**Otso Ovaskainen and Ilkka Hanski
University of Helsinki**

Metapopulation capacity (lM) measures the capacity of a highly fragmented landscape to support a viable metapopulation. If
extinction-colonization dynamics can be described by a deterministic, spatially realistic metapopulation model, the long-term
persistence depends on the condition

(lM>d in the text)

Here d=e/c is the ratio between the extinction and colonization rates of the focal species. The metapopulation capacity lM integrates the effects of habitat patch areas and connectivities, as specified by structural model assumptions. Mathematically, lM is the leading eigenvalue of an appropriate landscape

Metapopulation capacity (lM) can be calculated for different fragmented landscapes to rank them in terms of their capacity to support viable metapopulations.

Fig.1. Above the threshold lM>d, the fraction of occupied patches (weighted by the patch values) can be closely approximated by pl*=1-d/lM. This figure shows pl* in 25 Glanville fritillary butterfly patch networks. The dots are based on field data, whereas the continuous line shows the prediction according to the theory, with the threshold chosen to correspond to the average for those 11 networks with pl* > 0.3. The broken lines give the limits omitting the two most extreme estimates. |

Fig.2. The contributions of individual habitat patches to the metapopulation capacity, called the patch values, can be closely approximated by the components of the eigenvector corresponding to lM. The sizes of the dots are proportional to patch areas in panel (a) and to patch values in panel (b). The contour lines reveal the core of the network. |