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 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     

A Canopy Photosynthesis Model for the Dynamics of Size Structure and Self-thinning in Plant Populations

A dynamic model for growth and mortality of individual plantsin a stand was developed, based on the process of canopy photosynthesis,and assuming an allometric relationship between plant heightand weight, i.e. allocation growth pattern of plant height andstem diameter. Functions G(t, x), for the mean growth rate ofindividuals of size x at time t, and M(t,x), for the mortalityrate of individuals of size x at time t, were developed fromthis model and used in simulations. The dynamics of size structurewere simulated, combining the continuity equation model, a simpleversion of the diffusion model, with these functions. Simulationsreproduced several well-documented phenomena: (1) size variabilityin terms of coefficient of variation and skewness of plant weightincreases at first with stand development and then stabilisesor decreases with an onset of intensive self-thinning; (2) duringthe course of self-thinning, there is a power relationship betweendensity and biomass per unit ground area, irrespective of theinitial density and of the allocation-growth pattern in termsof the allometric parameter relating plant height and weight.The following were further shown by simulation: (a) competitionbetween individuals in a crowded stand is never completely one-sidedbut always asymmetrically two-sided, even though competitionis only for light; (b) plants of ‘height-growth’type exhibit a greater asymmetry in competition than plantsof ‘diameter-growth’ type, (c) the effect of competitionon the growth of individuals in a crowded stand converges toa stationary state, even when the stand structure still changesgreatly. All of these theoretical results can explain recentempirical results obtained from several natural plant communities.Finally, a new, general functional form for G(t, x) in a crowdedstand is proposed based on these theoretical results, insteadof a priori or empirical growth and competition functions. Canopy photosynthesis, competition mode, continuity equation, self-thinning, simulation, size distribution     

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     

Density Effects on the Size Structure of Annual Plant Populations: An Indication of Neighbourhood Competition

Size variability among plants has been observed to increasewith higher stand density, leading to the speculation that resourcedistribution among competing plants is primarily asymmetricrather than symmetric. The relationships between size variability,stand density, and type of resource distribution among competingplants were investigated using a spatially explicit, individual-plantmodel of annual plant population dynamics. When plants variedin neighbourhood competition, size variability increased withhigher stand densities whether shared resources were symmetricallyor asymmetrically distributed among competing plants. Size variabilitydid not increase with higher stand densities when neighbourhoodcompetition was constant for all plants. These simulations indicatethat increased size variability among competing plants doesnot distinguish between symmetric and asymmetric resource distribution,but rather is direct evidence for neighbourhood competition. Size hierarchy, neighbourhood competition, density effects, asymmetric competition, symmetric competition     

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.     

Inequality of size and size increment in Pinus banksiana in relation to stand dynamics and annual growth rate

BACKGROUND AND AIMS: Changes in size inequality in tree populations are often attributed to changes in the mode of competition over time. The mode of competition may also fluctuate annually in response to variation in growing conditions. Factors causing growth rate to vary can also influence competition processes, and thus influence how size hierarchies develop. METHODS: Detailed data obtained by tree-ring reconstruction were used to study annual changes in size and size increment inequality in several even-aged, fire-origin jack pine (Pinus banksiana) stands in the boreal shield and boreal plains ecozones in Saskatchewan and Manitoba, Canada, by using the Gini and Lorenz asymmetry coefficients. KEY RESULTS: The inequality of size was related to variables reflecting long-term stand dynamics (e.g. stand density, mean tree size and average competition, as quantified using a distance-weighted absolute size index). The inequality of size increment was greater and more variable than the inequality of size. Inequality of size increment was significantly related to annual growth rate at the stand level, and was higher when growth rate was low. Inequality of size increment was usually due primarily to large numbers of trees with low growth rates, except during years with low growth rate when it was often due to small numbers of trees with high growth rates. The amount of competition to which individual trees were subject was not strongly related to the inequality of size increment. CONCLUSIONS: Differences in growth rate among trees during years of poor growth may form the basis for development of size hierarchies on which asymmetric competition can act. A complete understanding of the dynamics of these forests requires further evaluation of the way in which factors that influence variation in annual growth rate also affect the mode of competition and the development of size hierarchies.     

