Mathematics in the Age of AI

Terence Tao 

True solitude is found in the wild places, where one is without human obligation. One’s inner voices become audible. One feels the attraction of one’s most intimate sources. In consequence, one responds more clearly to other lives.

Wendell Berry

Mutually beneficial interactions between bacteria and Arabidopsis promote phosphorus nutrition and growth 

Wang et al., 2026

It remains unknown whether plants establish mutualistic relationships with any bacteria to cope with phosphorus (P) limitation. We characterized root-bacterial microbiome members to show that many of them may cooperate with Arabidopsis to promote seedling P nutrition and growth. In-depth analyses uncovered an intricate interaction between Arabidopsis and Acinetobacter bacteria during P deficiency. Instead of a direct role in P-mining, malate secreted by P-deprived roots acts as a call-for-help signal that recruits bacteria to the rhizoplane, where Acinetobacter adopt a mutualistic lifestyle and utilize host-derived nutrients to robustly mobilize P normally inaccessible to plants. The rhizoplane, but not the surrounding space, served as a hotspot for P acquisition by both plants and bacteria. The interaction occurred in the context of a bacterial community and in P-impoverished soil. Our work reveals a mutualistic strategy between bacteria and a non-mycorrhizal plant that promotes P nutrition.

https://www.cell.com/cell/fulltext/S0092-8674(26)00917-7

The hidden dimensions of consciousness? are plants intelligent? 

Peter Singer and Michael Pollan

Resistant and Susceptible Lima Bean Genotypes Differentially Recruit Rhizosphere and Phyllosphere Bacteria in Response to the Fungal Pathogen Colletotrichum truncatum  

Novaes de Aquino et al., 2026

Los microbiomas asociados a las plantas desempeñan un papel fundamental en la salud del hospedero y en su resistencia a las enfermedades. En este estudio se evaluaron las comunidades bacterianas de la rizósfera y la filosfera de dos genotipos de frijol lima (Phaseolus lunatus) con diferente nivel de resistencia a la antracnosis, tanto en plantas inoculadas como no inoculadas con Colletotrichum truncatum. Para ello, se secuenció el gen 16S rRNA de las bacterias presentes en ambos compartimentos.

Los resultados mostraron que tanto el genotipo de la planta como la inoculación con el patógeno modificaron significativamente la estructura de las comunidades bacterianas. En el genotipo resistente se observaron cambios más marcados en la composición del microbioma después de la inoculación, tanto en la rizósfera como en la filosfera. En la rizósfera, las plantas susceptibles inoculadas presentaron una mayor diversidad bacteriana que las resistentes. Además, los genotipos resistentes exhibieron conjuntos bacterianos más diferenciados entre plantas inoculadas y no inoculadas, lo que sugiere una reorganización específica del microbioma en respuesta al patógeno.

El análisis de redes ecológicas reveló respuestas diferentes según el compartimento vegetal. En la filosfera de las plantas resistentes inoculadas se detectó una red bacteriana con mayor conectividad y predominio de interacciones positivas, indicando una comunidad más cooperativa y organizada durante la infección. En conjunto, los resultados demuestran que los genotipos resistentes remodelan activamente su microbioma frente al ataque de C. truncatum, favoreciendo el enriquecimiento de bacterias potencialmente beneficiosas y el establecimiento de redes microbianas más interconectadas y cooperativas, lo que probablemente contribuye a una mayor resistencia a la enfermedad.

https://bsppjournals.onlinelibrary.wiley.com/doi/10.1111/ppa.70234

The Personalised Ecology Index: A novel measure of an individual's direct sensory interactions with nature

Poznansky et al., 2026

El estudio presenta el Personalised Ecology Index (PEI), un nuevo indicador diseñado para cuantificar las interacciones directas de una persona con la naturaleza. El índice integra cuatro dimensiones: frecuencia de las visitas a espacios naturales, duración de esas visitas, diversidad de ambientes frecuentados e intensidad de la atención que la persona presta a los elementos naturales, como plantas, animales y paisajes.

