Models and tests of optimal density and maximal yield for crop plants

Multi-scale characterisation of cold response reveals immediate and long-term impacts on cell physiology up to seed composition in sunflower

Early sowing can help summer crops escape drought and can mitigate the impacts of climate change on them. However, it exposes them to cold stress during initial developmental stages, which has both immediate and long-term effects on development and physiology. To understand how early night-chilling stress impacts plant development and yield, we studied the reference sunflower line XRQ under controlled, semi-controlled and field conditions. We performed high-throughput imaging of the whole plant parts and obtained physiological and transcriptomic data from leaves, hypocotyls and roots. We observed morphological reductions in early stages under field and controlled conditions, with a decrease in root development, an increase in reactive oxygen species content in leaves and changes in lipid composition in hypocotyls. A long-term increase in leaf chlorophyll suggests a stress memory mechanism that was supported by transcriptomic induction of histone coding genes. We highlighted DEGs related to cold acclimation such as chaperone, heat shock and late embryogenesis abundant proteins. We identified genes in hypocotyls involved in lipid, cutin, suberin and phenylalanine ammonia lyase biosynthesis and ROS scavenging. This comprehensive study describes new phenotyping methods and candidate genes to understand phenotypic plasticity better in response to chilling and study stress memory in sunflower.

Toward systems agroecology: Design and control of intercropping

In view of changing climatic conditions and disappearing natural resources such as fertile soil and water, exploring alternatives to today's industrial monocrop farming becomes essential. One promising farming practice is intercropping (IC), in which two or more crop species are grown together. Many experiments have shown that, under certain circumstances, IC can decrease soil erosion and fertilizer use, improve soil health and land management, while preserving crop production levels. However, there have been no quantitative approaches to predict, design, and control appropriate IC implementation for given particular environmental and farming conditions, and to assess its robustness. Here, we develop such an approach, based on methods and concepts developed in data science and systems biology. Our dataset groups the results of 2258 IC experiments, involving 274 pairs of 69 different plants. The data include 4 soil characteristics and 5 environmental and farming conditions, together with 8 traits for each of the two intercropped plants. We performed a dimensional reduction of the resulting 25-dimensional variable space and showed that, from a few quantities, one can predict IC yield relative to sole cultivation with good accuracy. For given environmental conditions, our computational approach can help to choose a companion plant and appropriate farming practices. It also indicates how to estimate the robustness of IC to external perturbations. This approach, together with its results, can be viewed as an initial step toward "systems agriculture," which would ultimately develop systems of multiple plant grown together in appropriately designed and controlled settings.

An allometry perspective on crops

Understanding trait-trait coordination is essential for successful plant breeding and crop modeling. Notably, plant size drives variation in morphological, physiological, and performance-related traits, as described by allometric laws in ecology. Yet, as allometric relationships have been limitedly studied in crops, how they influence and possibly limit crop performance remains unknown. Here, we review how an allometry perspective on crops gains insights into the phenotypic evolution during crop domestication, the breeding of varieties adapted to novel conditions, and the prediction of crop yields. As allometry is an active field of research, modeling and manipulating crop allometric relationships can help to develop more resilient and productive agricultural systems to face future challenges.

Photosynthetic capacity and assimilate transport of the lower canopy influence maize yield under high planting density

Photosynthesis is a major trait of interest for the development of high-yield crop plants. However, little is known about the effects of high-density planting on photosynthetic responses at the whole-canopy level. Using the high-yielding maize (Zea mays L.) cultivars "LY66," "MC670," and "JK968," we conducted a 2-yr field experiment to assess ear development in addition to leaf characteristics and photosynthetic parameters in each canopy layer at 4 planting densities. Increased planting density promoted high grain yield and population-scale biomass accumulation despite reduced per-plant productivity. MC670 had the strongest adaptability to high-density planting conditions. A physiological analysis showed that increased planting density primarily led to decreases in the single-leaf area above the ear for LY66 and MC670 and below the ear for JK968. Furthermore, high planting density decreased chlorophyll content and the photosynthetic rate due to decreased canopy transmission, leading to severe decreases in single-plant biomass accumulation in the lower canopy. Moreover, increased planting density improved presilking biomass transfer, especially in the lower canopy. The yield showed significant positive relationships with photosynthesis and biomass in the lower canopy, demonstrating the important contributions of these leaves to grain yield under dense planting conditions. Increased planting density led to retarded ear development as a consequence of reduced glucose and fructose contents in the ears, indicating reductions in sugar transport that were associated with limited sink organ development, reduced kernel number, and yield loss. Overall, these findings highlighted the photosynthetic capacities of the lower canopy as promising targets for improving maize yield under dense planting conditions.

