Non-parametric upscaling of stochastic simulation models using transition matrices.

CIPRIOTTI, P; WIEGAND, T.; PUTZ, S.; BARTOLONI, N.J.; PARUELO, J.M.

Methods in Ecology and Evolution

Wiley Online Library

Año: 2016 vol. 7 p. 313 - 322

1.The pro blem of scaling up from tractable, sm all-scale observations and experiments to prediction of large-scale patterns is at the core of ecological theory and application, and one of the central problems in ecology.2. We present and test a general nonparametric framework to upscale spatially explicit and stochastic simulationmodels. The idea is to design a state space, defined by the important state variables of the small-scale model, andto divide it into a finite number of discrete states. Transition probabilities are then tallied by monitoring extensivesimulation runs of the small-scale model, covering the e ntire range of initial conditions, states and external dri-vers that may occur for the desired application. We exemplify our approach by upscaling an individual-basedmodel that simulates the spatiotemporal dynamics of Festuca pallescens step pes under sheep grazing in WesternPatagonia, Argentina, with a spatial resolution of 03m9 03manda015-ha extent. The upscaled model sim-ulates a 2500-ha paddock with 015-ha resolution and is enri ched with additional rules that describe heterogene-ity in the local stocking rate at the paddock scale.3. We obtained 24 transition matrices that governed the upsc aled model for different combinations of stockingrates and annual precipitation. The upscaled model produced excellent predictions for the long-term dynamics,but as expected, it did not fully capture t he interannual dynamics of the original model. Rules for heterogeneityin the local stockin g rate allowed for emergence of realistic vegetation patterns as commonly observed for waterpoints in arid rangelands.4. Our general nonparametric upscaling approach can be applied to a wide range of stochastic simulation mod-els in which the dynamics can be approximated by a set of states, transitions and external drivers. Because estima-tion of the transition probabilities can be done parallel, our approach can be applied to a wide range of models ofintermediate complexity. Our approach closes a gap in our ability to scale up from small scales, where the biolog-ical knowledge is available, to larger scales that are relevant for management.