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.     

Effect of Localized Placement of Nutrients on Root Competition in Self-thinning Populations

The hypothesis that increased root competition can lower theslope and/or intercept of the self-thinning line traversed byplant populations was tested using localized placement of nutrientsto increase root competition. Localized placement of nutrientswill result in increased root competition, if average inter-rootdistances are reduced, and if nutrients are in limiting supply.It was predicted that high-density, nutrient-limited populationsof Ocimum basilicum L. grown with localized placement of nutrientswould self-thin along a lower biomass–density line thannon-localized controls. This was tested at two fertility levelson a soil-based potting medium in expt 1, and at one fertilitylevel on washed sand in expt 2. Localized placement of nutrients significantly reduced the elevation(intercept) of the self-thinning line for both shoot and rootbiomass in expt 2. In expt 1, at the higher-fertility level,localized placement of nutrients had no significant effect;at the lower fertility level, localization had no significanteffect on thinning lines for shoot biomass, and resulted ina zero slope of the thinning line for root biomass. Canopy-based models of self-thinning failed to account for thereduction in the thinning-line intercept observed in expt 2.In both experiments, localized placement of nutrients resultedin a higher proportion of total root length being located inthe localization zone, which would result in a reduction inthe average inter-root distance. This would intensify root competitionunder conditions of nutrient limitation. The hypothesis thatintensified root competition would lower the self-thinning lineis supported by the results of expt 2. Localized placement of nutrients; root competition; shoot competition; root–shoot allocation; self-thinning; Ocimum basilicum ; sweet basil     

Relationship between the virtual dynamic thinning line and the self-thinning boundary line in simulated plant populations

The self-thinning rule defines a straight upper boundary line on log-log scales for all possible combinations of mean individual biomass and density in plant populations. Recently, the traditional slope of the upper boundary line, -3/2, has been challenged by -4/3 which is deduced from some new mechanical theories, like the metabolic theory. More experimental or field studies should be carried out to identify the more accurate self-thinning exponent. But it＇s hard to obtain the accurate self-thinning exponent by fitting to data points directly because of the intrinsic problem of subjectivity in data selection. The virtual dynamic thinning line is derived from the competition-density （C-D） effect as the initial density tends to be positive infinity, avoiding the data selection process. The purpose of this study was to study the relationship between the virtual dynamic thinning line and the upper boundary line in simulated plant stands. Our research showed that the upper boundary line and the virtual dynamic thinning line were both straight lines on log-log scales. The slopes were almost the same value with only a very little difference of 0.059, and the intercept of the upper boundary line was a little larger than that of the virtual dynamic thinning line. As initial size and spatial distribution patterns became more uniform, the virtual dynamic thinning line was more similar to the upper boundary line. This implies that, given appropriate parameters, the virtual dynamic thinning line may be used as the upper boundary line in simulated plant stands.     

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     

A Mechanistic Analysis of Self-thinning in Terms of the Carbon Balance of Trees

The self-thinning behavior of a monoculture forest is examinedfrom a mechanistic viewpoint, in terms of the carbon balanceof trees at the stand level. Two approaches are described: thefirst is based on simple assumptions concerning the balancebetween growth, photosynthesis and respiration; the second usesthe process-based I.T.E. EDINBURGH FOREST model, extended toinclude tree birth and death, to examined the assumptions ofthe first approach at a more mechanistic level and to interpretthe observed variation in the responses to shading and soilfertility in terms of a single model. The first approach leads to a power law relation m n ^-1/y betweenmean biomass per tree (m) and the number of trees per unit groundarea (n), where y is the exponent characterising the rate atwhich respiration (r) scales with biomass (i.e. r m^y). Forvalues of y less than 1, m and n are predicted to increase anddecrease, respectively, as powers of time (t) such that thebiomass per unit ground area (M) increases linearly with t forany value of y. When y equals 1, m and n vary exponentiallywith t and M remains constant. When r is assumed to be proportional to stem cambium surfacearea, the value of y is shown to lie in the range 0·5to 1 depending on the rate of stem taper. This leads to slopeson a log m vs. log n self-thinning plot in range -1 to -2 andtypically around -1·5 for rates of taper based on mechanicalrequirements. For the second approach, the I.T.E. EDINBURGH FOREST model,a previously published mechanistic model of plantation growthat the stand level (Thornley, 1991), is extended to naturalstands by introducing average stem birth and death rates thatare functions of the carbon and nitrogen substrate status oftrees. Growth of even-aged and mixed-age forest over about 500years is simulated under a variety of environmental and physiologicalconditions. In general, the forest model predicts a curved log m vs. logn thinning line, but has a reasonably well-defined linear sectionunder most conditions. The slope of the linear portion flattensas the rate at which cambium surface area scales with structuralbiomass increases, in qualitative agreement with the analyticalprediction of the first approach. Quantitative differences betweenthe two approaches are interpreted in terms of the process representedin the forest model. In general, the height of the thinningline increases with irradiance, but is relatively insensitiveto soil nitrogen, with no change in slope in either case. However,at very low irradiance or soil nitrogen levels, the slope flattenscontinuously and the entire thinning line becomes markedly non-linear.Even-aged stands and mixed-age stands have different thinningslopes.Copyright 1993, 1999 Academic Press Self-thinning, carbon balance, mechanistic model, forest growth, respiration     