China can be self-sufficient in maize production by 2030 with optimal crop management

Population growth and economic development in China has increased the demand for food and animal feed, raising questions regarding China's future maize production self-sufficiency. Here, we address this challenge by combining data-driven projections with a machine learning method on data from 402 stations, with data from 87 field experiments across China. Current maize yield would be roughly doubled with the implementation of optimal planting density and management. In the 2030 s, we estimate a 52% yield improvement through dense planting and soil improvement under a high-end climate forcing Shared Socio-Economic Pathway (SSP585), compared with a historical climate trend. Based on our results, yield gains from soil improvement outweigh the adverse effects of climate change. This implies that China can be self-sufficient in maize by using current cropping areas. Our results challenge the view of yield stagnation in most global areas and provide an example of how food security can be achieved with optimal crop-soil management under future climate change scenarios.

Density Management Is More Cost Effective than Fertilization for Chimonobambusa pachystachys Bamboo-Shoot Yield and Economic Benefits

Stand-density management and fertilization practices are the main two factors affecting bamboo-shoot yield. However, the appropriate density and fertilization rates are still unclear for improving the bamboo-shoot yield and its economic benefits, especially for a high economic value bamboo-shoot forest. To fill this gap, we conducted a two-year split-plot design experiment in a Chimonobambusa pachystachys shoot forest. The main plots were assigned to five density rates, 40,000, 50,000, 60,000, 70,000, and 100,000 culms ha−1, and the subplots were assigned to four fertilization rates (nitrogen:phosphorus:potassium = 23:3:15): 0, 820, 1640, and 2460 kg ha−1 a−1. Results showed that the bamboo-shoot yield increased first and then decreased with stand density, while it increased with fertilization rates. Density management and fertilization regulate bamboo-shoot yield by changing the soil’s Olsen P, available nitrogen, organic matter, and available potassium contents. The maximum bamboo-shoot yield was 9315.92 kg ha−1, which appeared in the density of 60,000 culms ha−1 and the fertilization of 2460 kg ha−1 a−1. However, the maximum bamboo-shoot net profit was 135,242.63 CNY ha−1, which appeared at the density of 60,000 culms ha−1 and the fertilization of 1640 kg ha−1 a−1. The economic-benefit analysis shows that density management achieves a net-profit growth comparable to fertilizer application at a much lower cost. The study results provide a basis for the scientific management of C. pachystachys shoot forests and bamboo farmers to improve their income.

Impacts of transpiration of agricultural crops and seeding on rainfall: Implications from a mathematical model

As the source of replenishment, rainfall has an extensive impact because its variability shapes biologically efficient pulses of soil moisture recharge across layers from rainfall events. In this paper, a mathematical model is proposed to explore the importance of transpiration from agricultural crops and aerosols on the pattern of rainfall. For the system without seeding, the simulation results show destabilizing roles of parameters related to formation of cloud drops due to transpiration of agricultural crops, formation of raindrops due to cloud drops and growth of agricultural crops due to rain. The model without seeding is extended to its stochastic counterpart to encapsulate the uncertainty observed in some important parameters. We observe the variability in the system’s variables and found their distributions at certain fixed times, which explore the importance of stochasticity in the system. Our findings show that transpiration through agricultural crops plays an important role in cloud formation, and thus, affects the effectiveness of different rainfall events. Moreover, the combined actions of transpiration and seeding are much more beneficial in producing rain. Finally, we see the behavior of system by considering seasonal variations of some rate parameters.

