A linear algebraic method for pricing temporary life annuities and insurance policies

We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims

Leaf morphological traits as adaptations to multiple climate gradients

1. Leaf morphological traits vary systematically along climatic gradients. However, recent studies in plant functional ecology have mainly analysed quantitative traits, while numerical models of species distributions and vegetation function have focused on traits associated with resource acquisition; both ignore the wider functional significance of leaf morphology. 2. A data set comprising 22 leaf morphological traits for 662 woody species from 92 sites, representing all biomes present in China, was subjected to multivariate analysis in order to identify leading dimensions of trait covariation (correspondence analysis), quantify climatic and phylogenetic contributions (canonical correspondence analysis with variation partitioning), and characterize co-occurring trait syndromes (k-means clustering) and their climatic preferences. 3. Three axes accounted for > 20% of trait variation in both evergreen and deciduous species. Moisture index, precipitation seasonality and growing-season temperature accounted for 8–10% of trait variation; family 15–32%. Microphyll or larger, mid- to dark green leaves with drip-tips in wetter climates contrasted with nanophyll or smaller glaucous leaves without drip-tips in drier climates. Thick, entire leaves in less seasonal climates contrasted with thin, marginal dissected, aromatic, and involute/revolute leaves in more seasonal climates. Thick, involute, hairy leaves in colder climates contrasted with thin leaves with marked surface structures (surface patterning) in warmer climates. Distinctive trait clusters were linked to the driest and most seasonal climates, for example the clustering of picophyll, fleshy and succulent leaves in the driest climates and leptophyll, linear, dissected, revolute or involute, and aromatic leaves in regions with highly seasonal rainfall. Several trait clusters co-occurred in wetter climates, including clusters characterised by microphyll, moderately thick, patent, and entire leaves or notophyll, waxy, dark green leaves. 4. Synthesis. The plastic response of size, shape, color and other leaf morphological traits to climate is muted, thus their apparent shift along climate gradients reflects plant adaptations to environment at a community-level as determined by species replacement. Information on leaf morphological traits, widely available in floras, could be used to strengthen predictive models of species distribution and vegetation function

Optimality-based modelling of wheat sowing dates globally

CONTEXT Sowing dates are currently an essential input for crop models. However, in the future, the optimal sowing time will be affected by climate changes and human adaptations to these changes. A better understanding of what determines the choice of wheat type and sowing dates is required to be able to predict future crop yields reliably. OBJECTIVE This study was conducted to understand how climate conditions affect the choice of wheat types and sowing dates globally. METHODS We develop a model integrating optimality concepts for simulating gross primary production (GPP) with climate constraints on wheat phenology to predict sowing dates. We assume that wheat could be sown at any time with suitable climate conditions and farmers would select a sowing date that maximises yields. The model is run starting on every possible climatically suitable day, determined by climate constraints associated with low temperature and intense precipitation. The optimal sowing date is the day which gives the highest yield in each location. We evaluate the simulated optimal sowing dates with data on observed sowing dates created by merging census-based datasets and local agronomic information, then predict their changes under future climate scenarios to gain insight into the impacts of climate change. RESULTS AND CONCLUSIONS Cold-season temperatures are the major determinant of sowing dates in the extra-tropics, whereas the seasonal cycle of monsoon rainfall is important in the tropics. Our model captures the timing of reported sowing dates, with differences of less than one month over much of the world; maximum errors of up to two months occur in tropical regions with large altitudinal gradients. Discrepancies between predictions and observations are larger in tropical regions than temperate and cold regions. Slight warming is shown to promote earlier sowing in wet areas but later in dry areas; larger warming leads to delayed sowing in most regions. These predictions arise due to the interactions of several influences on yield, including the effects of warming on growing-season length, the need for sufficient moisture during key phenological stages, and the temperature threshold for vernalization of winter wheat. SIGNIFICANCE The integration of optimality concepts for simulating GPP with climate constraints on phenology provides realistic predictions of wheat type and sowing dates. The model thus provides a basis for predicting how crop calendars might change under future climate change. It can also be used to investigate potential changes in management to mitigate the negative impacts of climate change

