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     

Foliage Profile, Size Structure and Stem Diameter-Plant Height Relationship in Crowded Plant Populations

The relationships between vertical foliage profile of an individualplant, competition between individuals, size structure and allocationpattern between stem diameter (D) and plant height (H) wereinvestigated using canopy photosynthesis and two-dimensionalcontinuity equation models including D and H as two independentvariables. Broad-leaved type plants (more foliage mass in theupper layer than in the lower layer of the canopy of an individualwhen grown in isolation) showed curvilinear D-H relationshipand bimodal H distribution, and underwent more asymmetric competitionthan coniferous type plants (more foliage mass in the lowerlayer than in the upper layer of the canopy of an individualwhen grown in isolation) under crowded conditions. Coniferoustype plants showed almost linear D-H relationship (i.e. simpleallometry) and unimodal H distribution, and underwent more symmetriccompetition than broad-leaved type plants under crowded conditions.However, in both the cases D distributions were unimodal. Allocationpatterns between D and H affected these features only a little.These simulation results can explain many actual data alreadypublished. The value of     

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     

A Model for Mortality in a Self-thinning Plant Population

A model for mortality process in a self-thinning plant populationis proposed. It considers the spacial process but does not requirepositional information of each individual plant due to the assumptionsthat plants with interacting neighbours all greater than themselvesare the first to die and neighbours' sizes are mutually independentat each growth stage. Mortality of plants of size x at age t,M(t, x), is given as M(t, x) = m{P(t, x)}ⁿ where P(t, x) isthe proportion of plants of size greater than x at age t, andm and n are parameters. This model fits data from an experimentalplantation of Abies sachalinensis and will be useful for furtherdevelopment of the theoretical study of plant population growth. Abies sachalinensis Fr. Schm., self-thinning, mortality, size distribution, neighbourhood effect, spacial process model     

On the Ordered Development of Plants 2. Self-thinning in Plant Communities

It is shown that the hypothesis that a growing point on a vegetativeplant requires a minimum rate of supply of assimilate to continuegrowth can quantitatively describe self-thinning in communitiesof Trifolium subterraneum. The hypothesis can also be used toexplain the different relationships observed between mean plantweight and plant density when plants are grown in full daylight,70 per cent shade, and transferred between the two light environments.The implications of the hypothesis to self-thinning in naturalplant communities are discussed. Self-thinning, assimilate, plant development     

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     

Effect of Water Deficit on Self-thinning Line in Spring Wheat （Triticum aestivum L.） Populations

Monocultures of spring wheat （Triticum aestivum L.） were grown at overcrowded densities （10 000 and 3 000 plants per m^2） under well-watered and water-stressed conditions to investigate the effects of water deficits on self-thinning. The results showed that density reduction in water-stressed populations was delayed compared with that In well-watered populations. Populations grown In well-watered conditions conformed to the -3/2- power law. Compared with the well-watered condition, there was no significant decrease of the self-thinning line under water-stressed conditions In this experiment, although the rate of average shoot blomass accumulatlon decreased. This result Implied that the exponent of the -3/2-power equation Is not as sensitive as the rate of average shoot blomass accumulation to water stress. Further analysis indicated that, In each density treatment, the lines of the height versus shoot blomass relationships did not differ significantly between the two water conditions. However, the Intercepts of the height versus shoot blomass relationships were greater In the higher-density populations （10 000/m^2） than those In the lower-density populations （3 000/m^2）. These results showed that water deficit did not change plant geometry In this experiment. That Is to say, shoot competition for light remains constant at a given blomass, although root competition for water becomes more serious In water deficit conditions. Based on these results and previous reports we propose that, to affect the thinning line slope, changes In symmetric competition are not as efficient as changes In asymmetric competition.     