Effects of biotic and abiotic factors on forest biomass fractions

The extent to which key factors at the global scale influence plant biomass allocation patterns remains unclear. Here, we provide a theory about how biotic and abiotic factors influence plant biomass allocation and evaluate its predictions using a large global database for forested communities. Our analyses confirm theoretical predictions that temperature, precipitation, and plant height and density jointly regulate the quotient of leaf biomass and total biomass, and that they have a much weaker effect on shoot (leaf plus stem) biomass fractions at a global scale. Moreover, biotic factors have larger effects than abiotic factors. Climatic variables act equally on shoot and root growth, and differences in plant body size and age, as well as community species composition, which vary with climate in ways that drown out the variations in biomass fractions. The theory and data presented here provide mechanistic explanations of why climate has little effect on biomass fractions.

Artificial selection for grain yield has increased net CO2 exchange of the ear leaf in maize crops

Identifying the physiological traits indirectly selected during the search for high-yielding maize hybrids is useful for guiding further improvements. To investigate such traits, in this study we focused on the critical period of kernel formation because kernel number is the main yield component affected by breeding. Our results show that breeding has increased the number of florets per ear and ear growth rate but not the vegetative shoot growth rate, suggesting localised effects around the ear. Consistent with this possibility, breeding has increased the net CO2 exchange of the ear leaf in field-grown crops grown at high population densities. This response is largely accounted for by increased light interception (which increases photosynthesis) and by reduced rates of respiration of the ear leaf in modern hybrids compared to older ones. Modern hybrids show increased ear-leaf area per unit leaf dry matter (specific leaf area), which accounts for the reduced respiratory load per unit leaf area. These observations are consistent with a model where the improved ear leaf CO2 exchange helps the additional florets produced by modern hybrids to survive the critical period of high susceptibility to stress and hence to produce kernels.

Growth, death, and resource competition in sessile organisms

Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.

Enhancing the productivity of ryegrass at elevated CO2 is dependent on tillering and leaf area development rather than leaf-level photosynthesis

Whilst a range of strategies have been proposed for enhancing crop productivity, many recent studies have focused primarily on enhancing leaf photosynthesis under current atmospheric CO2 concentrations. Given that the atmospheric CO2 concentration is likely to increase significantly in the foreseeable future, an alternative/complementary strategy might be to exploit any variability in the enhancement of growth/yield and photosynthesis at higher CO2 concentrations. To explore this, we investigated the responses of a diverse range of wild and cultivated ryegrass genotypes, with contrasting geographical origins, to ambient and elevated CO2 concentrations and examined what genetically tractable plant trait(s) might be targeted by plant breeders for future yield enhancements. We found substantial ~7-fold intraspecific variations in biomass productivity among the different genotypes at both CO2 levels, which were related primarily to differences in tillering/leaf area, with only small differences due to leaf photosynthesis. Interestingly, the ranking of genotypes in terms of their response to both CO2 concentrations was similar. However, as expected, estimates of whole-plant photosynthesis were strongly correlated with plant productivity. Our results suggest that greater yield gains under elevated CO2 are likely through the exploitation of genetic differences in tillering and leaf area rather than focusing solely on improving leaf photosynthesis.

Water content quantitatively affects metabolic rates over the course of plant ontogeny

Plant metabolism determines the structure and dynamics of ecological systems across many different scales. The metabolic theory of ecology quantitatively predicts the scaling of metabolic rate as a function of body size and temperature. However, the role of tissue water content has been neglected even though hydration significantly affects metabolism, and thus ecosystem structure and functioning. Here, we use a general model based on biochemical kinetics to quantify the combined effects of water content, body size and temperature on plant metabolic rates. The model was tested using a comprehensive dataset from 205 species across 10 orders of magnitude in body size from seeds to mature large trees. We show that water content significantly influences mass-specific metabolic rates as predicted by the model. The scaling exponents of whole-plant metabolic rate vs body size numerically converge onto 1.0 after water content is corrected regardless of body size or ontogenetic stage. The model provides novel insights into how water content together with body size and temperature quantitatively influence plant growth and metabolism, community dynamics and ecosystem energetics.

