Partha Sharathi Dutta

The complexity of many natural systems stems from the abundance of interactions that go beyond simple pairwise networks. While higher-order interactions (HOIs) are fundamental to the dynamics of complex networks, their role in shaping ecological communities through species dispersal remains poorly understood. Here, using chaotic tritrophic dynamics, we explore how synchronization emerges in networks characterized by both dyadic and three-body interactions. In random networks, HOIs reduce extreme asynchrony by promoting partial clustering, but never produce complete synchrony. By contrast, in globally connected networks, stronger HOIs drive the system from asynchronous states to full synchrony, with important consequences for community persistence. Employing the master stability function, we further demonstrate that global synchrony remains stable once a critical coupling threshold is crossed. Our findings reveal that HOI-mediated dispersal introduces topology dependence governed by the local triadic structure of the landscape network, which critically shapes the system's collective emergent dynamics.

Species persistence in ecosystems results from the interplay between ecological interactions and behavioural strategies. Classical niche theory explains how resource overlap determines the strength of interactions, while evolutionary game theory (EGT) describes how cooperation and defection strategies arise from payoff-dependent decisions. Most eco-evolutionary models assume that strategies remain fixed over generations, overlooking the potential for behavioural adjustments on ecological time scales. Here, we develop a mathematical framework that integrates Lotka–Volterra niche competition (LVNC) dynamics with an adaptive strategy model, allowing species to update their strategies based on the payoff-sensitive Fermi rule. We examine community outcomes on four symmetric games: prisoner's dilemma (PD), snowdrift, stag hunt (SH) and trivial (TR) (also known as harmony), implemented on networks with varying topologies and connectivity. We find that adaptive strategy updates significantly reduce the likelihood of species extinction in comparison to static strategies, enabling coexistence in payoff regions that would otherwise lead to collapse. The structure of the network plays an important role in determining persistence, particularly in snowdrift and PD games. Furthermore, regular ecological networks may experience abrupt extinction with changes in connectivity, whereas scale-free networks support persistence through cooperative hubs. Overall, our results demonstrate that behavioural adaptation is pivotal in promoting species persistence, more so than network architecture alone.

Strategic interactions between tumor cells have been hypothesized to arise through evolutionary processes in which cell actions are conditioned on their fitness payoffs. Temporal change in payoffs impacts cell strategies, leading to the evolution of unwanted traits and genetic variation. Consequently, understanding the stochastic game dynamics of tumor metabolism for fluctuating payoffs is an important problem. Here, we study a game-theoretic model of tumor metabolism with fluctuating payoffs. A key feature of this model is the metabolic exploration rate, a quantity that governs metabolic symbiosis in tumor cells and thereby affects tumor progression to metastasis. We find that intrinsic noise induces a transition from a dominance game to a coordination game for an increase in metabolic exploration rate. This transition coincides with a change in the payoffs for the tumor cells at the threshold for critical transitions of the corresponding stochastic system. As a result, our model suggests that variations in payoffs due to intrinsic fluctuations can lead to unexpected changes in tumor cell persistence, transitioning from dominance to coexistence. Additionally, we investigate some candidate early warning signals that we hypothesize may anticipate critical transitions in the stochastic tumor system, guiding therapy to decouple tumor metabolism and thereby prevent cancer proliferation.

Ongoing environmental change threatens the persistence of species in ecological communities. Plant-pollinator mutualistic networks, which support biodiversity and ecosystem functioning, are particularly vulnerable to such disturbances. Although environmental variation is known to modify demographic rates and weaken mutualistic interactions, how its pace and stochasticity jointly affect the stability of mutualistic networks remains largely unknown. Here, we analyse a high-dimensional mutualistic network model with time-varying demographic rates, such as mortality and competition alongside noisy fluctuations. A reduced two-dimensional model reveals that sufficiently fast parameter change can trigger rate-driven pollinator collapse, which is further expedited by noise. These dynamics persist in the high-dimensional mutualistic network. Using 30 empirical plant-pollinator communities, we show that network structure is associated with vulnerability to rapid change in demographic parameters, as measured by critical rates: higher connectance and nestedness increase tolerance to rapid changes across noise intensities, whereas higher modularity reduces stability, leading to collapse at lower rates of change. Overall, our results highlight that the pace and variability of demographic changes interact with network structure to shape the stability and persistence of mutualistic communities.

Ecological networks of interacting species are higher dimensional complex systems involving nonlinear coupling. Variations in the coupling strength can weaken the resilience of the network and result in tipping or critical transitions. Such networks are continuously subject to environmental perturbations, climate change and other anthropogenic activities, which can produce uncertainty in the system parameters, such as the growth rate of the species, further impacting tipping. Despite some studies successfully quantifying uncertainty in such networks, efforts to reduce this uncertainty are limited. Here, we advance by quantifying and minimizing uncertainty in tipping thresholds across a class of important ecological networks—mutualistic networks. This is done by deploying Bayesian inference on random ordinary differential equations, leveraging a universal dimension reduction technique to transform the high-dimensional system into a one-dimensional framework. Through Bayesian inference, we demonstrate how uncertainty in the occurrence of tipping points can be narrowed, providing estimates of tipping bounds. Further, we find the giant component of interaction matrices by considering near-neighbour interactions in mutualistic networks of different dimensions, which accurately captures the uncertainty present in the original networks. Our work is one of the first to mitigate uncertainty in tipping points in networks with applicability to higher dimensional systems spanning different domains. This article is part of the theme issue ‘Critical transitions and intelligent control in complex systems’.