An Individual Stand Growth Model for Mean Plant Size Based on the Rule of Self-thinning

A growth model for pure, even-aged stands of plants is asymptoticallybounded above by the self-thinning rule that relates maximumplant size to stand density. The model characterizes accretionin mean size as a deviation from the limiting size. It consistsof a function relating mean size to time and density and a companionsurvival model. The growth model is obtained by substitutingthe survival model for density in the mean size relationship.Model flexibility is demonstrated by fitting it to annual remeasurementsof mean size and number of plants per unit area in a stand ofPinus taeda L. 3/2-power rule, mortality, survival, stand dynamics, plant growth model, loblolly pine     

Growth of Individuals in Plant Populations

Relationships between individual plant weight and net photosynthesisper day (G(t, x) function of plant weight) in plant populationsof various stand structures were simulated based on a canopyphotosynthesis model. The G(t, x) functions of plant weightare determined mainly by LAI (leaf area index), the relationshipbetween individual plant weight and leaf area, canopy structureand extinction coefficient. The concave relationship betweenindividual plant weight and leaf area at small LAI (<2),at small extinction coefficient (< 0.5), or at the canopystructure having the maximum leaf area density at the bottomproduces a concave G(t, x) function, which generates negativeskewness of plant weight. The linear relationship between individualplant weight and leaf area at large LAI (> 2) produces aconvex G(t, x) function, which generates positive skewness ofplant weight. These simulation results coincide with G(t, x)functions obtained experimentally and with the well-known phenomenonof stand dynamics in which skewness of plant weight becomesnegative in the early growth stage and then increases to a positivevalue as a stand grows and becomes crowded. Helianthus annuus L., individual plant size, mean growth rate, canopy photosynthesis model, skewness, stand structure     

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 Distribution of Plant Populations

In studying the distribution of plant species in sample quadratsit may be assumed that the individuals are aggregated into groupsshowing a Poisson distribution, while the number of individualsin each group follows a logarithmic distribution. The resultingcompound distribution of individuals per quadrat is the negativebinomial. Evidence is produced to show that the distributionscalculated on this basis agree with those actually obtainedin the cases examined.     

On the Structure-Bounded Growth Processes in Plant Populations

If growing cells in plants are considered to be composed of increments (ICs) an extended version of the law of mass action can be formulated. It evidences that growth of plants runs optimal if the reaction–entropy term (entropy times the absolute temperature) matches the contact energy of ICs. Since these energies are small, thermal molecular movements facilitate via relaxation the removal of structure disturbances. Stem diameter distributions exhibit extra fluctuations likely to be caused by permanent constraints. Since the signal–response system enables in principle perfect optimization only within finite-sized cell ensembles, plants comprising relatively large cell numbers form a network of size-limited subsystems. The maximal number of these constituents depends both on genetic and environmental factors. Accounting for logistical structure–dynamics interrelations, equations can be formulated to describe the bimodal growth curves of very different plants. The reproduction of the S-bended growth curves verifies that the relaxation modes with a broad structure-controlled distribution freeze successively until finally growth is fully blocked thus bringing about “continuous solidification”.     

植物种群的繁殖对策

植物种群的繁殖对策钟章成（西南师范大学,重庆６３０７１５）ＲｅｐｒｏｄｕｃｔｉｖｅＳｔｒａｔｅｇｉｅｓｏｆＰｌａｎｔＰｏｐｕｌａｔｉｏｎｓ．￥ＺｈｏｎｇＺｈａｎｇｃｈｅｎｇ（ＳｏｕｔｈｗｅｓｔＣｈｉｎａＴｅａｃｈｅｒｓＵ－ｎｉｖｅｒｓｉｔｙ,Ｃｈｏｎ...     

A Test for Non-randomness in Plant Populations

A simple test for non-randomness suitable for use in samplingplant populations is suggested. The criterion used is where n_i is the number of quadrats containing i shoots. A tablegiving significant points of for various values of N, the totalnumber of quadrats, is provided. The test is applied to four sets of experimental data and theresults agree with tests carried out on the complete distributions.It is suggested that this type of criterion could be used inother fields where similar forms of non-randomness also exist.     

Notes on Contagious Distributions in Plant Populations

Past experience has shown that the Poisson series is often inadequateas a model for describing plant populations. Various alternativetwo-parameter models have been suggested in place of the Poissonseries, but they all depend on assumptions which may or maynot hold. In this paper a different approach is put forwardin that attention is concentrated on the mean number of plantsper quadrat and an index of ‘clumping’ or ‘contagiousness’.Examples are given as to the use of these concepts to test fordifferences between the distribution of a plant in two localitiesor between two plants in the same locality.     

Morphological Polyvariance of Ontogeny in Natural Plant Populations

The main patterns of expression of the morphological polyvariance of plants are discussed: diversity of biomorphs, pathways of ontogeny, and disturbances of morphogenesis. The diversity of biomorphs of tap root plants in different ecological conditions has been analyzed in detail. Promising directions of future studies have been formulated.