Agroecological genetics of biomass allocation in wheat uncovers genotype interactions with canopy shade and plant size.

How plants distribute biomass among organs influences resource acquisition, reproduction and plant-plant interactions, and is essential in understanding plant ecology, evolution, and yield production in agriculture. However, the genetic mechanisms regulating allocation responses to the environment are largely unknown. We studied recombinant lines of wheat (Triticum spp.) grown as single plants under sunlight and simulated canopy shade to investigate genotype-by-environment interactions in biomass allocation to the leaves, stems, spikes, and grains. Size-corrected mass fractions and allometric slopes were employed to dissect allocation responses to light limitation and plant size. Size adjustments revealed light-responsive alleles associated with adaptation to the crop environment. Combined with an allometric approach, we demonstrated that polymorphism in the DELLA protein is associated with the response to shade and size. While a gibberellin-sensitive allelic effect on stem allocation was amplified when plants were shaded, size-dependent effects of this allele drive allocation to reproduction, suggesting that the ontogenetic trajectory of the plant affects the consequences of shade responses for allocation. Our approach provides a basis for exploring the genetic determinants underlying investment strategies in the face of different resource constraints and will be useful in predicting social behaviours of individuals in a crop community.

Functional structure mediates the responses of productivity to addition of three nitrogen compounds in a meadow steppe.

Atmospheric nitrogen (N) deposition is altering grassland productivity and community structure worldwide. Deposited N comes in different forms, which can have different consequences for productivity due to differences in their fertilization and acidification effects. We hypothesize that these effects may be mediated by changes in plant functional traits. We investigated the responses of aboveground primary productivity and community functional composition to addition of three nitrogen compounds (NH4NO3, [NH4]2SO4, and CO[NH2]2) at the rates of 0, 5, 10, 20 g N m-2 yr-1. We used structural equation modeling (SEM) to evaluate how functional structure influences the responses of productivity to the three N compounds. Nitrogen addition increased community-level leaf chlorophyll content but decreased leaf dry matter content and phosphorus concentration. These changes were mainly due to intra-specific variation. Functional dispersion of traits was reduced by N addition through changes in species composition. SEM revealed that fertilization effects were more important than soil acidification for the responses of productivity to CO(NH2)2 addition, which enhanced productivity by decreasing functional trait dispersion. In contrast, the effects of (NH4)2SO4 and NH4NO3 were primarily due to soil acidification, influencing productivity via community-weighted means of functional traits. Our results suggest that N forms with different fertilizing and acidifying effects influence productivity via different functional traits pathways. Our study also emphasizes the need for in situ experiments with the relevant N compounds to accurately understand and predict the ecological effects of atmospheric N deposition on ecosystems.

Human total fertility rate affected by ambient temperatures in both the present and previous generations.

Elevated temperatures negatively affect human reproduction through several processes that regulate nutrient uptake and resource allocation in pregnant women. These can interfere with foetal development, resulting in low birth weight neonates with altered development trajectories. Temperatures that affect the current generation could, therefore, also have an impact on the following generation. We asked whether heat stress affected offspring fertility by asking if current and past ambient temperatures influenced total fertility rates (TFR) in human populations distributed across the world. We analysed time series data in 65 countries using simple regression analyses based on maximum temperatures and temperature amplitudes over 55 years. Supplemental longer time series (up to 100 years) provided information on response patterns in Northern Europe and Greenland's colder climates. There were clear and strong effects of temperatures on the TFR in the concurrent and the previous generation. Our temperature-based models account for 71-95% of the variation in TRF in European countries and Greenland, and 56-99% of the variation in 65 countries worldwide. Our findings are consistent with studies of seasonal variation in fertility and suggest that increased temperatures will negatively influence populations subjected to monthly maximum temperatures above 15-20 °C, while fertility in colder climates benefits from elevated temperatures. Our results provide strong evidence that ambient temperatures have important effects on human fertility, and that these effects persist into the following generation.

Latitudinal pattern of flowering synchrony in an invasive wind-pollinated plant.

