Size-asymmetric competition and size-asymmetric growth in a spatially explicit zone-of-influence model of plant competition

Size-asymmetric competition among plants is usually defined as resource pre-emption by larger individuals, but it is usually observed and measured as a disproportionate size advantage in the growth of larger individuals in crowded populations (“size-asymmetric growth”). We investigated the relationship between size-asymmetric competition and size-asymmetric growth in a spatially explicit, individual-based plant competition model based on overlapping zones of influence (ZOI). The ZOI of each plant is modeled as a circle, growing in two dimensions. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. We grew simulated populations with different degrees of size-asymmetric competition and at different densities and analyzed the size dependency of individual growth by fitting coupled growth functions to individuals. The relationship between size and growth within the populations was summarized with a parameter that measures the size asymmetry of growth. Complete competitive symmetry (equal division of contested resources) at the local level results in a very slight size asymmetry in growth. This slight size asymmetry of growth did not increase with increasing density. Increased density resulted in increased growth asymmetry when resource competition at the local level was size asymmetric to any degree. Size-asymmetric growth can be strong evidence that competitive mechanisms are at least partially size asymmetric, but the degree of size-asymmetric growth is influenced by the intensity as well as the mode of competition. Intuitive concepts of size-asymmetric competition among individuals in spatial and nonspatial contexts are very different.     

Competitive Asymmetry Reduces Spatial Effects on Size-Structure Dynamics in Plant Populations

The growth of each individual in plant populations was simulatedby a spatial competition model for five density levels and fourdifferent spatial distribution patterns of individuals, varyingfrom highly clumped to regular. The simulation results wereanalysed using the diffusion model for evaluating the effectsof density and distribution pattern on the size-structure dynamicsin relation to the degree of competitive asymmetry. At low densities,changes in statistics of plant weight over time such as mean,coefficient of variation, skewness, and Box-Cox-transformedkurtosis differed greatly among spatial patterns, irrespectiveof the degree of competitive asymmetry. In completely symmetriccompetition, the spatial effect on size-structure dynamics remainedrelatively large irrespective of densities, although mean plantweight became similar among the spatial patterns with increasingdensity. However, the spatial effect diminished with increaseddensity in strongly asymmetric competition, when similar sizedistributions were realized irrespective of the spatial patterns.Therefore, it was concluded that: (1) irrespective of the degreeof competitive asymmetry, spatial pattern is important for size-structuredynamics at low densities; (2) spatial pattern is nearly immaterialunder strongly asymmetric competition at high densities; and(3) under crowded conditions, neighbourhood effects are muchmore apparent at the population level in less asymmetric competition.These processes and outcomes are linked to the forms of thefunctions of mean growth rate of individuals [G(t,x) function]and variance in growth rate [D(t,x) function]. These functionsare variable depending on the spatial pattern under symmetriccompetition, but are rather stable under strongly asymmetriccompetition at high densities irrespective of the spatial patterns.Therefore, size structure under strongly asymmetric competitioncan be regarded as a stable system, whereas that under symmetriccompetition is regarded as a variable system in relation tothe spatial pattern and process. From this, it was inferredthat: (1) the goodness-of-fit of spatial competition modelsfor crowded plant populations is higher in less asymmetric competition;and (2) higher species diversity in plant communities is associatedwith the lower degree of competitive asymmetry.Copyright 1994,1999 Academic Press Asymmetric competition, diffusion model, neighbourhood effect, size-structure stability, spatial competition model, spatial distribution pattern, species diversity, symmetric competition     

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.     