Tradeoffs in the evolution of plant farming by ants

Diverse forms of cultivation have evolved across the tree of life. Efficient farming requires that the farmer deciphers and actively promotes conditions that increase crop yield. For plant cultivation, this can include evaluating tradeoffs among light, nutrients, and protection against herbivores. It is not understood if, or how, nonhuman farmers evaluate local conditions to increase payoffs. Here, we address this question using an obligate farming mutualism between the ant Philidris nagasau and epiphytic plants in the genus Squamellaria that are cultivated for their nesting sites and floral rewards. We focused on the ants' active fertilization of their crops and their protection against herbivory. We found that ants benefited from cultivating plants in full sun, receiving 7.5-fold more floral food rewards compared to shade-cultivated plants. The higher reward levels correlated with higher levels of crop protection provided by the ants. However, while high-light planting yielded the greatest immediate food rewards, sun-grown crops contained less nitrogen compared to shade-grown crops. This was due to lower nitrogen input from ants feeding on floral rewards instead of insect protein gained from predation. Despite this tradeoff, farming ants optimize crop yield by selectively planting their crops in full sun. Ancestral state reconstructions across this ant-plant clade show that a full-sun farming strategy has existed for millions of years, suggesting that nonhuman farmers have evolved the means to evaluate and balance conflicting crop needs to their own benefit.

A General Model for Seed and Seedling Respiratory Metabolism

The ontogeny of seed plants usually involves a dormant dehydrated state and the breaking of dormancy and germination, which distinguishes it from that of most organisms. Seed germination and seedling establishment are critical ontogenetic stages in the plant life cycle, and both are fueled by respiratory metabolism. However, the scaling of metabolic rate with respect to individual traits remains poorly understood. Here, we tested metabolic scaling theory during seed germination and early establishment growth using a recently developed model and empirical data collected from 41 species. The results show that (i) the mass-specific respiration rate (R_m) was weakly correlated with body mass, mass-specific N content, and mass-specific C content; (ii) R_m conformed to a single Michaelis-Menten curve as a function of tissue water content; and (iii) the central parameters in the model were highly correlated with DNA content and critical enzyme activities. The model offers new insights and a more integrative scaling theory that quantifies the combined effects of tissue water content and body mass on respiratory metabolism during early plant ontogeny.

Is timing of reproduction according to temperature sums an optimal strategy?

Temperature sums are widely used to predict the seasonal timing of yearly recurring biological events, such as flowering, budburst, and hatching. We use a classic energy allocation model for annual plants to compare a strategy for reproductive timing that follows a temperature sum rule (TSR) with a strategy that follows an optimal control rule (OCR) maximizing reproductive output. We show that the OCR corresponds to a certain TSR regardless of how temperature is distributed over the growing season as long as the total temperature sum over the whole growing season is constant between years. We discuss such scenarios, thus outlining under which type of variable growth conditions TSR maximizes reproductive output and should be favored by natural selection. By providing an ultimate explanation for a well-documented empirical pattern this finding enhances the credibility of temperature sums as predictors of the timing of biological events. However, TSR and OCR respond in opposite directions when the total yearly temperature sum changes between years, representing, for example, variation in the length of the growing season. Our findings have implications for predicting optimal responses of organisms to climatic changes and suggest under which conditions natural selection should favor photoperiod versus temperature control.

Clothing the Emperor: Dynamic Root-Shoot Allocation Trajectories in Relation to Whole-Plant Growth Rate and in Response to Temperature

