Mathematical Biology Lab

Research Interests:

Prediction and Mitigation of Tipping Points in Living Systems

Many natural systems can undergo sudden, large and often irreversible changes under the influence of small stochastic perturbations. Such qualitative sudden changes in the structure and function of a system are known as regime shift or critical transition. Critical transitions occur as a consequence of gradual changes in a system or an environmental parameters and unprecedented changes in environmental conditions project high importance on rate of change of theses parameters. The key objective is to study regime shift in various bi-stable biological systems. Well known examples of regime shifts in complex systems include: collapse of ecosystems (ecology), crash of markets in global finance (finance), systemic failures such as epileptic seizures (biology), and Arctic sea ice melting (climate). Each of these shifts has the potential to invoke serious and harmful consequences for environment as well as human well-being. Therefore, understanding the mechanisms of regime shifts and predicting them using early warning signals (EWS) are important issues due to the potential application in management and prevention of catastrophes in complex nonlinear systems.

Y. Sharma and P. S. Dutta*, Regime shifts driven by dynamic correlations in gene expression noise, Physical Review E, APS, Vol. 96 (2), 022409 (2017). DOI: https://doi.org/10.1103/PhysRevE.96.022409
P. S. Dutta*, Y. Sharma and K. C. Abbott, Robustness of early warning signals for catastrophic and non-catastrophic transitions, OIKOS, Wiley, Vol. 127(9), pp 1251-1263, (2018). DOI: https://doi.org/10.1111/oik.05172
S. Sarkar, S. Sinha, H. Levine, M. K. Jolly and P. S. Dutta*, Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination, PNAS, Vol. 116, Issue 52, 2019-13773, (2019). DOI: https://doi.org/10.1073/pnas.1913773116
T. Kaur, S. Sarkar, S. Chowdhury, S. Sinha, M. K. Jolly and P. S. Dutta*, Anticipating the novel coronavirus (COVID-19) pandemic, Frontiers in Public Health, Vol. 8, 569669, (2020). DOI: https://doi.org/10.3389/fpubh.2020.569669
S. Deb, S. Bhandary, and P. S. Dutta*, Evading tipping points in socio-mutualistic networks via structure mediated optimal strategy, Journal of Theoretical Biology, Elsevier, Vol. 567, 111494(10) (2023). DOI: https://doi.org/10.1016/j.jtbi.2023.111494
T. Kaur, and P. S. Dutta, Critical rates of climate warming and abrupt collapse of ecosystems, Proceedings of the Royal Society A, The Royal Society Publishing, Vol. 478 (2264), 2022.0086 (2022). DOI: https://doi.org/10.1098/rspa.2022.0086
D. A. O'Brien, S. Deb, G. Gal, S. Thackeray, P. S. Dutta, S. Matsuzaki, L. May, C. F. Clements, Early warning signals have limited applicability to empirical lake data, Nature Communications, 14, 7942 (2023). DOI: https://doi.org/10.1038/s41467-023-43744-8

Effects of Climate Change on Ecosystems

Ecosystems are witnessing the shrinking of glaciers, shifts in ranges of plants and animals, formation of ice sheets on the river due to changing climatic conditions. Current climatic projections pose a significant threat to the survival of species. Increasing emission of greenhouse gases in the atmosphere and various anthropogenic factors has caused our Earth’s surface to warm, creating colder/warmer or drier/wetter regions worldwide. Spatiotemporal evolution in ecological networks is an integral part of natural communities. Moreover, direct negative effects of warming can be altered by the subsequent indirect effects of warming in complex trophic structures. It is potentially essential to understand the calling of nature and investigate how complex interaction modules respond towards the changing global mean temperature as they form the reason for our being. We investigate ecological interactions by incorporating the influence of abiotic stress (temperature) on species biological processes consistent with studies based on the reaction kinetics and empirical data [1-2]. Our prime aim is to understand the different dynamics of ecological networks, their stability, and the impact of environmental warming on biodiversity sustainability.

