High Initial Density Research Articles

Verification of traffic-induced soil compaction after long-term ploughing and 10 years minimum tillage on clay loam soil in South-East Norway

Grain yields are presented from a 10-year field trial with four tillage regimes (annual ploughing, harrowing only, ploughing/harrowing alternate years and minimum tillage) on clay loam. We also present soil physical analyses and use the compaction verification tool (CVT) to assess compaction on plots with annual ploughing and minimum tillage, after using slurry tankers with contrasting wheel loads (4.1 Mg, 6.6 Mg) and wheeling intensities (1×/10×) in the 11th trial year, and yields monitored two years after compaction. Winter wheat yields in the period before compaction were strongly affected by tillage, with annual ploughing giving on average 24% higher yield than direct drilling. Both wheat and oats were far less affected in treatments with harrowing only or ploughing/harrowing alternate years, on average within 6% of annual ploughing. Yields after compaction were affected by both previous tillage and compaction intensity. In the first year, single wheeling after annual ploughing gave 23% yield reduction with 4.1 Mg wheel load and 28% reduction with 6.6 Mg wheel load, whilst multiple wheeling gave 14% reduction at 6.6 Mg wheel load. Yield reductions after minimum tillage ranged from 63% (single wheeling with 4.1 Mg) to 100% (multiple wheeling with 6.6 Mg). Similar trends were found in the second year. The soil physical data indicated that all wheeling led to changes in bulk density, pore sizes and permeability in both topsoil and subsoil on both sampled tillage plots. However, effects in the subsoil were partly masked by the soil's high initial bulk density, partly due to its high clay content. The CVT, which plots air capacity against hydraulic conductivity, suggested some harmful compaction on both plots, with the minimum tillage plot being less affected than the ploughed plot. However, yield results did not support this conclusion, indicating that other factors limited yields on the minimum tilled plot.

Density of founder cells affects spatial pattern formation and cooperation in Bacillus subtilis biofilms.

In nature, most bacteria live in surface-attached sedentary communities known as biofilms. Biofilms are often studied with respect to bacterial interactions. Many cells inhabiting biofilms are assumed to express 'cooperative traits', like the secretion of extracellular polysaccharides (EPS). These traits can enhance biofilm-related properties, such as stress resilience or colony expansion, while being costly to the cells that express them. In well-mixed populations cooperation is difficult to achieve, because non-cooperative individuals can reap the benefits of cooperation without having to pay the costs. The physical process of biofilm growth can, however, result in the spatial segregation of cooperative from non-cooperative individuals. This segregation can prevent non-cooperative cells from exploiting cooperative neighbors. Here we examine the interaction between spatial pattern formation and cooperation in Bacillus subtilis biofilms. We show, experimentally and by mathematical modeling, that the density of cells at the onset of biofilm growth affects pattern formation during biofilm growth. At low initial cell densities, co-cultured strains strongly segregate in space, whereas spatial segregation does not occur at high initial cell densities. As a consequence, EPS-producing cells have a competitive advantage over non-cooperative mutants when biofilms are initiated at a low density of founder cells, whereas EPS-deficient cells have an advantage at high cell densities. These results underline the importance of spatial pattern formation for competition among bacterial strains and the evolution of microbial cooperation.

Influence of initial plant density on sawn timber properties for Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco)

Mechanical wood properties are increasingly relevant for structural applications and are influenced by growing space availability. Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) has an increasing market share in Europe and is mainly processed to sawn timber. A sample of 164 thinning trees was taken from two Douglas-fir long-term forestry research plots in Germany. The end-use quality of about 2,000 side and center boards was analyzed as a function of initial plant density (1,000, 2,000, and 4,000 trees per hectare) and log position within the stem. Sawn timber quality was described by knottiness, density, modulus of elasticity, and strength. Explanatory parameters were radial position, longitudinal position, and initial plant density. All boards were strength graded visually and by the grading machine GoldenEye-706 using both X-rays for detecting densities and size as well as position of knots and laser interferometry for detecting eigenfrequency (DIN 4074, DIN 2012; EN 14081-2, CEN 2010). High plant density led to better mechanical sawn timber quality. Significant differences were especially observed between 1,000 and 2,000 trees per hectare. The yield of machine strength-graded center boards of strength class C24 increased from 50 to 89 % at low and high initial plant density, respectively. Foresters are able to improve end-product quality by controlling planting density in particular. The roundwood price that foresters get should be based on the proportion of higher strength classes within logs to give incentives for a more quality-oriented forest management.