Global leaf-trait mapping based on optimality theory

Aim Leaf traits are central to plant function, and key variables in ecosystem models. However recently published global trait maps, made by applying statistical or machine-learning techniques to large compilations of trait and environmental data, differ substantially from one another. This paper aims to demonstrate the potential of an alternative approach, based on eco-evolutionary optimality theory, to yield predictions of spatio-temporal patterns in leaf traits that can be independently evaluated. Innovation Global patterns of community-mean specific leaf area (SLA) and photosynthetic capacity (Vcmax) are predicted from climate via existing optimality models. Then leaf nitrogen per unit area (Narea) and mass (Nmass) are inferred using their (previously derived) empirical relationships to SLA and Vcmax. Trait data are thus reserved for testing model predictions across sites. Temporal trends can also be predicted, as consequences of environmental change, and compared to those inferred from leaf-level measurements and/or remote-sensing methods, which are an increasingly important source of information on spatio-temporal variation in plant traits. Main conclusions Model predictions evaluated against site-mean trait data from > 2,000 sites in the Plant Trait database yielded R2 = 73% for SLA, 38% for Nmass and 28% for Narea. Declining species-level Nmass, and increasing community-level SLA, have both been recently reported and were both correctly predicted. Leaf-trait mapping via optimality theory holds promise for macroecological applications, including an improved understanding of community leaf-trait responses to environmental change

Optimality principles explaining divergent responses of alpine vegetation to environmental change

Recent increases in vegetation greenness over much of the world reflect increasing CO2 globally and warming in cold areas. However, the strength of the response to both CO2 and warming in those areas appears to be declining for unclear reasons, contributing to large uncertainties in predicting how vegetation will respond to future global changes. Here, we investigated the changes of satellite-observed peak season absorbed photosynthetically active radiation (Fmax) on the Tibetan Plateau between 1982 and 2016. Although climate trends are similar across the Plateau, we identified robust divergent responses (a greening of 0.31 ± 0.14% year−1 in drier regions and a browning of 0.12 ± 0.08% year−1 in wetter regions). Using an eco-evolutionary optimality (EEO) concept of plant acclimation/adaptation, we propose a parsimonious modelling framework that quantitatively explains these changes in terms of water and energy limitations. Our model captured the variations in Fmax with a correlation coefficient (r) of .76 and a root mean squared error of .12 and predicted the divergent trends of greening (0.32 ± 0.19% year−1) and browning (0.07 ± 0.06% year−1). We also predicted the observed reduced sensitivities of Fmax to precipitation and temperature. The model allows us to explain these changes: Enhanced growing season cumulative radiation has opposite effects on water use and energy uptake. Increased precipitation has an overwhelmingly positive effect in drier regions, whereas warming reduces Fmax in wetter regions by increasing the cost of building and maintaining leaf area. Rising CO2 stimulates vegetation growth by enhancing water-use efficiency, but its effect on photosynthesis saturates. The large decrease in the sensitivity of vegetation to climate reflects a shift from water to energy limitation. Our study demonstrates the potential of EEO approaches to reveal the mechanisms underlying recent trends in vegetation greenness and provides further insight into the response of alpine ecosystems to ongoing climate change

The China plant trait database version 2

Plant functional traits represent adaptive strategies to the environment, linked to biophysical and biogeochemical processes and ecosystem functioning. Compilations of trait data facilitate research in multiple fields from plant ecology through to land-surface modelling. Here we present version 2 of the China Plant Trait Database, which contains information on morphometric, physical, chemical, photosynthetic and hydraulic traits from 1529 unique species in 140 sites spanning a diversity of vegetation types. Version 2 has five improvements compared to the previous version: (1) new data from a 4-km elevation transect on the edge of Tibetan Plateau, including alpine vegetation types not sampled previously; (2) inclusion of traits related to hydraulic processes, including specific sapwood conductance, the area ratio of sapwood to leaf, wood density and turgor loss point; (3) inclusion of information on soil properties to complement the existing data on climate and vegetation (4) assessments and flagging the reliability of individual trait measurements; and (5) inclusion of standardized templates for systematical field sampling and measurements

Rising CO2 and warming reduce global canopy deman for nitrogen

Nitrogen (N) limitation has been considered as a constraint on terrestrial carbon uptake in response to rising CO2 and climate change. By extension, it has been suggested that declining carboxylation capacity (Vcmax) and leaf N content in enhanced-CO2 experiments and satellite records signify increasing N limitation of primary production. We predicted Vcmax using the coordination hypothesis, and estimated changes in leaf-level photosynthetic N for 1982–2016 assuming proportionality with leaf-level Vcmax at 25˚C. Whole-canopy photosynthetic N was derived using satellite-based leaf area index (LAI) data and an empirical extinction coefficient for Vcmax, and converted to annual N demand using estimated leaf turnover times. The predicted spatial pattern of Vcmax shares key features with an independent reconstruction from remotely-sensed leaf chlorophyll content. Predicted leaf photosynthetic N declined by 0.27 % yr-1, while observed leaf (total) N declined by 0.2–0.25 % yr-1. Predicted global canopy N (and N demand) declined from 1996 onwards, despite increasing LAI. Leaf-level responses to rising CO2, and to a lesser extent temperature, may have reduced the canopy requirement for N by more than rising LAI has increased it. This finding provides an alternative explanation for declining leaf N that does not depend on increasing N limitation