Flowering synchrony can play an important role in plants' reproductive success, which is essential for the successful establishment and spread of invasive plants. Although flowering synchrony has been found to be closely related to climatic factors, the effects of variation in such factors along latitudinal gradient on flowering synchrony and the role of flowering synchrony in the reproductive success of invading populations remain largely unexplored. In a 2-year field study, we examined the latitudinal variation of flowering phenology, especially flowering synchrony, in an invasive plant, Spartina alterniflora, along coastal China, and its relationship with population seed set across three climatic zones. We found that first flowering date was delayed, and flowering synchrony increased with increasing latitude. Flowering synchrony was negatively related to temperature during flowering season but not to soil properties or precipitation, suggesting that climate has shaped the latitudinal pattern of flowering synchrony. Moreover, a positive correlation between flowering synchrony and seed set across latitudes indicates the possible role of flowering synchrony in the latitudinal pattern of sexual reproduction in S. alterniflora These results suggest that, in addition to the effects of climate on the growth of invasive species, climatic factors can play an important role in the invasion success of alien plants by regulating the flowering synchrony and thus the reproductive success of invasive plants.

Evolutionary agroecology: individual fitness and population yield in wheat (Triticum aestivum).

Although the importance of group selection in nature is highly controversial, several researchers have argued that plant breeding for agriculture should be based on group selection, because the goal in agriculture is to optimize population production, not individual fitness. A core hypothesis behind this claim is that crop genotypes with the highest individual fitness in a mixture of genotypes will not produce the highest population yield, because fitness is often increased by "selfish" behaviors, which reduce population performance. We tested this hypothesis by growing 35 cultivars of spring wheat (Triticum aestivum L.) in mixtures and monocultures, and analyzing the relationship between population yield in monoculture and individual yield in mixture. The relationship was unimodal, as predicted. The highest-yielding populations were from cultivars that had intermediate fitness, and these produced, on average, 35% higher yields than cultivars with the highest fitness. It is unlikely that plant breeding or genetic engineering can improve traits that natural selection has been optimizing for millions of years, but there is unutilized potential in traits that increase crop yield by decreasing individual fitness.

Effects of nitrogen and water addition on trace element stoichiometry in five grassland species.

A 9-year manipulative experiment with nitrogen (N) and water addition, simulating increasing N deposition and changing precipitation regime, was conducted to investigate the bioavailability of trace elements, iron (Fe), manganese (Mn), copper (Cu), and zinc (Zn) in soil, and their uptake by plants under the two environmental change factors in a semi-arid grassland of Inner Mongolia. We measured concentrations of trace elements in soil and in foliage of five common herbaceous species including 3 forbs and 2 grasses. In addition, bioaccumulation factors (BAF, the ratio of the chemical concentration in the organism and the chemical concentration in the growth substrate) and foliar Fe:Mn ratio in each plant was calculated. Our results showed that soil available Fe, Mn and Cu concentrations increased under N addition and were negatively correlated with both soil pH and cation exchange capacity. Water addition partly counteracted the positive effects of N addition on available trace element concentrations in the soil. Foliar Mn, Cu and Zn concentrations increased but Fe concentration decreased with N addition, resulting in foliar elemental imbalances among Fe and other selected trace elements. Water addition alleviated the effect of N addition. Forbs are more likely to suffer from Mn toxicity and Fe deficiency than grass species, indicating more sensitivity to changing elemental bioavailability in soil. Our results suggested that soil acidification due to N deposition may accelerate trace element cycling and lead to elemental imbalance in soil-plant systems of semi-arid grasslands and these impacts of N deposition on semi-arid grasslands were affected by water addition. These findings indicate an important role for soil trace elements in maintaining ecosystem functions associated with atmospheric N deposition and changing precipitation regimes in the future.

Does climate directly influence NPP globally?

The need for rigorous analyses of climate impacts has never been more crucial. Current textbooks state that climate directly influences ecosystem annual net primary productivity (NPP), emphasizing the urgent need to monitor the impacts of climate change. A recent paper challenged this consensus, arguing, based on an analysis of NPP for 1247 woody plant communities across global climate gradients, that temperature and precipitation have negligible direct effects on NPP and only perhaps have indirect effects by constraining total stand biomass (Mtot ) and stand age (a). The authors of that study concluded that the length of the growing season (lgs ) might have a minor influence on NPP, an effect they considered not to be directly related to climate. In this article, we describe flaws that affected that study's conclusions and present novel analyses to disentangle the effects of stand variables and climate in determining NPP. We re-analyzed the same database to partition the direct and indirect effects of climate on NPP, using three approaches: maximum-likelihood model selection, independent-effects analysis, and structural equation modeling. These new analyses showed that about half of the global variation in NPP could be explained by Mtot combined with climate variables and supported strong and direct influences of climate independently of Mtot , both for NPP and for net biomass change averaged across the known lifetime of the stands (ABC = average biomass change). We show that lgs is an important climate variable, intrinsically correlated with, and contributing to mean annual temperature and precipitation (Tann and Pann ), all important climatic drivers of NPP. Our analyses provide guidance for statistical and mechanistic analyses of climate drivers of ecosystem processes for predictive modeling and provide novel evidence supporting the strong, direct role of climate in determining vegetation productivity at the global scale.

