Leaf biomass changes with stand development in hinoki cypress (<Emphasis Type="Italic">Chamaecyparis obtusa</Emphasis> [Sieb. et Zucc.] Endl.)

We monitored a permanent plot of 3-year-old Chamaecyparis obtusa seedlings for 11 years after planting. As the stem cross-sectional area at the crown base can be regarded as a good predictor of leaf mass according to the pipe model theory, we measured this parameter to determine temporal trends in leaf biomass. The mean values showed asymptotic growth, maintaining a near-constant level after a stand age of 9 years. Peak values were found at 9 years, followed by a slight decrease because of a continuous reduction in stand density. This temporal trend suggests that the leaf biomass per unit land area attains a peak at an age of 9 years. As the stand density changes with stand age, the relationship between stand stem cross-sectional area at the crown base and stand density showed an optimum curve in which the optimum density was around 9200 ha⁻¹. We propose hypothetical trends in primary productivity and biomass density with stand age, based on the results of measurements of stem cross-sectional area at the crown base and stand density under the assumption of the 3/2 power law of self-thinning.     

Self-thinning lines differ with fertility level

The effect of variations in fertility level of the substrate on the self-thinning lines followed by populations of Ocimum basilicum L. was investigated experimentally by establishing populations over a range of densities at two fertility levels. Populations from each fertility level followed different self-thinning lines for shoot biomass. Self-thinning began at a lower biomass in populations grown at the higher fertility level; the subsequent slope of the thinning line was –0.5 for these stands on a log shoot biomass versus log density plot. The slope of the self-thinning line was flatter (–0.29) at the lower fertility level. Fitting the self-thinning line by the Structural Relationship rather than the Major Axis made little difference to line estimates. Biomass packing differed with fertility level, with plants from the higher fertility stands requiring more canopy volume for given shoot biomass than plants from lower fertility levels. Biologically, this would mean shoot competition intensified more rapidly at the higher fertility level as biomass accumulated in stands. The difference in slope between fertility levels was associated with changes above- and belowground. The radial extension of the canopy versus shoot mass relationships of individual plants differed with fertility level. Plants at the lower fertility level allocated more biomass to root growth, and had less leaf area per unit root length. The differences in slope of the self-thinning lines may have been because of differences in the radial extension of the canopy versus shoot mass relationships of individual plants at each fertility level, and/or to an increase in root competition at the lower fertility level.     

Maintenance cost, toppling risk and size of trees in a self-thinning stand

Wind routinely topples trees during storms, and the likelihood that a tree is toppled depends critically on its allometry. Yet none of the existing theories to explain tree allometry consider wind drag on tree canopies. Since leaf area index in crowded, self-thinning stands is independent of stand density, the drag force per unit land can also be assumed to be independent of stand density, with only canopy height influencing the total toppling moment. Tree stem dimensions and the self-thinning biomass can then be computed by further assuming that the risk of toppling over and stem maintenance per unit land area are independent of stand density, and that stem maintenance cost is a linear function of stem surface area and sapwood volume. These assumptions provide a novel way to understand tree allometry and lead to a self-thinning line relating tree biomass and stand density with a power between −3/2 and −2/3 depending on the ratio of maintenance of sapwood and stem surface.     

Density-dependent Mortality Induced by Low Nutrient Status of the Substrate

The hypothesis that changing the fertility level of the substratewould change the self-thinning line (different slope or intercept)followed by high-density populations was tested by sowing populationsof Ocimum basilicum L. at two densities on a soil-based pottingmix adjusted to three fertility levels (F0, F1 and F2). Fertilitylevel significantly affected the slope of the thinning linesfor both shoot and root biomass. For shoot biomass, more mortalityoccurred per unit increase in biomass as fertility level declined(the slope of the thinning line became flatter). The slope ofthe log shoot biomassvs. log density relationship was -0.5 atthe F2-, zero at the F1-, and 0.94 at the F0-fertility. Forthe log root biomassvs. log density lines, slopes were zeroat the F2- and F0-fertility levels, and -0.32 at F1. Packingof shoot biomass into canopies of individual plants correlatedwell with observed exponents of self-thinning lines at the F2-and F1-fertility level. Plants at the F2-fertility level requiredmore canopy space to support a given shoot biomass than plantsat F1, indicating that shoot competition was more intense atthe F2-fertility level for a given biomass. Leaf area indexand size inequality also increased with fertility level fora given shoot biomass. Density-dependent mortality in populationsgrown at the F0-fertility level was highly unusual in havinga positive slope for the shoot biomass vs. density relationship.Shoot growth per plant was static as density declined in theF0-populations; however, root growth per plant increased. Allmeasurements of shoot growth (mass, height, canopy extension,leaf area) remained static in the F0-populations: root massand length increased in comparison. It is argued that root competitionbecame sufficiently intense to cause the density-dependent mortalityseen at the F0-fertility level, with little contribution ofshoot competition to mortality. Copyright 1999 Annals of BotanyCompany Ocimum basilicum, self-thinning, root competition, shoot competition, fertility level and competition, density-dependent mortality, allometric self-thinning.     