Density Effects on Plant Height Growth and Inequality in Sunflower Populations

Comparisons between competing and non-competing sunflower （Helianthus annuus L.） populations demonstrate pronounced effects of density on plant height growth, height-to-crown width ratio, and s popuiaUon＇s height inequality. In the present study, non-destructive measurements of height and the prolected crown area of sunflower plants were taken at seven times from emergence to fruit maturation in even-aged monospeclflc stands with initial densities of 1, 4, 16, and 64 plants/m^2. The mean height of populations Increased and then decreased with increasing population density; the height Inequalities of uncrowded populations decreased during stand growth, whereas the height inequaiiUes of crowded popuisUons decreased first and then increased during stand development. The interindlvidual relationships between the relative height growth rate and height within uncrowded populations became significantly negative during population growth, whereas these relationships were negative first and then became positive during the development of crowded populations. In the uncrowded populations, the static Interindlvldual relationship between height-to-crown width ratio and volume was positive, whereas for the crowded population these relationships became negative with increasing competition for light. The data suggest that the plastic responses of plant height and height-to-crown width ratio to light competition will become more Intense with increasing competition Intensity. The results of the present study argue strongly for the Importance of size-dependent Individual-level plastic responses due to size-asymmetric light competition In generating the variations in population height inequality.     

Positive interactions can increase size inequality in plant populations

1.  Large variation in the size of individuals is a ubiquitous feature of natural plant populations. While the role of competition in generating this variation has been studied extensively, the potential effects of positive interactions among plants, which are common in high-stress environments, have not been investigated.
2.  Using an individual-based 'zone-of-influence' model, we investigate the effects of competition, abiotic stress and facilitation on size inequality in plant monocultures. In the model, stress reduces the growth rate of plants, and facilitation ameliorates the effects of stress. Both facilitation and competition occur in overlapping zones of influence. We tested some of the model's predictions with a field experiment using the clonal grass Elymus nutans in an alpine meadow.
3.  Facilitation increased the size inequality of model populations when there was no density-dependent mortality. This effect decreased with density as competition overwhelmed facilitation. The lowest size inequality was found at intermediate densities both with the model and in the field.
4.  When density-dependent mortality was included in the model, stress delayed its onset and reduced its rate by reducing growth rates, so the number of survivors at any point in time was higher under harsh than under more benign conditions. Facilitation increased size inequality during self-thinning.
5.   Synthesis . Our results demonstrate that facilitation interacts with abiotic stress and competition to influence the degree of size inequality in plant populations. Facilitation increased size inequality at low to intermediate densities and during self-thinning.     

Effects of competition,herbivory and substrate disturbance on growth and size structure in pin cherry (Prunus pensylvanica L.) seedlings

We examined separate and interactive effects of intraspecific competition, vertebrate browsing and substrate disturbance on the growth and size structure of pin cherry (Prunus pensylvanica L.) in the first two seasons of growth after clearcutting, in a hardwoods forest in New Hampshire, United States. Over the 15-month study period, 97.5% of 1801 individuals survived, and mean plant height increased from 4-fold at high density to 5-fold at low density. Relative height growth was significantly lower at higher plant densities in two of the three growth periods examined. Vertebrate browsers (moose and deer) significantly preferred taller plants. Browsed plants had higher relative height growth following browsing than unbrowsed plants (compensatory growth) at low and intermediate densities. The degree of compensation declined with density and compensation was not significant at the highest density level. At low and intermediate densities, plants browsed early in life regained height dominance through compensatory growth; they failed to regain dominance at high density. Because compensatory growth tended to offset the effects of size-selective browsing, there was no difference in the degree of size inequality between browsed and unbrowsed plots. However, size inequality increased with plant density. Substrate disturbance caused by logging had no significant effects on either relative height growth or size inequality. The slope of the relationship between relative height growth and initial height increased significantly with density and time, and was higher in unbrowsed than in browsed plots, suggesting that competition among plants was size-asymmetric. Despite the preference of browsers for large plants, there was a clear net growth advantage for plants of large initial size, when the effects of competition, browsing and compensatory growth were combined. The interactive effects of density and browsing demonstrate the importance of a multifactorial approach to the analysis of individual plant performance and population structure.     

