia Informatica Universalis, pages 33 à 61 34 V2CS special issue of Studia Informatica Universalis cropping cycles since the first forest clearing. It is then validated with the help of a Markovian model, comparing two transition matrices with χ metrics. The two transition matrices were respectively created with historical data of plot land use, and with simulated data produced by the land use ABM. We finish with a general discussion on the validation of such a complex system with a simple mathematical model.