Reduced global plant respiration due to the acclimation of leaf dark respiration coupled to photosynthesis

Leaf dark respiration (Rd) acclimates to environmental changes. However, the magnitude, controls and time scales of acclimation remain unclear and are inconsistently treated in ecosystem models. We hypothesized that Rd and Rubisco carboxylation capacity (Vcmax) at 25°C (Rd,25, Vcmax,25) are coordinated so that Rd,25 variations support Vcmax,25 at a level allowing full light use, with Vcmax,25 reflecting daytime conditions (for photosynthesis), and Rd,25/Vcmax,25 reflecting night-time conditions (for starch degradation and sucrose export). We tested this hypothesis temporally using a 5-yr warming experiment, and spatially using an extensive field-measurement data set. We compared the results to three published alternatives: Rd,25 declines linearly with daily average prior temperature; Rd at average prior night temperatures tends towards a constant value; and Rd,25/Vcmax,25 is constant. Our hypothesis accounted for more variation in observed Rd,25 over time (R2 = 0.74) and space (R2 = 0.68) than the alternatives. Night-time temperature dominated the seasonal time-course of Rd, with an apparent response time scale of c. 2 wk. Vcmax dominated the spatial patterns. Our acclimation hypothesis results in a smaller increase in global Rd in response to rising CO2 and warming than is projected by the two of three alternative hypotheses, and by current models

Leaf economics fundamentals explained by optimality principles

The life span of leaves increases with their mass per unit area (LMA). It is unclear why. Here, we show that this empirical generalization (the foundation of the worldwide leaf economics spectrum) is a consequence of natural selection, maximizing average net carbon gain over the leaf life cycle. Analyzing two large leaf trait datasets, we show that evergreen and deciduous species with diverse construction costs (assumed proportional to LMA) are selected by light, temperature, and growing-season length in different, but predictable, ways. We quantitatively explain the observed divergent latitudinal trends in evergreen and deciduous LMA and show how local distributions of LMA arise by selection under different environmental conditions acting on the species pool. These results illustrate how optimality principles can underpin a new theory for plant geography and terrestrial carbon dynamics

Global datasets of leaf photosynthetic capacity for ecological and earth system research

The maximum rate of Rubisco carboxylation (Vcmax) determines leaf photosynthetic capacity and is a key parameter for estimating the terrestrial carbon cycle, but its spatial information is lacking, hindering global ecological research. Here, we convert leaf chlorophyll content (LCC) retrieved from satellite data to Vcmax, based on plants’ optimal distribution of nitrogen between light harvesting and carboxylation pathways. We also derive Vcmax from satellite (GOME-2) observations of sun-induced chlorophyll fluorescence (SIF) as a proxy of leaf photosynthesis using a data assimilation technique. These two independent global Vcmax products agree well (r 2=0.79, RMSE=15.46 μmol m-2 s -1 25 , P<0.001) and compare well with 3672 ground-based measurements (r2=0.68, RMSE=13.55 μmol m-2 s -1 and P<0.001 for SIF; r2=0.55, RMSE=17.55 μmol m-2 s -1 and P<0.001 for LCC). The LCC-derived Vcmax product is also used to constrain the retrieval of Vcmax from TROPOMI SIF data to produce an optimized Vcmax product using both SIF and LCC information. The global distributions of these products are compatible with Vcmax computed from an ecological optimality theory using meteorological variables, but importantly reveal additional information on the influence of land cover, irrigation, soil pH and leaf nitrogen on leaf photosynthetic capacity. These satellite-based approaches and spatial Vcmax products are primed to play a major role in global ecosystem research. The three remote sensing Vcmax products based on SIF, LCC and SIF+LCC are available at https://doi.org/10.5281/zenodo.6466968 (Chen et al., 2020) and the code for implementing the ecological optimality theory is available at https://github.com/SmithEcophysLab/optimal_vcmax_R (Smith, 2020)