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We give elements towards the classification of quantum Airy structures based on the W.glr/-algebras at self-dual level based on twisted modules of the Heisenberg VOA of glr for twists by arbitrary elements of the Weyl group Sr. In particular, we construct a large class of such quantum Airy structures. We show that the system of linear ODEs forming the quantum Airy structure and determining uniquely its partition function is equivalent to a topological recursion à la Chekhov–Eynard–Orantin on singular spectral curves. In particular, our work extends the definition of the Bouchard–Eynard topological recursion (valid for smooth curves) to a large class of singular curves and indicates impossibilities to extend naively the definition to other types of singularities. We also discuss relations to intersection theory on moduli spaces of curves, giving a general ELSV-type representation for the topological recursion amplitudes on smooth curves, and formulate precise conjectures for application in open r-spin intersection theory.

Since the 5th Assessment Report of the Intergovernmental Panel on Climate Change (AR5) an extended concept of the energetic analysis of climate change including forcings, feedbacks and adjustment processes has become widely adopted. Adjustments are defined as processes that occur in response to the introduction of a climate forcing agent, but that are independent of global-mean surface temperature changes. Most considered are the adjustments that impact the Earth energy budget and strengthen or weaken the instantaneous radiative forcing due to the forcing agent. Some adjustment mechanisms also impact other aspects of climate not related to the Earth radiation budget. Since AR5 and a following description by Sherwood et al. (2015, ), much research on adjustments has been performed and is reviewed here. We classify the adjustment mechanisms into six main categories, and discuss methods of quantifying these adjustments in terms of their potentials, shortcomings and practicality. We furthermore describe aspects of adjustments that act beyond the energetic framework, and we propose new ideas to observe adjustments or to make use of observations to constrain their representation in models. Altogether, the problem of adjustments is now on a robust scientific footing, and better quantification and observational constraint is possible. This allows for improvements in understanding and quantifying climate change. Climate change is driven by perturbations to the atmospheric composition, to land use, or by changes of incoming solar radiation. It can be understood energetically by quantifying the perturbation to the Earth energy budget-the instantaneous radiative forcing-and the response of the climate system to this perturbation. This response can be split into feedbacks-mechanisms that act in response to global-mean surface temperature changes-and other processes that act independently of the global-mean surface temperature change. These latter processes are called adjustments

Values play a significant role in decision-making, especially regarding nature. Decisions impact people and nature in complex ways and understanding which values are prioritised, and which are left out is an important task for improving the equity and effectiveness of decision-making. Based on work done for the IPBES Values Assessment, this paper develops a framework to support analyses of how decision-making influences nature as well as whose values get prioritised. The framework is used to analyse key areas of environmental policy: a) the present model for nature protection in market economies, b) the role of valuation in bringing nature values into decisions, and c) values embedded in environmental policy instruments, exemplified by protected areas for nature conservation and payments for ecosystem services. The analyses show that environmental policies have been established as mere additions to decision-making structures that foster economic expansion, which undermines a wide range of nature's values. Moreover, environmental policies themselves are also focused on a limited set of nature's diverse values.

As countries consider new area-based conservation targets under the Convention on Biological Diversity, protected areas (PAs) and their impacts on people and nature are coming under increasing scrutiny. We review the evidence base on PA impacts, combining the findings from existing rigorous impact evaluations with local case studies developed for this study. We identify characteristics of PA establishment and management that improve the sustainability of biodiversity conservation and justice for local communities. We find that recognizing and respecting local values and knowledge about natural resource stewardship, colearning, and comanagement are key to achieving positive impacts for nature and people. Transforming PA governance toward more inclusive conservation depends upon the ability of PAs to be designed and implemented around the values and needs of local people. © 2023 Elsevier B.V.

Based on an extensive model intercomparison, we assessed trends in biodiversity and ecosystem services from historical reconstructions and future scenarios of land-use and climate change. During the 20th century, biodiversity declined globally by 2 to 11%, as estimated by a range of indicators. Provisioning ecosystem services increased several fold, and regulating services decreased moderately. Going forward, policies toward sustainability have the potential to slow biodiversity loss resulting from land-use change and the demand for provisioning services while reducing or reversing declines in regulating services. However, negative impacts on biodiversity due to climate change appear poised to increase, particularly in the higher-emissions scenarios. Our assessment identifies remaining modeling uncertainties but also robustly shows that renewed policy efforts are needed to meet the goals of the Convention on Biological Diversity.

