Ferenc Jordán

The trophic interactions among species can be represented by a food web. Since the functional importance of species in communities are largely due to their contribution to maintaining ecological processes, importance can be quantified by their network position in the food web. From this perspective, central species can be supposedly more important than peripheral ones. Over the past decade, another aspect of species importance has emerged that examines how unique a species is in its interaction pattern. This focuses on their functional replaceability, quantifying local redundancies in network structure. Originally, the concept of species uniqueness is related to how the field of influence of a species overlaps with other species (i.e., how similar are their network neighborhoods); and from a functional and trophic viewpoint, a species is unique if such an overlap is small. In the current methodology, however, overlap not only considers information within the field of influence, but also those outside it, and this deviates from the original concept of species uniqueness measurement. In this paper, by analysing 92 food webs, we demonstrate that out-of-field information can dominate when quantifying the uniqueness value of species for larger food webs; and we propose a modified approach to species uniqueness measurement just by including the within-field information alone. We find that species uniqueness ranking derived from our new approach and that from the current methodology correlate to various degree for those 92 food webs. We discuss how the difference depends on food web topology. Notably, negative correlation tends to be observed for food webs that are large in size and more sparse in its structural organization. This means that network size and density influence the relative importance of indirect effects in community dynamics.

Achieving sustainable human-wildlife coexistence in well-functioning ecosystems is a vitally important and major challenge under global change. In response, rewilding is an emerging paradigm in ecosystem service provision through the re-establishment of natural ecological processes in self-sustaining ecosystems. Effective prediction of ecological changes in rewilding projects requires tools integrating quantitative methods with social-economic dimensions and thinking. We consider the current state of such quantitative treatments, highlighting opportunities for harnessing mathematics and statistics. We present an emerging quantitative framework, encompassing four key areas of the rewilding process: design and planning, ecological modelling, metrics for assessment, and coupled social-ecological systems, informed by recent progress in mathematical, statistical, and ecological modelling. The adaptive cycle concept is used to integrate these four key areas. Dynamical systems modelling informed by empirical knowledge allows us to address trans-disciplinary feedbacks, nonlinearities, and anticipate the potential for emerging properties and critical transitions/regime shifts during rewilding, predicting the range and likelihood of alternative scenarios. Our framework provides a possible foundation and new opportunities for a more robust quantitative and predictive methodology for rewilding. We argue that a project is more likely to achieve its goals, and in a more cost-effective way, if mathematical scientists are included from the beginning.

This theme issue features 18 papers exploring ecological interactions, encompassing metabolic, social, and spatial connections alongside traditional trophic networks. This integration enriches food web research, offering insights into ecological dynamics. By examining links across organisms, populations, and ecosystems, a hierarchical approach emerges, connecting horizontal effects within organizational levels vertically across biological organization levels. The inclusion of interactions involving humans is a key focus, highlighting the need for their integration into ecology given the complex interactions between human activities and ecological systems in the Anthropocene. The comprehensive exploration in this theme issue sheds light on the interconnectedness of ecological systems and the importance of considering diverse interactions in understanding ecosystem dynamics. This article is part of the theme issue ‘Connected interactions: enriching food web research by spatial and social interactions’.

Climate change affects ecosystems at several levels: by altering the spatial distribution of individual species, by locally rewiring interspecific interactions, and by reorganizing trophic networks at larger scales. The dynamics of marine food webs are becoming more and more sensitive to spatial processes and connections in the seascape. As a case study, we study the atlantification of the Barents Sea: we compare spatio-temporal subsystems at three levels: the identity of key organisms, critically important interactions and the entire food web. Network analysis offers quantitative measurements, including centrality indices, trophic similarity indices, a topological measure of interaction asymmetry and network-level measures. We found that atlantification alters the identity of key species (boreal demersals becoming hubs), results in strongly asymmetric interactions (dominated by haddock), changes the dominant regulation regime (from bottom-up to wasp-waist control) and makes the food web less modular. Since the results of food web analysis may be quite sensitive to network construction, the aggregation of food web data was explicitly studied to increase the robustness of food web analysis. We found that an alternative, mathematical aggregation algorithm better preserves some network properties (e.g. density) of the original, unaggregated network than the biologically inspired aggregation into functional groups. This article is part of the theme issue ‘Connected interactions: enriching food web research by spatial and social interactions’.