In Defence of the -3/2 Boundary Rule: a Re-evaluation of Self-thinning Concepts and Status

The -3/2 power rule, or -3/2 self-thinning rule, was accepted10 years ago as an important generalization, but has recentlybeen questioned by a number of authors. This paper assesseswhat remains of the rule. While it has been empirically establishedthat size-density trajectories followed by self-thinning plantpopulations do not necessarily follow a -3/2 slope, a more generalpower rule describing a density-dependent upper limit to meanshoot biomass per plant (the '-3/2 boundary rule') remains largelyintact. Principal component analysis (PCA) overestimates the steepnessof the thinning slope if y:x variance ratio is greater than1:1. Lonsdale's (Ecology 71: 1373-1388) overall mean PCA slopeof -0·6 for biomass-density suggests a true mean slopeclose to the theoretical value of -0·5. Reduced majoraxis (RMA) regression appears a reasonable approximation forthe -3/2 but not the -1/2 formulation of the rule. Fitting ofa linear functional relationship (LFR) is a more appropriateslope estimation procedure, not previously used for data onthinning. None of these procedures estimates a boundary linethat is not transgressed by any data point except through errorsof measurement. Mortality due to overcrowding ensues when a small, suppressedplant no longer holds its leaves high enough in the canopy tomaintain a positive carbon balance. It follows that LAI shouldremain constant during thinning, and that self-thinning theoryshould be developed in terms of maximum leaf area index andthe biomass required to support it. A derivation is presentedand some of its consequences are examined.Copyright 1995, 1999Academic Press Self-thinning, -3/2 power rule, -3/2 self-thinning rule, boundary line, size-density compensation, regression methods     

A Mathematical Model for Leaf Photosynthesis of Mulberry

A mathematical model of leaf photosynthesis has been established. In this model, the processes of photosynthesis are divided into two parts, ie., the carboxylation process driven by light which is dependent on temperature and CO2 concentration, and the diffusion of CO2 from atmosphere to the carboxylation site. Finatly, CO2 uptake by the leaf is understood as dependent on 1), the CO2 response curve of the leaf mesophyll and 2). the CO2 partial pressure in the intercellular space in leaf. The COs response curve of the leaf photosynthesis is described mathematically in terms of carboxylation efficiency (Ca) or its initial slope and the photosynthetic capacity (Pm) or the CO2-saturated uptake rate of CO2 uptake, and dark respiration (Rd). The dependency of photosynthesis on leaf temperature and incident light intensity is incorporated into variations of those parameters which establish an appropriate response to internal CO2 pressure for particular light and temperature conditions prevailing at any time. Secondly the interactiion of stomata with photosynthesis is represented as an empirical relation between stomatal conductance and a combined environmental physiological index, APn·Hx/CaThe parameters used in the modelwere estimated with Marquardt-Newton method for non-linear function. Field measurements of mulberry leaf photosynthesis provided a data set for model testing. The resuks show that the simulated values of the model agree well with observed data. The model was used to analyse the response surface of leaf conductance and photosynthesis to environmental factors—Applications and limitations of the model are discussed     

