Advancing approaches for understanding the nature-people link.

• Bayesian Belief Multifunctionality Framework is a new tool that links socio-ecological research; • The framework acknowledges ecosystem complexity and multifunctionality; • Our framework links species and their traits to ecosystem functions and NCPs; • The trait set that supports a high level of metal sequestration also supports a high level of N-release; • The trait set that maximised secondary production contributes to higher sediment stability; • Increasing the density of organisms generally positively affects NCPs. Acknowledging complexity within relationships between fundamental ecology and societal research is critical in improving our current understanding of how natural ecosystems work and how they could be managed to achieve set management goals. Specifically, this challenge is linked to the multifunctional nature of ecosystems. We develop the Bayesian Belief Multifunctionality Framework to studying nature-people links that allows a holistic and transparent analysis of the relationships between species, their functional traits, multiple ecosystem functions and multiple nature's contributions to people (NCPs). We assess seven ecosystem functions common in marine soft-sediments (secondary production, metal sequestration, denitrification, N-release, sediment stability, primary production and sediment formation) and nine NCPs (food and feed, supporting services, climate regulation, regulation of coastal water quality, physical and psychological experience, habitat creation, learning, materials and erosion control). We use a case study based on an extensive and diverse intertidal sandflat macrofaunal community within Kaipara Harbour, New Zealand. By testing different scenarios in which we identify the set of traits responsible for the highest function performance for every function, we show that functional redundancy (i.e., the presence of multiple species that deliver the maximum performance for a specific function) was high for some functions but low for others. In our model, functional redundancy was the lowest for denitrification and secondary production, while primary production exhibited high functional redundancy. The network analysis also allowed us to gain insight into functional synergies and trade-offs, resulting from maximising individual function to a trait set. The trait set that maximised secondary production contributes to higher sediment stability; the trait set that maximised metal sequestration contributes to higher N-release; and the trait set that maximised denitrification contributes to high rates of metal sequestration and N-release. Negative effects were also apparent, e.g., the trait set that maximised metal sequestration resulted in a lower probability in sediment stability and secondary production. Finally, the scenario testing feature of the framework allowed for exploration of the changes in NCPs from changes in macrofauna density. High density of species with a trait set identified as important to individual functions generated an increase in the provision of the majority of considered NCPs. Thanks to its clear and transparent result presentation and flexible analysis, the BN Multifunctionality Framework can deliver insightful messages into multifunctionality links helping to reveal the multifunctional nature of diverse and complex natural ecosystems. Image, graphical abstract [ABSTRACT FROM AUTHOR]