Influence of pores on workability of porous Al/SiC composites fabricated through powder metallurgy + mechanical alloying

In the present work, the compressive formability of porous Al/SiC composites fabricated through mechanical alloying (MA) is investigated. Aluminum matrix composites consisting of pure Al reinforced with different amounts of 5, 10, 20wt.% SiC with mean particle size of 16μm and other composites containing 10wt.% SiC with particle sizes of 12, 16μm were produced by a powder metallurgy route. The effect of milling time on microstructure and mechanical properties of the composites was studied. The phased compression tests coupled with density measurement and continuous compression of the samples were indicative of increases in strength and decreases in ductility of the composites with increasing milling time, increasing amount of reinforcement particles and decreasing their size. Instantaneous density coefficient and instantaneous work hardening exponent of the samples, during deformation stages, show decreasing trends when density increased. It was also revealed that instantaneous work hardening exponent increase with increasing milling time, increasing weight percentage of the reinforcement and decreasing its particle size. The samples having higher initial densities, containing lower amounts of larger SiC particles show better workability.

Pre-Mainsequence Stellar Evolution in N-Body Models

AbstractWe provide a set of analytic fits to the radii of pre-mainsequence stars in the mass range 0.1 < M/M⊙ < 8.0. We incorporate the formulae in N-body cluster models for evolution from the beginning of pre-main sequence. In models with 1 000 stars and high initial cluster densities, pre-mainsequence evolution causes roughly twice the number of collisions between stars than in similar models with evolution begun only from the zero-age main sequence. The collisions are often all part of a runaway sequence that creates one relatively massive star.

Non-equilibrium grain boundaries in titanium nanostructured by severe plastic deformation: Computational study of sources of material strengthening

A computational model of ultrafine grained (UFG) or nanostructured titanium (Ti), based on a finite element (FE) unit cell model of the material and a dislocation density based model of plastic deformation has been developed. FE simulations of tensile deformation of UFG Ti with different fractions and properties of the grain boundary (GB) phase have been carried out. The effect of different degrees of deviation from the equilibrium state of the grain boundaries (GBs) on the mechanical behaviour of nanostructured Ti have been investigated using the combined composite/dislocation dynamics based model. In particular, the effects of different diffusion coefficients in the GB phase, of a high initial dislocation density in the grain boundaries, as well as of atomic scale precipitates are investigated for affecting the deformation behaviour of UFG or nanostructured Ti.

Soil Displacement and Soil Bulk Density Changes as Affected by Tire Size

<abstract><title><italic>Abstract.</italic></title> The selection of the appropriate tire size and inflation pressure for a particular load and soil condition is a critical consideration to ensure that the effects of vehicle traffic on soil compaction are minimized and that agricultural soils are managed in a sustainable manner. This study investigated the changes in soil bulk density from soil displacement data produced by a range of combine harvester tires (680/85R32, 800/65R32, and 900/60R32) with vertical load of 10.5 t and inflation pressures in the range of 0.19 to 0.25 MPa to provide a valuable indicator for tire selection. The study was conducted in a soil bin facility using a sandy loam soil (Cottenham series) maintained at 10% (w w^-1) moisture content. Results showed that the initial density (γ) was the main factor influencing soil displacement and soil bulk density changes beneath the tires. Increased tire size and low inflation pressure reduced soil displacement and the resultant increase in soil bulk density. After a single pass of the tires over the soil, these increases were approximately 26% for a low (γ = 1.20 g cm^-3), 17% for a medium (γ = 1.40 g cm^-3), and 4% for a high (γ = 1.60 g cm^-3) initial bulk density soil, respectively. The advantages of increasing tire size and lowering inflation pressure were also reflected in the results obtained from the cone penetrometer resistance data. The tire with the highest inflation pressure (0.25 MPa) produced a significantly (p < 0.05) higher increase in soil cone index (0 to 700 mm depth range) compared with the tires with lower inflation pressures (0.19 and 0.22 MPa, respectively), particularly at the centerline of the wheeling. Linear relationships (R² ≥ 0.98) between drop cone penetration and rut depth were established; these data were subsequently related to the calculated increase in soil bulk density determined from soil displacement data. The increase in soil bulk density resulting from a single pass of a tire over the soil can be determined for a range of tire configurations and initial soil conditions with the data produced by this study.