植物种群自疏过程中构件生物量与密度的关系

不论是在对植物种群自疏规律还是在对能量守衡法则的研究中,个体大小(M)大多针对植物地上部分生物量,地下部分和构件生物量及其动态十分重要又多被忽视。以1年生植物荞麦为材料研究了自疏种群地下部分生物量、包括地下部分的个体总生物量以及各构件生物量与密度的关系。结果表明:平均地上生物量和个体总生物量与密度的异速关系指数(γabove-ground和γindividual)分别为-1.293和-1.253,与-4/3无显著性差异(P>0.05),为-4/3自疏法则提供了有力证据;平均根生物量-密度异速指数γroot(-1.128)与-1无显著性差异(P>0.05),与最终产量恒定法则一致;平均茎生物量-密度异速指数γstem(-1.263)接近-4/3(P>0.05),平均叶生物量-密度异速指数γleaf(-1.524)接近-3/2(P>0.05),分别符合-4/3自疏法则与-3/2自疏法则;而繁殖生物量与密度的异速关系指数γreproductive(-2.005)显著小于-3/2、-4/3或-1(P<0.001)。因此,不存在一个对植物不同构件普适的生物量-密度之间的关系。光合产物在地上和地下构件的生物量分配格局以及构件生物量与地上生物量之间特异的异速生长关系导致不同构件具有不同的自疏指数。无论对于地上生物量还是个体总生物量,荞麦种群能量均守衡,而对于地下生物量,荞麦种群能量不守衡。     

Light Fluctuations and Photosynthesis

The effects of fluctuating light on photosynthesis are examined.A simple model of leaf photosynthesis is used so that the analysiscan be presented in explicit terms, the time-dependent problemis solved, and the response of photosynthesis to step changesin light-flux density is calculated. The presence of light fluctuationscan cause a discrepancy between measurements and estimates ofphotosynthesis; the relevant factors are the response time ofthe device used for measuring light-flux density, the responsetime of the photosynthetic system in the leaf, and the steady-statelight response curve with the degree of non-linearity and thevalue of the light-flux density for maximum photosynthesis beingespecially important. Some general methods for estimating practicallythe effects of light fluctuations on photosynthesis are described.The use of the methods of time-series analysis in such problemsis discussed.     

Effect of light interception by non-photosynthetic organs on canopy photosynthetic production

A canopy photosynthesis model was derived on the assumption that the light diminution within a canopy is caused by both leaves and non-photosynthetic organs. The light diminution by leaves and that by non-photosynthetic organs were taken into account separately in the Lambert-Beer equation of light extinction. The light flux density on the leaf surface at each depth was evaluated from the leaf's share of light. The light flux density on the leaf surface thus obtained was incorporated into the Monsi-Saeki model of canopy photosynthesis. The proposed model was applied for estimating gross canopy photosynthesis in a 19-year-oldLarix leptolepis plantation where 38% of the light diminution was due to non-photosynthetic organs. The daily canopy photosynthesis on one summer day calculated using the present model was about 22% less than that calculated by the conventional Monsi-Saeki model, in which light interception by non-photosynthetic organs is neglected. The degree of such reduction in canopy photosynthesis through shading by non-photosynthetic organs was assessed in relation to parameters affecting light extinction, leaf photosynthetic characteristics, and light regime above the canopy.     

The Influence of Carbon Dioxide and Daily Photon-flux Density on Optimal Leaf Nitrogen Concentration and Root: Shoot Ratio

Using a cost-benefit model, the leaf nitrogen concentrationand root : shoot ratio that maximize whole-plant relative growthrate are determined as a function of the above-ground environment(integrated daily photon flux density and the concentrationof carbon dioxide at the site of fixation within the leaf).The major advantage of this approach is that it determines theadaptive significance of leaf physiology by considering thefunctional integration of leaves and roots. The predicted responseto increasing daily photon flux densities is an increase inoptimal leaf N concentration (N_opt) and a concomitant increasein root: shoot ratio. Increased carbon dioxide concentrations,on the other hand, reduce N_opt and only slightly change root:shoot ratio. The observed increase in leaf nitrogen concentrationfound in plants growing at high altitudes (low CO₂ partial pressure)is also predicted. Since these responses to light and CO₂ maximizethe whole-plant relative growth rate, the observed adjustmentsthat plants make to light and carbon dioxide concentration appearto be adaptive. We show that the relationship between photosynthesis and leafnitrogen concentration is complex and depends on the light andCO₂ levels at which photosynthesis is measured. The shape ofthis function is important in determining N_opt and the oppositeresponse of leaf nitrogen to light and carbon dioxide is shownto be the result of the different effects of light and CO₂ onthe photosynthesis-leaf nitrogen curve. Plant growth, photosynthesis, leaf nitrogen, biomass allocation, optimization, carbon dioxide light     