We quantified how root-shoot biomass allocation and whole-plant growth rate co-varied ontogenetically in contrasting species in response to cooling. Seven grass and four forb species were grown for 56 days in hydroponics. Growth was measured repeatedly before and after day/night temperatures were reduced at 28 days from 20 °C/15 °C to 10 °C/5 °C; controls remained unchanged. Sigmoid trajectories of root and shoot growth were reconstructed from the experimental data to derive continuous whole-plant relative growth rates (RGRs) and root mass fractions (RMFs). Root mass fractions in cooled plants generally increased, but this originated from unexpected and previously uncharacterised differences in response among species. Root mass fraction and RGR co-trajectories were idiosyncratic in controls and cooled plants. The RGR-RMF co-trajectories responded to cooling in grasses, but not forbs. The RMF responses of stress-tolerant grasses were predictably weak but projected to eventually out-respond faster-growing species. Sigmoid growth constrains biomass allocation. Only when neither root nor shoot biomass is near-maximal can biomass allocation respond to environmental drivers. Near maximum size, plants cannot adjust RMF, which then reflects net above- and belowground productivities. Ontogenetic biomass allocations are not equivalent to those based on interspecific surveys, especially in mature vegetation. This reinforces the importance of measuring temporal growth dynamics, and not relying on "snapshot" comparisons to infer the functional significance of root-shoot allocation.

Environmental Stress: Salinity Ruins a Plant's Day in the Sun

New research reveals how low levels of salinity in soil inhibit a plant's ability to respond to shade through a signaling mechanism involving the plant stress hormone abscisic acid.

A canopy conundrum: can wind-induced movement help to increase crop productivity by relieving photosynthetic limitations?

Wind-induced movement is a ubiquitous occurrence for all plants grown in natural or agricultural settings, and in the context of high, damaging wind speeds it has been well studied. However, the impact of lower wind speeds (which do not cause any damage) on mode of movement, light transmission, and photosynthetic properties has, surprisingly, not been fully explored. This impact is likely to be influenced by biomechanical properties and architectural features of the plant and canopy. A limited number of eco-physiological studies have indicated that movement in wind has the potential to alter light distribution within canopies, improving canopy productivity by relieving photosynthetic limitations. Given the current interest in canopy photosynthesis, it is timely to consider such movement in terms of crop yield progress. This opinion article sets out the background to wind-induced crop movement and argues that plant biomechanical properties may have a role in the optimization of whole-canopy photosynthesis via established physiological processes. We discuss how this could be achieved using canopy models.

Nonlinear phenotypic variation uncovers the emergence of heterosis in Arabidopsis thaliana

Heterosis describes the phenotypic superiority of hybrids over their parents in traits related to agronomic performance and fitness. Understanding and predicting nonadditive inheritance such as heterosis is crucial for evolutionary biology as well as for plant and animal breeding. However, the physiological bases of heterosis remain debated. Moreover, empirical data in various species have shown that diverse genetic and molecular mechanisms are likely to explain heterosis, making it difficult to predict its emergence and amplitude from parental genotypes alone. In this study, we examined a model of physiological dominance initially proposed by Sewall Wright to explain the nonadditive inheritance of traits like metabolic fluxes at the cellular level. We evaluated Wright's model for two fitness-related traits at the whole-plant level, growth rate and fruit number, using 450 hybrids derived from crosses among natural accessions of A. thaliana. We found that allometric relationships between traits constrain phenotypic variation in a nonlinear and similar manner in hybrids and accessions. These allometric relationships behave predictably, explaining up to 75% of heterosis amplitude, while genetic distance among parents at best explains 7%. Thus, our findings are consistent with Wright's model of physiological dominance and suggest that the emergence of heterosis on plant performance is an intrinsic property of nonlinear relationships between traits. Furthermore, our study highlights the potential of a geometric approach of phenotypic relationships for predicting heterosis of major components of crop productivity and yield.

Genotype-aggregated planting improves yield in Jerusalem artichoke (Helianthus tuberosus) due to self/non-self-discrimination

