The effects of density, spatial pattern, and competitive symmetry on size variation in simulated plant populations

Patterns of size inequality in crowded plant populations are often taken to be indicative of the degree of size asymmetry of competition, but recent research suggests that some of the patterns attributed to size-asymmetric competition could be due to spatial structure. To investigate the theoretical relationships between plant density, spatial pattern, and competitive size asymmetry in determining size variation in crowded plant populations, we developed a spatially explicit, individual-based plant competition model based on overlapping zones of influence. The zone of influence of each plant is modeled as a circle, growing in two dimensions, and is allometrically related to plant biomass. The area of the circle represents resources potentially available to the plant, and plants compete for resources in areas in which they overlap. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. Theoretical plant populations were grown in random and in perfectly uniform spatial patterns at four densities under size-asymmetric and size-symmetric competition. Both spatial pattern and size asymmetry contributed to size variation, but their relative importance varied greatly over density and over time. Early in stand development, spatial pattern was more important than the symmetry of competition in determining the degree of size variation within the population, but after plants grew and competition intensified, the size asymmetry of competition became a much more important source of size variation. Size variability was slightly higher at higher densities when competition was symmetric and plants were distributed nonuniformly in space. In a uniform spatial pattern, size variation increased with density only when competition was size asymmetric. Our results suggest that when competition is size asymmetric and intense, it will be more important in generating size variation than is local variation in density. Our results and the available data are consistent with the hypothesis that high levels of size inequality commonly observed within crowded plant populations are largely due to size-asymmetric competition, not to variation in local density.     

Effects of Density and Extinction Coefficient on Size Variability in Plant Populations

The effects of density and extinction coefficient on size variability,as measured by the coefficient of variation of plant weightin even-aged monocultures, were investigated theoretically usinga diffusion model of growth and size distribution and a canopyphotosynthesis model over the range of densities at which self-thinning(size-dependent mortality) does not occur. Size inequality (thecoefficient of variation of plant weight) increases with increasingdensity or leaf area index at each growth stage. Plants witherect leaves are prone to lower size inequality than plantswith horizontal leaves. These results agree well with existingobservations on even-aged plant monocultures and suggest thatcompetition between plants is mainly one-sided (competitionfor light). One sided competition affects size variability througha G(t, x) function (mean growth of plants of size x at timet per unit time). Two-sided competition (including competitionfor nutrients) affects size variability through a D(t, x) function(variance of growth of plants of size x at time t per unit time).In this case, size inequality decreases with increasing density.The importance of studying size variability is emphasized. Helianthus annus L., size variability, size inequality, coefficient of variation, competition, density effect, extinction coefficient, diffusion model, canopy photosynthesis model     

Modeling the growth of individuals in plant populations: local density variation in a strand population of Xanthium strumarium (Asteraceae)

We studied the growth of individual Xanthium strumarium plants growing at four naturally occurring local densities on a beach in Maine: (1) isolated plants, (2) pairs of plants ≤1 cm apart, (3) four plants within 4 cm of each other, and (4) discrete dense clumps of 10-39 plants. A combination of nondestructive measurements every 2 wk and parallel calibration harvests provided very good estimates of the growth in aboveground biomass of over 400 individual plants over 8 wk and afforded the opportunity to fit explicit growth models to 293 of them. There was large individual variation in growth and resultant size within the population and within all densities. Local crowding played a role in determining plant size within the population: there were significant differences in final size between all densities except pairs and quadruples, which were almost identical. Overall, plants growing at higher densities were more variable in growth and final size than plants growing at lower densities, but this was due to increased variation among groups (greater variation in local density and/or greater environmental heterogeneity), not to increased variation within groups. Thus, there was no evidence of size asymmetric competition in this population. The growth of most plants was close to exponential over the study period, but half the plants were slightly better fit by a sigmoidal (logistic) model. The proportion of plants better fit by the logistic model increased with density and with initial plant size. The use of explicit growth models over several growth intervals to describe stand development can provide more biological content and more statistical power than "growth-size" methods that analyze growth intervals separately.     