Contrasts between whole-plant and local nutrient levels determine root growth and death in Ailanthus altissima (Simaroubaceae).

UNLABELLED: • PREMISE OF THE STUDY: There is an ongoing debate about the importance of whole-plant control vs. local modular mechanisms for root growth. We conducted a split-root experiment with different patch/background levels of nitrogen to examine whether local root growth and death are controlled by local resource levels or at the whole-plant level.• METHODS: Three microrhizotrons with 0, 10, and 100 µg N/g growth medium levels (74 g growth medium each) were attached to pots of high or low soil N in which one Ailanthus altissima individual was growing. One fine root was guided into each of the microrhizotrons and photographed every 4 d. Plants were harvested after 28 d; root growth and mortality in the microrhizotrons were recorded. Changes in root length, number of laterals, and interlateral length were determined from the photos and analyzed.• KEY RESULTS: While overall plant growth was influenced by background N level, both patch and background N levels influenced root growth and mortality in patches. Local roots proliferated most when the patch N level was high and background level low, and they proliferated least and showed highest mortality when patch N was low and the background level high.• CONCLUSIONS: The fate of roots growing in a patch is influenced by the resource environment of the plant's other roots as well as the resource levels in the patch itself. Thus, the growth and death of roots in patches is determined by both modular and whole-plant mechanisms.

Reduced Root Cortical Tissue with an Increased Root Xylem Investment Is Associated with High Wheat Yields in Central China.

Trait-based approaches are increasingly used to understand crop yield improvement, although they have not been widely applied to anatomical traits. Little is known about the relationships between root and leaf anatomy and yield in wheat. We selected 20 genotypes that have been widely planted in Luoyang, in the major wheat-producing area of China, to explore these relationships. A field study was performed to measure the yields and yield components of the genotypes. Root and leaf samples were collected at anthesis to measure the anatomical traits relevant to carbon allocation and water transport. Yield was negatively correlated with cross-sectional root cortex area, indicating that reduced root cortical tissue and therefore reduced carbon investment have contributed to yield improvement in this region. Yield was positively correlated with root xylem area, suggesting that a higher water transport capacity has also contributed to increased yields in this study. The area of the leaf veins did not significantly correlate with yield, showing that the high-yield genotypes did not have larger veins, but they may have had a conservative water use strategy, with tight regulation of water loss from the leaves. This study demonstrates that breeding for higher yields in this region has changed wheat's anatomical traits, reducing the roots' cortical tissue and increasing the roots' xylem investment.

The heme-responsive PrrH sRNA regulates Pseudomonas aeruginosa pyochelin gene expression.

Pseudomonas aeruginosa is an opportunistic pathogen that requires iron for growth and virulence, yet this nutrient is sequestered by the innate immune system during infection. When iron is limiting, P. aeruginosa expresses the PrrF1 and PrrF2 small RNAs (sRNAs), which post-transcriptionally repress expression of nonessential iron-containing proteins, thus sparing this nutrient for more critical processes. The genes for the PrrF1 and PrrF2 sRNAs are arranged in tandem on the chromosome, allowing for the transcription of a longer heme-responsive sRNA, termed PrrH. While the functions of PrrF1 and PrrF2 have been extensively studied, the role of PrrH in P. aeruginosa physiology and virulence is not well understood. In this study, we performed transcriptomic and proteomic studies to identify the PrrH regulon. In shaking cultures, the pyochelin synthesis proteins were increased in two distinct prrH mutants compared to the wild type, while the mRNAs for these proteins were not affected by the prrH mutation. We identified complementarity between the PrrH sRNA and the sequence upstream of the pchE mRNA, suggesting the potential for PrrH to directly regulate the expression of genes for pyochelin synthesis. We further showed that pchE mRNA levels were increased in the prrH mutants when grown in static but not shaking conditions. Moreover, we discovered that controlling for the presence of light was critical for examining the impact of PrrH on pchE expression. As such, our study reports on the first likely target of the PrrH sRNA and highlights key environmental variables that will allow for future characterization of PrrH function. IMPORTANCE In the human host, iron is predominantly in the form of heme, which Pseudomonas aeruginosa can acquire as an iron source during infection. We previously showed that the iron-responsive PrrF small RNAs (sRNAs) are critical for mediating iron homeostasis during P. aeruginosa infection; however, the function of the heme-responsive PrrH sRNA remains unclear. In this study, we identified genes for pyochelin siderophore biosynthesis, which mediates uptake of inorganic iron, as a novel target of PrrH regulation. This study therefore highlights a novel relationship between heme availability and siderophore biosynthesis in P. aeruginosa.

