Understanding the geospatial and socio-ecological effects of management interventions and environmental governance via embedded Gaussian processes

Background/Question/Methods

Analyses of ecological patterns in geographical space—such as species distributions, forest cover changes, and ecosystem service provision—are crucial to evaluate the effectiveness of management interventions and environmental governance. And an increasing number of publicly available data sets allow for studying these patterns at high resolutions and over wide regions. However, as ecological patterns emerge from a complex web of interacting variables, several covariates usually have to be included to properly estimate the effect of a variable of interest (such as the implementation of a specific policy, or management regime). We propose "embedded Gaussian processes" as a new approach that allows to include a set of interacting covariates, while addressing non-linear effects and spatial dependency. This approach consists in: (1) using a simple artificial neural network (a self-organizing map) to map the full covariate space onto a two-dimensional principal surface; and (2) capture the effect of the reduced covariate space as an isotropic Gaussian process. Compared to existing matching methods, this avoids subsampling—thus avoiding the introduction of spatial bias—and it more fully takes into account the topology of the covariate space. We used several hundred simulated landscapes to assess the the accuracy of inferences provided by our approach.

Results/Conclusions

For all landscapes, the covariate space could be adequately represented by the corresponding self-organizing maps (≥ 92% variance explained). The use of Gaussian processes formulated over the self-organizing maps then provided for more accurate inference on the variable of interest, when compared to coarsened exact matching and propensity score matching (judged by whether the true value was included within the 95% confidence interval of the estimate). Improvements were most pronounced in landscapes where the variable of interest and the covariates exhibited strong correlation in geographical space. Embedded Gaussian processes specifically increased accuracy in geographic areas where other matching methods would exclude samples. Increased non-linearity and auto-correlation in covariate space reduced the accuracy for all methods, although slightly less for embedded Gaussian processes. Uncertainty around estimates, however, increases more strongly for embedded Gaussian processes when the sample size is reduced. Our approach is thus likely to require larger sample sizes than other matching methods, depending on the complexity of the response variable and the number of covariates. In situations where data are not scarce, however, embedded Gaussian processes provide an effective tool to evaluate management and governance effectiveness in relation to conservation, land-use change, and ecosystem services.