Population distributions of plant size and light environment of giant ragweed (Ambrosia trifida L.) at three densities

Summary Plots in a naturally occurring population of giant ragweed (Ambrosia trifida L.) near Ames, Iowa, USA were left unthinned (high density,=693 plants/m²) or were thinned in early June 1989 to create low and medium densities of 10 and 50 plants/m². Size and light environment of individual plants were measured at monthly intervals from June to September. By September, low density plants had 15 times greater biomass/plant and 30 times greater leaf area/plant than high density plants, although biomass and leaf area per unit land area decreased with decreasing density. Plants at high density allocated more biomass to stem growth, but plants at medium and low density had successively higher leaf area ratios, higher potential photosynthetic rates, higher allocation to leaves, and higher growth rates. Average light on leaves decreased with increasing density and also decreased over the growing season in the low and medium densities. The distribution of light environments of individual plants was non-normal and skewed to the left in most months, in contrast to the rightwards skew of distributions of plant size parameters. Inequality in the distributions, as measured by coefficient of variation and Gini coefficients, increased over most of the growing season. There was little effect of density on inequality of stem diameter, height, or estimated dry weight, but inequality in reproductive output greatly increased with density. There was greater inequality in number of staminate flowers produced than in number of pistillate flowers and seeds produced. Path analysis indicated that early plant size was the most important predictor of final plant size and reproductive output; photosynthesis, conductance, and light environment were also significantly correlated with size and reproduction but usually were of minor importance. Variation in growth rate apparently increased inequality in plant size at low density, whereas belowground competition and death of smaller plants may have limited increases in inequality at high density.     

Differences in Fine-Root Biomass of Trees and Understory Vegetation among Stand Types in Subtropical Forests

Variation of total fine-root biomass among types of tree stands has previously been attributed to the characteristics of the stand layers. The effects of the understory vegetation on total fine-root biomass are less well studied. We examined the variation of total fine-root biomass in subtropical tree stands at two sites of Datian and Huitong in China. The two sites have similar humid monsoon climate but different soil organic carbon. One examination compared two categories of basal areas (high vs. low basal area) in stands of single species. A second examination compared single-species and mixed stands with comparable basal areas. Low basal area did not correlate with low total fine-root biomass in the single-species stands. The increase in seedling density but decrease in stem density for the low basal area stands at Datian and the quite similar stand structures for the basal-area contrast at Huitong helped in the lack of association between basal area and total fine-root biomass at the two sites, respectively. The mixed stands also did not yield higher total fine-root biomasses. In addition to the lack of niche complementarity between tree species, the differences in stem and seedling densities and the belowground competition between the tree and non-tree species also contributed to the similarity of the total fine-root biomasses in the mixed and single-species stands. Across stand types, the more fertile site Datian yielded higher tree, non-tree and total fine-root biomasses than Huitong. However, the contribution of non-tree fine-root biomass to the total fine-root biomass was higher at Huitong (29.4%) than that at Datian (16.7%). This study suggests that the variation of total fine-root biomass across stand types not only was associated with the characteristics of trees, but also may be highly dependent on the understory layer.     

Influence of biotic and abiotic factors on the morphology and reproduction of Suaeda maritima on a salt marsh

The aim of this study was to estimate the influence of biotic and abiotic factors on Suaeda maritima reproduction on a salt marsh. Individuals of Suaeda maritima were submitted in natural conditions to four series of densities (100, 1,000, 4,000 and 8,000 plants/m2). When density increases, individuals tend to be less or non-branched, while individual biomass decreases. Consequently, individual seed production decreases as density increases. Despite morphological modifications, Suaeda maritima present density-dependent mortality. For a unit area, total biomass and seed production are higher at intermediate density (1,000 plants/m2). Environmental factors could interfere with self-thinning. They seem to limit the effect of competition on mortality and to have an influence on individual and total seed production. This experiment stressed the importance of a biotic factor such as intra-specific competition, which occurs at the same time as abiotic factors, in Suaeda maritima dynamics in the field.     

