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1. Origin of exponential growth in nonlinear reaction networks

   https://doi.org/10.1073/pnas.2013061117  

   Lin, Wei-Hsiang; Kussell, Edo; Young, Lai-Sang; Jacobs-Wagner, Christine (November 2020, Proceedings of the National Academy of Sciences of the United States of America)

   null (Ed.)

   Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlin- ear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of long- term growth: scalability of flux functions and ergodicity of the rescaled systems. Our theory shows that nonlinear fluxes can gen- erate not only balanced growth but also oscillatory or chaotic growth modalities, explaining nonequilibrium dynamics observed in cell cycles and ecosystems. Our mathematical framework is broadly useful in predicting long-term growth rates from natural and synthetic networks, analyzing the effects of system noise and perturbations, validating empirical and phenomenological laws on growth rate, and studying autocatalysis and network evolution. 

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2. Acquisitive plants exhibit stronger phenological shifts in response to warming: insights from meta-analysis and long-term monitoring

   https://doi.org/10.1038/s41467-026-70474-4  

   Xiong, Kexin; Reich, Peter B; Ciais, Philippe; Lu, Chunyan; Zhou, Huimin; Wang, Xinxin; Peñuelas, Josep; Wu, Chaoyang; Liu, Huiying (December 2026, Nature Communications)

   Abstract As climate warming accelerates, shifts in plant phenology are reshaping the functioning and stability of terrestrial ecosystems. While the roles of climatic drivers in shaping phenological responses to warming are well established, the influence of intrinsic plant functional traits remains poorly understood. Here, we combine two complementary approaches through a meta-analysis of 124 field warming experiments and an analysis of long-term phenological monitoring networks (CPON and USA‑NPN) to evaluate phenological responses to warming across a spectrum of resource-use strategies in seasonally cold biomes. Our meta-analysis demonstrates that resource-acquisitive plants, characterized by higher nutrient concentrations and thinner leaves, show significantly stronger phenological responses to experimental warming. This pattern is observed consistently across both leaf-out in spring and senescence in autumn. These results from meta-analysis are further supported by two long-term observational datasets, which also show more pronounced phenological shifts in acquisitive species under long-term warming. Our findings present a trait-climate integration framework that extends beyond conventional environmental drivers, providing a mechanistic foundation to enhance the accuracy of forecasts for plant responses to climate change. 

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3. Responses of Coastal Ecosystems to Climate Change: Insights from Long-Term Ecological Research

   https://doi.org/10.1093/biosci/biac006  

   Reed, Daniel C; Schmitt, Russell J; Burd, Adrian B; Burkepile, Deron E; Kominoski, John S; McGlathery, Karen J; Miller, Robert J; Morris, James T; Zinnert, Julie C (August 2022, BioScience)

   abstract Coastal ecosystems play a disproportionately large role in society, and climate change is altering their ecological structure and function, as well as their highly valued goods and services. In the present article, we review the results from decade-scale research on coastal ecosystems shaped by foundation species (e.g., coral reefs, kelp forests, coastal marshes, seagrass meadows, mangrove forests, barrier islands) to show how climate change is altering their ecological attributes and services. We demonstrate the value of site-based, long-term studies for quantifying the resilience of coastal systems to climate forcing, identifying thresholds that cause shifts in ecological state, and investigating the capacity of coastal ecosystems to adapt to climate change and the biological mechanisms that underlie it. We draw extensively from research conducted at coastal ecosystems studied by the US Long Term Ecological Research Network, where long-term, spatially extensive observational data are coupled with shorter-term mechanistic studies to understand the ecological consequences of climate change. 

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4. Model-assisted deep learning of rare extreme events from partial observations

   https://doi.org/10.1063/5.0077646  

   Asch, Anna; J. Brady, Ethan; Gallardo, Hugo; Hood, John; Chu, Bryan; Farazmand, Mohammad (April 2022, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the training data are obtained from numerical simulations, as opposed to observations, with adequate samples from extreme events. However, to ensure the trained networks are applicable in practice, the training is not performed on the full simulation data; instead, we only use a small subset of observable quantities, which can be measured in practice. We investigate the feasibility of this model-assisted framework on three different dynamical systems (Rössler attractor, FitzHugh–Nagumo model, and a turbulent fluid flow) and three different deep neural network architectures (feedforward, long short-term memory, and reservoir computing). In each case, we study the prediction accuracy, robustness to noise, reproducibility under repeated training, and sensitivity to the type of input data. In particular, we find long short-term memory networks to be most robust to noise and to yield relatively accurate predictions, while requiring minimal fine-tuning of the hyperparameters. 

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5. A New Conceptual Model of Tropical Seagrass Eutrophication: Evidence for Single Nutrient Management

   https://doi.org/10.1111/conl.13133  

   Shayka, Bridget F; Allgeier, Jacob E (September 2025, Conservation Letters)

   ABSTRACT Nutrient enrichment is one of the greatest threats to seagrass ecosystems globally. Current management is based on a temperate conceptual model of seagrass eutrophication where epiphytes and then phytoplankton cause light limitation and seagrass die‐off. However, producers in tropical and subtropical systems respond differently to nutrients, suggesting a need for an updated conceptual model for these ecosystems. Using a long‐term multifactorial seagrass enrichment experiment of nitrogen and phosphorus supply rates and ratios, we showed that seagrass growth was enhanced with increased phosphorus but not nitrogen supply and was never inhibited by epiphytes or shifts in seagrass community structure. A parallel experiment showed phytoplankton primarily responded to nitrogen enrichment. Our findings provide evidence for a new nutrient enrichment conceptual model in subtropical and tropical seagrass ecosystems, with a larger role played by phytoplankton. We suggest that management efforts to mitigate nitrogen supply alone may offer an effective starting point for reducing negative impacts of eutrophication, one of the most ubiquitous stressors to these imperiled ecosystems. 

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