Asymmetric facilitation can reduce size inequality in plant populations resulting in delayed density‐dependent mortality

Size inequality in plant populations is a ubiquitous feature that has received much attention due to ecological and evolutionary implications. The mechanisms driving size inequality were mainly attributed to different modes of competition (symmetric versus asymmetric), while the potential effects of different modes of facilitation (symmetric versus asymmetric) to this pattern have not yet been fully explored. We employed an individual‐based model to explore the relative roles of both competition and facilitation simultaneously along an environmental stress gradient. Special emphasis was given to the assessment of symmetric facilitation (plants receive benefit from each other equally or proportionally to benefactors’ sizes) and asymmetric facilitation (beneficiary plants receive benefits from benefactor plants that are higher than proportional to the benefactors’ size) in altering plant size inequality. We found that independent of the particular mode of competition, symmetric facilitation generally increased size inequality, whereas asymmetric facilitation decreased it. This pattern was consistent along the stress gradient. Because of their different effects on size inequality, symmetric facilitation accelerated self‐thinning, whereas asymmetric facilitation delayed the onset of density‐dependent mortality, promoting survival under intermediate stress conditions. We compared our model predictions with both 1) a previous modelling study focusing on the effect of (symmetric) facilitation on the size inequality, and 2) re‐analysed data from a published experiment generating asymmetric facilitation of plants against enhanced ultraviolet‐B (UV‐B). Whereas our model predictions and the results of the empirical experiment were consistent, we found that previous theoretical results that solely relied on symmetric facilitation need to be re‐adjusted. Our study showed that combinations of different modes of competition and facilitation can alter size inequality in different ways and with important consequences for the onset of density‐dependent mortality during population development. Explicitly considering different modes and mechanisms of interactions (both facilitation and competition) will improve mechanistic understanding in plant ecology.     

Nutrient availability and atmospheric CO2 partial pressure modulate the effects of nutrient heterogeneity on the size structure of populations in grassland species

BACKGROUND AND AIMS: Size-asymmetric competition occurs when larger plants have a disproportionate advantage in competition with smaller plants. It has been hypothesized that nutrient heterogeneity may promote it. Experiments testing this hypothesis are inconclusive, and in most cases have evaluated the effects of nutrient heterogeneity separately from other environmental factors. The aim of this study was to test, using populations of Lolium perenne, Plantago lanceolata and Holcus lanatus, two hypotheses: (a) nutrient heterogeneity promotes size-asymmetric competition; and (b) nutrient heterogeneity interacts with both atmospheric CO2 partial pressure (P(CO2)) and nutrient availability to determine the magnitude of this response. METHODS: Microcosms consisting of monocultures of the three species were grown for 90 d in a factorial experiment with the following treatments: P(CO2) (37.5 and 70 Pa) and nutrient availability (NA; 40 and 120 mg of N added as organic material) combined with different spatial distribution of the organic material (NH; homogeneous and heterogeneous). Differences in the size of individual plants within populations (size inequality) were quantified using the coefficient of variation of individual above-ground biomass and the combined biomass of the two largest individuals in each microcosm. Increases in size inequality were associated with size-asymmetric competition. KEY RESULTS: Size inequality increased when the nutrients were heterogeneously supplied in the three species. The effects of NH on this response were more pronounced under high nutrient supply in both Plantago and Holcus (significant NA x NH interactions) and under elevated P(CO2) in Plantago (significant P(CO2) x NA x NH interaction). No significant two- and three-way interactions were found for Lolium. CONCLUSIONS: Our first hypothesis was supported by our results, as nutrient heterogeneity promoted size-asymmetric competition in the three species evaluated. Nutrient supply and P(CO2) modified the magnitude of this effect in Plantago and Holcus, but not in Lolium. Thus, our second hypothesis was partially supported.     

Size-dependent growth and the development of inequality in maize,sunflower and soybean

Links were investigated between allometry of plant growth and dynamics of size structure of well-fertilized, irrigated crops of soybean (Glycine max L.), sunflower (Helianthus annuus L.) and maize (Zea mays L.) grown at standard plant-population densities (D), as in commercial crops (D = 30, 6 and 8.5 plants m-2, respectively), and at high densities (2D). Patterns of size-dependent growth of shoot and seed mass accumulation were distinctly different among species. In soybean and sunflower, non-linear relationships between size and subsequent growth led to strong hierarchical populations in terms of both shoot and seed biomass. Curvilinear (soybean) and sigmoid (sunflower) size-dependent growth determined strongly asymmetrical (soybean) and bimodal (sunflower) frequency distributions of shoot biomass indicating predominantly size asymmetrical competition among individuals. In comparison, a lower plant-to-plant variation coupled with a typical linear allometry of growth to plant size indicated symmetrical two-sided plant interference in maize. Despite the weak development of hierarchies in shoot biomass, a strong inequality in reproductive output developed in crowded populations of maize indicating an apparent breakage of reproductive allometry.     