不同倍性冬小麦种内竞争能力的比较研究

通过3个不同倍性冬小麦材料(两倍体栽培一粒、四倍体栽培两粒、六倍体现代品种长武134),在不同水分条件下进行密度实验,研究了不同材料的株高、生物量累积和分蘖动态的变化,以及产量对密度变化的反应。结果表明随着群体的增大,不同倍性材料个体间竞争明显加剧,相互抑制作用增强,种群内部个体大小等级差异增大;在不同群体下各倍性材料的个体生长存在差异,表现为四倍体栽培两粒竞争能力两倍体栽培一粒六倍体现代品种长武134,且长武134受种群大小影响最为显著,但长武134产量累积的投入比例最高,产量最高,低竞争能力的个体更适合生产上的需求,是群体高产的基础。研究结果为旱地小麦的高产栽培和育种提供了理论基础。     

Planting densities and bird and rodent absence affect size distributions of four dicots in synthetic tallgrass communities

Variability in the size distributions of populations is usually studied in monocultures or in mixed plantings of two species. Variability of size distributions of populations in more complex communities has been neglected. The effects of seeding density (35 or 350 seeds/species/m²) and presence of small vertebrates on the variability of size distributions were studied for a total of 1,920 individuals of 4 species in replicated synthetic communities of 18 species in northern Illinois. End-of season height and above-ground biomass were measured for prairie perennials Dalea purpurea (purple prairie clover), Echinacea purpurea (purple coneflower), Desmanthus illinoensis (Illinois bundleflower) and Heliopsis helianthoides (early sunflower). Variability in biomass distribution of the four target species was twice as great at low than at high densities when small vertebrates were excluded. Our results suggest that inter- and intraspecific competition may affect all individuals more under high-density conditions, thereby reducing the variability in their biomass distributions within this community. This result, a consequence of plant-plant interaction, is obscured when small birds or mammals are present, presumably because either or both add variance that overwhelms the pattern.     

三峡水库消落区植被在差异性水淹环境中的分布格局

人工水库修建引发的差异性水文节律是决定消落区植被群落格局的主要因素,高强度水淹环境中水淹胁迫是影响植被的重要因子而低强度水淹环境中物种竞争是影响植被的重要因子。为了探究差异性水淹环境中三峡水库消落区植物的水淹耐受能力及光资源竞争能力(植物株高)对植被群落分布格局的影响,对三峡水库典型消落区不同水淹强度下生长的植被进行了研究,结果表明:(1)典型消落区调查共发现有植物41种,其中高耐淹低竞争能力型植物4种,其生物量在所有物种生物量中的占比达70.99%,低耐淹高竞争能力型植物23种,其生物量占比为28.02%,低耐淹低竞争能力型植物14种,生物量占比不足1%,消落区内无高耐淹高竞争能力型植物物种分布;(2)高耐淹低竞争能力型植物在水淹强度大的消落区区域占优,低耐淹高竞争能力型植物在植物物种竞争压力大的消落区区域占据主导,低耐淹低竞争能力型植物在消落区中仅有零星分布;(3)消落区植被生物量格局随着高程增加呈现出先增加后减少的趋势。研究差异性水淹环境对三峡水库消落区植被分布的影响,可以为深入理解消落区植被分布格局的形成机制和大型水库消落区植被恢复与重建提供理论依据。     

Relatedness and competitive asymmetry – the growth and development of common frog tadpoles

Individuals can compete either through direct interference or uptake of limiting resources. If competing individuals are able to recognize their relatives, relatedness of competitors may evoke kin selection, which favours relatively even resource share among relatives. Resource competition is often size-symmetric, i.e. proportional to an individual's biomass, while interference competition is asymmetric giving large individuals a disproportionate advantage over small individuals. Kin-selection is predicted to reduce the intensity of direct interference and competitive asymmetry, leading to increased mean and decreased variation in individual size. We tested these predictions by investigating the effects of relatedness on age and size at metamorphosis in the common frog Rana temporaria tadpoles in a laboratory experiment. We reared related (full- and half-sibs) and unrelated tadpoles of different sizes (small, large, small and large together) at two densities until metamorphosis. Relatedness had little effect on mean growth, but it reduced size variation, as measured with coefficient of variation. Furthermore, there was a significant interaction between relatedness and density in size at metamorphosis, so that relatives always grew better in lower density, but growth was less affected by density among unrelated individuals. This indicates that the effects of relatedness on tadpole performance may be context dependent. Initial size differences in the mixed size treatment evened out during the course of the experiment, and initially small tadpoles were able to compensate the early growth losses, although it took longer for them to reach metamorphosis. We conclude that although relatedness may have rather small effects on the growth and development of R. temporaria tadpoles, it increases the symmetry of resource share decreasing between-individual variation in size at metamorphosis.     

