Discover network dynamics with neural symbolic regression

Yu et al., 2025

Discovering network dynamics—automatically

Complex systems are everywhere: from ecosystems and gene networks to epidemics and social behavior. Each consists of many interacting components whose collective dynamics are notoriously difficult to model. Traditionally, scientists have relied on intuition and simplified equations—but for most real systems, the governing laws remain unknown.

Zihan Yu, Jingtao Ding & Yong Li  introduce ND2, a neural symbolic regression framework that discovers network dynamics directly from data. The key insight is to reduce the overwhelming search space of possible equations—normally exploding with the number of nodes—to an equivalent one-dimensional symbolic problem. ND2 combines graph neural networks and transformers (via a pretrained model called NDformer) with Monte Carlo tree search to automatically uncover concise, interpretable formulas that explain how networks evolve.

Applied to ten benchmark systems, ND2 correctly recovered the governing equations of classics such as Kuramoto oscillators, FitzHugh–Nagumo neurons, and Lotka–Volterra populations. More impressively, when tested on real data, it corrected existing biological models—reducing prediction errors by 60% in gene regulation and 56% in microbial communities—by revealing hidden higher-order interactions. In epidemic networks, ND2 uncovered transmission laws that explain cross-country differences in intervention effects and even captured the same power-law patterns across scales.

This study demonstrates how machine-driven discovery can bridge observational data and theoretical understanding, advancing complexity science from describing what we observe to deriving why it happens—directly from the data itself.

Abstract:

Network dynamics are fundamental to analyzing the properties of high-dimensional complex systems and understanding their behavior. Despite the accumulation of observational data across many domains, mathematical models exist in only a few areas with clear underlying principles. Here we show that a neural symbolic regression approach can bridge this gap by automatically deriving formulas from data. Our method reduces searches on high-dimensional networks to equivalent one-dimensional systems and uses pretrained neural networks to guide accurate formula discovery. Applied to ten benchmark systems, it recovers the correct forms and parameters of underlying dynamics. In two empirical natural systems, it corrects existing models of gene regulation and microbial communities, reducing prediction error by 59.98% and 55.94%, respectively. In epidemic transmission across human mobility networks of various scales, it discovers dynamics that exhibit the same power-law distribution of node correlations across scales and reveal country-level differences in intervention effects. These results demonstrate that machine-driven discovery of network dynamics can enhance understandings of complex systems and advance the development of complexity science.

https://www.nature.com/articles/s43588-025-00893-8

Rafael Araujo

GEOMETRY/Flight

http://rafael-araujo.com

AI is helping to decode animals’ speech. Will it also let us talk with them?

Rachel Fieldhouse

Deep in the rainforests of the Democratic Republic of the Congo, Mélissa Berthet found bonobos doing something thought to be uniquely human.

During the six months that Berthet observed the primates, they combined calls in several ways to make complex phrases1. In one example, bonobos (Pan paniscus) that were building nests together added a yelp, meaning ‘let’s do this’, to a grunt that says ‘look at me’. “It’s really a way to say: ‘Look at what I’m doing, and let’s do this all together’,” says Berthet, who studies primates and linguistics at the University of Rennes, France.

In another case, a peep that means ‘I would like to do this’ was followed by a whistle signalling ‘let’s stay together’. The bonobos combine the two calls in sensitive social contexts, says Berthet. “I think it’s to bring peace.”

The study, reported in April, is one of several examples from the past few years that highlight just how sophisticated vocal communication in non-human animals can be. In some species of primate, whale and bird, researchers have identified features and patterns of vocalization that have long been considered defining characteristics of human language. These results challenge ideas about what makes human language special — and even how ‘language’ should be defined.

Perhaps unsurprisingly, many scientists turn to artificial intelligence (AI) tools to speed up the detection and interpretation of animal sounds, and to probe aspects of communication that human listeners might miss. “It’s doing something that just wasn’t possible through traditional means,” says David Robinson, an AI researcher at the Earth Species Project, a non-profit organization based in Berkeley, California, that is developing AI systems to decode communication across the animal kingdom.

