The Drape: a new way to characterize ecosystem states, dynamics, and tipping points from process-based models

There are many ways to study ecosystem dynamics, all having several issues. Main limitations of differential equation systems are the necessarily small number of interactions between few variables used, and parameter values to be set before the system dynamics can be studied. Main drawbacks of large-scale snapshot observation datasets to build a stability landscape are assuming that the most represented conditions are the most stable states, and using the computed landscape to directly study the system's dynamics. To remedy these aforementioned shortcomings and study complex systems based on the processes that characterize them without having to limit the number of variables, neither set parameter values, nor to use observations serving both model buildup and system's dynamics analysis, we propose a geometric model as an additional and novel aid to study ecosystem dynamics. The Drape is a generic multi-dimensional analysis, derived from process-based model datasets that include disturbances. We illustrate the methodology to apply our concept on a continental-scale system and by using a mechanistic vegetation model to obtain values of state variables. The model integrates long-term dynamics in ecosystem components beyond the theoretical stability and potential landscape representations currently published. Our approach also differs from others that use resolution of differential equation systems. We used Africa as example, representing it as a grid of 9395 pixels. We simulated each pixel to build the ecosystem domain and then to transform it into the Drape - the mean response surface. Then, we applied a textural analysis to this surface to discriminate stable states (flat regions) from unstable states (gradient or crest regions), which likely represent tipping points. Projecting observed data onto the Drape surface allows testing ecological hypotheses, such as illustrated here with the savanna-forest alternative stable states, that are still today debated topics, mainly due to methods and data used. The Drape provides new insights on all ecosystem types and states, identifying likely tipping points (represented as narrow ridges versus stable states across flat regions), and allowing projection and analysis of multiple ecosystem types whose state variables are based on the same three variables.