Do plant communities show constant final yield?

Total biomass production of plant monocultures growing over a range of densities and harvested after a period of growth increases monotonically with density and then levels out at higher densities. This pattern is called constant final yield (CFY) and is considered one of the most general phenomena in plant ecology. If CFY applies to plant communities, it would be a key to understanding and predicting many community-level phenomena. We tested two primary hypotheses experimentally: (1) Mixtures of several species show CFY. (2) If so, the proportion of biomass production by the component species in a mixture does not change at densities above the density that reaches CFY. We performed a series of glasshouse experiments over 3 years using a "community density series," in which the overall density of five species was varied while their proportions remained unchanged. In the first experiment, we grew a mixture of annual and perennial herbaceous species in mesocosms, and all species were also grown in monocultures at the corresponding densities. A similar experiment was performed in the second and third years, but only with annuals. A third experiment with mixtures only was performed in pots over 2 years. In all cases, aboveground biomass was harvested, separated by species, dried, and weighed. Perennials with underground storage organs produced maximum aboveground biomass at low or intermediate densities. In the second experiment, two of the species produced maximum biomass at the second-highest density in monoculture, while mixtures of all five species showed classical CFY behavior, and the contribution of the species to the mixture changed very little above the lowest density producing CFY. The results of the third experiment were also consistent with the hypotheses. In conclusion, CFY in aboveground biomass production was observed in communities of annual species, and the contribution of the individual species was relatively insensitive to an increase in density above that reaching CFY, i.e., competitive performance of the species changed with density until CFY was reached. Evidence for CFY was stronger in mixture than in monoculture. Coexistence theory must include density as well as frequency dependence if densities are below CFY.

Biomass Allocation Responses to Root Interactions in Wheat Cultivars Support Predictions of Crop Evolutionary Ecology Theory.

The goal of agriculture is to optimize the population yield, but natural selection has produced active competition among plants, which decreases population performance. Therefore, cultivar breeding should be based on group selection, increasing yield by weakening individual competitive responses. We hypothesize that this has occurred inadvertently to some degree, so modern cultivars have weakened competitive traits and responses, such as reduced root proliferation in response to neighboring roots. We conducted a field experiment with eight cultivars of spring wheat that have been released over the last hundred years, which we grew at two densities. Two contrasting wheat cultivars, a landrace and a modern cultivar, were used in a second field experiment on competition within and between the two cultivars to quantify their competitiveness. Finally, a greenhouse experiment was conducted with these two cultivars gown (a) in mixture and monoculture, (b) at four densities, (c) two watering levels, and (d) with permeable vs. non-permeable soil dividers, to study root proliferation responses to competition. Results of field experiment 1 showed that the population aboveground biomass (AGB) had increased, while belowground biomass had decreased over the course of breeding, so that the root to shoot ratio (R/S) was negatively correlated with the release year of the cultivar. The landrace had stronger competitiveness than the modern cultivar in the field experiment 2. There was clear evidence of root proliferation and a resultant reduction in AGB in response to neighboring roots in the greenhouse experiment, and the modern variety showed less root proliferation in response to neighbors. We conclude that the newer cultivar was a weaker competitor but higher-yielding in two ways: (1) it had higher reproductive effort and therefore less allocation to structures that increase competitive ability, and (2) it had reduced root proliferation in response to the roots of neighboring plants. Our results show that wheat plants change their biomass allocation in response to resource levels and the presence of neighboring roots. The presence of root proliferation in the modern cultivar, albeit less than in the landrace, suggests that further increases in yield via group selection are possible.

Arbuscular mycorrhizal fungi alter plant allometry and biomass-density relationships.

