Elasticity and loop analyses: tools for understanding forest landscape response to climatic change in spatial dynamic models

Spatially explicit dynamic forest landscape models have been important tools to study large-scale forest landscape response under global climatic change. However, the quantification of relative importance of different transition pathways among different forest types to forest landscape dynamics stands as a significant challenge. In this study, we propose a novel approach of elasticity and loop analyses to identify important transition pathways contributing to forest landscape dynamics. The elasticity analysis calculates the elasticity to measure the importance of one-directional transitions (transition from one forest type directly to another forest type); while the loop analysis is employed to measure the importance of different circular transition pathways (transition from one forest type through other forest types back to itself). We apply the proposed approach to a spatially explicit dynamic model, LANDIS-II, in a study of forest landscape response to climatic change in the Boundary Waters Canoe Area (BWCA) incorporating the uncertainties in climatic change predictions. Our results not only corroborate the findings of the previous studies on the most likely future forest compositions under simulated climatic variability, but also, through the novel application of the elasticity and loop analyses concepts, provide a quantitative assessment of the specific mechanisms leading to particular forest compositions, some of which might remain undetected with conventional model evaluation methods. By quantifying the importance of specific processes (transitions among forest types) to forest composition dynamics, the proposed approach can be a valuable tool for a more quantitative understanding of the relationship between processes and landscape composition/patterns.