TY - JOUR A1 - Menz, Stephan A1 - Latorre, Juan C. A1 - Schütte, Christof A1 - Huisinga, Wilhelm T1 - Hybrid stochastic-deterministic solution of the chemical master equation JF - Multiscale modeling & simulation : a SIAM interdisciplinary journal N2 - The chemical master equation (CME) is the fundamental evolution equation of the stochastic description of biochemical reaction kinetics. In most applications it is impossible to solve the CME directly due to its high dimensionality. Instead, indirect approaches based on realizations of the underlying Markov jump process are used, such as the stochastic simulation algorithm (SSA). In the SSA, however, every reaction event has to be resolved explicitly such that it becomes numerically inefficient when the system's dynamics include fast reaction processes or species with high population levels. In many hybrid approaches, such fast reactions are approximated as continuous processes or replaced by quasi-stationary distributions in either a stochastic or a deterministic context. Current hybrid approaches, however, almost exclusively rely on the computation of ensembles of stochastic realizations. We present a novel hybrid stochastic-deterministic approach to solve the CME directly. Our starting point is a partitioning of the molecular species into discrete and continuous species that induces a partitioning of the reactions into discrete-stochastic and continuous-deterministic processes. The approach is based on a WKB (Wentzel-Kramers-Brillouin) ansatz for the conditional probability distribution function (PDF) of the continuous species (given a discrete state) in combination with Laplace's method of integral approximation. The resulting hybrid stochastic-deterministic evolution equations comprise a CME with averaged propensities for the PDF of the discrete species that is coupled to an evolution equation of the related expected levels of the continuous species for each discrete state. In contrast to indirect hybrid methods, the impact of the evolution of discrete species on the dynamics of the continuous species has to be taken into account explicitly. The proposed approach is efficient whenever the number of discrete molecular species is small. We illustrate the performance of the new hybrid stochastic-deterministic approach in an application to model systems of biological interest. KW - chemical master equation KW - hybrid model KW - multiscale analysis KW - partial averaging KW - asymptotic approximation KW - WKB ansatz Y1 - 2012 U6 - https://doi.org/10.1137/110825716 SN - 1540-3459 VL - 10 IS - 4 SP - 1232 EP - 1262 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Schibalski, Anett A1 - Körner, Katrin A1 - Maier, Martin A1 - Jeltsch, Florian A1 - Schröder, Boris T1 - Novel model coupling approach for resilience analysis of coastal plant communities JF - Ecological applications : a publication of the Ecological Society of America N2 - Resilience is a major research focus covering a wide range of topics from biodiversity conservation to ecosystem (service) management. Model simulations can assess the resilience of, for example, plant species, measured as the return time to conditions prior to a disturbance. This requires process-based models (PBM) that implement relevant processes such as regeneration and reproduction and thus successfully reproduce transient dynamics after disturbances. Such models are often complex and thus limited to either short-term or small-scale applications, whereas many research questions require species predictions across larger spatial and temporal scales. We suggest a framework to couple a PBM and a statistical species distribution model (SDM), which transfers the results of a resilience analysis by the PBM to SDM predictions. The resulting hybrid model combines the advantages of both approaches: the convenient applicability of SDMs and the relevant process detail of PBMs in abrupt environmental change situations. First, we simulate dynamic responses of species communities to a disturbance event with a PBM. We aggregate the response behavior in two resilience metrics: return time and amplitude of the response peak. These metrics are then used to complement long-term SDM projections with dynamic short-term responses to disturbance. To illustrate our framework, we investigate the effect of abrupt short-term groundwater level and salinity changes on coastal vegetation at the German Baltic Sea. We found two example species to be largely resilient, and, consequently, modifications of SDM predictions consisted mostly of smoothing out peaks in the occurrence probability that were not confirmed by the PBM. Discrepancies between SDM- and PBM-predicted species responses were caused by community dynamics simulated in the PBM and absent from the SDM. Although demonstrated with boosted regression trees (SDM) and an existing individual-based model, IBC-grass (PBM), our flexible framework can easily be applied to other PBM and SDM types, as well as other definitions of short-term disturbances or long-term trends of environmental change. Thus, our framework allows accounting for biological feedbacks in the response to short- and long-term environmental changes as a major advancement in predictive vegetation modeling. KW - Baltic Sea KW - hybrid model KW - Lolium perenne KW - model coupling KW - Scirpus maritimus KW - transient dynamics Y1 - 2018 U6 - https://doi.org/10.1002/eap.1758 SN - 1051-0761 SN - 1939-5582 VL - 28 IS - 6 SP - 1640 EP - 1654 PB - Wiley CY - Hoboken ER -