El PEI fue validado utilizando encuestas realizadas a más de 29000 personas en el Reino Unido. Los resultados demostraron que el índice posee una sólida validez estadística, distingue adecuadamente entre distintos niveles de interacción con la naturaleza y presenta valores más altos en personas que viven en zonas rurales o con mayor disponibilidad de áreas verdes.

Los autores proponen que el PEI puede utilizarse para investigar la relación entre la experiencia cotidiana con la naturaleza, la salud, el bienestar y los comportamientos proambientales, además de servir como herramienta para evaluar políticas públicas orientadas a incrementar el contacto de la población con los ecosistemas naturales. Aunque reconocen limitaciones, como su enfoque en interacciones principalmente intencionales y su desarrollo inicial para el contexto británico, concluyen que constituye un instrumento novedoso y útil para estudiar la ecología personalizada de las personas y su relación con la conservación de la biodiversidad.

https://besjournals.onlinelibrary.wiley.com/doi/10.1002/pan3.70389

Assembly of plant holobionts is governed by nematode communities and their associated microbiota, conditioned by preceding plants

Heuer et al., 2026

Pants form holobionts by associating with diverse microbiota. Self-organization gives rise to emergent properties of the holobiont, such as increased resistance to pathogens. However, the local factors contributing to the self-organization are not well understood. We hypothesized that nematode communities and their associated microbiota govern the rhizobiome of the model plant holobiont tomato in terms of its suppression of root invasion by the parasite Meloidogyne hapla, and that the soil legacy influences the suppressive potential mediated by these biota. In pot experiments, a resistant tomato holobiont was favored by assembly in the presence of a nematode community conditioned by tomato plants, compared to oilseed rape or fallow soil. Nematode communities conditioned by tagetes could enhance resistance even better than tomato. Microbiota from crushed tomato-conditioned nematode communities increased resistance of the tomato holobiont, compared to microbiota of nematode communities conditioned by maize, or heat-inactivated microbiota. The 0.2 µm-filtered microbiota from crushed nematodes had the same effect, suggesting a role of nematode-associated bacteriophages in holobiont assembly. The results indicate that soil nematodes and their associated microbiota play a role in the local organization and stabilization of plant holobionts. They can influence the resistance of plants that subsequently grow in the same soil. From an applied perspective, crop rotation schemes that alter nematode–microbiota communities could be harnessed to engineer crop holobionts.

https://www.biorxiv.org/content/10.64898/2026.07.02.736003v1.full

Random motility regulation as a generic mechanism of community formation 

Dinelli et al., 2026

The self-organization of microbial ecosystems involves a large variety of mechanisms, ranging from biochemical signaling to population dynamics. Among these, the role of motility regulation has been little studied, despite the importance of active migration processes. Here we show how weak, random motility regulation suffices to induce complex forms of organization in bacterial mixtures comprising a large number of coexisting strains. First, we simulate microscopic models of run-and-tumble bacteria whose self-propulsion speeds are weakly regulated by the local density of each strain, mimicking the impact of weak, random metabolic interactions. Our simulations reveal that, as the heterogeneity of the interaction network increases, the system undergoes a phase transition leading to the emergence of distinct, spatially segregated communities. To account for these results and assess their robustness, we use random-matrix theory to analyze the hydrodynamic description of the bacterial mixture, obtaining a quantitative agreement with our microscopic simulations. Our results hold for a variety of motility-regulation mechanisms and highlight the need to characterize the role of motility regulation in experimentally relevant situations.

https://journals.aps.org/pre/abstract/10.1103/cl1f-mfgp

PrePrint:

https://arxiv.org/abs/2503.12692

The host–microbiome dimension of ecological regime shifts 

Rindi et al., 2026

Regime-shift research has largely overlooked host-associated microbiomes, even though they can buffer stress, speed recovery, and mediate chemical interactions that sustain reinforcing feedbacks and lock in alternative states.

Host–microbiome partnerships bolster stress-tolerance to perturbations and support recovery across marine foundation species.

