Effects of positive interactions, size symmetry of competition and abiotic stress on self-thinning in simulated plant populations

Background and Aims

Competition drives self-thinning (density-dependent mortality) in crowded plant populations. Facilitative interactions have been shown to affect many processes in plant populations and communities, but their effects on self-thinning trajectories have not been investigated.

Methods

Using an individual-based ‘zone-of-influence’ model, we studied the potential effects of the size symmetry of competition, abiotic stress and facilitation on self-thinning trajectories in plant monocultures. In the model, abiotic stress reduced the growth of all individuals and facilitation ameliorated the effects of stress on interacting individuals.

Key Results

Abiotic stress made the log biomass – log density relationship during self-thinning steeper, but this effect was reduced by positive interactions among individuals. Size-asymmetric competition also influenced the self-thinning slope.

Conclusions

Although competition drives self-thinning, its course can be affected by abiotic stress, facilitation and competitive symmetry.     

Competitive regulation of plant allometry and a generalized model for the plant self-thinning process

Taking into account the individual growth form (allometry) in a plant population and the effects of intraspecific competition on allometry under the population self-thinning condition, and adopting Ogawa's allometric equation 1/y = 1/axb + 1/c as the expression of complex allometry, the generalized model describing the change mode of r (the self-thinning exponential in the self-thinning equation, log M = K + log N, where M is mean plant mass, K is constant, and N is population density) was constructed. Meanwhile, with reference to the changing process of population density to survival curve type B, the exponential, r, was calculated using the software MATHEMATICA 4.0. The results of the numerical simulation show that (1) the value of the self-thinning exponential, r, is mainly determined by allometric parameters; it is most sensitive to change of b of the three allometric parameters, and a and c take second place; (2) the exponential, r, changes continuously from about -3 to the asymptote -1; the slope of -3/2 is a transient value in the population self-thinning process; (3) it is not a 'law' that the slope of the self-thinning trajectory equals or approaches -3/2, and the long-running dispute in ecological research over whether or not the exponential, r, equals -3/2 is meaningless. So future studies on the plant self-thinning process should focus on investigating how plant neighbor competition affects the phenotypic plasticity of plant individuals, what the relationship between the allometry mode and the self-thinning trajectory of plant population is and, in the light of evolution, how plants have adapted to competition pressure by plastic individual growth.     

The role of belowground competition and plastic biomass allocation in altering plant mass–density relationships

Metabolic scaling theory (MST) predicts a ‘universal scaling law’ for plant mass–density relationships, but empirical observations are more variable. Possible explanations of this variability include plasticity in biomass allocation between the above‐ and belowground compartment and different modes of competition, which can be asymmetric or symmetric. Although complex interactions of these factors are likely to occur, so far the majority of modelling and empirical studies has focussed on mono‐factorial explanations. We here present a generic individual‐based model, which allows exploring the plant mass–density relationship in realistic settings by representing plasticity of biomass allocation and different modes of competition in the above‐ and belowground compartment. Plants grew according to an ontogenetic growth model derived from MST. To evaluate the behavior of the simulated plants related to the allocation patterns and to validate model predictions, we conducted greenhouse experiments with tree seedlings. The model reproduced empirical patterns both at the individual and population level. Without belowground resource limitation, aboveground processes dominated and the slopes of mass–density relationships followed the predictions of MST. In contrast, resource limitation led to an increased allocation of biomass to belowground parts of the plants. The subsequent dominance of symmetric belowground competition caused significantly shallower slopes of the mass–density relationship, even though the growth of individual plants followed MST. We conclude that changes in biomass allocation induced by belowground resource limitation explain the deviations from the mass–density relationship predicted by MST. Taking into account the plasticity of biomass allocation and its linkage to the above‐ and belowground competition is critical for fully representing plant communities, in particular for correctly predicting their response of carbon storage and sequestration to changing environmental conditions.     