Cell-Derived Polymer/Extracellular Matrix Composite Scaffolds for Cartilage Regeneration, Part 1: Investigation of Cocultures and Seeding Densities for Improved Extracellular Matrix Deposition

This study investigated the coculture of chondrocytes and mesenchymal stem cells (MSCs) on electrospun fibrous polymer scaffolds to produce polymer/extracellular matrix (ECM) hybrid constructs with the objective of reducing the number of chondrocytes necessary to produce ample cartilage-like ECM within the scaffolds. To generate these hybrid constructs, electrospun poly(ɛ-caprolactone) fibrous scaffolds were seeded at both high and low initial densities with five different ratios of chondrocytes to MSCs: 1:0, 1:1, 1:3, 1:5, and 0:1, and cultured for 7, 14, and 21 days. Glycosaminoglycan production and distribution within the three coculture groups was similar to quantities generated by chondrocyte-only controls. Conversely, as the concentration of chondrocytes was increased, the collagen content of the constructs also increased at each time point, with a 1:1 chondrocyte to MSC ratio approximating the collagen production of chondrocytes alone. Histological staining suggested that cocultured constructs mimicked the well-distributed ECM patterns of chondrocyte generated constructs, while improving greatly over the restricted distribution of matrix within MSC-only constructs. These results support the capacity of cocultures of chondrocytes and MSCs to generate cartilaginous matrix within a polymeric scaffold. Further, the inclusion of MSCs in these cocultures enables the reduction of chondrocytes needed to produce cell-generated ECM.

Nonconservative scheme with the isentropic condition in rarefaction waves as applied to the compressible Euler equations

A previously developed secondorder accurate quasimonotone scheme is tested using the Riemann problem with high initial pressure and density ratios. For shock waves, the scheme is conser� vative, while, in rarefaction waves, the isentropic condition along the trajectory of a Lagrangian parti� cle is used instead of conservativeness in energy. It is shown that the shock front position produced by the scheme has no considerable errors typical of a representative set of conservative quasimonotone schemes of various orders of accuracy. The numerical accuracy is significantly improved in the case of moving grids with a contact discontinuity explicitly introduced in the form of a grid node. It is shown how the method can be extended to cover the multidimensional case and the presence of additional terms in the original equations. DOI: 10.1134/S0965542513110055

Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope

The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, \((g_o^{\prime } Q)^{1/3}\), which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.

Effects of crystal orientation on the dissolution of calcite by chemical and microscopic analysis

The purpose of this work was to examine the effects of polished crystal-surface orientation and degree of solution undersaturation on the dissolution kinetics of calcite. Crystallographic surface orientations utilized in this study included natural calcite specimens polished approximately parallel to the (104) plane, giving rise to surfaces with flat terraces with few steps, as well as fully kinked surfaces created by sectioning approximately parallel to the (001) plane. Results from inductively coupled plasma optical emission spectroscopy (ICP-OES) and vertical scanning interferometry (VSI) investigations revealed how crystallographic orientations of calcite with initially higher energy surface morphologies were associated with greater extent of reaction, greater surface retreat, and therefore, greater initial transient dissolution rates than those with lower energy initial surface morphologies. However, both the ICP-OES and atomic force microscopy (AFM) results confirm that the effects of crystal orientation become minimal under long-term conditions because (1) variously oriented calcite surfaces exhibited similar “long-term” rates and (2) orientations with high initial reactive site densities developed lower energy morphologies. Estimating a step rate coefficient from the experimental data from a miscut sample suggest that these coefficients may be highly morphology dependent. Results from this study are significant for predicting long term calcite dissolution rates because they suggest that the “long-term” dissolution rate of calcite will be governed by the rates of the rhombohedral faces and microfacets and the time-scale for approaching such conditions is of the order of days at room temperature and slightly alkaline solution conditions.

