Dynamic reserve site selection under contagion risk of deforestation

Recently, dynamic reserve site selection models based on stochastic dynamic programming (SDP) have been proposed. The models consider a random development pattern in which the probability that a site will be developed is independent of the development status of other sites. However, development often takes the form of a contagion process in which the sites most likely to be developed are near sites that already have been developed. To consider site selections in such cases, we propose improved algorithms that make use of a graph representation of the sites network. The first formulation is an exact, dynamic programming algorithm, with which theoretical and experimental complexities are evaluated. The exact method can be applied only to small problems (less than 10 sites), but real-world problems may have hundreds or thousands of sites, implying that heuristic selection methods must be used. We provide a general framework for describing such heuristic solution methods, and propose a new heuristic method based on a parameterised reinforcement learning algorithm. The method allows us to compute a heuristic function by performing and exploiting many simulations of the deforestation process. We show that the method can be applied to problems with hundreds of sites, and demonstrate experimentally that it outperforms previously proposed heuristic methods in terms of the average number of species conserved.