How does fertility of the substrate affect intraspecific competition? Evidence and synthesis from self-thinning

When dense populations of even-aged plant monocultures are subject to intense competition, mortality can occur in a process known as self-thinning, in which changes in biomass are accompanied by decreases in density. On a plot of log biomass versus log density, self-thinning populations show a linear relationship called the self-thinning line. Variations in the fertility level of the substrate are known to affect self-thinning in a number of ways. Populations from substrates with different fertility levels have been observed to self-thin along the same line, or along different lines. A review of several experiments using the one species grown at different fertility levels was undertaken to look for any mechanisms that might account for the different patterns observed. It was postulated that the critical difference between whether populations followed a common or different line was the way in which competition developed in the stands as biomass accumulated. For the common-line pattern, data on the canopy volume required to support a given biomass showed that biomass packing did not differ between fertility levels, supporting the model of a common competitive mechanism operating at all fertility levels. When different lines were observed, the development of competition differed as plants increased in size and biomass accumulated at each fertility level. Over the upper range of fertility levels, biomass packing values per plant increased as fertility declined and the position of self-thinning lines followed predictions from biomass packing data. At the low end of the fertility scale, biomass packing values still decreased with fertility level, but the position of self-thinning lines was not linked to the biomass packing of individual plants: root interactions were presumed to dominate competition and the trajectory of self-thinning lines.     

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.     

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.     

The importance of conspecific facilitation during recruitment and regeneration: A case study in degraded mangroves

Facilitation can affect positively the survival, growth and fitness of neighboring plants and is able to promote the establishment of plant species under harsh environmental conditions. This study is one of the few to focus on conspecific nurse plants enabling the establishment of tree followers and the generally unknown interplay between facilitation and competition during recruitment and establishment.Field studies were conducted in an hypersaline area in north Brazil where the hydrological regime was disturbed by road construction in 1974. Avicennia germinans shrubs were able to recolonize subareas.Three different stages of re-colonization were identified by satellite imagery based on the vegetation coverage and were defined as the early, middle, and late stages. Different plant parameters, including height and crown radius of individual trees, were measured, and all plants separating mangrove seedlings and larger plants were stem-mapped.The Hegyi index was adapted to measure local interaction intensity, considering both positive (facilitation) and negative (competition) interactions among neighboring plants. Spatial point pattern analyses were combined with the interaction index to obtain a better overview of the strength and importance of the plant interactions within the different recolonizing stages.The spatial patterns displayed aggregation for all plants in all developmental stages. This is supported by the interaction index calculated for seedlings. The index, however, provides an early signal for the switching of plant interactions from facilitation to competition as the developmental stage increased. This feature remains undetected in the spatial patterns because self-thinning processes are linked to individual growth processes and require more time to take place.This study broadens the ecological concept of nurse plants from hetero- to conspecific, including the importance and strength of plant interactions. The studied degraded areas are recolonizing naturally, and conclusions can be drawn for restoration projects, which usually do not take facilitation effects into account.     

Density-dependence in single-species populations of plants

The general form of yield-density relationships in plant populations is discussed with reference to reciprocal equations and the $\text{3}\text{2}$ power law, which describes the concomitant changes in plant weight and density during self-thinning. A model to describe the pattern of mortality in high density populations is also discussed with particular reference to the nature of intraspecific competition within plant populations.A reparameterized version of a reciprocal equation proposed by Bleasdale & Nelder is used to describe the relationship between individual plant weight and surviving plant density. The biological interpretation of the parameters is discussed in relation to the dry matter production of isolated plants, the density at which mutual interference between neighbours becomes appreciable, and the efficiency of resource utilization at high densities.The reparameterized equation is then used together with an equation which describes mortality during self-thinning as the basis for a new model to describe the relation between total plant yield and sowing density. The law of allometry is used in conjunction with the model to describe the relationship between the weight of a plant part and density, and this then forms the basis for a model of the population dynamics of annual plants with effectively discrete generations. Finally the dynamical behaviour of plant populations is discussed. It is concluded that most plant populations will show neighbourhood stability with exponential or perhaps oscillatory damping towards an equilibrium.     