Accumulating evidence indicates that plants are capable of self/non-self and kin/stranger discrimination. Plants increase biomass of and resource allocation to roots when they encounter roots of conspecific non-self-neighbors, but not when they encounter self roots. Root proliferation usually occurs at the expense of reproductive investment. Therefore, if clonal crops are capable of self/non-self-discrimination, spatially aggregated planting with seedlings of the same genotype may decrease root proliferation and produce a higher yield than planting without considering seedling genotype. To test this idea, we grew Helianthus tuberosus (Jerusalem artichoke) in pot and field conditions and examined self/non-self-discrimination and the effectiveness of genotype-aggregated planting. Plants grown in self pairs allocated less to root biomass than plants grown in non-self pairs in both pot and field conditions; in field conditions, the self pairs produced 40% more tubers by weight than the non-self pairs. When six sprouts from seed tuber of two different genotypes were grown together, with the two genotypes planted aggregately (AGG) or alternately (ALT), plants in the AGG group produced 14% more tubers than plants in the ALT group. These results suggest that spatial aggregation of genotypes increases tuber production in H. tuberosus. Because we found no evidence for trade-offs between root biomass and tuber production, suppression of root proliferation may not be the only mechanism behind the benefits of genotype aggregation. By applying the concept of self/non-self-discrimination, farmers can increase crop production without additional external inputs or expansion of agricultural land use.

Molecular control of crop shade avoidance

The shade avoidance response (SAR) in crops can be detrimental to yield, as precious carbon resources are redirected to stem or petiole elongation at the expense of biomass production. While breeding efforts have inadvertently attenuated this response in staple crops through correlated selection for yield at high density, it has not been eliminated. The extensive work done in Arabidopsis has provided a detailed understanding of the SAR and can be used as a framework for understanding the SAR in crop species. Recent crop SAR works point to auxin as a key factor in regulating the SAR in several crop species. These works also clearly demonstrate that one model for crop SAR will not fit all, and thus we need to move forward with studying the genetic players of the SAR in several model crop species. In this review, we provide the current knowledge of the SAR as reported at the physiological and molecular levels.

Constrained growth flips the direction of optimal phenological responses among annual plants

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.

Space resource utilisation: a novel indicator to quantify species competitive ability for light

Species richness and productivity are two fundamental aspects of ecosystems. As a result, the relationship between species richness and productivity has been widely studied. A series of fertilisation experiments in an alpine meadow on the Tibetan Plateau were performed to study the relationship between species richness and productivity. In this paper, we present a novel indicator, i.e., space resource utilisation (SRU), which is calculated by a volume formula (V_i  =  h_i · S_i; h_i = plant height of species i, S_i = quadrat area × percent cover of species i). SRU more fully reflected species competitive ability for light in both horizontal and vertical dimensions compared with plant height and cover. We used this novel indicator to investigate the effects of SRU on the changes in species richness and productivity following fertilisation. We found that the SRU of the community was correlated with increasing productivity and decreasing species richness following fertilisation and was a better predictor of species richness than productivity. The changes in SRU following fertilisation vary among species. These results demonstrate that SRU can be a more useful tool in explaining plant biodiversity loss and predicting the fate of different species than each of height, cover and productivity.

Scaling the respiratory metabolism to phosphorus relationship in plant seedlings

There are empirical indications of an isometric scaling relationship between plants' respiratory metabolism rates and nitrogen contents. To test the hypothesis that there may be a similar relationship between plants' respiratory metabolism and phosphorus contents we used data obtained from 150 laboratory and field-grown seedlings representing 30 herbaceous species and 20 woody deciduous species. Our results show that whole-plant respiration rates strongly scaled to the 0.81-power of the whole-plant phosphorus content, across wide ranges of growth conditions and functional classifications. Moreover, we also found a similar scaling exponent between whole-plant respiration rates and total nitrogen contents for the same set of samples. The similarities of the metabolic scaling relationships suggest that similar mechanisms may be involved in the transport and storage of phosphorus and nitrogen in plants.

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.)Hook.) plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF). Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc.) on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.

A theoretical framework for whole-plant carbon assimilation efficiency based on metabolic scaling theory: a test case using Picea seedlings