Light acquisition and use by individuals competing in a dense stand of an annual herb, Xanthium canadense

The importance of light acquisition and utilization by individuals in intraspecific competition was evaluated by determining growth and photosynthesis of individual plants in a dense monospecific stand of an annual, Xanthium canadense. Photosynthesis of individual plants in the stand was calculated using a canopy photosynthesis model in which leaf photosynthesis was assumed to be function of leaf nitrogen content and light availability. The estimated photosynthetic rates of individuals were strongly correlated with the measured growth rates. Photosynthetic rates per unit aboveground mass (RPR, relative photosynthetic rate) increased with increasing aboveground mass, suggesting asymmetric (one-sided) competition in the stand. However, larger individuals had similar RPRs, suggesting symmetric (two-sided) competition. These results were consistent with the observation that size inequality over the whole stand increased with growth, but it remained stable among the larger individuals. The RPR of an individual was calculated as the product of absorbed photon flux per unit aboveground mass (Φ_mass) and light use efficiency (LUE, photosynthesis per unit absorbed photon flux). Φ_mass indicates the efficiency of light acquisition, and was higher in larger individuals in the stand, while LUE was highest in individuals with intermediate aboveground mass. LUE depends on leaf nitrogen content. At an early stage, leaf nitrogen contents of smaller individuals were similar to those that maximize LUE. Light availability to smaller individuals decreased as they grew, while their nitrogen contents did not change markedly, which decreased their LUE. We concluded that asymmetric competition among individuals in the stand resulted mainly from lower efficiencies in both light acquisition and light use by smaller individuals. Received: 31 January 1998 / Accepted: 12 November 1998     

Allometry and Competition between Saplings of Picea jezoensis and Abies sachalinensis in a Sub-boreal Coniferous Forest, northern Japan

The crown shape and the mode of competition between saplings(<2m in height) of the two conifers,Picea jezoensis andAbiessachalinensis, of a sub-boreal forest, northern Japan, wereinvestigated based on the diffusion model. A model for individualsapling growth considering both inter- and intraspecific competitionwas developed. The effect of species-specific crown shape onthe sapling growth and competition of the two species were examined.PiceajezoensisandAbies sachalinensissaplings had deep conic and shallowflat crowns, respectively.Picea jezoensishad more foliage massthanAbies sachalinensisof the same sapling mass. It was suggestedthat thePicea jezoensissapling has a high cost for assimilation–respirationbalance under dark conditions of closed canopies, whereas theAbiessachalinensissapling maintains effective assimilation even undersuppressed conditions. Widely spaced saplings, such as gap successors,ofPicea jezoensishad a greater relative growth rate (a₀) thanwidely spacedAbies sachalinensis. The crown shape of saplingsof the two species shows different adaptations for efficientpersistence in the sub-boreal forest. Saplings ofPicea jezoensisandAbies sachalinensiswere not uniformlydistributed, but aggregated in different sites as the saplingsgrew, indicating habitat segregation between the two speciesat the sapling stage. Intraspecific sapling competition wasone-sided in each of the two conifers. Interspecific saplingcompetition was one-sided in the direction only fromAbies sachalinensistoPiceajezoensis. Therefore, asymmetric competition prevailed at thesapling stage of the two species. These results contrast withweak symmetric competition or the almost absence of competitionbetween trees (2m in height) of the two species (Kubota andHara,Annals of Botany76: 503–512, 1995). The mode of competitionchanged with the life-history stage from the sapling (intenseand asymmetric) to the tree (weak and symmetric or almost absent). In conclusion (1) asymmetric and intense competition betweensaplings brought about habitat segregation between the dominantspecies,Picea jezoensisandAbies sachalinensis, in the earlystage of life-history; (2) therefore, the coexistence ofPiceajezoensisandAbies sachalinensisof the sub-boreal forest wasdetermined by the boundary conditions for the growth dynamicsof the trees, as segregation of establishment sites resultingfrom asymmetric and intense competition between saplings; (3)then the species composition of the forest was maintained byweak symmetric competition or the almost absence of competitionbetween trees. Crown shape; growth dynamics; species coexistence; habitat segregation; diffusion model     

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.     

