The spatially explicit metapopulation model - Incidence Function Model

The Incidence Function Model describes presence/absence of a species in the patches of a highly fragmented landscape at discrete time intervals (years) as the result of colonization and extinction processes. The IFM ignores local dynamics sin ce they are faster than metapopulation dynamics in producing changes in the size of local populations (Hanski, 1994).
In the IFM, the process of occupancy of patch i is described by a first-order Markov chain with two states, {O, i} (empty and occupied, respectively). The extinction probability of a population in a patch is constant in time and is assumed to decrease with increasing patch area, and the colonization probability is assumed to be a sigmoidal function increasing with connectivity. The IFM is the best known spatially explicit metapopulation model in literature.
This model has been applied to conservation problems and to area-wide pest-management.
First, a short introduction to discrete time, finite space, homogeneous Markov chain will be provided, aiming at understanding the basic mathematics of the IFM. Then, the IFM model will be discussed by deeply considering (a) the role of the parameters and how they affect metapopulation dynamics; (b) variations to the basic model (rescue effect, time-dependent colonization probabilities). Finally, we will move on to the use of the free software R to deal with simulation and parameter estimation.