Intraspecific Competition in a Natural Stand of Betula ermanii

Density and size of naturally regenerated Betula ermanii weremonitored for six years in a 100 m² plot located in Hokkaido,northern Japan. Natural thinning of 10- to 15-year-old treesoccurred at a negative exponential rate related to tree volume,demonstrating the –3/2 power rule of self-thinning. Diameterdistributions were unimodal at ages 10–13 years and bimodalat 14 and 15 years. Changes in diameter distribution were accompaniedby changes in structure, from a one- to two-storied stand. Mortalitywas highest among smaller trees and where density was greatest.The spatial distribution of trees changed from random to uniformwith increased stand age. Betula ermanii Cham., Self-thinning, mortality, spatial distribution, size distribution     

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.     

Response of Self-thinning to Artificially Reduced Levels of Leaf Area in Monocultures of Trifolium pratense

Greenhouse grown monocultures of Trifolium pratense L, werepartially defoliated to test the hypothesis that the constantof proportionality (K) in the self-thinning rule is a functionof leaf area. This constant equates mean weight (w) and density(p) in self-thinning populations by the equation Pruning leaflets did not affect the pattern or occurrence ofdensity-related mortality but, as predicted, did affect K, whichwas reduced by 25 per cent as leaf area was decreased from anaverage of 7.3 to 3.9 m²m^–2. For both self-thinning andnon-self-thinning populations, leaf area was substituted forK in eqn (1) to give Multiple linear regression showed that this expression was significantfor all three defoliation treatments. Regressions with treedata grouped by genera were also significant and indicate thateqn (2) may be a more general expression of the relation betweenmean weight and density in even-aged monocultures. The self-thinningrule may be a special case of eqn (2) which expresses itselfwhen leaf area attains some upper limit. Trifolium pratense, red clover, leaf area, self-thinning, defoliation     

The effect of clipping on self-thinning in Trifolium pratense

The self-thinning rule describes mortality in a crowded even-aged stand as a function only of biomass accumulation. We tested this prediction by stopping biomass accumulation with clipping treatments in Trifolium pratense. Moderate levels of clipping slowed thinning mortality considerably, but did not stop it entirely.     

The difference between above- and below-ground self-thinning lines in forest communities

Quantifying the self-thinning process in various plant communities has been a long-standing issue in both theoretical and empirical studies. Most studies on plant self-thinning have centered only on aboveground parts, and rarely on belowground parts. There is still a general lack of comparison between above- and belowground self-thinning processes, especially for forest communities. The fundamental mechanistic difference and the functional association between above- and belowground competition indicate that the self-thinning process of belowground parts may be different from that of aboveground parts. We investigated the self-thinning lines for above-ground (M _A), below-ground (M _B), and total biomass (M _T), respectively, across forest communities in China. The results showed that neither the classical self-thinning rule (−3/2 exponent) nor the universal scaling rule (−4/3 exponent) can apply to all the self-thinning relationships across these forest communities and that the self-thinning lines for belowground biomass were flatter and lower than those for aboveground biomass across most of these forest communities.     