The effective radiative forcing (ERF) is a robust predictor of future equilibrium warming. It is generally assumed that the ERF depends only on changes in atmospheric constituents and is independent of the background climate state. Building on recent work demonstrating that, in contrast, the instantaneous radiative forcing (IRF) for CO2 is strongly state-dependent, we show that the ERF for CO2 also increases in warmer climate states. We analyse a 4×CO2 atmosphere-only forcing in both control and warmer climate states in eight CMIP6-era models. Four models participated in the Cloud Feedback Model Intercomparison Project (CFMIP) which used pre-industrial SSTs in its control state and SSTs from near the end of the same model’s coupled abrupt-4×CO2 run in its warm state. In the other four models we used an AMIP climatology as the control state and a uniform increase in SSTs of 4 K above this AMIP climatology in the warm state. All eight models show an increase in 4×CO2 ERF, ranging from 0.1-0.5 W m-2, translating to a relative increase of 0.02-0.09 W m-2 K-1 or 0.2-1.1 % K-1. The increase is statistically significant in five of the eight models. Our findings have implications for derivation of simplified relationships of climate warming, for instance in the calculations of global warming metrics and in economic models, from which future climate change risks being underpredicted without a temperature adjustment. We also run aerosol forcing experiments under the +4 K climate, for which there is less agreement between models, but some show large changes in aerosol ERF under the warmer climate state, with potential implications for our ability to discern transient warming even with a more accurate understanding of present-day aerosol forcing.

We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called r-ELSV formula, as well as its orbifold generalization, the so-called qr-ELSV formula.

We generalise a result of Kazarian regarding Kadomtsev–Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting problems or hypergeometric tau-functions. The proof uses recent results on the relations between hypergeometric tau-functions and topological recursion, as well as the DOSS correspondence between topological recursion and cohomological field theories. As a particular case, we recover the result of Alexandrov of KP integrability for triple Hodge integrals with a Calabi-Yau condition.

We prove the conjecture of Do and Karev that the monotone orbifold Hurwitz numbers satisfy the Chekhov-Eynard-Orantin topological recursion.

The great expansion of economic activity since the end of World War II has caused an unprecedented rise in living standards, but it has also caused rapid changes in earth systems. Nearly all types of natural capital—the world’s stock of resources and services provided by nature—are in decline. Clean air, abundant and clean water, fertile soils, productive fisheries, dense forests, and healthy oceans are critical for healthy lives and healthy economies. Mounting pressures, however, suggest that the trend of declining natural capital may cast a long shadow into the future. "Nature’s Frontiers: Achieving Sustainability, Efficiency, and Prosperity with Natural Capital" presents a novel approach to address these foundational challenges of sustainability. A methodology combining innovative science, new data sources, and cutting-edge biophysical and economic models builds sustainable resource efficiency frontiers to assess how countries can sustainably use their natural capital more efficiently. The analysis provides recommendations on how countries can better use their natural capital to achieve their economic and environ mental goals. The report indicates that significant efficiency gaps exist in nearly every country. Closing these gaps can address many of the world’s pressing economic and environmental problems—economic productivity, health, food and water security, and climate change. Although the approach outlined in this report will entail demanding policy reforms, the costs of inaction will be far higher.

As countries consider new area-based conservation targets under the Convention on Biological Diversity, protected areas (PAs) and their impacts on people and nature are coming under increasing scrutiny. We review the evidence base on PA impacts, combining the findings from existing rigorous impact evaluations with local case studies developed for this study. We identify characteristics of PA establishment and management that improve the sustainability of biodiversity conservation and justice for local communities. We find that recognizing and respecting local values and knowledge about natural resource stewardship, colearning, and comanagement are key to achieving positive impacts for nature and people. Transforming PA governance toward more inclusive conservation depends upon the ability of PAs to be designed and implemented around the values and needs of local people.