Combining innovative microbiome manipulations with regime-shift mapping tools can reveal whether altering microbiomes shifts thresholds.

Host-associated microbiome-based indicators may precede host-based metrics and enable earlier, more targeted interventions.

A holobiont lens on regime-shift dynamics may help translate microbiome-assisted restoration into actionable tools for managing ecosystems under accelerating change.

Rising climate and local pressures increase the risk of regime shifts, yet despite progress, thresholds remain difficult to identify early enough to take action. We argue that this shortfall reflects a host-centric view that largely omits host-associated microbiomes, which can shape resilience by modulating stress tolerance, aiding recovery, and stabilizing alternative states through inhibitory chemical interactions. We propose a research agenda that integrates host-associated microbiomes into regime-shift ecology by combining novel microbiome manipulations in laboratory and field settings with regime-shift mapping tools, while simultaneously developing microbiome-based early warning indicators. Reframing regime-shift theory through a host-associated microbiome lens can provide practical tools to anticipate collapse, improve monitoring, and inform timely interventions, thereby supporting more adaptive and robust conservation under accelerating global change.

https://www.cell.com/trends/ecology-evolution/abstract/S0169-5347(26)00148-5

Environmental microbes as modulators of plant volatile landscapes: Implications for plant–insect chemical communication 

Zhang et al., 2026

Free-living environmental microbes at four plant-atmosphere interfaces (leaf, nectar, fruit, and bark surfaces) intercept, biotransform, and augment plant volatile signals, shaping what herbivores, pollinators, and parasitoids detect. This forum article reviews how microbes remodel these signals, the threats posed by climate change and land-use intensification, and priorities for translating microbial volatile ecology into sustainable pest management.

The global phyllosphere spans an estimated 1 billion square kilometres of above-ground plant surface, placing surface-dwelling epiphytes, carposphere colonisers, and nectar inhabitants at the plant-atmosphere boundary. At the plant-atmosphere interface, these microbes occupy a biochemical gatekeeper role: intercepting, consuming, and transforming plant-emitted volatile organic compounds (VOCs) before those signals reach insect receivers. Isoprene monooxygenases in Rhodococcus and Variovorax catalyse the oxidation and biocapture of isoprene emitted from leaf surfaces, while fungal cytochrome P450 monooxygenases, reductases, and Baeyer–Villiger oxidases execute stereoselective biotransformations, including regioselective hydroxylation of inactivated C–-H bonds, enantioselective carbonyl reduction, and lactone-forming oxidations.

Biotransformation can redirect a plant monoterpene into functionally divergent chemical spaces. For example, Aspergillus niger DSM 821 and Corynespora cassiicola DSM 62475 can convert (±)-linalool into furanoid and pyranoid linalool oxides, while A. niger DSM 821 and Botrytis cinerea additionally produce lilac aldehydes and lilac alcohols as byproducts through a pathway postulated to proceed via 8-hydroxylinalool. Furanoid linalool oxide is electroantennographically active in bee pollinators and attracts hoverflies, while lilac aldehyde acts as a repellent to the same hoverfly species. Thus, fungal biotransformations can generate compounds with opposing semiochemical functions within the same receiver community. Plant VOCs, in turn, shape phyllosphere microbial community composition, establishing bidirectional exchanges with direct consequences for herbivore, pollinator, and parasitoid perception.

linkinghub.elsevier.com/retrieve/pii/S0966842X26001605

Metarhizium – Insect Interactions: Implications for Nitrogen Cycling

Tang et al., 2026

Los hongos endófitos entomopatógenos desempeñan un doble papel ecológico como mutualistas de las plantas y patógenos de insectos. A través de esta doble función, transfieren a las plantas nitrógeno derivado de los insectos, contribuyendo de manera significativa al ciclo del nitrógeno en los ecosistemas. Sin embargo, los mecanismos que regulan esta transferencia han permanecido poco explorados.

