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More extreme climatic events (ECEs) are among the most prominent consequences of climate change. Despite a long-standing recognition of the importance of ECEs by paleo-ecologists and macro-evolutionary biologists, ECEs have only recently received a strong interest in the wider ecological and evolutionary community. However, as with many rapidly expanding fields, it lacks structure and cohesiveness, which strongly limits scientific progress. Furthermore, due to the descriptive and anecdotal nature of many ECE studies it is still unclear what the most relevant questions and long-term consequences are of ECEs. To improve synthesis, we first discuss ways to define ECEs that facilitate comparison among studies. We then argue that biologists should adhere to more rigorous attribution and mechanistic methods to assess ECE impacts. Subsequently, we discuss conceptual and methodological links with climatology and disturbance-, tipping point- and paleo-ecology. These research fields have close linkages with ECE research, but differ in the identity and/or the relative severity of environmental factors. By summarizing the contributions to this theme issue we draw parallels between behavioural, ecological and evolutionary ECE studies, and suggest that an overarching challenge is that most empirical and theoretical evidence points towards responses being highly idiosyncratic, and thus predictability being low. Finally, we suggest a roadmap based on the proposition that an increased focus on the mechanisms behind the biological response function will be crucial for increased understanding and predictability of the impacts of ECE. This article is part of the themed issue ‘Behavioural, ecological and evolutionary responses to extreme climatic events’.

Carbon dioxide (CO2) emissions affect local temperature; quantifying that local response is important for learning about the earth system, the impacts of mitigation, and adaptation needs. We assume the climate system can be represented as a time‐dependent linear system, diagnosing Green's Functions for the spatial temperature response to CO2 emissions based on CMIP6 earth system models. This allows us to emulate the linear component of the temperature response to CO2. This approach is sufficient to capture the spatial temperature response of CMIP6 experiments within one standard deviation of the multimodel spread across most regions, though accuracy is lower in the Southern Ocean and the Arctic. Our approach reveals where nonlinear feedbacks are important in current CMIP6 models, and where the local system response is well represented by a time‐dependent linear differential operator. It incorporates emissions path dependency and may be useful for evaluating large ensembles of emission scenarios. Plain Language Summary Carbon dioxide (CO2) emissions impact surface temperature. It is well established that the global mean temperature change is proportional to the cumulative emissions of CO2. This has led to the creation of carbon budgets to reach temperature goals. We test this relationship at the spatio‐temporal scale, quantifying a simple approach that estimates the local temperature response to CO2 emissions alone. We use an approach built from the Climate Model Intercomparison Project Phase 6 (CMIP6) Earth System Models, based on the concept that an additional unit of CO2 can be scaled for larger emissions and summed over time to estimate cumulative impacts. We evaluate this with additional CMIP6 experiments, showing that this approach captures the temperature response in most locations with lower accuracy in the Arctic and Southern Ocean. This type of approach may be useful to evaluate many policy scenarios and to better understand earth system processes that are represented in the models, as it takes around one second to quantify 90 years' worth of temperature change on a local computer, while Earth System Models can require weeks of runtime on supercomputers. Key Points With a Green's Function approach, we emulate the linear component of the spatially resolved temperature response to CO2 emissions We reproduce the temperature response well within multi‐model uncertainty except in the Arctic and Southern Ocean This approach allows expedient quantification of the spatial and temporal temperature response to varying CO2 emissions pathways

Increasing the accuracy of crop productivity estimates is a key element in planning adaptation strategies to ensure global food security under climate change. Process-based crop models are effective means to project climate impact on crop yield, but have large uncertainty in yield simulations. Here, we show that variations in the mathematical functions currently used to simulate temperature responses of physiological processes in 29 wheat models account for is greater than 50% of uncertainty in simulated grain yields for mean growing season temperatures from 14 C to 33 C. We derived a set of new temperature response functions that when substituted in four wheat models reduced the error in grain yield simulations across seven global sites with different temperature regimes by 19% to 50% (42% average). We anticipate the improved temperature responses to be a key step to improve modelling of crops under rising temperature and climate change, leading to higher skill of crop yield projections.