Reproductive allocation patterns in different density populations of spring wheat

The effects of increased intraspecific competition on size hierarchies （size inequality） and reproductive allocation were investigated in populations of the annual plant, spring wheat （Triticurn aestivurn）. A series of densities （100, 300, 1 000, 3 000 and 10 000 plants/m^2） along a gradient of competition intensity were designed in this experiment. The results showed that average shoot biomass decreased with increased density. Reproductive allocation was negatively correlated to Gini coefficient （R^2 = 0.927）, which suggested that reproductive allocation is inclined to decrease as size inequality increases. These results suggest that both vegetative and reproductive structures were significantly affected by intensive competition. However, results also indicated that there were different relationships between plant size and reproductive allocation pattern in different densities. In the lowest density population, lacking competition （100 plants/m^2）, individual reproductive allocation was size independent but, in high density populations （300, 1 000, 3 000 and 10 000 plants/m^2）, where competition occurred, individual reproductive allocation was size dependent： the small proportion of larger individuals were winners in competition and got higher reproductive allocation （lower marginal reproductive allocation; MRA）, and the larger proportion of smaller individuals were suppressed and got lower reproductive allocation （higher MRA）. In conclusion, our results support the prediction that elevated intraspecific competition would result in higher levels of size inequality and decreased reproductive allocation （with a negative relationship between them）. However, deeper analysis indicated that these frequency- and size-dependent reproductive strategies were not evolutionarily stable strategies.     

EFFECTS OF POSTDISPERSAL SEED PREDATION ON SPATIAL INEQUALITY AND SIZE VARIABILITY IN AN ANNUAL PLANT,ERODIUM CICUTARIUM (GERANIACEAE)

By decreasing seed density, ants introduced into flats of uniformly sown seeds of Erodium cicutarium (Geraniaceae) created differences in the neighbor-free area available to individual plants. The changes in spatial patterns brought about by the ants were greater when a higher proportion of seeds was removed but were independent of initial seed density. These spatial changes and differences in seed density were examined for their effects on plant size and reproduction. Gini values were calculated to determine inequalities. As the inequality in space among individual plants increased, the variation in final biomass increased. The number of individuals reproducing was constant among treatments, and yet seed production per plant was significantly greater for populations in which the spatial pattern was influenced by seed predation. The decrease in density and changed spatial pattern, due to previous seed predation, resulted in a few individuals having much more space than others and consequently producing many more seeds. The increase in reproductive effort per flat was much greater than could be explained by the changing density alone. Our experiment demonstrates that spatial inequality, such as that generated by seed predators, can be more important than density in generating size inequalities in plant populations. This result can profoundly alter the competitive interactions between plants and determine which plants produce seed for the next generation.     

Growth and competition in clonal plants-persistence of shoot populations and species diversity

This paper reviews studies on growth and size-structure dynamics of shoots and clones in clonal plants in comparison with those in non-clonal plants, and discusses the characteristics of clonal plants. The mode of competition between individuals (symmetric versus asymmetric, degree of competitive asymmetry), growth dynamics of individuals, allocation pattern between organs and spatial pattern of individuals are closely correlated with each other in non-clonal plant populations. Theoretical and field studies based on the diffusion model revealed that plants of “height-growth” type (mostly early-successional tree species) and plants of “diameter-growth” type (mostly late-successional tree species) tend to exhibit asymmetric competition and symmetric competition respectively. Moreover, asymmetrically competing plants show smaller effects of variation in individual growth rate and spatial pattern on the size-structure dynamics of the population than symmetrically competing plants. Thefefore, the spatial pattern of inviduals should be considered especially for plants undergoing symmetric competition. These results for non-clonal plants should have a significant implication also for the growth dynamics and competition in clonal plants. The mean growth rate of shoots [G(t,x) function] and hence the mode of competition between shoots differs among clonal plant species as in non-clonal plants. However, a large magnitude and size-independence (or slightly negative size-dependence) of the variation in growth rate of shoots [D(t,x) function], especially at the early stage in a growing season is a common characteristic of many clonal plant species, in contrast to the positively size-dependent variation in individual growth rate in non-clonal plants. This type of variation in shoot growth rate leads to the persistence of stable shoot populations even when the mean growth rate function is changed, and also in cases where the shoot population structure would be unstable in the absence of variation in growth rate. It is suggested that competition between clones is symmetric in most clonal plant species, which brings about small-scale spatio-temporal changes in species abundance and hence species diversity.     