The Nature Futures Framework (NFF) is a heuristic tool for co-creating positive futures for nature and people. It seeks to open up a diversity of futures through mainly three value perspectives on nature – Nature for Nature, Nature for Society, and Nature as Culture. This paper describes how the NFF can be applied in modelling to support decision-making. First, we describe key considerations for the NFF in developing qualitative and quantitative scenarios: i) multiple value perspectives on nature as a state space where pathways improving nature toward a frontier can be represented, ii) mutually reinforcing key feedbacks of social-ecological systems that are important for nature conservation and human wellbeing, iii) indicators of multiple knowledge systems describing the evolution of complex social-ecological dynamics. We then present three approaches to modelling Nature Futures scenarios in the review, screening, and design phases of policy processes. This paper seeks to facilitate the integration of relational values of nature in models and strengthen modelled linkages across biodiversity, nature’s contributions to people, and quality of life.

Sustaining the organisms, ecosystems and processes that underpin human wellbeing is necessary to achieve sustainable development. Here we define critical natural assets as the natural and semi-natural ecosystems that provide 90% of the total current magnitude of 14 types of nature’s contributions to people (NCP), and we map the global locations of these critical natural assets at 2 km resolution. Critical natural assets for maintaining local-scale NCP (12 of the 14 NCP) account for 30% of total global land area and 24% of national territorial waters, while 44% of land area is required to also maintain two global-scale NCP (carbon storage and moisture recycling). These areas overlap substantially with cultural diversity (areas containing 96% of global languages) and biodiversity (covering area requirements for 73% of birds and 66% of mammals). At least 87% of the world’s population live in the areas benefitting from critical natural assets for local-scale NCP, while only 16% live on the lands containing these assets. Many of the NCP mapped here are left out of international agreements focused on conserving species or mitigating climate change, yet this analysis shows that explicitly prioritizing critical natural assets and the NCP they provide could simultaneously advance development, climate and conservation goals.

Twenty-five years since foundational publications on valuing ecosystem services for human well-being, addressing the global biodiversity crisis still implies confronting barriers to incorporating nature’s diverse values into decision-making. These barriers include powerful interests supported by current norms and legal rules such as property rights, which determine whose values and which values of nature are acted on. A better understanding of how and why nature is (under)valued is more urgent than ever. Notwithstanding agreements to incorporate nature’s values into actions, including the Kunming-Montreal Global Biodiversity Framework (GBF) and the UN Sustainable Development Goals, predominant environmental and development policies still prioritize a subset of values, particularly those linked to markets, and ignore other ways people relate to and benefit from nature. Arguably, a ‘values crisis’ underpins the intertwined crises of biodiversity loss and climate change, pandemic emergence and socio-environmental injustices. On the basis of more than 50,000 scientific publications, policy documents and Indigenous and local knowledge sources, the Intergovernmental Platform on Biodiversity and Ecosystem Services (IPBES) assessed knowledge on nature’s diverse values and valuation methods to gain insights into their role in policymaking and fuller integration into decisions. Applying this evidence, combinations of values-centred approaches are proposed to improve valuation and address barriers to uptake, ultimately leveraging transformative changes towards more just (that is, fair treatment of people and nature, including inter- and intragenerational equity) and sustainable futures.

Sustaining ecosystem services (ES) critical to human well-being is hindered by many practitioners lacking access to ES models ("the capacity gap") or knowledge of the accuracy of available models ("the certainty gap"), especially in the world's poorer regions. We developed ensembles of multiple models at an unprecedented global scale for five ES of high policy relevance. Ensembles were 2 to 14% more accurate than individual models. Ensemble accuracy was not correlated with proxies for research capacity, indicating that accuracy is distributed equitably across the globe and that countries less able to research ES suffer no accuracy penalty. By making these ES ensembles and associated accuracy estimates freely available, we provide globally consistent ES information that can support policy and decision-making in regions with low data availability or low capacity for implementing complex ES models. Thus, we hope to reduce the capacity and certainty gaps impeding local- to global-scale movement toward ES sustainability.