Simultaneous and accurate measurements of whole-plant instantaneous carbon-use efficiency (ICUE) and annual total carbon-use efficiency (TCUE) are difficult to make, especially for trees. One usually estimates ICUE based on the net photosynthetic rate or the assumed proportional relationship between growth efficiency and ICUE. However, thus far, protocols for easily estimating annual TCUE remain problematic. Here, we present a theoretical framework (based on the metabolic scaling theory) to predict whole-plant annual TCUE by directly measuring instantaneous net photosynthetic and respiratory rates. This framework makes four predictions, which were evaluated empirically using seedlings of nine Picea taxa: (i) the flux rates of CO(2) and energy will scale isometrically as a function of plant size, (ii) whole-plant net and gross photosynthetic rates and the net primary productivity will scale isometrically with respect to total leaf mass, (iii) these scaling relationships will be independent of ambient temperature and humidity fluctuations (as measured within an experimental chamber) regardless of the instantaneous net photosynthetic rate or dark respiratory rate, or overall growth rate and (iv) TCUE will scale isometrically with respect to instantaneous efficiency of carbon use (i.e., the latter can be used to predict the former) across diverse species. These predictions were experimentally verified. We also found that the ranking of the nine taxa based on net photosynthetic rates differed from ranking based on either ICUE or TCUE. In addition, the absolute values of ICUE and TCUE significantly differed among the nine taxa, with both ICUE and temperature-corrected ICUE being highest for Picea abies and lowest for Picea schrenkiana. Nevertheless, the data are consistent with the predictions of our general theoretical framework, which can be used to access annual carbon-use efficiency of different species at the level of an individual plant based on simple, direct measurements. Moreover, we believe that our approach provides a way to cope with the complexities of different ecosystems, provided that sufficient measurements are taken to calibrate our approach to that of the system being studied.

Bayesian inference of baseline fertility and treatment effects via a crop yield-fertility model

To effectively manage soil fertility, knowledge is needed of how a crop uses nutrients from fertilizer applied to the soil. Soil quality is a combination of biological, chemical and physical properties and is hard to assess directly because of collective and multiple functional effects. In this paper, we focus on the application of these concepts to agriculture. We define the baseline fertility of soil as the level of fertility that a crop can acquire for growth from the soil. With this strict definition, we propose a new crop yield-fertility model that enables quantification of the process of improving baseline fertility and the effects of treatments solely from the time series of crop yields. The model was modified from Michaelis-Menten kinetics and measured the additional effects of the treatments given the baseline fertility. Using more than 30 years of experimental data, we used the Bayesian framework to estimate the improvements in baseline fertility and the effects of fertilizer and farmyard manure (FYM) on maize (Zea mays), barley (Hordeum vulgare), and soybean (Glycine max) yields. Fertilizer contributed the most to the barley yield and FYM contributed the most to the soybean yield among the three crops. The baseline fertility of the subsurface soil was very low for maize and barley prior to fertilization. In contrast, the baseline fertility in this soil approximated half-saturated fertility for the soybean crop. The long-term soil fertility was increased by adding FYM, but the effect of FYM addition was reduced by the addition of fertilizer. Our results provide evidence that long-term soil fertility under continuous farming was maintained, or increased, by the application of natural nutrients compared with the application of synthetic fertilizer.

Interspecific differences in whole-plant respiration vs. biomass scaling relationships: a case study using evergreen conifer and angiosperm tree seedlings

PREMISE OF THE STUDY

Empirical studies and theory indicate that respiration rates (R) of small plants scale nearly isometrically with both leaf biomass (ML) and total plant biomass (MT). These predictions are based on angiosperm species and apply only across a small range of body mass. Whether these relationships hold true for different plants, such as conifers, remains unclear.

METHODS

We tested these predictions using the whole-plant maintenance respiration rates and the biomass allocation patterns of the seedlings of two conifer tree species and two angiosperm tree species. Model Type II regression protocols were used to compare the scaling exponents (α) and normalization constants (β) across all four species and within each of the four species.

KEY RESULTS

The data show that the scaling exponents varied among the four species and that all differed significantly from isometry. For conifers, scaling exponents for R vs. MT, and R and ML were numerically smaller than those of the broadleaved angiosperm species. However, across the entire data set, R scaled isometrically with ML and with MT as predicted by the West, Brown, and Enquist (WBE) theory. We also observed higher respiration rates for small conifer seedlings compared to comparably sized angiosperm seedlings.

CONCLUSIONS

Our data add credence to the view that the R vs. M scaling relationship differs among species, and that in general, the numerical values of this interspecific scaling relationship will depend on the species pooled in the analysis and on the range of body sizes within the data set.