Since the definition of Natural Capital was proposed (Costanza et al., 2014), a wide range of quantitative and qualitative modeling research on ES become available. However, while many were supported by poor flexibility of software packages, other had difficulties in eliciting expert knowledge and were limited by the inability to model feedback loop (Landuyt et al., 2013). Bayesian Networks (BN) and Bayesian belief networks (BBNs) are semi-quantitative modeling approaches that have recently gained importance in ES modeling. A main advantage is their capability to incorporate, in a single cause-effect network, causal relationships from very different sources, such as expert judgement, literature, process-based models and empirical data, allowing to deal directly and explicitly with uncertainty (Keshtkar et al., 2013). Furthermore, they can be used in both directions along the network: as a prognostic tool, e.g. to check the outcome by fixing management scenarios; or as diagnostic tool, e.g. to help identifying and prioritizing targets of management actions by fixing the outcome. If BBNs are combined with information on the costs and expected benefits of an action, one can derive guidelines about the best option to adopt given the network structure and the associated cost and utility functions, using varying management scenarios.

Models will be developed if possible for costs and benefits of management actions concerning Supporting services (A3) Carbon Stocks and Sequestration (A4) and Socio-cultural values (A5). Non-market prices will be set for Cultural ES, using the willingness of people to pay water taxes or the actual travelling cost to riverine landscapes, and proxies of market prices for Carbon sequestration. Conversion of BBN models into a user friendly toolbox in open-access will be made using Netica Application Programmer, or other. Those Application Programmer Interfaces, API, will ultimately enable decision-makers to quantify trade-offs associated with alternative management options, such as land-use alternatives and to identify areas where investment in natural capital can enhance ES provided by riparian forests.