Relationships between biodiversity and multiple ecosystem functions (that is, ecosystem multifunctionality) are context-dependent. Both plant and soil microbial diversity have been reported to regulate ecosystem multifunctionality, but how their relative importance varies along environmental gradients remains poorly understood. Here, we relate plant and microbial diversity to soil multifunctionality across 130 dryland sites along a 4,000 km aridity gradient in northern China. Our results show a strong positive association between plant species richness and soil multifunctionality in less arid regions, whereas microbial diversity, in particular of fungi, is positively associated with multifunctionality in more arid regions. This shift in the relationships between plant or microbial diversity and soil multifunctionality occur at an aridity level of ∼0.8, the boundary between semiarid and arid climates, which is predicted to advance geographically ∼28% by the end of the current century. Our study highlights that biodiversity loss of plants and soil microorganisms may have especially strong consequences under low and high aridity conditions, respectively, which calls for climate-specific biodiversity conservation strategies to mitigate the effects of aridification.

We introduce a theoretical framework that predicts the optimum planting density and maximal yield for an annual crop plant. Two critical parameters determine the trajectory of plant growth and the optimal density, N opt , where canopies of growing plants just come into contact, and competition: (i) maximal size at maturity, M max , which differs among varieties due to artificial selection for different usable products; and (ii) intrinsic growth rate, g, which may vary with variety and environmental conditions. The model predicts (i) when planting density is less than N opt , all plants of a crop mature at the same maximal size, M max , and biomass yield per area increases linearly with density; and (ii) when planting density is greater than N opt , size at maturity and yield decrease with −4/3 and −1/3 powers of density, respectively. Field data from China show that most annual crops, regardless of variety and life form, exhibit similar scaling relations, with maximal size at maturity, M max , accounting for most of the variation in optimal density, maximal yield, and energy use per area. Crops provide elegantly simple empirical model systems to study basic processes that determine the performance of plants in agricultural and less managed ecosystems. E fficiency of agriculture will need to increase to feed the growing human population as arable land, water, and fertilizers become increasingly limited (1, 2). A relevant question is, What is the optimal density to plant seeds of an annual crop? The answer should be of interest to applied plant scientists who want to predict planting densities that maximize yields and to basic plant scientists who want to better understand the fundamental processes of growth and competition.Here we develop and test analytical models that predict the optimal seeding density that maximizes yield for annual crop plants. These models were inspired by theories and data on plant scaling relations (3-10). We modify the theories to model the growth and maturation of annual crops as a function of density and mature plant size. We evaluate the models using data from agricultural crops in controlled experiments in China. Empirical and Conceptual BackgroundThere is an intermediate seeding density for an annual crop that maximizes yield at harvest. When seeds are planted at lower density, yields are reduced because the plants grow to mature size without using all available resources. When seeds are planted at higher density, plants compete for resources and mature at smaller sizes; total yield declines because mature size per individual decreases faster than number of individuals per area increases.The dynamics of crop production can be modeled as the outcome of four interacting processes. First, the growth of an individual annual plant from germination to maturity traces a sigmoidal trajectory that reflects allocation of energy and biomass to new tissue as a function of plant size. Second, size at maturity depends on density: Initially all plants grow at nearmaximal rates, but if individuals ...

There is general agreement that competition for resources results in a tradeoff between plant mass, M, and density, but the mathematical form of the resulting thinning relationship and the mechanisms that generate it are debated. Here, we evaluate two complementary models, one based on the space-filling properties of canopy geometry and the other on the metabolic basis of resource use. For densely packed stands, both models predict that density scales as M −3/4 , energy use as M 0 , and total biomass as M 1/4 . Compilation and analysis of data from 183 populations of herbaceous crop species, 473 stands of managed tree plantations, and 13 populations of bamboo gave four major results: (i) At low initial planting densities, crops grew at similar rates, did not come into contact, and attained similar mature sizes; (ii) at higher initial densities, crops grew until neighboring plants came into contact, growth ceased as a result of competition for limited resources, and a tradeoff between density and size resulted in critical density scaling as M −0.78 , total resource use as M −0.02 , and total biomass as M 0.22 ; (iii) these scaling exponents are very close to the predicted values of M −3/4 , M 0 , and M 1/4 , respectively, and significantly different from the exponents suggested by some earlier studies; and (iv) our data extend previously documented scaling relationships for trees in natural forests to small herbaceous annual crops. These results provide a quantitative, predictive framework with important implications for the basic and applied plant sciences.allometric scaling | energy equivalence | plant energetics | self-thinning T he structure and dynamics of plant populations and communities often reflect the interacting consequences of three fundamental processes: (i) competition for resources, (ii) the effect of body size on resource use, and (iii) the effect of plant density on growth and mortality (1-4). Two approaches traditionally have been used to study these interactions. One focuses on theoretical models and empirical measurements of abundance, spacing, survival, mortality, and recruitment as functions of plant size in relatively undisturbed natural populations and communities, especially forests (4-11), where the thinning process is complicated by effects of shading and other factors on asymmetries in resource supply and resulting growth and mortality rates (11-16). The second approach focuses on the structure and dynamics of plants in agricultural settings (17)(18)(19)(20)(21)(22), where plants of nearly identical age grow under controlled conditions. Studies of such simplified agricultural systems have led to theoretical and empirical selfthinning relationships that characterize the temporal trajectory of decreasing population density as a function of increasing plant size as stands develop under conditions of resource limitation and competition (17)(18)(19). These exhibit a characteristic phenomenology in which plants grow with minimal mortality until they reach a size-dependent critical density, ...

Summary• The homoploid hybrid species Pinus densata is restricted to alpine habitats that exceed the altitude range of its two parental species, Pinus tabulaeformis and Pinus yunnanensis. Alpine habitats usually generate cold-induced water stress in plants. To understand the ecological differentiation between these three species, we examined their physiological responses to drought stress.• Potted seedlings of three species were subjected to low, mild, moderate and severe water stress in an automatic-controlled glasshouse. Fifteen indicators of fitness were measured for each species in each treatment, and most of these decreased as drought increased.• Pinus densata exhibited higher fitness than both parental species in terms of total dry mass production (TDM) and long-term water use efficiency (WUE L ) across all treatments; several other ecophysiological traits were also extreme but not across every treatment, and not always in the highest stress treatment.• These results indicate that extreme characters that have become well fixed in P. densata, confer a faster seedling growth rate and more efficient water use, which in turn should confer increased drought tolerance. These traits of P. densata likely promoted its ecological separation from its parental species and facilitated its successful colonization and establishment in high-altitude habitats.

The energetic equivalence rule, which is based on a combination of metabolic theory and the self-thinning rule, is one of the fundamental laws of nature. However, there is a progressively increasing body of evidence that scaling relationships of metabolic rate vs. body mass and population density vs. body mass are variable and deviate from their respective theoretical values of 3/4 and −3/4 or −2/3. These findings questioned the previous hypotheses of energetic equivalence rule in plants. Here we examined the allometric relationships between photosynthetic mass (M p) or leaf mass (M L) vs. body mass (β); population density vs. body mass (δ); and leaf mass vs. population density, for desert shrubs, trees, and herbaceous plants, respectively. As expected, the allometric relationships for both photosynthetic mass (i.e. metabolic rate) and population density varied with the environmental conditions. However, the ratio between the two exponents was −1 (i.e. β/δ = −1) and followed the trade-off principle when local resources were limited. Our results demonstrate for the first time that the energetic equivalence rule of plants is based on trade-offs between the variable metabolic rate and population density rather than their constant allometric exponents.