A Petri net modeling approach to explore the temporal dynamics of the provision of multiple ecosystem services

The representation of the temporal dynamics of ecosystem services (ES) is a crucial research frontier in the field of ES modeling. In fact, most current ES models focus on static ES assessments, that need to be repeated with different inputs per time step to explore potential changes in ES. Here, we present a new approach for the dynamic modeling of multiple ES, based on the Petri Net modeling framework. The key features are: (i) multiple ES are modeled together as a single network, using a social-ecological systems (SES) perspective; (ii) the model accounts for the interactions occurring among ES, by distinguishing between the ES whose provision is mediated by some type of human input, which can produce some side-effects on the system, and those that are generated directly through ecosystem functions and do not generate side-effects; (iii) the model can reproduce the effects of changing drivers on the elements of the SES. These features allow to use the model to explore how ES can evolve over time under different "what-if" scenarios. The importance of considering the ES interactions is tested, showing that failing to include them in the model remarkably affects the results. Due to its complexity, the model should be used as an exploratory tool, focusing on the analysis of the general trends of multiple ES provision, rather than on the generation of quantitative projections. A first conceptual application to the Venice lagoon, Italy, is presented, in which the trends of 13 different ES are simulated. This application shows the potential of the model in exploring the development produced by climate change and socio-economic pressures, and the effects of a set of possible management actions. This modeling approach can contribute to generate new perspectives on the dynamic modeling of multiple ES and on the integrated management of SES.