Ecological Archives A016-020-A3

Örjan Bodin, Maria Tengö, Anna Norman, Jakob Lundberg, and Thomas Elmqvist. 2006. The value of small size: loss of forest patches and thresholds in southern Madagascar. Ecological Applications 16:440–451.

Appendix C. Rate of movement estimation for Lemur catta.

In our model, the dispersal flux rate (i.e., rate of movements) between any two habitat patches depends on: (1) The geographical distance between the habitat patches and (2) the area of the habitat patches. The geographical distance has a much stronger impact than the area on the dispersal flux rate. Distances between all pair of patches were measured using the Landsat image, and a measure Sij, representing a metric proportional to the dispersal flux rate, was calculated using a negative exponential dispersal kernel (Eq. C.1). This model partly captured the underlying assumptions behind the Incident Function Model (Hanski 1994).


Sij = Metric proportional to the dispersal flux rate from patch i to patch j
Aj = Area of patch j (m2)
Dij = Distance between patch i and patch j (m)
= constant (1/m)
C = cut-off value
b = constant (1/m)

The minimum hospitable patch area for Lemur catta was estimated to be 1 ha (Ganzhorn et al. 1999). The parameters were set such that only 5% of the maximum Sij remained between patches of 1 ha, if separated by a distance Dij equal to the chosen level of vagility. This level of Sij was also set as the cut-off, i.e., an infinitesimal increase in distance or an infinitesimal decrease in patch jís area would disconnect these patches. Thus, pairs of patches with a Sij below the cut-off were not considered as connected, i.e. no edge connected such pairs of nodes. We did not consider the directionality of the edges. Instead we set both Sij and Sji to the mean value of Sij and Sji. In addition, in the search for components, we did not take the numerical values of Sij in account as long as they were above the cut-off.


Hanski, I. 1994. A practical model of metapopulation dynamics. Journal of Animal Ecology 63:151–162.

Ganzhorn, J. U., J. Fietz, E. Rakotovao, D. Schwab, and D. Zinner. 1999. Lemurs and the regeneration of dry deciduous forest in Madagascar. Conservation Biology 13:794–804.

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