Three Interpretations of the Self-thinning Rule

The self-thinning rule states that w, the mean biomass per plantin a dense monospecific stand, is related to p, the number ofplants in a unit area of that stand, by the power law relationshipw = Kp^–, where is approximately three-halves. The supportfor this rule, theoretical as well as experimental, has thusfar been largely empirical. In an effort to provide a firmertheoretical basis for it, three different and somewhat independenttheoretical models are propounded and shown to lead to powerlaw relationships with characteristic exponents in the vicinityof three-halves. theoretical models, mathematical model, three-halves law, density-effect, self-thinning     

The Nitrogen Content of Plants and the Self-thinning Rule of Plant Ecology: A Test of the Core-skin Hypothesis

The ‘core-skin’ hypothesis postulates that secondarilythickened plants behave energetically as an inert ‘core’covered by an active ‘skin’, the ‘skin’being two-imensional, the ‘core’ three-dimensional.This would explain the ‘self-thinning ‘or‘–3/2’ rule of plant ecology, that is, the tendencyfor log (dry weight per plant) and log (number of plants perunit area) to progress along a straight line relationship, withslope = – 3/2’. The hypothesis was tested as follows. Plant nitrogen contentwas used as an estimate of the mass of ‘skin’ perplant, and dry weight as an estimate of the mass of the ‘core’.As plants mature the slope of the relationship between y = log(mass of nitrogen per plant) and x = log (mass of dry matterper plant) is expected to decline from an initial value of 1.0towards a final value of 0.66. The intercept of the relationshipis expected to reflect the intrinsic content of ‘skin’per unit of ‘core’. Genotypic variation in thisparameter should cause genotypic differences in the maximumattainable yield of biomass per unit area. The expectations were investigated by fitting the function y= p+qx+r exp – x to 30 sets of data on plant nitrogencontent, plant weight and time in 18 different vegetables. Simplelinear regressions of y on x were fitted to more limited setsof data on weights and nitrogen contents of mature trees. Theexpectations were, with some minor exceptions, confirmed. Nitrogen, yield, plant competition, 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.     

Yield-density Relationships: the Influence of Resource Availability on Growth and Self-thinning in Populations of Vulpia fasciculata

Monocultures of Vulpia fasciculata were grown over a wide rangeof densities to investigate the influence of crowding and nutrientsupply on growth and self-thinning. For a given time and densityseries the relationship between mean yield per plant (w) andthe density of survivors (N) could be described by the equation w= w_m (1+aN)^–b. where w_m is the yield of an isolated plant, a is the area requiredto achieve a yield of w_m and b describes the effectiveness withwhich resources are taken up from the area. All three parametersincreased with time. Adding nutrients changed not only the rate at which the effectsof crowding occurred but also the intensity of crowding since w_m = C(a^b)^D. where C and D are constants. The addition of nutrients resultedin an increase in the value of C. Such an increase means thata larger weight can be supported by a given area because theresources within that area are greater. During the early phases of growth, populations of V. fasciculataconformed to the –3/2 power law, w = cN^–3/2, butonly at very high densities with a plentiful supply of nutrients.However, once the maximum standing crop had been reached thetrajectory of the thinning line switched to a slope of justless than –1 when weight was ploted against density onlogarithmic scales. The intercept of the –3/2 thinningline was considerably higher (log c = 5.74) than those for mosttrees and forbs but was similar to those of a number of othergrasses. Vulpia fasciculata, dune fescue, yield-density models, self-thinning, density-dependence, nutrient supply     

Modelling the Time Course of Self-thinning in Crowded Plant Populations

A logarithmic model for the self-thinning of plants is proposed.This model describes the time course of self-thinning very welland fits data from forest stands and yield tables, which followthe 3/2 power law. An approximated expression of this modelshows that plant density decreases with age along a Gompertzcurve. This appears to be a basic property of the time courseof self-thinning in plants. Pinus strobus L., Pinus densiflora Sieb, et Zucc., stand development, self-thinning, 3/2 power law, logarithmic model, mortality     

Survivorship,growth and self-thinning in Banksia ericifolia

High-density (dense) and low-density (sparse) plots were set up in naturally sown monospecific stands of Banksia ericifolia in coastal heath, 3 years after fire. This was done both in high-growth and low-growth areas. Plant mortality was recorded quarterly, and two harvests were made at 6 and 9 years to sample growth. Density-independent mortality at an exponential rate was observed in the low-growth treatments at both densities, and in the high-growth sparse treatment. Growth level affected mortality, with the half-life of populations in the high-growth sparse plots being double that of populations in the low-growth plots. Density-dependent mortality (self-thinning) was seen only in the high-growth dense plots. Seasonal effects on mortality were slight; maximum mortality was observed in the spring-summer period in plots subject to density-independent mortality, and in the winter-spring quarter in plots that had self-thinned. Yields in the high-growth plots and the low-growth dense plots were high for heath vegetation. The self-thinning populations did not exceed White's (1985) upper boundary for thinning lines of log intercept (K) = 5 on standardized axes. The data suggested a log intercept value in the range 4.8–4.9 in the high-growth stands assuming a thinning-line slope of – 1.5. Banksia ericifolia (a large shrub/small tree) has a high mean plant weight per given thinning density compared with trees, where an upper limit of log K= .4 has been suggested by White (1985). The volume of canopy space per plant in B. ericifolia is not unusual compared with other species. The amount of biomass packed into a given volume of canopy space was high in this Banksia, achieved by having leaves with a low ratio of area to weight (specific leaf area, SLA). For given values of density, leaf area index and proportion of shoot as leaf, plants with a low SLA will be several times heavier than plants with a high SLA. This achieves a high biomass to volume ratio without an erectophile canopy and may explain the high intercept seen for thinning lines of conifers.     

