How do different matrix representations affect connectivity assessments?

Authors and Affiliations: 

Ziółkowska E. (1), Ostapowicz K. (1), Radeloff V. C. (2), Kuemmerle T. (3)

(1) Institute of Geography and Spatial Management, Jagiellonian University, Gronostajowa 7, 30-387 Krakow, Poland

(2) Department of Forest and Wildlife Ecology, University of Wisconsin-Madison, 1630 Linden Drive, Madison, WI 53706-1598, USA

(3) Geography Department, Humboldt-University Berlin, Unter den Linden 6, 10099 Berlin, Germany


Assessing landscape connectivity is important for conservation decisions and for evaluating alternative conservation strategies. There are various approaches for assessing connectivity and metapopulation dynamics (e.g., Kindlmann and Burel 2008, Rayfield et al. 2011). Many of these use different representations of the matrix (i.e. area between habitat patches), but the influence of this on the results obtained when assessing connectivity has not been systematically evaluated.

Our goal was to investigate the effects of different matrix representations (binary, categorical and continuous) on the connectivity assessment, i.e., the delineation of connections among habitat patches, and prioritization of patches based on different connectivity measures. We also analyzed whether that effect is dependent on the spatial pattern of habitat patches in the landscape.

We tested our approach on 50 x 50 km subsets of a continuous European bison habitat suitability map (HSM; spatial resolution of 100 m) for the Carpathians (Kuemmerle et al., 2010; Fig. 1). Habitat patches were defined as groups of pixels larger than 1 km2 with a habitat suitability index above with a habitat suitability index above a certain threshold. We used three different thresholds of habitat suitability index (i.e., 50, 60, and 70) to produce maps with different spatial patterns. The matrix was considered either as not influencing the movements of species (model M1), or influencing it. In the latter case, two different definitions of surface resistance for movement were used: a categorical movement cost surface based on a land-cover map (model M2), and continuous cost surface based on the inverted HSM (model M3; Fig. 1).

Connections among habitat patches were constructed either as the shortest lines (model M1), or as least-cost paths connecting edges of patches (models M2 and M3). We compared connections, as well as the relative importance of habitat patches for overall landscape connectivity based on (1) isolation, (2) incidence functional, and (3) graph theory measures. Connectivity measures were derived using Conefor Sensinode 2.6 (Saura and Torné, 2009) and scripts written in Python.

Our results showed that matrix representation affect the connections among habitat patches much more than the prioritization of patches for overall connectivity. The biggest differences occurred between models M1 and M3 (Fig. 1). Connections delineated based on models M2 and M3 were much longer than the shortest connections between habitat patches (model M1). The sums of movement costs along connections for model M3 were approximately two times greater than for model M1. In contrast, the effect of different matrix representations on patch prioritizations was small, though largest again between models M1 and M3. For smaller migration distances the matrix representation had a higher influence on differences in patch prioritizations (Fig. 2). The definition of patch attribute used for calculation of connectivity metrics also significantly affected the results (Fig. 2). In summary, our analyses highlight the importance of the way the matrix is represented in connectivity analysis, especially when the goal is to identify the most important connections for species movement.

Acknowledgments: Research project supported by the National Science Centre (program SONATA, project no 2011/03/D/ST10/05568), and by the Doctus (doctoral scholarship) programme.


Kindlmann P and Burel F (2008) Connectivity measures: a review. Landscape Ecology 23: 879–890.

Kuemmerle T, Perzanowski K, Chaskovskyy O, Ostapowicz K, Halada L, Bashta A-T, Kruhlov I, Hostert P, Waller DM, and Radeloff VC (2010) European Bison habitat in the Carpathian Mountains. Biological Conservation 143, 908-916.

Rayfield B, Fortin M-J, and Fall A (2011) Connectivity for conservation: A framework to classify network measures. Ecology 92: 847–858.

Saura S and Torné J (2009) Conefor Sensinode 2.2: a software package for quantifying the importance of habitat patches for landscape connectivity. Environmental Modelling & Software 24, 135-139.