People depend on benefits provided by ecological systems. Understanding how these ecosystem services – and the ecosystem properties underpinning them – respond to drivers of change is therefore an urgent priority. We address this challenge through developing a novel risk‐assessment framework that integrates ecological and evolutionary perspectives on functional traits to determine species’ effects on ecosystems and their tolerance of environmental changes. We define Specific Effect Function (SEF) as the per‐gram or per capita capacity of a species to affect an ecosystem property, and Specific Response Function (SRF) as the ability of a species to maintain or enhance its population as the environment changes. Our risk assessment is based on the idea that the security of ecosystem services depends on how effects (SEFs) and tolerances (SRFs) of organisms – which both depend on combinations of functional traits – correlate across species and how they are arranged on the species’ phylogeny. Four extreme situations are theoretically possible, from minimum concern when SEF and SRF are neither correlated nor show a phylogenetic signal, to maximum concern when they are negatively correlated (i.e., the most important species are the least tolerant) and phylogenetically patterned (lacking independent backup). We illustrate the assessment with five case studies, involving both plant and animal examples. However, the extent to which the frequency of the four plausible outcomes, or their intermediates, apply more widely in real‐world ecological systems is an open question that needs empirical evidence, and suggests a research agenda at the interface of evolutionary biology and ecosystem ecology. We offer a new synthesis integrating in a single, coherent framework the evolution of organismal traits, ecosystem process and services, and their security or vulnerability in the face of specific kinds of environmental change. Our risk assessment integrates ecological and evolutionary perspectives on functional traits to determine species’ effects on ecosystems and their tolerance of different environmental threats. Applying the assessment to five case studies, we show that the security of ecosystem services depends on how effects and tolerances of organisms – which both depend on combinations of functional traits – correlate across species and how they are arranged on the phylogenetic tree. Our framework highlights the importance of phylogenetic redundancy in species’ effects and the risks of strong phylogenetic patterning in species’ tolerances, and suggests a concrete, new research agenda at the interface of evolutionary biology and ecosystem ecology.

Terrestrial biosphere models (TBMs) are highly sensitive to model representation of photosynthesis, in particular the parameters maximum carboxylation rate and maximum electron transport rate at 25°C (V c,max.25 and J max.25, respectively). Many TBMs do not include representation of Arctic plants, and those that do rely on understanding and parameterization from temperate species. We measured photosynthetic CO2 response curves and leaf nitrogen (N) content in species representing the dominant vascular plant functional types found on the coastal tundra near Barrow, Alaska. The activation energies associated with the temperature response functions of V c,max and J max were 17% lower than commonly used values. When scaled to 25°C, V c,max.25 and J max.25 were two- to five-fold higher than the values used to parameterize current TBMs. This high photosynthetic capacity was attributable to a high leaf N content and the high fraction of N invested in Rubisco. Leaf-level modeling demonstrated that current parameterization of TBMs resulted in a two-fold underestimation of the capacity for leaf-level CO2 assimilation in Arctic vegetation. This study highlights the poor representation of Arctic photosynthesis in TBMs, and provides the critical data necessary to improve our ability to project the response of the Arctic to global environmental change.

In this paper, we propose a conceptual approach to assign a “mathematical meaning” to the non-local function χ ( r , r ′ ) . Mathematical evaluation of this kernel remains difficult since it is a function depending on six Cartesian coordinates. The idea behind this approach is to look for a limit process in order to explore mathematically this non-local function. According to our approach, the bra ⟨ χ r ′ ξ | is the linear functional that corresponds to any ket | ψ ⟩ , the value ⟨ r ′ | ψ ⟩ . In condensed writing ⟨ χ r ′ ξ | ⟨ r | ψ ⟩ = ⟨ r ′ | ψ ⟩ , and this is achieved by exploiting the sifting property of the delta function that gives it the sense of a measure, i.e. measuring the value of ψ ( r ) at the point r ′ . It is worth noting that ⟨ χ r ′ ξ | is not an operator in the sense that when it is applied on a ket, it produces a number ψ ( r = r ′ ) and not a ket. The quantity χ r ′ ξ ( r ) proceed as nascent delta function, turning into a real delta function in the limit where ξ → 0 . In this regard, χ r ′ ξ ( r ) acts as a limit of an integral operator kernel in a convolution integration procedure.