En este estudio, los autores demuestran que el consorcio planta-hongo formado por la especie ampliamente distribuida Metarhizium robertsii constituye un modelo idóneo para comprender la biología y el funcionamiento ecológico de los hongos endófitos entomopatógenos. Los resultados muestran que este hongo es capaz de degradar la caulilexina C, un compuesto antifúngico producido por las raíces de las plantas, generando como producto el compuesto volátil 1-metoxiindol, cuya función ecológica no había sido descrita previamente.

El 1-metoxiindol actúa como un potente atrayente de insectos. En particular, es detectado por el receptor olfativo Or74a de las larvas de Drosophila melanogaster y atrae a diversas especies de dípteros hacia el sistema planta-Metarhizium. Una vez reclutados, estos insectos son infectados y consumidos por el hongo, lo que incrementa la transferencia de nitrógeno derivado de los insectos hacia las plantas asociadas.

Estos hallazgos revelan un mecanismo ecológico auto-reforzante que integra la química vegetal, el metabolismo fúngico y el comportamiento de los insectos. Este proceso fortalece la simbiosis planta-hongo y constituye una vía previamente desconocida mediante la cual los hongos endófitos entomopatógenos contribuyen al flujo y reciclaje del nitrógeno en los ecosistemas terrestres.

t.co/qpEXbwp2Ky

Global density and biomass of arbuscular mycorrhizal fungal networks 

Stewart et al., 2026

Most species of plants form underground associations with arbuscular mycorrhizal (AM) fungi, which provide plant roots with nutrients in exchange for carbon. AM fungi form networks of hyphae that act as tubes spreading carbon and connecting plants, but the global scale of these networks is unknown because of the difficulty of observing them underground. Compiled field and experimental data on hyphal density and used machine learning to predict how AM density varies across the globe. They then predicted hyphal biomass using high-resolution image analysis of hyphal network length from two globally distributed fungal species grown on transparent media in the lab. The authors predicted a large and spatially variable extent of AM fungi across the globe.

Arbuscular mycorrhizal fungi form symbioses with ~70% of plant species, building hyphal networks that exchange nutrients for host-derived carbon. These tubular networks move ~1 billion metric tons of carbon per year into Earth’s soils. However, we have no quantitative understanding of the hyphal infrastructure required to carry out this resource transfer. We assembled data from 322 studies representing more than 16,000 soil cores across nine biomes and developed machine-learning models to predict hyphal densities globally. With robotic imaging of more than 300,000 hyphae, we calibrated a biomass model from our spatial predictions. We estimate that global topsoils contain 1.10 × 1017 ± 0.13 × 1017 SD kilometers of living hyphae, weighing ~300 ± 60 SD megatons, ~4- to 6-fold the biomass of humans. Our uncertainty analyses identified undersampled ecosystems that require additional empirical attention.

https://www.science.org/doi/10.1126/science.adu4373

Maps:

https://a-hidden-infrastructure.spun.earth/story/mycorrhizal-infrastructure-map

https://www.spun.earth/underground-atlas/mycorrhizal-biodiversity

Agricultural intensification, microbial homogenization and loss of rare microbiota

Banerjee et al., 2026

To meet the needs of a growing human population, agricultural management practices have undergone substantial intensification, specialization and industrialization. This has contributed to biotic homogenization and a loss of diversity in microbial communities within agricultural systems. In this Perspective, we summarize recent studies that report microbial homogenization due to agricultural intensification. We propose a definition of microbial homogenization and explore how intensive agricultural practices can cause taxonomic, physiological, genetic and functional homogenization of microbial communities. Our analysis indicates that globally the diversity of rare taxa is lower in intensively managed agricultural lands compared with less-intensive lands and that agricultural intensification suppresses beneficial microorganisms and promotes pathogenic taxa. We identify microbial taxa that are sensitive to intensification and discuss how the disproportionate impact on rare microbiota can threaten agro-ecosystem functions and food security. Finally, we outline key challenges and suggest areas that require further research.

