Spatial renormalization as a multiscale approach to determining the security of landscapes

Background/Question/Methods

A landscape is a heterogeneous mosaic in which the contribution of each location to organismal fitness, particularly security, varies along a continuum from detrimental to optimal.  Yet, currently available connectivity indices provide a discrete categorization of landscapes: patches have value, the matrix does not.  Additionally, these indices cannot be easily adjusted to address security at scales relevant to different species that inhabit the same landscape.  

Here we use majority rule renormalization to measure security of individual cells across entire landscapes.  Simulated landscapes, lattices of equal-sized cells that are classified as secure (value = 1) or vulnerable (value = 0) habitat, are sampled with non-overlapping 2 x2 cell windows.   All cells within the window are reclassified to the same value as the majority of the 4 cells.  The process is repeated using a window with a resolution twice as coarse as that used in the previous renormalization until the size of the window equals the scale of interest.  The sum of values derived from all renormalizations is the Security Index (SI) for each cell.

In simulated landscapes, we randomly classified cells as secure in densities of p = 0.1 to 0.9 and calculated SI across a range of scales.   We also introduced different-sized disturbances onto simulated landscapes and measured changes in SI (DSI).  

Results/Conclusions

We conducted 100 trials for each combination of habitat density, scale, and size of disturbance.  In undisturbed landscapes, SI increased with habitat density at all scales and was highest in the interior of patches and lowest in the matrix.  However, as scale increased a phase transition in SI became evident between low and high densities of habitat at p =0.5.   

Mean DSI increased with size of disturbance, scale, and habitat density.  It decreased by >50% from the disturbance to adjacent cells but at much lower rates with greater distances from disturbances.  SI was unaffected beyond 10 cells from small disturbances at low and medium densities of habitat and beyond 20 cells at high densities.  Medium and large disturbances affected SI more than 25 cells from all disturbances.

Our results are consistent with empirical data on the value of landscapes in providing security for organisms that occupy them.  This technique can contribute to more accurate evaluations of translocation sites, corridors, and impacts of disturbances.