  Model uncertainty and limited data are fundamental challenges to robust
management of human intervention in a natural system. These challenges are
acutely highlighted by concerns that many ecological systems may contain
tipping points, such as Allee population sizes. Before a collapse, we do not
know where the tipping points lie, if they exist at all. Hence, we know neither
a complete model of the system dynamics nor do we have access to data in some
large region of state-space where such a tipping point might exist. We
illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian
Process (GP) prior provides a flexible representation of this inherent
uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework
in order to make robust management predictions with both model uncertainty and
limited data. We use simulations to evaluate this approach as compared with the
standard approach of using model selection to choose from a set of candidate
models. We find that model selection erroneously favors models without tipping
points -- leading to harvest policies that guarantee extinction. The GPDP
performs nearly as well as the true model and significantly outperforms
standard approaches. We illustrate this using examples of simulated
single-species dynamics, where the standard model selection approach should be
most effective, and find that it still fails to account for uncertainty
appropriately and leads to population crashes, while management based on the
GPDP does not, since it does not underestimate the uncertainty outside of the
observed data.
