Behind the scenes of landscape connectivity: Optimization, thresholding. (April 2022) - Pomianowski, Wojciech
Abstract: Optimization is underlying technique of many graph-theoretic algorithms, including shortest paths and minimum spanning tree and hence – hidden component of landscape connectivity methods. Optimization solutions have different selectivity but it remains unexplored. Indeterminate solutions happen without warning and may be spatially biased. Errors are hidden. These issues may undermine connectivity measures and conclusions. Two optimization targets may be distinguished: mobile agent and connectivity provider, with different requirements. Review of how are they handled in literature finds them entangled and often misspecified, owing to inconclusive results, especially pronounced when conservation and explanatory goals are mixed. I categorize graph structures against targets and show how initial choice of structure introduces implicit optimization. Allowing for stochasticity of mobile agent resolves omniscience problem. Lastly, I advocate against creating landscape graphs with thresholds in favor of complete planar graphs. Thresholding is impractical, biased by design and yields non-optimal solutions due to simplistic partitioning. Highlights: Network distances depend of successful optimization, which is not guaranteed. Optimization delivers best graph structures but does not inform about their quality and errors. It's unlikely to change soon. Attempts to improve or extend proven algorithms (e.g. shortest paths) are risky. Conservation-oriented and explanation-oriented studies should be separated. Graph thresholding delivers wrong results.