BACKGROUND AND AIMS: Plant biomass-density relationships during self-thinning are determined mainly by allometry. Both allometry and biomass-density relationship have been shown to vary with abiotic conditions, but the effects of biotic interactions have not been investigated. Arbuscular mycorrhizal fungi (AMF) can promote plant growth and affect plant form. Here experiments were carried out to test whether AMF affect plant allometry and the self-thinning trajectory. METHODS: Two experiments were conducted on Medicago sativa L., a leguminous species known to be highly dependent on mycorrhiza. Two mycorrhizal levels were obtained by applying benomyl (low AMF) or not (high AMF). Experiment 1 investigated the effects of AMF on plant growth in the absence of competition. Experiment 2 was a factorial design with two mycorrhizal levels and two plant densities (6000 and 17 500 seeds m(-2)). Shoot biomass, root biomass and canopy radius were measured 30, 60, 90 and 120 d after sowing. The allometric relationships among these aspects of size were estimated by standardized major axis regression on log-transformed data. KEY RESULTS: Shoot biomass in the absence of competition was lower under low AMF treatment. In self-thinning populations, the slope of the log (mean shoot biomass) vs. log density relationship was significantly steeper for the high AMF treatment (slope = -1·480) than for the low AMF treatment (-1·133). The canopy radius-biomass allometric exponents were not significantly affected by AMF level, but the root-shoot allometric exponent was higher in the low AMF treatment. With a high level of AMF, the biomass-density exponent can be predicted from the above-ground allometric model of self-thinning, while this was not the case when AMF were reduced by fungicide. CONCLUSIONS: AMF affected the importance of below-ground relative to above-ground interactions and changed root vs. shoot allocation. This changed allometric allocation of biomass and altered the self-thinning trajectory.

Allometry and Yield Stability of Cereals.

Crop plants grow, and then, they allocate resources to different structures, including seeds and fruits, which represent yield in most crops. We define the yield stability of a genotype as its ability to reduce the effects of temporal variation in resources and conditions on yield production, and we argue that yield stability can be understood in terms of two processes: (1) crop survival and growth (biomass production): the ability of the crop plants to survive and produce biomass under the range of conditions to which it is exposed and (2) the pattern of allocation of this biomass to yield across this range of conditions. Plant breeders and crop physiologists have focused on (1), but much less attention has been paid to (2). We hypothesize that (2) is primarily the result of reproductive allometry: the quantitative relationship between vegetative and reproductive biomass. Ecological theory and the allometric models we present predict a tradeoff between (a) the ability of a genotype to produce yield over a wide variety of conditions and (b) its ability to produce very high yields under optimal or near-optimal conditions. We reanalyze the data from two recent studies, and the results are consistent with this hypothesis. Yield stability in crops corresponds to bet-hedging in evolutionary ecological theory. It is the most appropriate strategy for smallholder farmers in developing countries, a group that comprises most of the farmers in the world. Researchers and crop breeders need to rethink their objectives if they want to develop optimal varieties for these farmers.

Effects of positive interactions, size symmetry of competition and abiotic stress on self-thinning in simulated plant populations.

BACKGROUND AND AIMS: Competition drives self-thinning (density-dependent mortality) in crowded plant populations. Facilitative interactions have been shown to affect many processes in plant populations and communities, but their effects on self-thinning trajectories have not been investigated. METHODS: Using an individual-based 'zone-of-influence' model, we studied the potential effects of the size symmetry of competition, abiotic stress and facilitation on self-thinning trajectories in plant monocultures. In the model, abiotic stress reduced the growth of all individuals and facilitation ameliorated the effects of stress on interacting individuals. KEY RESULTS: Abiotic stress made the log biomass-log density relationship during self-thinning steeper, but this effect was reduced by positive interactions among individuals. Size-asymmetric competition also influenced the self-thinning slope. CONCLUSIONS: Although competition drives self-thinning, its course can be affected by abiotic stress, facilitation and competitive symmetry.

Effects of Intra- and Interspecific Plant Density on Rhizosphere Bacterial Communities.

