Modification of the effective mesh size for measuring landscape fragmentation to solve the boundary problem

Patch-based landscape metrics can be biased by the boundaries and the extent of a reporting unit if the boundaries fragment patches. We call this the “boundary problem”. The effective mesh size m eff is a convenient method to quantify landscape fragmentation, that is based on the probability that two points chosen randomly in a region will be connected, e.g., not be separated by roads, railroads, or urban development. The cutting-out (CUT) procedure, used in the original computation of m eff, suffers from the boundary problem because the boundaries of the reporting units are considered to be additional barriers. Therefore, m eff will be underestimated, particularly if reporting units are embedded within the broader landscape. In this paper, we present a solution to overcome this limitation by a new method called “cross-boundary connections” (CBC) procedure. It attributes the connections between two points that are located in different reporting units to both reporting units. We systematically compare the CBC procedure to the CUT procedure and show that the boundary problem is intrinsic to the CUT procedure, while the CBC procedure is independent of the size and administrative boundaries of reporting units. In addition, we elucidate the superior performance of the new procedure in the case study of South Tyrol where m eff is being used for sustainability reporting on the level of municipalities. The new CBC procedure eliminates the bias due to the boundaries and the size of reporting units in measuring landscape fragmentation through m eff.