Impulse response functions (IRF), the response in a climate parameter to an emission pulse of CO2, are used to characterize Earth system response timescales and to calculate Global Warming Potentials (GWPs). GWPs are widely used to compare emissions of different greenhouse gases and to compute CO2 equivalent emissions as reported by governments to the United Nations Framework Convention on Climate Change (UNFCCC). The GWP of any gas x is the absolute GWP of gas x Absolute and relative Global Warming Potential (AGWPx) divided by AGWP of CO2. Ideally, AGWP CO2 and GWPx would be independent of atmospheric CO2 and climate. However, AGWP CO2 , and, in turn, GWPx change under rising atmospheric CO2 and global warming, affecting the emission reporting under the UNFCCC. Here, we apply perturbed parameter ensemble simulations, constrained in a Bayesian approach by observational data, to investigate how AGWP CO2 and IRF vary under different atmospheric background CO2 levels (CO 2,bg ). We provide analytical formulations to compute AGWP CO2 and IRF for CO2, ocean and land carbon uptake, global mean surface air temperature, steric sea level, and ocean heat content, and to adjust these metrics to different CO 2,bg . AGWP CO2 , given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 101.8(±13.5) 10−15 yr W m−2 kg-CO 2−1 for CO 2,bg = 425 ppm and decreases by 7% for CO 2,bg = 500 ppm. The decrease is driven by a decrease in the radiative efficiency of CO2, partly canceled by a concomitant increase of IRF CO2 due to muted ocean and land carbon uptake under higher CO2 levels. We recommend regularly adjusting AGWP CO2 and, in turn, GWPs of long-lived gases to contemporary atmospheric CO2 and climate.

Vector Error Correction Model is a cointegrated VAR model. This idea of Vector Error Correction Model (VECM), which consists of a VAR model of the order p - 1 on the differences of the variables, and an error-correction term derived from the known (estimated) cointegrating relationship. Intuitively, and using the stock market example, a VECM model establishes a short-term relationship between the stock prices, while correcting with the deviation from the long-term comovement of prices. An Impulse Response Function traces the incremental effect of a 1 unit (or one standard deviation) shock in one of the variables on the future values of the other endogenous variables. Impulse Response Functions trace the incremental effect of the marketing action reflected in the shock. The data used in this analysis are 4 (four) daily plantation stocks prices in Indonesia with time period of January to July in three years which are 2018, 2019, and 2020. The objective of this study is to determine the relationship among 4 (four) stocks prices with VECM and to know the behaviour of each stocks prices with Impulse Response.

Within-field variability of crop yield levels has been extensively investigated, but the spatial variability of crop yield responses to agronomic treatments is less understood. On-farm precision experimentation (OFPE) can be a valuable tool for the estimation of in-field variation of optimal input rates and thus improve agronomic decisions. Therefore, the objectives of this study were to investigate the spatial variability of optimal input rates in OFPE and the potential economic benefit of site-specific input management. Mixed geographically weighted regression (GWR) models were used to estimate local yield response functions. The methodology was applied to investigate the spatial variability in corn response to nitrogen and seed rates in four cornfields in Illinois, USA. The results showed that spatial heterogeneity of model parameters was significant in all four fields evaluated. On average, the RMSE of the fitted yield decreased from 1.2 Mg ha−1 in the non-spatial global model to 0.7 Mg ha−1 in the GWR model, and the r-squared increased from 10 to 68%. The average potential gain of using optimized uniform rates of seed and nitrogen was US$ 65.00 ha−1, while the added potential gain of the site-specific application was US$ 58.00 ha−1. The combination of OFPE and GWR proved to be an effective tool for testing precision agriculture’s central hypothesis of whether optimal input application rates display adequate spatial variability to justify the costs of the variable rate technology itself. The reported results encourage more research on response-based input management recommendations instead of the still widespread focus on yield-based algorithms.

Following the emergence of the Internet, the Internet of things (IOT) brought about another wave of technological and economic revolutions. Through the lens of the production process, this study utilises the dynamic network slack-based measure model in data envelopment analysis to evaluate 32 IOT companies in Taiwan in terms of their innovation efficiency, operational efficiency and overall efficiency for the period of 2007–2017. Empirical results reveal that the average operational and overall efficiencies of IOT companies in Taiwan have been decreasing considerably since 2008. However, their average innovation efficiency remains stable over the sample period owing to government reductions in enterprise research and development (R&D) tax credit incentives. Through the impulse response function method, this study further confirms that the Statute for Industrial Innovation, which was implemented in 2010 and revised and reimplemented in 2016, specifically, policies concerning enterprise R&D tax credits, affect the efficiencies of IOT companies in Taiwan. Overall, this study reveals the performance evaluation process of IOT companies by showing that their innovation capability affects their operational efficiency. Thus, the government is advised to incorporate innovation measures into relevant industrial policies to achieve policy effectiveness.