Biomass accumulation and shading effects of epiphytes on leaves of the seagrass, Heterozostera tasmanica, in Victoria,Australia

A method is described for estimating the rate of accumulation of epiphyte biomass on leaves of the seagrass, Heterozostera tasmanica (Martens ex Aschers.) den Hartog and for estimating the effect of epiphyte biomass on photosynthesis of the seagrass. Epiphyte biomass was determined by comparison of the weight per unit area of epiphyte-covered and epiphyte-free leaf blades. Epiphyte weight increased as age of the seagrass leaves increased. Linear regression on epiphyte biomass vs. leaf age estimated the rate of biomass accumulation. Rates varied from 5.7 to 104 μg epiphyte dry weight per cm² of leaf surface per day at three sites in Western Port and Port Phillip Bay, Victoria. Rates of accumulation of epiphyte biomass were generally higher during December through March (summer) than in May (autumn), August (winter) or October (Spring). Light attenuation by epiphytes increase linearly with biomass. The rate of biomass accumulation of epiphytes was compared with leaf growth rate, ambient photon flux density in H. tasmanica beds and the photosynthesis—photon flux density curve of H. tasmanica. This comparison demonstrated that epiphyte biomass can accumulate fast enough to shade H. tasmanica leaves and significantly reduce the time (to less than one half of the leaf life span) in which positive net photosynthesis of the leaf blade is possible.     

Response of Growth Dynamics of Two Spring Geophytes to Light Regime in a Lime-Beech Forest

Blomaee accumulation, leaf longevity and growth rate of two spring forest geophytes, Scllla blfolla L. and Arum maculatum L. were estimated separately for three size groups within each population of these species. Despite the differences in leaf longevity, both species showed a similar pattern of blomass accumulation In relation to their phenologles and reproductive demands. Eco-physlological acclimation to changing light environment was assumed through photosynthetic parameters and dynamics of leaf area Index In the predominant size group of each species. A light response curve was measured under natural light for each species through the continuum of Its phenology to quantify the photosynthetic photon flux density at light saturation, light-saturated photosynthetic rate, light compensation point, and dark respiration. Light-saturated assimilation per leaf area basis, dark respiration rate and light compensation points were significantly higher in S. blfolla relative to A. maculatum. However, the acclimation of photosynthesis that would respond to light changes in environment was not found in S. bifolla. In contrast, In A. maculatum a marked shift In the light dependence of photosynthesis through the season was noticed, which resulted In a strong photosynthetic acclimation to the low-light conditions. Accompanied by significant leaf area Index, this efficient low-light photosynthesis enabled greater leaf longevity, and consequently longer accumulative period to A. maculatum. From the different parameters that we determined （both photosynthetic acclimation and growth strategy） it would appear that these species belong to two distinct subgroups： S. blfolla to the early and A. maculatum to the late vernals.     

A Modified Self-thinning Equation to Describe Size/Density Relationships for Defoliated Swards

Use of the self-thinning rule to describe size/density compensation(SDC) in defoliated swards is examined. It is shown that defoliationrelated variation in leaf area and associated morphogeneticchanges in plant structure necessitate slope corrections, designatedC_a and C_r , respectively. The theory predicts that reduced leafarea in more heavily defoliated swards will result in SDC atslopes more negative than -3/2 (variable leaf area SDC), andthat there will be a transition to -3/2 (constant leaf area)SDC at higher herbage mass. Empirical data from previous experiments with Lolium perenneL. and Medicago sativa L. are examined, and appear to confirmthe theoretical predictions, including the slope change at thepoint of transition from variable to constant leaf area SDC.This transition point, designated d_i , is subject to interspecificvariation and is related to the mature shoot size of a particularspecies. Some applications of this theory are discussed, andin particular a sward productivity index is proposed.Copyright1995, 1999 Academic Press Variable leaf area self-thinning, size/density compensation, Lolium perenne, Medicago sativa, sward productivity index     