T. Kaur and P. S. Dutta*, Persistence and stability of interacting species in response to climate warming: The role of trophic structure, Theoretical Ecology, Springer, Vol. 13, Issue 3, pp 333-348, (2020). DOI: https://doi.org/10.1007/s12080-020-00456-9
A. Narang, S. Bhandary, T. Kaur, A. Gupta, T. Banerjee and P. S. Dutta*, Long-range dispersal promotes species persistence in climate extremes, CHAOS, AIP, Vol. 29, Issue 10, pp 103136 (2019). DOI: https://doi.org/10.1063/1.5120105
A. Narang, and P. S. Dutta, Climate warming and dispersal strategies determine species persistence in a metacommunity, Theoretical Ecology, Springer, Vol. 15, Issue 1, pp 81-92 (2022). DOI: https://doi.org/10.1007/s12080-022-00531-3
T. Kaur, and P. S. Dutta, Critical rates of climate warming and abrupt collapse of ecosystems, Proceedings of the Royal Society A, The Royal Society Publishing, Vol. 478 (2264), 2022.0086 (2022). DOI: https://doi.org/10.1098/rspa.2022.0086
S. Bhandary, S. Deb, and P. S. Dutta*, Rising Temperature Drives Tipping Points in Mutualistic Networks, Royal Society Open Science, The Royal Society Publishing, Vol. 10(2), 221363(17) (2023). DOI: https://doi.org/10.1098/rsos.221363

Spatio-temporal Dynamics of Coupled Ecological Systems

Synchrony and stability are two important dynamical phenomena which are widely observed in population ecology. These two phenomena have great importance for better management of ecosystem functioning and theoretical understanding of these two phenomena in population dynamics is still demanding. We investigate spatial ecological interactions consistently found in nature to understand mechanisms driving synchronous dynamics as well as stability of ecosystems [1-2]. Various mathematical models of ecological systems and the concepts of nonlinear dynamics are taken into account, the relationship between synchrony and stability is characterized in terms of time and space.

A. Gupta, T. Banerjee and P. S. Dutta*, Increased persistence via asynchrony in oscillating ecological populations with long-range interaction, Physical Review E, APS, Vol. 96 (4), 042202 (2017). DOI: https://doi.org/10.1103/PhysRevE.96.042202
R. Arumugam and P. S. Dutta*, Synchronization and entrainment of metapopulations: A trade-off among time-induced heterogeneity, dispersal and seasonal force, Physical Review E, APS, Vol. 97 (6), 062217, (2018). DOI: https://doi.org/10.1103/PhysRevE.97.062217
S. Bhandary, D. Biswas, T. Banerjee and P. S. Dutta*, Effects of time-varying habitat connectivity on metacommunity persistence, Physical Review E, APS, Vol. 106 (1), 014309 (12) (2022). DOI: https://doi.org/10.1103/PhysRevE.106.014309
A. Narang, T. Banerjee, and P. S. Dutta*, Noise-induced symmetry breaking in a network of excitable ecological systems, Physical Review E, APS, Vol. 107 (2), 024410(6) (2023). DOI: https://doi.org/10.1103/PhysRevE.107.024410

Network Resilience

Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties, for instance collapse of pollinator communities and cascading failures in power grids. Such a sudden transition demonstrates a network’s resilience, which is the ability of a system to persist in the face of perturbations. Most resilience research has focused on equilibrium network states which suddenly shifts to an alternative state at a threshold value of a driver. Although presence of non-equilibrium dynamics in a number of nodes may advance or delay sudden transitions, and give early warning signals of an impeding collapse – has never been studied. We try to bridge this gap by studying network models with diverse topology, in which non-equilibrium dynamics may appear in the network even before the transition to an alternative state, in response to environmental stress deteriorating their external conditions [1]. The percentage of uncoupled nodes exhibiting non-equilibrium dynamics plays an important role in determining the transition type of the network.

S. Bhandary, T. Kaur, T. Banerjee and P. S. Dutta*, Network resilience of FitzHugh-Nagumo neurons in the presence of non-equilibrium dynamics, Physical Review E, APS, Vol. 103 (2), 022314 (12), (2021). DOI: https://doi.org/10.1103/PhysRevE.103.022314
S. Bhandary, S. Deb, and P. S. Dutta*, Rising Temperature Drives Tipping Points in Mutualistic Networks, Royal Society Open Science, The Royal Society Publishing, Vol. 10(2), 221363(17) (2023). DOI: https://doi.org/10.1098/rsos.221363

Ongoing External Projects:

"Abrupt Transitions and its Indicators in Living Systems" funded by SERB, Govt. of India (CRG/2019/002402) for the period Nov. 2019 -- Nov. 2022.
"Collective Dynamics in Adaptive Ecological Networks" funded by SERB, Govt. of India (MTR/2021/000148) for the period Feb. 2022 -- Feb. 2025.

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