DOES PHENOTYPIC PLASTICITY FOR ADULT SIZE VERSUS FOOD LEVEL IN DROSOPHILA MELANOGASTER EVOLVE IN RESPONSE TO ADAPTATION TO DIFFERENT REARING DENSITIES?

Recent studies with Drosophila have suggested that there is extensive genetic variability for phenotypic plasticity of body size versus food level. If true, we expect that the outcome of evolution at very different food levels should yield genotypes whose adult size show different patterns of phenotypic plasticity. We have tested this prediction with six independent populations of Drosophila melanogaster kept at extreme densities for 125 generations. We found that the phenotypic plasticity of body size versus food level is not affected by selection or the presence of competitors of a different genotype. However, we document increasing among population variation in phenotypic plasticity due to random genetic drift. Several reasons are explored to explain these results including the possibility that the use of highly inbred lines to make inferences about the evolution of genetically variable populations may be misleading.     

Consumer–plant interaction strength: importance of body size,density and metabolic biomass

Explaining variability in the strength and sign of trophic interactions between primary consumers and plants is a long‐standing research challenge. Consumer density and body size vary widely in space and time and are predicted to have interactive effects on consumer–plant interactions. In a southern US salt marsh, we used replicate field enclosures to orthogonally manipulate the body size (mass) and density of a dominant consumer (a snail). We investigated impacts (leaf damage and biomass) on monocultures of cordgrass, the foundation species, over three months. Increasing consumer density and body size increased leaf damage additively and, as predicted, multiplicatively reduced plant biomass. Notably, size and density determined the sign of consumer impact on plants: low to medium densities of small consumers enhanced, while high densities of large consumers strongly suppressed, plant biomass. Finally, total consumer metabolic biomass (mass^0.75) within an enclosure parsimoniously explained plant biomass response, supporting theoretical predictions and suggesting that multiplicative effects of density and body size resulted from their effects on total metabolic biomass. The consequences of changes in consumer density and body size resulting from anthropogenic perturbations may therefore be predicted based on metabolic biomass. Synthesis Consumer size, density and biomass can all strongly affect consumer–plant interactions. Though density and body size have been extensively studied as drivers of variation in interaction strength, the role of biomass as the ultimate driver has been less appreciated. We manipulated body size and density of a single consumer species and, based on metabolic theory, integrated these into a single variable: total metabolic biomass. Our results suggest that changes in interaction strength attributed to size or density may in fact be due to changes in metabolic biomass. This metric could thus serve as a useful tool in further understanding species interactions.     

Size symmetry of competition alters biomass-density relationships

As crowded populations of plants develop, the growth of some plants is accompanied by the death of others, a process called density-dependent mortality or 'self-thinning'. During the course of density-dependent mortality, the relationship between total population biomass (B) and surviving plant density (N) is allometric: B = aN(b). Essentially, increasing population biomass can be achieved only through decreasing population density. Variation in the allometric coefficient a among species has been recognized for many years and is important for management, assessment of productivity and carbon budgets, but the causes of this variation have not been elucidated. Individual-based models predict that size-dependent competition causes variation in the allometric coefficient. Using transgenic Arabidopsis with decreased plasticity, we provide experimental evidence that morphological plasticity of wild-type populations decreases the size asymmetry of competition for light and thereby decreases density-dependent mortality. This decrease in density-dependent mortality results in more biomass at a given density under size-symmetric compared with size-asymmetric competition.     