Effects of Ultraviolet-B Irradiance on Intraspecific Competition and Facilitation of Plants: Self-Thinning,Size Inequality,and Phenotypic Plasticity

(1) The effects of facilitation on the structure and dynamics of plant populations have not been studied so widely as competition. The UV-B radiation, as a typical environmental factor causing stress, may result in direct stress and facilitation. (2) The effects of UV-B radiation on intraspecific competition and facilitation were investigated based on the following three predictions on self-thinning, size inequality, and phenotypic plasticity: i) Self-thinning is the reduction in density that results from the increase in the mean biomass of individuals in crowded populations, and is driven by competition. In this study, the mortality rate of the population is predicted to decrease from UV-B irradiance. ii) The size inequality of a population increases with competition intensity because larger individuals receive a disproportionate share of resources, thereby leaving limited resources for smaller individuals. The second hypothesis assumes that direct stress decreases the size inequality of the population. iii) Phenotypic plasticity is the ability to alter one’s morphology in response to environmental changes. The third hypothesis assumes that certain morphological indices can change among the trade-offs between competition, facilitation, and stress. These predictions were tested by conducting a field pot experiment using mung beans, and were supported by the following results: (3) UV-B radiation increased the survival rate of the population at the end of self-thinning. However, this result was mainly due to direct stress rather than facilitation. (4) Just as competitor, facilitation was also asymmetric. It increased the size inequality of populations during self-thinning, whereas stress decreased the size inequality. (5) Direct stress and facilitation influence plants differently on various scales. Stress inhibited plant growth, whereas facilitation showed the opposite on an individual scale. Stress increased survival rate, whereas facilitation increased individual variability on the population scale. (6) Trade-offs between competitions, facilitation, and direct stress varied in different growing stages.     

The Roles of Spatial Pattern and Size Variation in Shaping Height Inequality of Plant Population

Game-theoretic models predict that there is an ESS height for the plant population to which all individual plants should converge. To attain this conclusion, the neighborhood factors were assumed to be equal for all the individual plants, and the spatial pattern and size variation of population were left without consideration, which is clearly not right for the scenario of plant competition. We constructed a spatially-explicit, individual-based model to explore the impacts of spatial structure and size variation on individual plant’s height and population’s height hierarchies under the light competition. The monomorphic equilibrium of height that all the individual plants will converge to only exists for a population growing in a strictly uniform spatial pattern with no size variation. When the spatial pattern of the population is non-uniform or there’s size variation among individual plants, the critical heights that individual plants will finally reach are different from each other, and the height inequality at the end of population growth will increase when the population’s spatial pattern’s degree of deviation from uniform and population’s size variation increase. Our results argue strongly for the importance of spatial pattern and neighborhood effects in generating the diversity of population’s height growth pattern.     

