Generalizing matrix structure affects the identification of least-cost paths and patch connectivity

Understanding and assessing landscape connectivity is often a primary goal when studying patchy or spatially structured populations. It is commonly accepted that the matrix plays a role in determining connectivity; however, it is not clear how the process of assessing connectivity is impacted by different ways in which the matrix may be represented, particularly if matrix structure is generalized to expedite analysis. We conducted a controlled experiment using computer simulations to evaluate the impact of increasing levels of matrix generalization on connectivity assessment using a constant arrangement of habitat patches. We varied matrix generalization for six simulated landscape patterns by adjusting the number of classes and level of pattern grain in 16 ways to yield sets of landscapes for which the matrix ranged from not generalized (i.e., heterogeneous) to completely generalized (i.e., homogeneous) while habitat placement was held constant. Least-cost paths were calculated for each landscape, and a spatial interaction model (SIM) was implemented to model the counts of patch inflows (immigration) and pairwise exchange. Applying a SIM allowed us to generate absolute outputs and explicitly compare the effect of changes to matrix generalization on connectivity. We found that both assessment of connections (i.e., measured distance and spatial delineation of least-cost paths) and patch inflows/pairwise exchange were highly sensitive to matrix generalization and that effects were inconsistent and unpredictable across the range of matrix representations, especially when estimating connectivity for individual patches. We conclude that matrix pattern may have an underappreciated effect on connectivity and that least-cost path delineation and connectivity assessment may be very sensitive to generalizations of the matrix. We suggest that sensitivity analysis of the matrix representation should be performed when conducting connectivity analyses.