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Redressing global patterns of biodiversity loss requires quantitative frameworks that can predict ecosystem collapse and inform restoration strategies. By applying a network-based dynamical approach to synthetic and real-world mutualistic ecosystems, we show that biodiversity recovery following collapse is maximized when extirpated species are reintroduced based solely on their total number of connections in the original interaction network. More complex network-based strategies that prioritize the reintroduction of species that improve ‘higher order’ topological features such as compartmentalization do not provide meaningful performance improvements. These results suggest that it is possible to design nearly optimal restoration strategies that maximize biodiversity recovery for data-poor ecosystems in order to ensure the delivery of critical natural services that fuel economic development, food security, and human health around the globe. 

Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL) hyperparameters, specifically, the depth, width and ensemble size, for robust function mapping with uncertainty quantification, is still emerging. This paper attempts to further our understanding by mapping Bayesian connectionist representations to polynomials of different orders with varying noise types and ratios. We examine the noise-contaminated polynomials to search for the combination of hyperparameters that can extract the underlying polynomial signals while quantifying uncertainties based on the noise attributes. Specifically, we attempt to study the question that an appropriate neural architecture and ensemble configuration can be found to detect a signal of any n-th order polynomial contaminated with noise having different distributions and signal-to-noise (SNR) ratios and varying noise attributes. Our results suggest the possible existence of an optimal network depth as well as an optimal number of ensembles for prediction skills and uncertainty quantification, respectively. However, optimality is not discernible for width, even though the performance gain reduces with increasing width at high values of width. Our experiments and insights can be directional to understand theoretical properties of BDL representations and to design practical solutions. 

Abstract Natural climate variability, captured through multiple initial condition ensembles, may be comparable to the variability caused by knowledge gaps in future emissions trajectories and in the physical science basis, especially at adaptation-relevant scales and projection horizons. The relations to chaos theory, including sensitivity to initial conditions, have caused the resulting variability in projections to be viewed as the irreducible uncertainty component of climate. The multiplier effect of ensembles from emissions-trajectories, multiple-models and initial-conditions contribute to the challenge. We show that ignoring this variability results in underestimation of precipitation extremes return periods leading to maladaptation. However, we show that concatenating initial-condition ensembles results in reduction of hydroclimate uncertainty. We show how this reduced uncertainty in precipitation extremes percolates to adaptation-relevant-Depth-Duration Frequency curves. Hence, generation of additional initial condition ensembles therefore no longer needs to be viewed as an uncertainty explosion problem but as a solution that can lead to uncertainty reduction in assessment of extremes.