This is a study-lab course in which topics are presented by short texts, practical sessions are introduced and explained and assignments are completed  by students. It is made of seven units: three theoretical units, each followed by a practical unit. In order to exemplify the use of the proposed  methods and models, a final unit is devoted to a case study on benthic macroinvertebrates in the Po River delta, providing the data, the R code and some interpretative comments. Practical units are based on the use of the R software, with purpose-specific libraries and functions. Quizzes are given following every unit, together with practical assignments to be addressed with the R software.

After this introductory unit, the first practical unit will be devoted to briefly introduce the R software. Biodiversity partitioning will be the subject of the next two units, where methodology and software for γ , α and β diversity profiling will be described and applied to a sample data set. The theory behind mixed effects modeling will be sketched and applied to investigate the variation of biodiversity measures. The last practical unit exemplifies the use of the R implementation of mixed effects modeling routines with data from ecological surveys. Finally we will summarize and exemplify the proposed methods with the complete analysis of a case study.

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.