Arbuscular mycorrhizal fungi alter plant allometry and biomass-density relationships

Background and Aims

Plant biomass–density relationships during self-thinning are determined mainly by allometry. Both allometry and biomass–density relationship have been shown to vary with abiotic conditions, but the effects of biotic interactions have not been investigated. Arbuscular mycorrhizal fungi (AMF) can promote plant growth and affect plant form. Here experiments were carried out to test whether AMF affect plant allometry and the self-thinning trajectory.

Methods

Two experiments were conducted on Medicago sativa L., a leguminous species known to be highly dependent on mycorrhiza. Two mycorrhizal levels were obtained by applying benomyl (low AMF) or not (high AMF). Experiment 1 investigated the effects of AMF on plant growth in the absence of competition. Experiment 2 was a factorial design with two mycorrhizal levels and two plant densities (6000 and 17 500 seeds m⁻²). Shoot biomass, root biomass and canopy radius were measured 30, 60, 90 and 120 d after sowing. The allometric relationships among these aspects of size were estimated by standardized major axis regression on log-transformed data.

Key Results

Shoot biomass in the absence of competition was lower under low AMF treatment. In self-thinning populations, the slope of the log (mean shoot biomass) vs. log density relationship was significantly steeper for the high AMF treatment (slope = –1·480) than for the low AMF treatment (–1·133). The canopy radius–biomass allometric exponents were not significantly affected by AMF level, but the root–shoot allometric exponent was higher in the low AMF treatment. With a high level of AMF, the biomass–density exponent can be predicted from the above-ground allometric model of self-thinning, while this was not the case when AMF were reduced by fungicide.

Conclusions

AMF affected the importance of below-ground relative to above-ground interactions and changed root vs. shoot allocation. This changed allometric allocation of biomass and altered the self-thinning trajectory.     

Mortality and Self-thinning in Postfire Black Spruce

Using age-structure determinations on both living and dead stemsin censused plots, coupled with stem analysis techniques, anhistorical picture of mortality and above-ground tree stem growthwas recreated for ten stands dominated by black spruce in northeasternOntario, Canada. No evidence of mortality was seen in any plot prior to 30 yearsfollowing postfire initiation. Each of the eight oldest standsshowed a linear decline in numbers for a 20–25 year period.The steepness of the mortality slope was proportional to initiallive stem density within and among plots during this phase.The final 10–20 years was marked by a less steep declinein numbers. The log density vs log mean tree volume curves in the eightoldest stands were doubly asymptotic and were fitted to a logisticcurve very tightly in each case. At the point of inflectionthe curves' slopes ranged from –2.14 to –3.89. However,log density vs log mean stem volume among stands at this pointof inflection had a slope of –0.96. Reasons for the inconsistency between within-stand and among-standself-thinning estimates are considered, as well as the poorfit to the –3/2 rule. Ecosystem processes related to thechange in nutrient relations during stand growth are identifiedas a prime influence on self-thinning behaviour in natural blackspruce stands. Mortality, stem analysis, self-thinning, Picea mariana, black spruce     

The allometric interpretation of the self-thinning rule

Plant populations growing at high densities undergo density-dependent mortality or self-thinning. The density of survivors ({ρ}) is related to their mean biomass (w) by the power equation w = K_ρ^?a, where a is $\text{3}\text{2}$. This is known as the “self-thinning rule”. This relationship is very general for plant populations and represents both an asymptotic time-trajectory for a particular population and a boundary line for juxtaposed joint values of w and p of separate populations. The traditional allometric derivation of the rule is outlined and shown to be unrealistic. An attempt to reformulate the self-thinning rule, based on the traditional allometric derivation, is shown to be unsatisfactory and an alternative allometric derivation is presented. The rule in its traditional statement $\text{w = K}{}_{\mathrm{\rho }}{}^{\mathrm{?3}}\text{2}$ is still its best expression. The nature of the constant K is discussed with particular reference to its dimensionality.