Throughflow centrality is a global indicator of the functional importance of species in ecosystems

To better understand and manage complex systems like ecosystems it is critical to know the relative contribution of system components to system functioning. Ecologists and social scientists have described many ways that individuals can be important; This paper makes two key contributions to this research area. First, it shows that throughflow, the total energy-matter entering or exiting a system component, is a global indicator of the relative contribution of the component to the whole system activity. It is global because it includes the direct and indirect exchanges among community members. Further, throughflow is a special case of Hubbell status as defined in social science. This recognition effectively joins the concepts, enabling ecologists to use and build on the broader centrality research in network science. Second, I characterize the distribution of throughflow in 45 empirically-based trophic ecosystem models. Consistent with expectations, this analysis shows that a small fraction of the system components are responsible for the majority of the system activity. In 73% of the ecosystem models, 20% or less of the nodes generate 80% or more of the total system throughflow. Four or fewer dominant nodes are required to account for 50% of the total system activity. 121 of the 130 dominant nodes in the 45 ecosystem models could be classified as primary producers, dead organic matter, or bacteria. Thus, throughflow centrality indicates the rank power of the ecosystems components and shows the power concentration in the primary production and decomposition cycle. Although these results are specific to ecosystems, these techniques build on flow analysis based on economic input-output analysis. Therefore these results should be useful for ecosystem ecology, industrial ecology, the study of urban metabolism, as well as other domains using input-output analysis.Comment: 7 figures, 2 table

Weighting and indirect effects identify keystone species in food webs

Species extinctions are accelerating globally, yet the mechanisms that maintain local biodiversity remain poorly understood. The extinction of species that feed on or are fed on by many others (i.e. ‘hubs’) has traditionally been thought to cause the greatest threat of further biodiversity loss. Very little attention has been paid to the strength of those feeding links (i.e. link weight) and the prevalence of indirect interactions. Here, we used a dynamical model based on empirical energy budget data to assess changes in ecosystem stability after simulating the loss of species according to various extinction scenarios. Link weight and/or indirect effects had stronger effects on food‐web stability than the simple removal of ‘hubs’, demonstrating that both quantitative fluxes and species dissipating their effects across many links should be of great concern in biodiversity conservation, and the potential for ‘hubs’ to act as keystone species may have been exaggerated to date

Functional Integration of Ecological Networks through Pathway Proliferation

Large-scale structural patterns commonly occur in network models of complex systems including a skewed node degree distribution and small-world topology. These patterns suggest common organizational constraints and similar functional consequences. Here, we investigate a structural pattern termed pathway proliferation. Previous research enumerating pathways that link species determined that as pathway length increases, the number of pathways tends to increase without bound. We hypothesize that this pathway proliferation influences the flow of energy, matter, and information in ecosystems. In this paper, we clarify the pathway proliferation concept, introduce a measure of the node--node proliferation rate, describe factors influencing the rate, and characterize it in 17 large empirical food-webs. During this investigation, we uncovered a modular organization within these systems. Over half of the food-webs were composed of one or more subgroups that were strongly connected internally, but weakly connected to the rest of the system. Further, these modules had distinct proliferation rates. We conclude that pathway proliferation in ecological networks reveals subgroups of species that will be functionally integrated through cyclic indirect effects.Comment: 29 pages, 2 figures, 3 tables, Submitted to Journal of Theoretical Biolog

Beyond the black box: Promoting mathematical collaborations for elucidating interactions in soil ecology

© 2019 The Authors. Understanding soil systems is critical because they form the structural and nutritional foundation for plants and thus every terrestrial habitat and agricultural system. In this paper, we encourage increased use of mathematical models to drive forward understanding of interactions in soil ecological systems. We discuss several distinctive features of soil ecosystems and empirical studies of them. We explore some perceptions that have previously deterred more extensive use of models in soil ecology and some advances that have already been made using models to elucidate soil ecological interactions. We provide examples where mathematical models have been used to test the plausibility of hypothesized mechanisms, to explore systems where experimental manipulations are currently impossible, or to determine the most important variables to measure in experimental and natural systems. To aid in the development of theory in this field, we present a table describing major soil ecology topics, the theory previously used, and providing key terms for theoretical approaches that could potentially address them. We then provide examples from the table that may either contribute to important incremental developments in soil science or potentially revolutionize our understanding of plant-soil systems. We challenge scientists and mathematicians to push theoretical explorations in soil systems further and highlight three major areas for the development of mathematical models in soil ecology: Theory spanning scales and ecological hierarchies, processes, and evolution