https://www.nature.com/articles/s41579-026-01315-w

From Math to Bio and Back: Reflections on a Two Way Street 

Steven Strogatz

Status of mycorrhiza research in 2026

Dallaire and Kameoka, 2026

Mycorrhizal symbiosis improves the nutrition of most land plants and plays key roles in nutrient cycling and ecosystem function. To understand and leverage the biology of mycorrhizal symbioses for sustainable agriculture and silviculture and the preservation of terrestrial ecosystems, molecular mechanisms enabling its establishment, function, and regulation are being investigated. Technological and conceptual advances are transforming the field and provide a detailed understanding of the mycorrhizal symbiosis on both the fungal and plant sides. In this viewpoint, we summarize recent advances that move the field toward a mechanistic understanding of mycorrhizal symbiosis, with a particular focus on studies presented at the 7th International Molecular Mycorrhiza Meeting (iMMM) held in Munich in September 2025.

https://nph.onlinelibrary.wiley.com/doi/10.1111/nph.71119

Balancing mutualism: choice and sanctions in root–microbe symbioses

Madhavan et al., 2026

Plant roots form symbioses with beneficial microorganisms to enhance nutrient acquisition. Most terrestrial plants form arbuscular mycorrhizal symbiosis (AMS) with obligate biotrophic Glomeromycotina fungi, which supply hosts with mineral nutrients in exchange for carbon through specialized symbiotic hyphal structures (arbuscules) that develop within root cortex cells. Legumes form root nodule symbiosis (RNS) with nitrogen-fixing rhizobia, which are housed as differentiated bacteroids within specialized symbiotic organs (nodules) and provide plants with ammonia in return for carbon. RNS exhibits high partner specificity, occurring only between compatible hosts and microbes. Conversely, AMS is less specific, although symbiosis outcomes are context-dependent and influenced by host and fungal genotype, environmental conditions, and microbial competition. In both cases, plants favor high-performing microsymbionts by recognizing them during symbiosis initiation or by punishing low-performing symbionts through postcolonization sanctions. Microbes, in turn, employ strategies to manipulate plants for their own benefit. Here, we review the molecular mechanisms underlying partner preference in beneficial plant–microbe interactions and discuss how host partner selection strategies maintain mutualistic stability in AMS and RNS, alongside microbial strategies to evade host control. Understanding the dynamic interplay of functionally diverse plant–microbe symbioses provides a basis for improving mutualisms in both natural and agricultural systems.

https://nph.onlinelibrary.wiley.com/doi/10.1111/nph.71107

Plant nutritional and structural diversity shape multitrophic arthropod communities and grassland productivity 

Lu et al., 2026

1. Arthropod communities, comprising diverse trophic groups such as herbivores, predators and parasitoids, are intricately linked to plant traits that provide food and habitat. While it is well-established that changes in plant functional diversity (e.g. trait identity and diversity) can significantly alter arthropod diversity across trophic levels, the cascading effects on ecosystem functions remain less understood. Particularly, the role of multitrophic arthropod diversity in mediating the relationship between plant functional diversity and grassland productivity presents a critical knowledge gap in ecosystem ecology.
2. We employed a long-term plant removal experiment in the Inner Mongolian grassland to systematically investigate how variations in the community-weighted mean and diversity of multiple plant traits influence the diversity (measured by taxon richness and abundance) of herbivores and their natural enemies. Furthermore, we explored how trophic interactions between herbivores and their natural enemies influence plant community productivity.
3. Our findings indicate that high diversity in plant nutritional traits (e.g. nitrogen, phosphorus and sodium contents) negatively impacts plant productivity through both direct and indirect pathways. The adverse effect was mediated by an increase in the richness of sucking and chewing herbivores, which exploited high resource complementarity yet collectively suppressed plant productivity. In contrast, higher community-weighted means of plant structural traits (e.g. vegetative height and leaf lateral spread) were associated with greater plant productivity. This positive effect appears to arise from enhanced top-down control, whereby predators—particularly spiders—reduced both the richness and abundance of herbivores.
4. Synthesis. Our study reveals that herbivores and their natural enemies respond distinctly to the variation in the composition and diversity of plant nutritional and structural traits. We show that cross-trophic interactions—specifically, diversity within herbivore and predator guilds—constitute a primary pathway through which plant functional diversity influences grassland productivity. By disentangling the links between plant trait spectra, arthropod community structure and ecosystem functioning, our findings provide key insights for biodiversity conservation and the design of ecosystem management strategies in grasslands.