Nitrogen use efficiency in instantaneous and daily photosynthesis of leaves in the canopy of a Solidago altissima stand

Photosynthetic capacity was measured on detached leaves sampled in a canopy of Solidago altissima L. Non-rectangular hyperbola fitted the light response curve of photosynthesis and significant correlations were observed between leaf nitrogen per unit area and four parameters which characterize the light-response curve. Using regressions of the parameters on leaf nitrogen, a model of leaf photosynthesis was constructed which gave the relationships between leaf nitrogen, photon flux density (PFD) and photosynthesis. Curvilinear relations were obtained between leaf nitrogen and photosynthetic rate on both an instantaneous and a daily basis. Nitrogen use efficiency (NUE, photosynthesis per unit leaf nitrogen) was calculated against leaf nitrogen under varying PFDs. The optimum nitrogen content per unit leaf area that maximizes NUE shifted to higher values with increasing PFD. Field measurements of PFD showed high positive correlations between the distribution of leaf nitrogen in the canopy and relative PFD. The predicted optimum leaf nitrogen content for each level in the canopy, to achieve maximized NUE during a clear day, was close to the actual nitrogen distribution as found through sampling.     

Theoretical Relationships Between Mean Plant Size, Size Distribution and Self Thinning under One-sided Competition

As yet there is no comprehensive theory in plant populationecology to explain relationships between mean plant size, sizedistribution and self-thinning. In this paper, a new synthesisof plant monocultures is proposed. If the reciprocal relationshipbetween plant biomass and plant population density among variousstands of even-aged plant populations holds, the same reciprocalrelationship must exist between cumulative mass and cumulativenumber of plants from the largest individual within a population,assuming strict one-sided competition (which is an extreme conditionfor competition for light among plants). The two parametersof the relationship between cumulative mass and cumulative numberwithin a stand both correlate with maximum plant height in thestand. One parameter equals the reciprocal of the potentialmaximum plant mass per area, which is expressed by the productof maximum plant height and dry-matter density. The other parametercorrelates with the potential maximum individual plant mass,which is allometrically related to maximum plant height. Asa stand develops, the growth rate of the smallest individualswill become zero due to suppression from larger individuals,and they will die; i.e. self-thinning will occur. The slopeof the self-thinning line is expressed through the coefficientsof allometry between height and mass and between dry matterdensity and height. When the former coefficient is 3 and thelatter is 0, the gradient exactly corresponds to the value expectedfrom the 3/2 power rule, but it can take various values dependingon the values of the two coefficients. Competition among individualsdetermines size-density relationships among stands, which inturn determine the size structure of the stand. The size structureconstrains the growth of individuals and results in self-thinningwithin the stand.Copyright 1999 Annals of Botany Company. Monoculture, plant population, self-thinning, competition, hierarchy, size-structure.     

Stand and self-thinning dynamics in natural <Emphasis Type="Italic">Abies</Emphasis> stands in northern Hokkaido,Japan

Stand dynamics and self-thinning were analyzed in relation to the dynamics of above-ground biomass in natural Abies sachalinensis stands growing on sand dunes in northern Hokkaido, Japan. This was done in order to examine wave-type regeneration in the stands. Fifty-two plots were established in almost pure Abies stands that ranged from saplings to the mature and collapsing growth stages. Above-ground biomass and tree height reached asymptotic levels prior to the collapsing phase, unlike wave-regeneration Abies stands in central Japan and North America. Stand density was high in the young growth stages, but the self-thinning rate, that is, the density decrease per biomass growth in the study stands was greater than in wave-regeneration stands in central Japan, as indicated by a large self-thinning exponent (–1.26 by reduced major axis regression). The range of tree height distribution was very narrow, and the stands vertical structure was typically single-layered. The slenderness ratio of trees was large, except in young stands. In mature and collapsing stands, advanced seedling density increased markedly. These stand and tree characteristics were considered to be correlated with the wave-type regeneration in the study stands, and it is assumed that prevailing winds affect tree mortality.     