Limited effects of soil nutrient heterogeneity on populations of Abutilon theophrasti (Malvaceae)

An experiment was conducted to determine if spatial nutrient heterogeneity affects mean plant size or size hierarchies in experimental populations of the weedy annual Abutilon theophrasti Medic. (Malvaceae). Heterogeneity was imposed by alternating 8 × 8 × 10 cm blocks of low and high nutrient soil in a checkerboard design, while a homogeneous soil treatment consisted of a spatially uniform mixture of the two soil types (mixed soil). Populations were planted at three densities. The effect of soil type on the growth of individuals was determined through a bioassay experiment using potted plants. The high nutrient, low nutrient, and mixed soil differed in their ability to support plant growth as indicated by differences in growth rates and final aboveground biomass. Concentrations of N, K, P, and Mg, measured at the end of the growing season in the experimental plots, also differed among all three soil types. Nevertheless, nutrient heterogeneity had little effect at the population level. Mean maximum leaf width measured at midseason was greater for populations on heterogeneous soil, but soil treatment did not affect midseason measurements of plant height, total number of leaves per plant, or canopy width. Population density affected all these parameters except plant height. When aboveground biomass was harvested at the end of the growing season, soil treatment was found to have no main effect on mean plant biomass, total population biomass, the coefficient of variation in plant biomass, or the combined biomass of the five largest plants in the population, but mean plant biomass was greater for populations on heterogeneous soils at the intermediate planting density. Mean plant biomass, total population biomass, and the coefficient of variation in plant biomass all varied with planting density. Mortality was low overall but significantly higher on homogeneous soil across all three densities. Soil heterogeneity had its strongest effect on individuals. In heterogeneous treatments plant size depended on the location of the plant stem with respect to high and low nutrient patches. Thus, soil nutrient heterogeneity influenced whether particular individuals were destined to be dominant or subordinate within the population but had little effect on overall population structure.     

Effect of local competition on resprouting of Arbutus unedo after clipping

Abstract. To evaluate the effects of local competition on the growth and size variability of sprouts following disturbance in a natural population of Arbutus unedo in Catalonia, plants were cut at the base and a neighbor removal experiment was performed. Removal of neighbors resulted in an increase in the number and biomass of sprouts at 2 and 7.5 months after clipping. Number and biomass of sprouts was also correlated with initial plant size (stump area). Inter-genet competition appeared to be symmetric, and acted to delay the onset of interference among sprouts within a genet. Size variability of sprouts on an individual was positively correlated with their density on the stump, supporting the hypothesis that competition among ramets (sprouts) within a genet is asymmetric. Reduced inter-genet competition from neighbor removal resulted in an increase in the number and biomass of sprouts growing from a stump. This resulted in an increase in the asymmetry of competition among sprouts, and therefore an increase in the size variability of these sprouts.     

Above-ground competition does not alter biomass allocated to roots in Abutilon theophrasti

We tested whether plants allocate proportionately less biomass to roots in response to above-ground competition as predicted by optimal partitioning theory. Two population densities of Abutilon theophrasti were achieved by planting one individual per pot and varying spacing among pots so that plants in the two densities experienced the same soil volume but different degrees of canopy overlap. Density did not affect root:shoot ratio, the partitioning of biomass between fine roots and storage roots, fine root length, or root specific length. Plants growing in high density exhibited typical above-ground responses to neighbours, having higher ratios of stem to leaf biomass and greater leaf specific area than those growing in low density. Total root biomass and shoot biomass were highly correlated. However, storage root biomass was more strongly correlated with shoot biomass than was fine-root biomass. Fine-root length was correlated with above-ground biomass only for the small subcanopy plants in crowded populations. Because leaf surface area increased with biomass, the ratio between absorptive root surface area and transpirational leaf surface area declined with plant size, a relationship that could make larger plants more susceptible to drought. We conclude that A. theophrasti does not reallocate biomass from roots to shoots in response to above-ground competition even though much root biomass is apparently involved in storage and not in resource acquisition.     