Light induced changes in the amorphous—crystalline silicon heterointerface

The photostability of the amorphous—crystalline silicon heterointerface is investigated. It is revealed that the metastability of hydrogenated amorphous silicon (a-Si:H) causes significant light induced changes in the heterointerface. Unlike bulk a-Si:H, the photostability of the heterointerface is not controlled by the microstructural properties of a-Si:H but rather by the initial heterointerface properties. Interfaces that initially have low interface defect density show the greatest degradation while those that initially have high interface defect density actually show light-induced improvement. It is shown that the degree of light induced change in the interface defect density is linearly proportional to the natural logarithm of the initial interface defect density. Further, it is revealed that the kinetics of light-induced change in the heterointerface defect density can be faster or slower than light-induced changes in bulk a-Si:H films depending on the initial properties of the heterointerface. Light soaking measurements on heterointerfaces with doped a-Si:H films reveal that interface defect density of these structures improves with light soaking. It is proposed that this is caused by a combination of the high initial interface defect density of samples using doped a-Si:H films and reduced generation of defects near the heterointerface due to the enhanced field effect provided by the doped films.

Dynamic balance between grain refinement and grain growth during high-pressure torsion of Cu powders

High-pressure torsion (HPT) was applied to unmilled coarse-grained (CG) Cu powders with low initial dislocation density and cryomilled nanocrystalline (nc) Cu powders with high initial dislocation density, with identical processing parameters. HPT of unmilled CG Cu powders resulted in exceptional grain refinement and increase in dislocation density, whereas significant grain growth and decrease in dislocation density occurred during HPT of cryomilled nc Cu powders. Equilibrium structures were achieved under both conditions, with very similar stable grain sizes and dislocation densities, suggesting dynamic balances between deformation-induced grain refinement and grain growth, and between deformation-induced dislocation accumulation and dislocation annihilation. The equilibrium structures are governed by these two dynamic balances.

Listeria monocytogenes responds to cell density as it transitions to the long-term-survival phase

Listeria monocytogenes was recently found to enter a long-term-survival (LTS) phase, which may help explain its persistence in natural environments and within food processing plants. The purpose of this study was to investigate the effects of initial cell density, initial pH and type of broth (fresh vs. spent) on the transition of L. monocytogenes to the LTS phase and model the change in viable population density with time. Initial cell density (~106–~1010CFU/ml) and initial pH (5.36–6.85) both significantly affected the transition of L. monocytogenes to the LTS phase (P<0.001) with initial cell density being the main determining factor. In contrast, type of broth did not significantly affect cell density change during the transition of stationary-phase cells at high initial density to the LTS phase (P>0.05). After 30-d incubation no significant differences in cell densities were observed between either type of broth or between any of the initial cell density/pH treatment combinations (P>0.05), where the mean viable cell density was 4.3±1.1×108CFU/ml. L. monocytogenes responded to viable cell density in accordance with the logistic equation during transition to the LTS phase. The Agr quorum-sensing system does not appear to play a role in the transition to the LTS phase. Further research is needed to better understand the control mechanisms utilized by L. monocytogenes as it transitions to a coccoid, resistant and stable density state in the LTS phase.