Ozone effects on wheat in relation to CO2: modelling short‐term and long‐term responses of leaf photosynthesis and leaf duration

A combined stomatal–photosynthesis model was extended to simulate the effects of ozone exposure on leaf photosynthesis and leaf duration in relation to CO₂. We assume that ozone has a short‐term and a long‐term effect on the Rubisco‐limited rate of photosynthesis, A_c. Elevated CO₂ counteracts ozone damage via stomatal closure. Ozone is detoxified at uptake rates below a threshold value above which A_c decreases linearly with the rate of ozone uptake. Reduction in A_c is transient and depends on leaf age. Leaf duration decreases depending on accumulated ozone uptake. This approach is introduced into the mechanistic crop simulation model AFRCWHEAT2. The derived model, AFRCWHEAT2‐O3, is used to test the capability of these assumptions to explain responses at the plant and crop level. Simulations of short‐term and long‐term responses of leaf photosynthesis, leaf duration and plant and crop growth to ozone exposure in response to CO₂ are analysed and compared with experimental data derived from the literature. The model successfully reproduced published responses of leaf photosynthesis, leaf duration, radiation use efficiency and final biomass of wheat to elevated ozone and CO₂. However, simulations were unsatisfactory for cumulative radiation interception which had some impact on the accuracy of predictions of final biomass. There were responses of leaf‐area index to CO₂ and ozone as a result of effects on tillering which were not accounted for in the present model. We suggest that some model assumptions need to be tested, or analysed further to improve the mechanistic understanding of the combined effects of changes in ozone and CO₂ concentrations on leaf photosynthesis and senescence. We conclude that research is particularly needed to improve the understanding of leaf‐area dynamics in response to ozone exposure and elevated CO₂.     

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     

Density effects and self-thinning in even-aged pure stands ofEucalyptus camaldulensis Dehn

The competition density effect and changes of mean total tree weight (w) and stand density (ρ) during course of self-thinning were examined in even-aged pure stands ofEucalyptus camaldulensis Dehn. which were planted in the tropical monsoon region. The level of competition was controlled by changing the initial stand density from 625 trees ha⁻¹ to 40,000 trees ha⁻¹. Hozumi's model was used to describe thew-ρ trajectory with aging of each stand and thew-ρ relation between stands of different densities at each time. The higher density produced trees of smaller mean tree sizes. The higher the density, the sooner self-thinning began. The growth curve ofE. camaldulensis followed the logistic growth curve where both maximum size and intrinsic growth rate change with time. Mean intrinsic growth rate was maximized at initiation of growth after lag time and then gradually decreased as time progressed. Hozumi's model was considered to be the best model with wide applicability for describing and comparing the growth characteristics during the course of self-thinning among different species, especially in tropical forest plantations, in which many diverse species were used for reforestation.     

Allometry of territory size and metabolic rate as predictors of self-thinning in young-of-the-year Atlantic salmon

1. Self-thinning is a progressive decline in population density caused by competitively induced losses in a cohort of growing individuals and can be depicted as: log₁₀ (density) = c − β log₁₀ (body mass).
2. In mobile animals, two mechanisms for self-thinning have been proposed: (i) the space hypothesis predicts that maximum population density for a given body size is the inverse of territory size, and hence, the self-thinning slope is the negative of the slope of the allometric territory-size relationship; (ii) the energetic equivalence hypothesis predicts that the self-thinning slope is the negative of the slope of the allometric metabolic rate relationship, assuming a constant supply of energy for the cohort.
3. Both hypotheses were tested by monitoring body size, population density, food availability and habitat for young-of-the-year Atlantic salmon ( Salmo salar ) in Catamaran Brook, New Brunswick. The results were consistent with the predictions of the space hypothesis. Observed densities did not exceed the maximum densities predicted and the observed self-thinning slope of −1·16 was not significantly different from the slope of −1·12, predicted by the allometry of territory size for the population under study.
4. The observed self-thinning slope was significantly steeper than −0·87, predicted by the allometry of metabolic rate, perhaps because of a gradual decline in food abundance over the study period. The decline in density was more rapid in very shallow sites and may have been partly caused by a seasonal change in water depth and an ontogenetic habitat shift rather than solely by competition for food or space.
5. The allometry of territory size may be a useful predictor of self-thinning in populations of mobile animals competing for food and space.