Savannas are grass-dominated ecosystems with scattered shrubs and savanna trees, often coexisting with tropical forests. They host a diverse range of plants and animals, act as a major carbon sink, regulate the global climate and support local economies. However, rapid environmental change is degrading these ecosystems, ultimately leading to a decline in biodiversity. Here, we consider a mathematical model of savanna–forest ecosystems to investigate rate-induced tipping (R-tipping) between distinct states under rapid variations in fitness parameters of different functional types (i.e. grass, savanna saplings and adult trees and forest trees) over time. To establish the existence of R-tipping, we determine basin instability (BI) in the corresponding frozen system with fixed-in-time inputs. Since time-dependent parameters make the model non-autonomous, it lacks compact invariant sets, which preclude the use of classical bifurcation theory. To address this, we reformulate the non-autonomous system with bi-asymptotically constant inputs as an autonomous one using compactification with an additional bounded variable. Furthermore, compactification enables us to identify the R-tipping threshold, which is crossed when tipping occurs. Overall, our analysis reveals distinct rate-induced transitions, including shifts to dominant states of grass, adult savanna trees and oscillatory dynamics.

Identifying sudden transitions during phenotypic decision-making of complex biological systems can be crucial for our ability to control a cellular state. Yet, prior determination of these sudden transitions or tipping points remains challenging, as biological systems often exhibit only subtle early changes, which are often masked by inherent noise or rapid transition dynamics. Using Notch signaling as a model, we systematically analyze dynamical transitions in Notch-Delta (ND), Notch-Delta-Jagged (NDJ), and Fringe-mediated NDJ systems for both one and two-cell contexts. In the one-cell ND system, critical slowing down (CSD)-based early warning signals (EWSs) reliably capture transitions between sender (S) and receiver (R) states and remain robust to variation in forcing rate. We further find that flickering is a precursor to transitions in one-cell NDJ system. In contrast, flickering does not occur in the two-cell Notch model due to the presence of a supercritical bifurcation. Our analysis also offers insight into how NICD (Notch Intracellular Domain)-driven and Fringe-mediated asymmetries, along with the strength of external signals, control the emergence of flickering. Overall, this study identifies sudden transitions in Notch signaling under demographic noise and can be extended to other noisy biological systems, with potential applications in drug development and targeted therapeutic interventions.

Widespread exploitation of biological resources raises concerns about the emergence of tipping points characterizing abrupt ecosystem collapse. Mitigating these tipping points is crucial for the sustainability of our being. However, our understanding of how the feedback loop between human exploitation strategies and the environment influences the mechanisms governing these tipping points remains elusive. This study employs an eco-evolutionary game-theoretic framework to explore the coupled dynamics of a renewable resource undergoing a sudden collapse. We investigate the co-evolution of strategic interactions and environmental dynamics using six possible game combinations representing diverse social dilemmas. We find that, depending on the choice of environment-dependent payoff structure, the tipping point can be shifted or even completely eluded. Additionally, this study emphasizes the impact of monitoring and punishment mechanisms against high-effort exploitation strategists on the system’s resilience. Our results unveil a rich spectrum of dynamics, spanning from multi-stability to oscillation, thereby presenting formidable challenges to resource management. While addressing the tragedy of the commons resulting from heightened harvesting efforts, targeted penalties for high-effort strategists emerge as a mitigating factor. Overall, our study highlights the interplay between ecological tipping points, individual decision-making and external control mechanisms within the realm of resource management.

The Cdc2-cyclin B/Wee1 kinase system exhibits bistability due to mutual inhibition. We explore the direction of critical slowing down near a tipping point to reveal the key biochemical species to best detect an upcoming transition.

We study rate-induced phase-tipping (RP-tipping) between two stable limit cycles of a birhythmic oscillator. We say that such an oscillator RP-tips when a time variation of an input parameter preserves the bistability of the limit cycles but induces transitions from one stable limit cycle to the other, causing abrupt changes in the amplitude and frequency of the oscillations. Crucially, these transitions occur when: the rate of change of the input is in a certain interval bounded by critical rate(s) , and the system is in certain phases of the cycle. We focus on two illustrative examples: the birhythmic van der Pol oscillator and the birhythmic Decroly–Goldbeter glycolysis model, each subjected to monotone and non-monotone shifts in their input parameters. We explain RP-tipping in terms of properties of the autonomous frozen system, including the phase of a cycle and partial basin instability along the parameter path traced by the changing input. We show that RP-tipping can occur as an irreversible one-way transition or as a series of transitions between the stable limit cycles. Finally, we present RP-tipping diagrams showing combinations of the rate and magnitude of parameter shifts and the phases of the oscillation that give rise to this genuine non-autonomous instability.