Impact of developmental variance on behavior of models for insect populations II. Models for populations with density dependent restrictions on growth

The impact of variation in developmental times on behavior of models for insect populations is investigated with special reference to models which include various types of intraspecific competition. At low densities, increases in developmental variation led to decreases in reproductive rate. At high densities, increases in developmental variation led to increases in reproductive rate. There was little change in the relationship between developmental variance and generation time as density increased.     

Experimental and model analyses of the effects of competition on individual size variation in wood frog (Rana sylvatica) tadpoles

1. Size variation is a ubiquitous feature of animal populations and is predicted to strongly influence species abundance and dynamics; however, the factors that determine size variation are not well understood. 2. In a mesocosm experiment, we found that the relationship between mean and variation in wood frog (Rana sylvatica) tadpole size is qualitatively different at different levels of competition created by manipulating resource supply rates or tadpole density. At low competition, relative size variation (as measured by the coefficient of variation) decreased as a function of mean size, while at high competition, relative size variation increased. Therefore, increased competition magnified differences in individual performance as measured by growth rate. 3. A model was developed to estimate the contribution of size-dependent factors (i.e. based on size alone) and size-independent factors (i.e. resulting from persistent inherent phenotypic differences other than size that affect growth) on the empirical patterns. 4. Model analysis of the low competition treatment indicated that size-dependent factors alone can describe the relationship between mean size and size variation. To fit the data, the size scaling exponent that describes the dependence of growth rate on size was determined. The estimated value, 0-83, is in the range of that derived from physiological studies. 5. At high competition, the model analysis indicated that individual differences in foraging ability, either size-based or due to inherent phenotypic differences (size-independent factors), were much more pronounced than at low competition. The model was used to quantify the changes in size-dependent or size-independent factors that underlie the effect of competition on size-variation. In contrast to results at low competition, parameters derived from physiological studies could not be used to describe the observed relationships. 6. Our experimental and model results elucidate the role of size-dependent and size-independent factors in the development of size variation, and highlight and quantify the context dependence of individual (intrapopulation) differences in competitive abilities.     

Genetic variation in resistance and tolerance to insect herbivory in Salix cordata

1. This study investigated whether sand-dune willow Salix cordata , exhibits genetic variation in resistance and tolerance to herbivory.
2. A field experiment using cuttings from nine willow clones demonstrated genetic variation in resistance to the specialist herbivore Altica subplicata , as measured by beetle densities. Willow clones differed significantly in both total biomass and leaf trichome densities, and herbivore densities were marginally correlated with both of these parameters.
3. Tolerance to herbivory was measured in a greenhouse experiment by comparing growth response of plants experiencing 50% artificial defoliation and plants experiencing no defoliation. Clones showed significant differences in tolerance to herbivory for some growth measures (changes in height and number of leaves), but not for other growth measures (stem diameter growth and final biomass).
4. Despite the significant genetic variation in both resistance and tolerance, no trade-off was found between resistance and tolerance to herbivory.     

Density dependence constrains mean growth rate while enhancing individual size variation in stream salmonids

The objective of this study was to elucidate the effects of density dependence on the individual size variation of brown trout (Salmo trutta) juveniles. Recruitment (the abundance of the youngest juveniles in May when they were 2 months old); the mean size attained by those individuals in September (6 months old) and the corresponding size variability around the mean size quantified with the coefficient of variation (CV) were examined in 22 year-classes at seven sites of two contrasting tributaries of the Rio Esva drainage (north-western Spain). Both mean size and CV tended to be site-specific but density dependence in the form of recruitment dependence affected both mean size and CV: the mean size depicted negative power relationships with increased recruitment whereas the CV increased positively with increased recruitment. However, this pattern differed among sites. At two out of seven sites, there was no obvious relationship between the mean size and recruitment. The CV increased positively with increased recruitment at all sites, although at several sites the CV described linear relationships and at others described power relationships. As a consequence, the stronger effects of density dependence on mean size occurred at low densities with minor effects at high densities, whereas density dependence operated on CV with continuous effects within the whole range of recruitment variation except at several sites where lower effects occurred at high densities. Thus, the occurrence, shape and intensity of competitive interactions underlying density dependence as a major cause of size variation differed across temporal and spatial scales.