Master regulators of biological systems in higher dimensions

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions.

Kernel-based joint independence tests for multivariate stationary and non-stationary time series

Multivariate time-series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the d-variable Hilbert-Schmidt independence criterion to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate, neuroscience and socio-economic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.

Flickering Emergences: The Question of Locality in Information-Theoretic Approaches to Emergence

"Emergence", the phenomenon where a complex system displays properties, behaviours, or dynamics not trivially reducible to its constituent elements, is one of the defining properties of complex systems. Recently, there has been a concerted effort to formally define emergence using the mathematical framework of information theory, which proposes that emergence can be understood in terms of how the states of wholes and parts collectively disclose information about the system's collective future. In this paper, we show how a common, foundational component of information-theoretic approaches to emergence implies an inherent instability to emergent properties, which we call flickering emergence. A system may, on average, display a meaningful emergent property (be it an informative coarse-graining, or higher-order synergy), but for particular configurations, that emergent property falls apart and becomes misinformative. We show existence proofs that flickering emergence occurs in two different frameworks (one based on coarse-graining and another based on multivariate information decomposition) and argue that any approach based on temporal mutual information will display it. Finally, we argue that flickering emergence should not be a disqualifying property of any model of emergence, but that it should be accounted for when attempting to theorize about how emergence relates to practical models of the natural world.

Opinion Dynamics with Higher-Order Bounded Confidence

The higher-order interactions in complex systems are gaining attention. Extending the classic bounded confidence model where an agent's opinion update is the average opinion of its peers, this paper proposes a higher-order version of the bounded confidence model. Each agent organizes a group opinion discussion among its peers. Then, the discussion's result influences all participants' opinions. Since an agent is also the peer of its peers, the agent actually participates in multiple group discussions. We assume the agent's opinion update is the average over multiple group discussions. The opinion dynamics rules can be arbitrary in each discussion. In this work, we experiment with two discussion rules: centralized and decentralized. We show that the centralized rule is equivalent to the classic bounded confidence model. The decentralized rule, however, can promote opinion consensus. In need of modeling specific real-life scenarios, the higher-order bounded confidence is more convenient to combine with other higher-order interactions, from the contagion process to evolutionary dynamics.

Capturing complex interactions in disease ecology with simplicial sets

Network approaches have revolutionized the study of ecological interactions. Social, movement and ecological networks have all been integral to studying infectious disease ecology. However, conventional (dyadic) network approaches are limited in their ability to capture higher-order interactions. We present simplicial sets as a tool that addresses this limitation. First, we explain what simplicial sets are. Second, we explain why their use would be beneficial in different subject areas. Third, we detail where these areas are: social, transmission, movement/spatial and ecological networks and when using them would help most in each context. To demonstrate their application, we develop a novel approach to identify how pathogens persist within a host population. Fourth, we provide an overview of how to use simplicial sets, highlighting specific metrics, generative models and software. Finally, we synthesize key research questions simplicial sets will help us answer and draw attention to methodological developments that will facilitate this.

Non-additive biotic interactions improve predictions of tropical tree growth and impact community size structure

Growth in individual size or biomass is a key demographic component in population models, with wide-ranging applications from quantifying species performance across abiotic or biotic conditions to assessing landscape-level dynamics under global change. In forest ecology, the responses of tree growth to biotic interactions are widely held to be crucial for understanding forest diversity, function, and structure. To date, most studies on plant-plant interactions only examine the additive competitive or facilitative interactions between species pairs; however, there is increasing evidence of non-additive, higher-order interactions (HOIs) impacting species demographic rates. When HOIs are present, the dynamics of a multispecies community cannot be fully understood or accurately predicted solely from pairwise outcomes because of how additional species "interfere" with the direct, pairwise interactions. Such HOIs should be particularly prevalent when species show non-linear functional responses to resource availability and resource-acquisition traits themselves are density dependent. With this in mind, we used data from a tropical secondary forest-a system that fulfills both of these conditions-to build an ontogenetic diameter growth model for individuals across 10 woody-plant species. We allowed both direct and indirect interactions within communities to influence the species-specific growth parameters in a generalized Lotka-Volterra model. Specifically, indirect interactions entered the model as higher-order quadratic terms, i.e., non-additive effects of conspecific and heterospecific neighbor size on the focal individual's growth. For the whole community and for four out of 10 focal species, the model that included HOIs had more statistical support than the model that included only direct interactions, despite the former containing a far greater number of parameters. HOIs had comparable effect sizes to direct interactions, and tended to further reduce the diameter growth rates of most species beyond what direct interactions had already reduced. In a simulation of successional stand dynamics, the inclusion of HOIs led to rank swaps in species' diameter hierarchies, even when community-level size distributions remained qualitatively similar. Our study highlights the implications, and discusses possible mechanisms, of non-additive density dependence in highly diverse and light-competitive tropical forests.

A framework and standardized terminology to facilitate the study of predation-risk effects

The very presence of predators can strongly influence flexible prey traits such as behavior, morphology, life history, and physiology. In a rapidly growing body of literature representing diverse ecological systems, these trait (or "fear") responses have been shown to influence prey fitness components and density, and to have indirect effects on other species. However, this broad and exciting literature is burdened with inconsistent terminology that is likely hindering the development of inclusive frameworks and general advances in ecology. We examine the diverse terminology used in the literature, and discuss pros and cons of the many terms used. Common problems include the same term being used for different processes, and many different terms being used for the same process. To mitigate terminological barriers, we developed a conceptual framework that explicitly distinguishes the multiple predation-risk effects studied. These multiple effects, along with suggested standardized terminology, are risk-induced trait responses (i.e., effects on prey traits), interaction modifications (i.e., effects on prey-other-species interactions), nonconsumptive effects (i.e., effects on the fitness and density of the prey), and trait-mediated indirect effects (i.e., the effects on the fitness and density of other species). We apply the framework to three well studied systems to highlight how it can illuminate commonalities and differences among study systems. By clarifying and elucidating conceptually similar processes, the framework and standardized terminology can facilitate communication of insights and methodologies across systems and foster cross-disciplinary perspectives.