As the research advances, there is increasing interest in using AI tools not only to listen in on animal speech, but also to potentially talk back.

Continue reading:

https://www.nature.com/articles/d41586-025-02917-9

Common mycorrhizal networks facilitate plant disease resistance by altering rhizosphere microbiome assemblyAuthor links open overlay panel

Zhang et al., 2025

Arbuscular mycorrhizal fungi can interconnect the roots of individual plants by forming common mycorrhizal networks (CMNs). These symbiotic structures can act as conduits for interplant communication. Despite their importance, the mechanisms of signal transfer via CMNs and their implications for plant community performance remain unknown. Here, we demonstrate that CMNs act as a pathway to elicit defense responses in healthy receiver plants connected to pathogen-infected donors. Specifically, we show that donor plants infected by the phytopathogen Botrytis cinerea transfer jasmonic acid via CMNs, which then act as a chemical signal in receiver plants. This signal transfer to receiver plants induces shifts in root exudates, promoting the recruitment of specific microbial taxa (Streptomyces and Actinoplanes) that are directly linked to the suppression of B. cinerea infection. Collectively, our study reveals that CMNs act as interplant chemical communication conduits, transferring signals that contribute to plant disease resistance via modulation of the rhizosphere microbiota.

https://www.sciencedirect.com/science/article/pii/S1931312825003427

Meta-analysis shows that planting nitrogen-fixing species increases soil organic carbon stock

Sun et al., 2025

Nitrogen (N)-fixing species are widely used in forestation and agriculture. The effects of planting N-fixing species on soil organic carbon (SOC) stock, however, remain uncertain, limiting policy development and their application towards a possible climate change mitigation strategy. Here we conduct a global meta-analysis of 385 datapoints from 136 studies comparing SOC stock with planting N-fixing versus non-N-fixing species. Planting N-fixing species increases SOC stock by 16% compared with non-N-fixing species. This SOC increase is closely accompanied by soil N increases, with an average accumulation of 7.8 g of SOC per gram of soil N increase. Climate mediates SOC responses, with greater SOC sequestration observed in drier and warmer regions, particularly in the tropics. We estimate that an additional increase of 0.29–0.75 PgC yr−1 in global SOC stock could be achieved by adopting N-fixing species for forestation, agriculture and regeneration of marginal lands, highlighting their potential for climate change mitigation.

Global distribution of the selected studies testing the effects of planting N-fixing species on SOC stock in this meta-analysis. Green and orange dots represent the geographic locations of studies on tree and crop planting, respectively. The green and orange shaded areas show the distribution ranges of planted forests and croplands, respectively. Inset: the distribution of the sites in the global biomes based on climatic conditions: MAT and MAP. Black dots indicate study sites in this meta-analysis.

https://www.nature.com/articles/s41559-025-02861-x.epdf

Advances in microbial based bio-inoculum for amelioration of soil health and sustainable crop production

Samantaray et al., 2024

The adoption of sustainable agricultural practices is increasingly imperative in addressing global food security and environmental concerns, with microbial based bio-inoculums emerging as a promising approach for nurturing soil health and fostering sustainable crop production.This review article explores the potential of microbial based bio-inoculumsor biofertilizers as a transformative approach to enhance plant disease resistance and growth. It explores the commercial prospects of biofertilizers, highlighting their role in addressing environmental concerns associated with conventional fertilizers while meeting the growing demand for eco-friendly agricultural practices. Additionally, this review discusses the future prospects of biofertilizers, emphasizing the ongoing advancements in biotechnology and formulation techniques that are expected to enhance their efficacy and applicability. Furthermore, this article provides insights into strategies for the successful acceptance of biofertilizers among farmers, including the importance of quality control, assurance, and education initiatives to raise awareness about their benefits and overcome barriers to adoption. By synthesizing the current research findings and industrial developments, this review offers valuable guidance for stakeholders seeking to exploit the potential of biofertilizers or beneficial microbes to promote soil health, ensure sustainable crop production, and addressing the challenges of modern agriculture.

