This study aimed at comparing six patch connectivity measures by fitting them to field data. We used occupancy data for eight beetle and two pseudoscorpion species from 281 hollow oaks in southeast Sweden. Species occupancy was modelled in relation to tree characteristics and one measure of patch connectivity at a time. For each connectivity measure we searched for the spatial scale that generated the best fit to field data. Connectivity measures that only include occupied patches provided better model fits than those that include all patches. When occupancy data are absent for surrounding habitat patches, information that reflects occurrence probabilities can be included in the connectivity measure. However, in this study incorporation of such information resulted in only a slight improvement of model fit. A frequently used connectivity measure based on the negative exponential function was relatively poor in explaining species' occurrence; for eight species out of nine a buffer measure was better. A better fit was obtained when the negative exponential function was modified to take into account that habitat patches may "compete" for the immigrants. The spatial scale with the best fit tended to be larger when we used connectivity measures in which dispersal sources are identified with lower precision. Thus, the outcomes from different multiple-scale studies are not directly comparable if the density of dispersal sources is not measured in the same way. Overall we conclude that buffer measures are useful, as they give good predictions and are easy to understand and use. If a biologically more realistic measure is needed, one that up-weights the closest patches should be used. Finally, the possibility that habitat patches may compete with each other for immigrants should be considered when selecting a connectivity measure.

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Journal Ecography
Ranius, T. (Thomas), Johansson, V. (Victor), & Fahrig, L. (2010). A comparison of patch connectivity measures using data on invertebrates in hollow oaks. Ecography, 33(5), 971–978. doi:10.1111/j.1600-0587.2009.06363.x