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     

Individual variability and mortality required for constant final yield in simulated plant populations

When plant monocultures are sown over a wide range of densities for a given period of time, the total biomass yield increases with density at low densities and then levels off at high densities, a phenomenon called constant final yield (CFY). There are several reported cases, however, where the total yield decreases at very high densities, but the reasons for such exceptions are not known. We used a spatially explicit, individual-based “field of neighborhood” simulation model to investigate the potential roles of spatial pattern, individual variation, and competitive stress tolerance for CFY. In the model, individual plants compete asymmetrically for light when their fields overlap, and this competition decreases growth and increases mortality. We varied (1) the initial size variation, (2) the spatial pattern, and (3) ability to survive intense competition and examined the effects on the density-biomass relationship. CFY was always observed when there was high variability among individuals, but not always when variability was low. This high size variation could be the result of high initial size variability or variation in the degree of local crowding. For very different reasons, very high and very low tolerance for competition resulted in decreasing total biomass at very high densities. Our results emphasize the importance of individual variation for population processes and suggest that we should look for exceptions to CFY in homogeneous, even-aged, regularly spaced populations such as plantations.     

Modeling the growth of individuals in crowded plant populations

Aims We present an improved model for the growth of individuals in plant populations experiencing competition.Methods Individuals grow sigmoidally according to the Birch model, which is similar to the more commonly used Richards model, but has the advantage that initial plant growth is always exponential. The individual plant growth models are coupled so that there is a maximum total biomass for the population. The effects of size-asymmetric competition are modeled with a parameter that reflects the size advantage that larger individual have over smaller individuals. We fit the model to data on individual growth in crowded populations of Chenopodium album .Important findings When individual plant growth curves were not coupled, there was a negative or no correlation between initial growth rate and final size, suggesting that competitive interactions were more important in determining final plant size than were plants' initial growth rates. The coupled growth equations fit the data better than individual, uncoupled growth models, even though the number of estimated parameters in the coupled competitive growth model was far fewer, indicating the importance of modeling competition and the degree of size-asymmetric growth explicitly. A quantitative understanding of stand development in terms of the growth of individuals, as altered by competition, is within reach.     

Gall insects and selection on plant vigor: can susceptibility compromise success in competition?

Gall insects select vigorously growing plants and plant parts when initiating gall formation. Vigor is associated with rapid growth rate, and in turn, rapid growth confers competitiveness. Are there conditions under which the cost of vigor, in the form of increased susceptibility to attack, outweighs the benefit of competitive success? I present a simulation model to explore the interaction between susceptibility and competition on the selective advantage of increased growth rate. Assuming size-symmetric competition, the model shows that in general, vigor is favored (benefit > cost) at low to intermediate gall loads. At very high plant densities, however, plants with high gall loads may lose standing in the competitive size hierarchy from which they cannot recover. The details of this result, however, change somewhat when competition is size-asymmetric, that is, when a larger focal plant suppresses smaller neighbors, but smaller neighbors cannot exert a reciprocal effect on the focal. At low densities, the pattern of selection on growth rate is qualitatively similar to the size-symmetric case. At higher plant densities, however, fast-growing genotypes can suppress slow ones so much during the preattack phase that even at the highest gall loads they maintain their standing in the competitive hierarchy. Thus, heavy gall insect attack on vigorous plants can impose selection against high intrinsic growth rates under strong symmetric competition, but not strong asymmetric competition. While life history traits can evolve as a correlated response to selection on defensive traits that reduce susceptibility, this model reveals that susceptibility can evolve as a correlated response to selection on basic life history traits.     

Asymmetric competition as a natural outcome of neighbour interactions among plants: results from the field-of-neighbourhood modelling approach

Numerous attempts have been made to infer the mode of competition from size or biomass distributions of plant cohorts. However, since the relationship between mode of competition and size distributions may be obscured by a variety of factors such as spatial configuration, density or resource level, empirical investigations often produce ambiguous results. Likewise, the findings of theoretical analyses of asymmetric competition are equivocal. In this paper, we analyse the mode of competition in an individual-based model which is based on the new field-of-neighbourhood approach. In this approach, plants have a zone of influence that determines the distance up to which neighbours are influenced. Additionally, a superimposed field within the zone of influence defines phenomenologically the strength of influence of an individual on neighbouring plants. We investigated competition at both individual and population level and characterised the influence of density and of the shape of the field-of-neighbourhood on occurrence and degree of competitive asymmetry. After finding asymmetric competition emerging in all scenarios, we argue that asymmetric competition is a natural consequence of local competition among neighbouring plants.     

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.