Using Maximum Lyapunov Exponents to Quantify the Spatial and Temporal Dynamics of Woody-Encroachment in Grasslands

Woody encroachment is occurring in grasslands around the globe. We investigate the spatial and temporal dynamics of this encroachment in relation to climate and fire regimes in the central U.S. A low-dimensional water balance model is used to assess stability of species composition using maximum Lyapunov exponents. Six years of eddy covariance data at a paired grassland and woody encroachment site at the Konza Prairie LTER site are used to verify carbon and water dynamics. Spatial changes in faction of woody species are quantified using historical aerial photography and remote sensing. The maximum Lyapunov exponents are used to quantify the stability of state variables including soil moisture and vegetation and diagnose the presence of tipping points in relation to woody fraction, fire frequency and precipitation variability. The sensitivity of woody encroachment to the controlling parameters of fire frequency and precipitation timing and magnitude are assessed using 100-year simulations with varying parameters. Understanding these spatial and temporal dynamics is essential for understanding how these ecosystems may respond to future climate change.