Detecting bifurcations and alternate stable states in vegetation with remote sensing: when hypotheses and errors align

Background/Question/Methods

Multiple stable states, bifurcations and thresholds have been observed in a variety of aquatic, marine and terrestrial systems.  Empirical observations are supported by conceptual and numerical models of how biotic and edaphic interactions can generate non-linear dynamics and ‘ecosystem surprises’.  Bifurcations have also been observed in savannas, where the coexistence of trees and grasses depends on climatic and edaphic constraints, and their interactions with demographic constraints imposed by fire, herbivory and other factors impacting woody recruitment and mortality.  In particular, it seems clear that a positive feedback exists in savannas where grass fires reduce tree density and cover, releasing grass growth and leading to increased fire frequency or intensity. This positive feedback can drive a bifurcation between high woody cover-low fire savannas and low woody cover-high fire savannas.  Recently, however, several authors have attempted to quantify the prevalence of alternate stable states in global savannas and boreal forests using a satellite-derived woody cover product.  While interesting, we wondered whether the statistical methodologies underlying the satellite tree cover product may limit our ability to draw inferences regarding multiple stable states. In particular, classification and regression tree (CART) methods may impose discontinuities in satellite tree cover estimates not present in reality. 

Results/Conclusions

To explore whether CART-based methods may lead to erroneous conclusions regarding discontinuities in tree-cover we present complimentary statistical and empirical analysis approaches:  (1) we generated a random-uniform “pseudo-tree cover” dataset representing woody cover in Africa and pseudo-satellite reflectance responses. We emulated the CART methods used in the satellite tree cover product by extracting a sample of points across the continent for regression tree analysis, with terminal nodes smoothed using residual regressions.  We found that these CART-based tree cover estimates show strongly non-uniform probability density functions (apparent discontinuities) where the underlying data were perfectly uniformly distributed; and (2) we analyze an independently-derived tree cover product, derived from field and remote sensing data using continuous linear and non-linear regression techniques. We conclude that, while state-bifurcations may indeed be a feature of savannas and boreal forests, inference at global scales using satellite-derived products should be approached with extreme caution.  More generally our conclusions serve as a reminder that the statistical and functional models used to estimate earth surface properties from remotely sensed radiances may interact with subsequent ecological or biophysical interpretations and hypothesis-testing.