https://besjournals.onlinelibrary.wiley.com/doi/10.1111/1365-2745.70316

The island biology of the host microbiome 

Sarkar et al., 2026

Highlights

The extraordinary biodiversity of the host-associated gut microbiome cannot be explained exclusively by host traits.

Researchers have interpreted hosts as biological islands suitable for microbial colonisation and have applied ecological theories of island biogeography and metacommunity ecology to further understand microbiome composition and variation.

To benefit from the host-as-island metaphor, the metacommunity processes characterising macroscopic and microbial diversity should be explicitly compared. On geological islands, these processes include interspecies interactions, local selection, interisland dispersal, and ecological stochasticity. In host islands, these processes are paralleled by interactions between microbes, host selection, microbial transmission, and microbial stochasticity, respectively.

A critical difference between host islands and geological islands is that host islands are mobile and undergo adaptive evolution, whereas geological islands do not.

Abstract

Microbiomes perform critical functions for their hosts, and understanding microbiome variation is important for both basic and applied science. However, host traits alone cannot explain the entirety of microbiome variation, because, alongside host traits, microbiomes are shaped by multiple ecological processes. Researchers have thus turned to theories of island biology, conceptualising animal hosts as islands and animal microbiomes as metacommunities that assemble within and disperse between host islands. To develop realistic models, this host-as-island metaphor must be examined by explicitly comparing geological and host islands. Here, we critically examine the host-as-island metaphor by evaluating how microbiome variation is shaped by the four metacommunity processes that explain biodiversity on geological islands: local interspecies interactions, local selection, dispersal, and stochasticity. Key differences between host islands and geological islands include the complexity of microbiome transmission networks arising from host mobility and sociality and the capacity of hosts to evolve to control their microbiomes. We conclude with discussions of how eco-evolutionary dynamics differ between geological islands and host islands, and the reciprocal relevance of island biology and microbiome science.

https://www.cell.com/trends/microbiology/abstract/S0966-842X(26)00040-5?

Soil microbial diversity associates with lower prevalence of human bacterial pathogens across global soils

Author links open overlay panel

Xiong et al., 2026

Soil-inhabiting pathogens threaten human health, but their biogeography and associations with soil biodiversity remain poorly understood. Here, we present global patterns of dominant human bacterial pathogens by integrating 1,602 soil metagenomes from 59 countries across continents. We show that dominant human pathogens are more prevalent (i.e., relative abundance) in wet (tropical and temperate) ecosystems and are particularly abundant in cropland soils. We find a global negative association between soil microbiome diversity and pathogen prevalence. We further reveal a significant and positive correlation between the abundance of dominant human pathogens and both disease virulence and global patterns of mortality associated with infectious diseases. Many dominant pathogens are likely to increase their proportion under global change scenarios. Our work provides a global atlas of dominant soil-inhabiting human pathogens and reveals their biogeography and ecology. These findings can guide the development of effective surveillance and risk management strategies to reduce outbreaks and pandemics.

https://www.sciencedirect.com/science/article/abs/pii/S1931312826001198

The rhizosphere microbiome as a decentralized immune system

Araujo et al., 2026

Plant immunity should be reconsidered beyond the boundaries of the plant genome. We propose that the rhizosphere microbiome may function analogously to a decentralized immune system, contributing adaptive defenselike properties and memory effects. In this forum article, we discuss how this perspective reframes immunity as an emergent property of plant–microbiome interactions, shifting the focus from a solitary host toward an integrated holobiont

https://www.cell.com/trends/microbiology/abstract/S0966-842X(26)00065-X