https://www.sciencedirect.com/science/article/pii/S2666517424000336

Mutualism provides a basis for biodiversity in eco-evolutionary community assembly

Gui Araujo,Miguel Lurgi

Ecological communities are considerably more complex than simple collections of species sharing the same environment. The large number of ecological interactions among species drives changes in populations through time that dictate the persistence of the entire community. Most research into the mechanisms of biodiversity considers different interaction types (mutualism, competition, consumer-resource) in isolation in either ecological or evolutionary contexts. In this study, we developed a community growth model that incorporates mutualism, competition, and consumer-resource interactions and considers both ecological and evolutionary mechanisms of assembly together. We found that communities formed via evolutionary speciation can reach higher species richness and exhibit greater proportions of mutualistic interactions than purely ecological models, resulting in more complex community structures. High levels of mutualism lead to communities more resilient to disturbances, such as the arrival of new species or sudden changes in abundances. Our research extends previous efforts by aiming to understand how evolutionary processes shape the diversity of ecological interactions and the role of these interactions in species persistence. Such knowledge is essential for preserving and restoring ecosystems in the face of growing environmental degradation.

https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013402

Natural selection

Paul Nurse

Application of microbial inoculants significantly  enhances crop productivity: A meta-analysis of studies from 2010 to 2020

Li et al, 2022

Abstract

Introduction

With the rapid development of microbial technology, microbial inoculant is considered as a promising tool in sustainable agricultural systems. Mechanisms by which microbial inoculants improve crop yield include improving plant nutrient availability and alleviating abiotic/biotic stresses (e.g., drought, salt and disease). However, the field efficacy of microbial inoculants remains inconsistent, which constrains large-scale adoptions. Identity of dominant mechanisms that underpin the positive impacts of different microbial inoculants is limited. Thus, a comprehensive quantitative assessment of known inoculants on crop performance is needed to provide guidance for the development of effective microbial tools from both research and commercial perspectives.

Materials and Methods

Based on 97 peer-reviewed publications, we conducted a meta-analysis to quantify the benefits of different microbial inoculants on crop yield, and to identify the key mechanisms that underpin enhanced crop yield.

Results

Result showed that (i) alleviation of stresses was the major mechanism (53.95%, n = 53) by which microbial inoculants enhance crop yield, while improving plant nutrient availability accounted for 22.25% (n = 58) of crop yield enhancement. (ii) Pseudomonas was the most effective microbial inoculant in enhancing crop yield through alleviating stresses (63.91%, n = 15), whereas Enterobacter was the most effective in improving plant nutrient availability (27.12%, n = 5). (iii) Considering both mechanisms together, Pseudomonas (49.94%, n = 21), Enterobacter (27.55%, n = 13) and Bacillus (25.66%, n = 32) were the largest sources of microbial inoculants to enhance crop yield, and the combination of diazotroph Burkholderia with its legume host had the highest effect on improving the yield (by 196.38%). Microbial inoculants also improve nutritional quality by enhancing mineral contents in the produce.

Conclusion

Our analysis provides evidence that microbial inoculants can enhance agricultural productivity and nutritional quality and can be used either alone or in combination with reduced amount of agrochemicals to promote sustainable agriculture.

https://onlinelibrary.wiley.com/doi/full/10.1002/sae2.12028

Revisiting the cry-for-help hypothesis in plant–microbe interactions

Tharp et al., 2025

The ‘cry-for-help hypothesis’ (CHH) is broadly used to study how root exudate modulation under stress influences recruitment of beneficial microbes in the rhizosphere. Here, we explored common misconceptions and limitations of the CHH and advocate for the reassessment of this prevalent hypothesis to unfold the ecological complexities of plant–microbe interactions.

https://www.cell.com/trends/plant-science/abstract/S1360-1385(25)00223-7