Mechanisms determining the degree of size asymmetry in competition among plants

When plants are competing, larger individuals often obtain a disproportionate share of the contested resources and suppress the growth of their smaller neighbors, a phenomenon called size-asymmetric competition. We review what is known about the mechanisms that give rise to and modify the degree of size asymmetry in competition among plants, and attempt to clarify some of the confusion in the literature on size asymmetry. We broadly distinguish between mechanisms determined primarily by characteristics of contested resource from those that are influenced by the growth and behavior of the plants themselves. To generate size asymmetric resource competition, a resource must be “pre-emptable.” Because of its directionality, light is the primary, but perhaps not the only, example of a pre-emptable resource. The available data suggest that competition for mineral nutrients is often size symmetric (i.e., contested resources are divided in proportion to competitor sizes), but the potential role of patchily and/or episodically supplied nutrients in causing size asymmetry is largely unexplored. Virtually nothing is known about the size symmetry of competition for water. Plasticity in morphology and physiology acts to reduce the degree of size asymmetry in competition. We argue that an allometric perspective on growth, allocation, resource uptake, and resource utilization can help us understand and quantify the mechanisms through which plants compete. Received: 17 February 1997 / Accepted: 8 October 1997     

Tree Competition and Species Coexistence in a Sub-boreal Forest, Northern Japan

The growth and mortality patterns and the mode of competitionof six tree species forming a sub-boreal climax forest in Hokkaido,northern Japan, were investigated based on the diffusion modelat the level of the individual tree 2 m height in a 2·3-hastudy site. Picea jezoensis, Picea glehnii, Betula ermanii andAbies sachalinensis were dominant species, occupying approx.94% of the total basal area. Sorbus commixta and Acer ukurunduensewere subordinate species occupying approx. 6% of the total basalarea. A model for individual growth was developed, consideringboth intra- and inter-specific competition and the degree ofcompetitive asymmetry. Asymmetry was found in intraspecificcompetition of Sorbus commixta and Acer ukurunduense. Piceajezoensis, Betula ermanii and Abies sachalinensis showed symmetricintraspecific competition. There was little interspecific competitionamongst Picea jezoensis, Picea glehnii and Betula ermanii. Abiessachalinensis competed symmetrically with Picea jezoensis (onlyvery weakly, P < 0·1) and Betula ermanii (P < 0·01).Picea glehnii gave no indication of inter- or intra-specificcompetition. The growth of the four dominant species was neveraffected by the two subordinate species; the growth of the twosubordinate species was governed by the abundances of the fourdominant species, the sum of which almost amounted to standcrowdedness (i.e. symmetric competitive effect and one-sidedcompetitive direction). On the scale of 2·3 ha of thesub-boreal forest, symmetric competition prevailed over one-sidedor asymmetric competition although statistical evidence forany competitive effects was rather weak. This was probably dueto the relatively low tree density and stand crowdedness ofthis climax forest. Little competition between the dominantspecies suggested by relatively low proportions of r²-valuesattributable to competitive effects indicates weak organizationamongst the component species (i.e. species were more or lessindependent of each other) at the level of the individual tree 2 m height on the 2·3-ha scale.Copyright 1995, 1999Academic Press Climax forest, diffusion model, individual growth, one-sided competition, size structure, symmetric competition     

Shoot Growth and Mortality Patterns of Urtica dioica, a Clonal Forb

The growth and mortality patterns of the clonal forb Urticadioica were investigated at the level of the individual shootin two growing seasons, 1991 and 1992, in a natural stand. Shootheight and diameter at ground level of each shoot tagged inspring were measured repeatedly five times during the growingseason. Dry weights of these repeatedly measured shoots wereestimated using an allometric relationship between dry weight,height and diameter of harvested shoots. A large decrease inshoot density occurred with stand development from the beginningof the growing season in both the years: (1) shoot survivalrate was about 30% at the end of the growing season; (2) shootmortality rate per 10 x 10 cm subplot between censuses was positivelydependent on shoot density per subplot; (3) the mortality rateof individual shoots was negatively dependent on shoot size(height, diameter and weight) at each growing stage, suggestingone-sided competition between living and dying shoots; (4) shootsize (height, diameter and weight) variability in terms of thecoefficient of variation and skewness decreased in accordancewith shoot mortality. Symmetric competition between living shootswas detected by regression analysis based on a model for individualshoot growth considering the degree of competitive asymmetry.However, the competitive effect on individual shoot growth wasvery small (nearly absent). The mortality pattern of Urticadioica indicates that shoot self-thinning occurred from theearly growing stage as in non-clonal crowded monospecific stands,and contrasts with many clonal plants where shoot self-thinningrarely occurs or, if any, is confined only to a short periodof the later growing stage. The pattern of growth and competitionbetween living shoots of Urtica dioica contrasts with non-clonalcrowded plants undergoing intense competition (usually asymmetric)between individuals, but is a common feature of many clonalplants where shoot competition is supposed to be reduced by'physiological integration' between shoots. These form a newpattern not reported yet for clonal plants. It is pointed outthat clonal plants show a wider spectrum of the growth, competitionand mortality patterns of shoots than non-clonals. Some possiblemechanisms for the pattern of Urtica dioica are discussed.Copyright1995, 1999 Academic Press Shoot competition, diffusion model, individual shoot growth, shoot self-thinning, shoot size variability, Urtica dioica L     