There have been very few studies on the effects of plant competition on the rhizosphere bacterial community. To investigate the impacts of intra- and interspecific plant competition, we analyzed the responses of rhizosphere bacterial communities to plant density as determined by 16S rRNA gene targeted sequencing. We included five weedy plant species growing in field soil in monocultures and mixed cultures at three densities in a greenhouse experiment. The rhizosphere bacterial community of each species changed more with density in a mixture of all five plant species than in monocultures, so intra- and interspecific plant competition had different effects on the bacterial community. For the dominant plant competitor, Centaurea cyanus, neither intra- nor interspecific competition had major effects on the composition of its rhizosphere bacterial communities. In contrast, the bacterial communities of the weakest competitor, Trifolium repens, were affected differently by intra- and interspecific competition. During increasing intraspecific competition T. repens maintained a highly specialized bacterial community dominated by Rhizobium; while during interspecific competition, the relative abundance of Rhizobium declined while other nitrogen fixing and potentially plant growth promoting taxa became more abundant. Contrary to previous observations made for soil microbial communities, the bacterial rhizosphere community of the weakest competitor did not become more similar to that of the dominant species. Thus, the process of competition, as well as the plant species themselves, determined the rhizosphere bacterial community. Our results emphasize the role of plant-plant interactions for rhizosphere bacterial communities. These effects may feedback to affect plant-plant interactions, and this is an important hypothesis for future research.

Variation in local density results in a positive correlation between plant neighbor sizes.

A positive correlation between the sizes of plants and the sizes of their nearest neighbors has been observed in many plant populations and is most often attributed to variation in microsite quality. We demonstrate another potentially important cause, using a simple spatial simulation model in which a plant's size is determined by its available area plus stochastic variation. If the spatial arrangement of individuals is nonuniform and local crowding reduces individual size, a positive correlation between the size of a plant and the size of neighboring individuals is to be expected. If a plant is small because it is crowded, its nearest neighbors will also tend to be crowded and therefore small. Such positive correlations will be observed whenever any trait of an object is related to the area available to it. Looking at the performance of neighboring objects without explicitly considering distance can give a very misleading signal.

Looking in the Wrong Direction for Higher-Yielding Crop Genotypes.

A misunderstanding of evolution via natural selection has led many plant physiologists and genetic engineers to look in the wrong direction for higher-yielding crop genotypes. Large investments in attempts to make 'better' plants by improving basic physiological processes are not likely to succeed because natural selection has been optimizing these for millions of years. Increases in yield from plant breeding have usually resulted from decreases, not increases, in plant fitness. Examples include reduced plant height and more vertical root growth in cereals. Plant scientists and breeders should generate hypotheses based on what evolutionary biologists call 'group selection', looking for attributes that increase yield in ways that decrease fitness, rather than attempting to improve upon the achievements of natural selection.

Evolutionary agroecology: Trends in root architecture during wheat breeding.

Root system characteristics determine soil space exploration and resource acquisition, and these characteristics include competitive traits that increase individual fitness but reduce population performance. We hypothesize that crop breeding for increased yield is often a form of "group selection" that reduces such "selfish" traits to increase population yield. To study trends in root architecture resulting from plant breeding and test the hypothesis that increased yields result in part from group selection on root traits, we investigated root growth and branching behavior in a historical sequence of wheat (Triticum aestivum) cultivars that have been widely grown in northwestern China. Plants were grown in gel-filled chambers to examine growth angles, numbers, and lengths of seminal roots, and in soil-filled chambers under eight soil resource levels for fractal analysis of root system architecture. Yield in field was evaluated at standard and low planting densities. Newer cultivars produced higher yields than older ones only at the higher sowing density, showing that increased yield results from changes in competitive behavior. Seminal root number and growth angles were negatively correlated with yield, while primary seminal root length was positively correlated with yield. Roots of higher-yielding modern varieties were simpler and less branched, grew deeper but spread less laterally than modern varieties. The fractal dimension of root branching was negatively correlated with the yield of cultivars at all resource levels. Root:shoot ratio was negatively correlated with yield under high soil resource levels. The results are consistent with the hypothesis that the success of wheat breeding for higher yields over past 100 years in northwestern China has been in part due to unconscious group selection on root traits, resulting in smaller, less branched, and deeper roots, suggesting a direction for further increases in crop yield in the future.

Balance between facilitation and resource competition determines biomass-density relationships in plant populations.

Theories based on competition for resources predict a monotonic negative relationship between population density and individual biomass in plant populations. They do not consider the role of facilitative interactions, which are known to be important in high stress environments. Using an individual-based 'zone-of-influence' model, we investigated the hypothesis that the balance between facilitative and competitive interactions determines biomass-density relationships. We tested model predictions with a field experiment on the clonal grass Elymus nutans in an alpine meadow. In the model, the relationship between mean individual biomass and density shifted from monotonic to humped as abiotic stress increased. The model results were supported by the field experiment, in which the greatest individual and population biomass were found at intermediate densities in a high-stress alpine habitat. Our results show that facilitation can affect biomass-density relationships.