Size‐symmetric competition in a shade‐tolerant invasive plant

AbstractPlant responses to crowding have been investigated extensively in stands of light‐demanding species, but shade‐tolerant species may react differently. In the present study, we investigated the effect of density on the mortality, size inequality, and biomass allocation of Alternanthera philoxeroides, a shade‐tolerant invasive species. Stem fragments of A. philoxeroides were grown at either low or high densities (6 vs. 24 plants per pot) under three light levels (10%, 34%, and 100% full sun). After 8 weeks, survival was 31% lower in pots with a higher initial density. Both high density and low light levels reduced plant size substantially. Mean plant biomass ranged from 0.23 g in high‐density and low‐light pots to 4.41 g in low‐density and high‐light pots. There were no strong or significant effects of density or light level on size inequality of survivors. Most of the variation in allocation and morphology in response to light level and crowding were due to plant size and allometric growth, with little evidence of true plasticity. There was a small but significant increase in shoot allocation, in the direction predicted by optimal allocation theory, at low light levels. Our results show that intense competition need not be size asymmetric, and suggest that tolerance to low light levels involves a reduction in phenotypic plasticity. Responses of the invasive A. philoxeroides to crowding may be an example of an invasive plant's success in establishing dense stands of closely related individuals that are shade tolerant, cooperative, and follow a relatively fixed allometric trajectory with low plasticity.

Strong radial variation in wood density follows a uniform pattern in two neotropical rain forests

Summary Wood density (WD) affects plant biomechanics, drought and decay resistance. As a consequence, WD is an important functional trait related to plant demography and ecosystem processes, which is also used to estimate tree biomass. Radial variation in WD (changes from the centre of the stem to the cambium) affects the strength of the entire stem, but also reflects any changes in wood functional properties that might occur during a tree's lifetime. To understand how WD and radial WD gradients, which were defined as the slope of the relationship between WD and distance to the centre, are related to demographic traits of species, we investigated WD in 335 tree species from a Panamanian moist forest and 501 species from an Ecuadorian rain forest and radial density gradients in 118 and 186 species, respectively, and compared WD with tree growth, mortality and size. WD was negatively related to tree growth and mortality. WD tended to increase towards the outside in trees with low initial density and to decrease towards the outside in trees with high initial density. Radial WD gradients were largely unrelated to tree size and demographic traits, but some families had higher or lower WD gradients at a given inner WD. Inner WD was by far the best predictor of radial WD gradients (r2 = 0·39 for Panama and 0·45 for Ecuador) and this relationship was indistinguishable between the two rain forests. This suggests a broadly uniform function of WD variation, likely responding to mechanical requirements during ontogeny. We discuss the factors potentially driving radial increases or decreases in WD and suggest ways to elucidate the relative importance of tree mechanics, hydraulic safety or decay resistance. We also discuss that not accounting for radial WD gradients may result in substantial errors in WD of the whole stem and consequently biomass estimates, and recommend sampling density gradients when obtaining density data from tree cores.

Field Evaluation of Predacious Mites (Acari: Phytoseiidae) for Biological Control of Citrus Red Mite,Panonychus citri(Trombidiformes: Tetranychidae)

ABSTRACT We evaluated 3 species of predacious mites (Acari: Phytoseiidae), Galendromus occidentalis (Nesbitt), Phytoseiulus persimilis Athias-Henriot and Neoseiulus californiens (McGregor), as biological control agents for citrus red mite, Panonychus citri (McGregor) (Trombidiformes: Tetranychidae), on citrus in southern Alabama. Three separate experiments were carried out during 2008 and 2011 to evaluate various factors (i.e. release rate, release frequency and initial prey density) that may impact the performance of the predacious mites. In the first experiment conducted in 2008 on trees with moderate initial prey densities (i.e. < 4 P. citri motiles per leaf), one single release of P. persimilis or G. occidentalis at a rate of 100 or 200 per tree effectively prevented the prey from exceeding the economic threshold (5 motiles/leaf) for the entire duration (35 d) of the experiment. The result of the second experiment in 2008 on trees with high initial prey densities (i.e. ≥ 5 motiles per leaf) showed tha...