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 competitive asymmetry on a local density model of plant interference

Although competition between plants is usually asymmetric (i.e. larger plants have a disproportionate effect on smaller plants) almost all models of plant competition at the local level have assumed symmetric competition. We add a simple version of competitive asymmetry to the local density neighborhood models of plant interference and population dynamics developed by Pacala & Silander (1985, Am. Nat. 125, 385-411; 1987, Oikos 48, 217-224) by assuming that plants within a neighborhood can be put in a linear dominance hierarchy based upon their initial size. The size of a focal plant is a function of the number of dominant and the number of subordinate neighbors within its neighborhood, with subordinate neighbors having less of an effect than dominant ones. Asymmetry prevents precipitous changes in focal plant size with changes in local density, making the relationship between focal plant size and local density hyperbolic, even if the symmetric model is not hyperbolic. Thus, asymmetry makes the model conform to the law of constant final yield, irrespective of the form of the relationship between plant size and local crowding. Asymmetry also prevents population dynamic oscillations in the model in cases in which it would occur in the absence of asymmetry. The results show that asymmetry has major effects on a model of local interference in plants, and point to the importance of including it in such models.     

Competitive asymmetry, foraging area size and coexistence of annuals

Individuals allocate resources to the expansion of their foraging area and those resources are no longer available for the traits that determine how well those individuals are able to protect their foraging area against competitors. The resulting trade‐off between foraging area size and the traits associated with the ability to compete for the resources within the foraging area applies to ecological scenarios as different as territorial defence by individuals and colonies, and light competition in plants. Whether the trade‐off affects species performance in competition for resources at the area of overlap between foraging areas depends on the symmetry of resource division. In symmetric competition resources are divided equally between the competitors, while in asymmetric competition the individual with the smallest foraging area, and consequently the greatest competitive ability, gains all the resources. Competition may also be a combination of the symmetric and asymmetric processes. I studied the effects of competitive asymmetry on population dynamics and coexistence of two annual species with different sized foraging areas using an individual‐based spatially explicit simulation model. Symmetric competition favoured the species with the larger foraging area and did not allow coexistence. Competitive asymmetry favoured the species with smaller foraging area and allowed coexistence, which was due to the consequences of losing an asymmetric competition being more severe than losing a symmetric competition. The mechanism of coexistence is the larger foraging area's superiority in low population densities (little competition) and the smaller foraging area's ability to win a large foraging area when competition was intense. Competitive asymmetry and small size of both foraging areas led to population dynamics dominated by long‐term fluctuations of small intensity. Symmetric competition and large size of the foraging areas led to large short‐term fluctuations, which often resulted in the extinction of one or both of the species due to demographic stochasticity.     

Potential Yield in Carrots (Daucus carota L.): Theory, Test, and an Application

There is little published information on the physiological behaviourof carrots at the crop level. Here we derive and test a simplemodel for the potential yield of carrot crops. The model calculatesgreen leaf area index (L) using a daily time step. Dry matterproduction is related linearly to light interception, calculatedfromL and canopy light extinction coefficient (k). Two stagesof growth are distinguished. In stage 1, leaf expansion on eachplant is unaffected by neighbouring plants. Stage 2 commenceswhen L reaches a critical value and the plants start to interact.Compared to stage 1, stage 2 has slower leaf expansion and ak which varies with plant density. Dry matter partitioning betweenshoots and the storage root depends on L. We calibrated themodel for two processing cultivars, ‘Chantenay Red Core’and ‘Red Hot’, using data from a 1997–98 plantdensity experiment in Hawke's Bay, New Zealand. The model accountedfor 72% of the observed variation in root size and 79% of thevariation in yield. We tested the model against results fromtwo experiments in 1995–96 and 1996–97. In bothexperiments the same two cultivars were sown at three differentsowing times. Overall, the model accounted for 72% of the observedvariation in root size and 66% of the variation in yield, showingthat it is portable to other environments. Finally, we appliedthe model to interpret the effects of sowing date in these twoexperiments. Previous attempts were confounded by variationin plants m^-2with sowing date. The model allowed us to separatethe effects of these factors, and indicated that early sowingsubstantially benefited yield. Copyright 2000 Annals of BotanyCompany Carrot, Daucus carota L., day-degrees, genetic algorithm, growth modelling, plant density, potential yield, thermal time     

