Dynamic Optimization of Ecosystem Services: A Comparative Analysis of Non-Spatial and Spatially-Explicit Models

This study develops and solves a stochastic, multi-year, discrete space-time model that allows the comparative analysis between non-spatial and spatially explicit models. The solution to this model implies the Stochastic Space-Time Natural Enemy-adjusted Economic Threshold (SST-NEET) to guide the choice of the optimal level of a pest that warrants management intervention. Using numerical simulation experiments over a generated synthetic geography, we derive three major conclusions. First, a unified framework for optimal control of a biological invasion must consider the simultaneous complexities of stochasticity, space, time and spatial spillovers. Second, the suggested SST-NEET is the most generalized version of the spatially explicit NEET model that can be simply reduced to a spatially homogenous or non-spatial model by giving conditions of each model assumed. Finally, accounting for spatial environmental heterogeneity and spatial spillovers are important factors to consider when making pest control decisions. Considering the fact that the initial distributions of pests and natural enemies are determined by the distribution of their habitat, conservation policies that increase spatial heterogeneity and spatial spillovers can be an effective way to use pest control ecosystem services to manage a biological invasion. An application to biological control of the soybean aphid using the natural enemy ladybird beetles is developed using field measurements in Newton County, Indiana, USA. After empirical parameterization of the equations of motion in a predator-prey system, the optimal economic threshold (aphids/plant) for using pesticides to control aphids is derived under three different forms of spatial heterogeneity. For a given set of input and output prices, the optimal economic threshold is derived numerically for three different forms of spatial heterogeneity.