Applying optimal control theory to a spatial simulation model of sudden oak death: ongoing surveillance protects tanoak while conserving biodiversity.

Sudden oak death has devastated tree populations across California. However, management might still slow disease spread at local scales. We demonstrate how to unambiguously characterize effective, local management strategies using a detailed, spatially explicit simulation model of spread in a single forest stand. This pre-existing, parameterized simulation is approximated here by a carefully calibrated, non-spatial model, explicitly constructed to be sufficiently simple to allow optimal control theory (OCT) to be applied. By lifting management strategies from the approximate model to the detailed simulation, effective time-dependent controls can be identified. These protect tanoak-a culturally and ecologically important species-while conserving forest biodiversity within a limited budget. We also consider model predictive control, in which both the approximating model and optimal control are repeatedly updated as the epidemic progresses. This allows management which is robust to both parameter uncertainty and systematic differences between simulation and approximate models. Including the costs of disease surveillance then introduces an optimal intensity of surveillance. Our study demonstrates that successful control of sudden oak death is likely to rely on adaptive strategies updated via ongoing surveillance. More broadly, it illustrates how OCT can inform effective real-world management, even when underpinning disease spread models are highly complex.BBSRC DTP Studentshi

Combining local- and large-scale models to predict the distributions of invasive plant species

Habitat-distribution models are increasingly used to predict the potential distributions of invasive species and to inform monitoring. However, these models assume that species are in equilibrium with the environment, which is clearly not true for most invasive species. Although this assumption is frequently acknowledged, solutions have not been adequately addressed. There are several potential methods for improving habitat-distribution models. Models that require only presence data may be more effective for invasive species, but this assumption has rarely been tested. In addition, combining modeling types to form ‘ensemble’ models may improve the accuracy of predictions. However, even with these improvements, models developed for recently invaded areas are greatly influenced by the current distributions of species and thus reflect near- rather than long-term potential for invasion. Larger scale models from species’ native and invaded ranges may better reflect long-term invasion potential, but they lack finer scale resolution. We compared logistic regression (which uses presence/absence data) and two presence-only methods for modeling the potential distributions of three invasive plant species on the Olympic Peninsula in Washington State, USA. We then combined the three methods to create ensemble models. We also developed climate-envelope models for the same species based on larger scale distributions and combined models from multiple scales to create an index of near- and long-term invasion risk to inform monitoring in Olympic National Park (ONP). Neither presence-only nor ensemble models were more accurate than logistic regression for any of the species. Larger scale models predicted much greater areas at risk of invasion. Our index of near- and long-term invasion risk indicates that \u3c4% of ONP is at high near-term risk of invasion while 67-99% of the Park is at moderate or high long-term risk of invasion. We demonstrate how modeling results can be used to guide the design of monitoring protocols and monitoring results can in turn be used to refine models. We propose that by using models from multiple scales to predict invasion risk and by explicitly linking model development to monitoring, it may be possible to overcome some of the limitations of habitat-distribution models

Transform-based particle filtering for elliptic Bayesian inverse problems

We introduce optimal transport based resampling in adaptive SMC. We consider elliptic inverse problems of inferring hydraulic conductivity from pressure measurements. We consider two parametrizations of hydraulic conductivity: by Gaussian random field, and by a set of scalar (non-)Gaussian distributed parameters and Gaussian random fields. We show that for scalar parameters optimal transport based SMC performs comparably to monomial based SMC but for Gaussian high-dimensional random fields optimal transport based SMC outperforms monomial based SMC. When comparing to ensemble Kalman inversion with mutation (EKI), we observe that for Gaussian random fields, optimal transport based SMC gives comparable or worse performance than EKI depending on the complexity of the parametrization. For non-Gaussian distributed parameters optimal transport based SMC outperforms EKI