Partitioning of Stored Resources Between Shoots in a Clone, and its Effects on Shoot Size Hierarchy

A theoretical study is described of the effects of the patternof partitioning of stored resources between the shoots of aclone on the development of shoot size hierarchy. When thereis an increasing convex relationship between the amount of resourcesavailable to a shoot at the start of growth and its biomassat maturity, the mode of competition between the shoots is asymmetricand the sharing of stored resources between shoots will notmaximize above-ground biomass of the clone at maturity. Underthis condition, the plant is predicted to allocate a smalleramount of its resources to storage, producing a lower below/above-groundbiomass ratio. Clonal species in which shoots compete asymmetricallyare known to have smaller below/above-ground biomass ratios.When there is an increasing concave relationship between theamount of resources available to a shoot at the start of growthand shoot biomass at maturity, the mode of competition willbe symmetric, and equal sharing of stored resources betweenall shoots at the start of growth will maximize the above-groundbiomass of the clone at maturity. If sharing of resources isthe optimal pattern of partitioning, all shoots of the cloneare predicted to be equal in size at maturity and, therefore,a size hierarchy will not develop within a clone. Copyright2001 Annals of Botany Company Clonal plants, pattern of partitioning, stored resources, shoot competition, size hierarchy, sharing of resources, symmetric competition     

Effects of Physiological and Environmental Variations on Size-Structure Dynamics in Plant Populations

Sensitivity analysis was conducted, based on the canopy photosynthesisand continuity equation models which were developed in a previouspaper (Yokozawa and Hara, 1992), to investigate effects of variationin physiological parameters (maximal photosynthetic rate perunit leaf area, respiration rate per unit leaf area, maintenancerespiration rate per unit weight, growth respiration rate perunit weight, light extinction coefficient of the canopy, etc.)on the size-structure dynamics in plant populations. As thedegree of asymmetry in competition between individuals increased,effects of variation in physiological parameters diminished.Therefore, a population undergoing one-sided competition (mostasymmetric competition) is a stable system, little affectedby temporal and spatial variations in the environmental conditionswhich lead to variation in physiological parameters, whereasa population undergoing symmetric two-sided competition is sensitiveto these fluctuations. It was also shown by simulation thatthe degree of asymmetry in competition decreases (through effectson canopy photosynthesis) as nutrient level in the soil is reduced.It is suggested that symmetric two-sided competition is associatedwith non-transitivity of competition between species (i.e. frequentreversals of rank order of species), and hence with speciesdiversity. Several other ecological phenomena are discussedin relation to allometry (i.e. allocation-growth pattern) andthe degree of asymmetry in competition.Copyright 1994, 1999Academic Press Allometry, canopy photosynthesis, competition mode, continuity equation, parameter sensitivity, stability of stand structure     

The Processes of Height-rank Determination Among Individuals and Neighbourhood Effects inChenopodium albumL. Stands

The height ofChenopodium albumL. plants grown in monocultureat three different densities was followed throughout the growingseason to examine size-rank determination processes with specialreference to the effects of neighbourhood conditions. Changesin height rank of plants in the stands were assessed by therank correlation between final height and the height at eachmeasurement during the growing season. The height ranks of plantswere almost fixed 1–2 weeks after canopy closure whenthe stand height was 10–20% of final stand height, andfixation occurred earlier in the denser plot. At each measurement,the effects of neighbourhood were evaluated as the partial correlationcoefficient between height growth and neighbourhood index withheight held constant (r_GN.H), in which competitive asymmetrywas incorporated. During the early period of the growing season,r_GN.Hwasnon-significant or positive (plants with taller and/or closerneighbours elongated faster), indicating no local competition.Just after canopy closure,r_GN.Hbecame negative, indicating localcompetition. A plant's rank changed only in an initial shortperiod of the competition. Plants occupying the upper canopyof stands at the end of the growing season were distinguishedby greater height growth during the initial short period ofcompetition after canopy closure, although these plants werenot necessarily taller before the onset of local competition.These results suggest that the fate of a plant in a crowdedstand is determined in the early stage of stand development.Copyright1999 Annals of Botany Company Height growth, neighbourhood competition, local competition, height-rank of plants in population, size difference, asymmetric competition,Chenopodium albumL.