Global sensitivity analysis for complex ecological models: a case study of riparian cottonwood population dynamics

Abstract

Mechanism-based ecological models are a valuable tool for understanding the drivers of complex ecological systems and for making informed resource-management decisions. However, inaccurate conclusions can be drawn from models with a large degree of uncertainty around multiple parameter estimates if uncertainty is ignored. This is especially true in nonlinear systems with multiple interacting variables. We addressed these issues for a mechanism-based, demographic model of Populus fremontii (Fremont cottonwood), the dominant riparian tree species along southwestern U.S. rivers. Many cottonwood populations have declined following widespread floodplain conversion and flow regulation. As a result, accurate predictive models are needed to analyze effects of future climate change and water management decisions. To quantify effects of parameter uncertainty, we developed an analytical approach that combines global sensitivity analysis (GSA) with classification and regression trees (CART) and Random Forest, a bootstrapping CART method. We used GSA to quantify the interacting effects of the full range of uncertainty around all parameter estimates, Random Forest to rank parameters according to their total effect on model predictions, and CART to identify higher-order interactions. GSA simulations yielded a wide range of predictions, including annual germination frequency of 10-100%, annual first-year survival frequency of 0-50%, and patch occupancy of 0-100%. This variance was explained primarily by complex interactions among abiotic parameters including capillary fringe height, stage-discharge relationship, and floodplain accretion rate, which interacted with biotic factors to affect survival. Model precision was primarily influenced by well-studied parameter estimates with minimal associated uncertainty and was virtually unaffected by parameter estimates for which there are no available empirical data and thus a large degree of uncertainty. Therefore, research to improve model predictions should not always focus on the least-studied parameters, but rather those to which model predictions are most sensitive. We advocate the combined use of global sensitivity analysis, CART, and Random Forest to: (1) prioritize research efforts by ranking variable importance; (2) efficiently improve models by focusing on the most important parameters; and (3) illuminate complex model properties including nonlinear interactions. We present an analytical framework that can be applied to any model with multiple uncertain parameter estimates.