Two main approaches have been considered for modelling the dynamics of the SIS model oncomplex metapopulations, i.e, networks of populations connected by migratory flows whoseconfigurations are described in terms of the connectivity distribution of nodes (patches)and the conditional probabilities of connections among classes of nodes sharing the samedegree. In the first approach migration and transmission/recovery process alternatesequentially, and, in the second one, both processes occur simultaneously. Here we followthe second approach and give a necessary and sufficient condition for the instability ofthe disease-free equilibrium in generic networks under the assumption of limited (orfrequency-dependent) transmission. Moreover, for uncorrelated networks and under theassumption of non-limited (or density-dependent) transmission, we give a bounding intervalfor the dominant eigenvalue of the Jacobian matrix of the model equations around thedisease-free equilibrium. Finally, for this latter case, we study numerically theprevalence of the infection across the metapopulation as a function of the patchconnectivity.

The distribution of fossorial water voles Arvicola terrestris on 15 small islands in the Sound of Jura, Argyll, Scotland, was established and populations were characterized in terms of size, structure and genetic composition (12 microsatellites). The results are compared with similar data from four metapopulations of riparian water voles in mainland Scotland. Water voles occurred on six islands, one of which was occupied in 1994, but not on two islands occupied during the 1960s. Probability of occupancy was significantly associated with proximity to the nearest occupied island. Unlike voles on the mainland, which occupy fragmented patches of exclusively riparian habitat, voles on islands were fossorial and occupied large areas of continuous habitat. Spring population sizes were c. 10 times higher on the islands than colonies of mainland metapopulations. Individuals from three islands were genotyped and these populations had 50% lower levels of microsatellite polymorphism than the mainland metapopulations. Rates of inferred contemporary dispersal among islands separated by 1 km or more of sea were very low, according to large differences among islands in genetic composition, proportions of coat colour types and incidence of skin infection. None the less, the long-term persistence of the island populations is likely to depend on such dispersal. Comparisons between island populations and mainland metapopulations indicate that in both fragmented systems the level of dispersal is the primary factor influencing genetic structure. The low genetic variability in the island populations may reflect either past historical events (founder effect and genetic drift) or present ecology (lack of immigration in closed and temporally fluctuating populations).