Refining intra-patch connectivity measures in landscape fragmentation and connectivity indices

Context. Measuring intra-patch connectivity, i.e. the connectivity within a habitat patch, is important to evaluate landscape fragmentation and connectivity. However, intra-patch connectivity is mainly measured with patch size, which can conceal diverse intra-patch connectivity patterns for similar patch size distributions. Objectives. We suggest a method to refine the intra-patch connectivity component of fragmentation and connectivity indices. This method allows for distinguishing different intra-patch connectivity patterns for similar patch size distributions. Methods. We used normalized patch complexity indices to weight patch size in common fragmentation and connectivity indices. Patch complexity indices included two existing geometrical indices (SHAPE and FRAC), and a new index derived from spatial network analysis, the mean detour index (MDI). We analyzed the behaviours of adjusted fragmentation and connectivity indices theoretically and empirically on both artificial and real landscapes. Results. While maintaining the mathematical properties of fragmentation and connectivity indices, our method could distinguish landscapes with identical patch size distributions but different spatial configurations. The mean detour index had a different response than geometrical indices. This result indicates that, at the patch level, topological complexity can exhibit different patterns from geometrical complexity. Conclusions. Measuring intra-patch connectivity with patch size in fragmentation and connectivity indices cannot distinguish landscapes having similar patch sizes distribution but different spatial configurations. This paper introduces a method to distinguish such patterns relying on geometrical and topological indices and shows to which extent it can impact conservation planning.