In recent years, parallel developments in disparate disciplines have focused on what has come to be termed connectivity; a concept used in understanding and describing complex systems. Conceptualisations and operationalisations of connectivity have evolved largely within their disciplinary boundaries, yet similarities in this concept and its application among disciplines are evident. However, any implementation of the concept of connectivity carries with it both ontological and epistemological constraints, which leads us to ask if there is one type or set of approach(es) to connectivity that might be applied to all disciplines. In this review we explore four ontological and epistemological challenges in using connectivity to understand complex systems from the standpoint of widely different disciplines. These are: (i) defining the fundamental unit for the study of connectivity; (ii) separating structural connectivity from functional connectivity; (iii) understanding emergent behaviour; and (iv) measuring connectivity. We draw upon discipline-specific insights from Computational Neuroscience, Ecology, Geomorphology, Neuroscience, Social Network Science and Systems Biology to explore the use of connectivity among these disciplines. We evaluate how a connectivity-based approach has generated new understanding of structural-functional relationships that characterise complex systems and propose a ‘common toolbox’ underpinned by network-based approaches that can advance connectivity studies by overcoming existing constraints.

The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines—from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity—one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes—excitations, regular and chaotic oscillators—and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.

This study provides a new perspective on understanding the intricacies of water‐mediated connectivity in ecosystems, bridging landscape ecology and geomorphology through network science. We highlight dryland and river‐floodplain ecosystems as distinct examples of contrasting water‐controlled systems. We (1) discuss central considerations in developing structural connectivity and functional connectivity networks of water‐mediated connectivity; (2) quantify the emergent patterns in these networks; and (3) evaluate the capacity of network science tools for investigating connectivity characteristics. With a focus on strength (weights) and direction, connectivity is quantified using seven parameters at both network and node levels. We find that link density, betweenness centrality and page rank centrality are highly sensitive to directionality; global efficiency and degree centrality are particularly sensitive to weights; and relative node efficiency remains unaffected by weights and directions. Our study underscores how network science approaches can transform how we quantify and understand water‐mediated connectivity, especially in consideration of the role(s) of weights and directionality. This interdisciplinary perspective, linking ecology, hydrology and geomorphology, has implications for both theoretical insights and practical applications in environmental management and conservation efforts.

In this study, we explore the conditions that led to the unprecedented wildfire that occurred in the Chernobyl Exclusion Zone in April 2020 and the effect of this fire on ¹³⁷Cs dispersal, as wildfires are important drivers of ¹³⁷Cs resuspension, with potentially harmful consequences for the receiving ecosystems. We characterised the historical wildfire record between 2000 and 2020 using the MCD64A1.006 MODIS Burned Area Monthly Global 500 m dataset and assessed the climatic conditions associated with these wildfire events using ERA5-Land reanalysis data. We also examined fire danger indices at the time of these wildfires. We then explored the widespread effects of the April 2020 wildfire on ¹³⁷Cs resuspension and subsequent deposition using the NOAA-HYSPLIT model, concluding that the impacts of such resuspension on areas further afield were minimal. Results show that climatic conditions leading to severe wildfires are increasing, especially during March and April. High soil moisture, relative humidity and extreme temperature anomalies are associated with the largest wildfires on record, and fire risk indices at the time of the April 2020 fire were higher than for other large fires on record. We have estimated that 3854 GBq of ¹³⁷Cs resuspended during the CPPF, with atmospheric transport dominant over Russia, Ukraine, Moldova and Kazakhstan. The observed increase in large wildfires will have implications for wildfire-driven soil erosion processes, which will further exacerbate the effects of atmospheric-driven ¹³⁷Cs redistribution.