Collapse of Primordial Filamentary Clouds under Far-Ultraviolet Radiation

The collapse and fragmentation of primordial filamentary clouds under isotropic dissociation radiation was investigated with one-dimensional hydrodynamical calculations. We investigate the effect of the dissociation photon on the filamentary clouds by calculating non-equilibrium chemical reactions. With the external radiation assumed to turn on when the filamentary cloud forms, a filamentary cloud with low initial density ($n_0$$\le$ 10$^{2}\ $ cm$^{-3}$ ) suffers a photodissociation of hydrogen molecules. In such a case, since the main coolant is lost, the temperature increases adiabatically enough to suppress the collapse. As a result, the filamentary cloud fragments into very massive clouds ($\sim$ 10$^{5}\ M_\odot$ ). On the other hand, the evolution of the filamentary clouds with high initial density ($n_0$$&amp;gt;$ 10$^{2}\ $ cm$^{-3}$ ) is hardly affected by the external radiation. This is because the filamentary cloud with high initial density shields itself from the external radiation. It is found that the fragment mass increases owing to the external radiation. This result is consistent with previous results with one-zone models. It is also found that the fragment mass decreases owing to the external dissociation radiation in the case with a sufficiently large line mass.

Long-term growth and yield effects of respacing natural regeneration of Sitka spruce in Britain

Stands of Sitka spruce (Picea sitchensis (Bong.) Carr.) originating from natural regeneration can be extremely dense with high mortality, poor growth form and low volume production. Although costly, respacing (pre-commercial thinning) can reduce resource competition for the remaining trees, altering the final crop produced. Three experiments were established to examine the effect of respacing 1–2 m tall trees to different target densities. The impact on stand growth and yield was measured 11–17 years after respacing, and the longer-term impact was modelled to year 50. Unrespaced control treatments self-thinned at a similar and constant rate at two sites. At the third, extremely high initial density resulted in a higher rate of self-thinning and lower density after 11 years. Wider respacing treatments resulted in larger mean tree diameter, but there was no significant effect of respacing on stand volume 11–17 years after respacing; greater diameter growth did not compensate for low tree number. Results indicate a volume penalty associated with delaying respacing until trees were 4 m tall, but this treatment was unreplicated. Modelled stand volume in year 50 was higher for the 2.6 m × 2.6 m respacing treatment than for the 1.8 m × 1.8 m, 2.1 m × 2.1 m or 3.3 m × 3.3 m treatments. However, open-grown conditions may reduce timber quality compared to closer spacing treatments. The results are presented using a stand density management diagram for Sitka spruce growing in Canada and support recent suggestions that British stands have a shallower size–density relationship than Canadian stands.

Initial density affects biomass–density and allometric relationships in self‐thinning populations of Fagopyrum esculentum

Summary The form and generality of the biomass–density relationship, especially during self‐thinning of crowded stands, have been intensively debated in recent years. All models of self‐thinning assume that the trajectory is independent of the initial pre‐thinning density, so populations differing in initial density can be analysed together. As plant allometry is a determinant of the self‐thinning trajectory, and competition alters plants' allometric growth, initial density may have consequences for the self‐thinning trajectory. To ask whether initial density can influence allometric relationships and the biomass–density trajectory, we grew Fagopyrum esculentum populations at three high densities and measured shoot biomass, density and the height and diameter of individual plants at six harvests. Initial density did not affect the slope of the log biomass–log density relationship, but there was a clear and significant effect on the intercept. Populations sown at higher densities had significantly more biomass at a given density of survivors. If the data for all densities and harvests are analysed together, the log biomass–log density relationship is linear with a slope of −0.377, which is consistent with the predictions of Metabolic Scaling Theory. If the independent variable initial density is included as a factor, the estimated slope of the log B–log N relationship is much steeper and consistent with the classical ‘Self‐thinning Rule’. The position of the self‐thinning trajectory is determined in part by the biomass density: the relationship between mass and volume. Initial density could affect this by altering allometric growth in a way that influences architectural compactness. An alternative hypothesis is that competition at higher initial density is more size symmetric, which has been shown to reduce growth and mortality. Synthesis. The self‐thinning trajectory is not always independent of initial population density. Interpopulation scaling patterns, even within one species, do not reflect processes within populations, and this conflation lies behind much of the current debate about size–density relationships in plant populations and communities. Interactions among plants and allometry are more important than internal physiological scaling mechanisms in determining the self‐thinning trajectory of crowded stands.