A model of physiological and allometric factors in the self-thinning curve

A generalized self-thinning curve for plants is derived from the modified Von Bertallanfy equation. When an asymptotic relation between photosynthesis per unit of leaf area and stocking density is assumed, the self-thinning curve thus derived is also asymptotic on a log-log scale but is fitted quite well by a log-linear approximation. The model predicts that the slope of the log-linear approximation is a function of (a) photosynthetic response to density and (b) the relation between leaf area and total aboveground biomass. Intercept of the log-linear approximation is a function of these plus maximum attainable biomass, site productivity, density at which maximum photosynthesis is attained, and the nature of carbon loss within the plant community. Linkages between various parameters within the model act to reduce differences in slope and intercept for species with different life history's and physiological requirements.     

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

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

Positive interactions can increase size inequality in plant populations

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

Ecological and mathematical considerations on self-thinning in even-aged pure stands

It is emphasized in growth analysis of self-thinning populations that relative mortality rate pertains to the difference between relative growth rates and net assimilation rates, each of which are definable on a mean plant size basis or on a biomass basis. The time trends of the ratio of relative mortality rate to relative growth rates to be expected according to Tadaki's, Shinozaki's and Hozumi's models are compared with that of the eastern white pine population, and a good agreement is exhibited. As an alternative to Hozumi's model, a new model is constructed to unite the logistic theory of plant growth and the 3/2 power law concerning self-thinning, which so far have usually been applied independently to growth analysis. To construct the model the following assumptions are made: the fundamental equation to relate mean plant weight with density in self-thinning population proposed by Shinozaki, and a special population with a specific initial density which follows thew-p trajectory of the 3/2 power law type and has an exponential decrease in its density with biological time. Properties of the model are examined from ecological and mathematical viewpoints.     

Emergent properties of plants competing in silico for space and light: Seeing the tree from the forest

A spatially explicit, reiterative algorithm (SERA) is presented and used to predict multiple aspects of plant population and community dynamics. Using simple physical principles and empirically derived relationships, SERA provides an analytical venue to test alternative hypotheses about individual functional traits governing ecological or evolutionary processes at the population or community level of complexity. Our analyses show that, as a result of competition for light and space, individual-level features scale up to produce species ensemble properties such as the scaling of self-thinning, size-dependent mortality, realistic size-frequency distributions, and a broad spectrum of empirically observed relationships for the species examined. SERA also predicts the competitive exclusion of conifers by angiosperms and the age at which reproductive maturity is achieved by different species. SERA serves as a null hypothesis by demonstrating that biologically complex phenomena, including widely observed scaling relationships at the species-ensemble level, can emerge from the operation of simple and transparent "rules" governing competition for space and light.     

The effects of salt stress and arbuscular mycorrhiza on plant neighbour effects and self-thinning

Abiotic and biotic factors can alter the nature and strength of plant–plant interactions and therefore self-thinning (density-dependent mortality), but few studies have looked at how such factors interact. We investigated how salt stress and arbuscular mycorrhizal fungi (AMF) influence plant neighbour effects and self-thinning in experimental populations of Medicago sativa. We obtained two mycorrhizal levels by applying the fungicide benomyl (low AMF) or not (high AMF) at three salinity levels (0.05%, 0.2% and 0.5%). In experiment 1, we investigated how salinity and AMF interact to influence plant interaction intensity using a neighbour removal treatment. In experiment 2, we investigated how self-thinning dynamics vary under salinity conditions and different AMF levels at two initial plant densities (6000 and 17,500 seeds m^?2). Shoot biomass and plant density were measured 30, 60 and 90 days after sowing. Standardized major axis regression was used to estimate self-thinning parameters. In experiment 1, AMF increased competitive plant neighbour effects when there was no salinity stress, but this enhancement was not significant with increasing salinity. In experiment 2, there were effects of salinity and AMF on the self-thinning trajectory. The slope of the log (mean shoot biomass per unit area) vs. log density relationship was significantly steeper for the high AMF treatment than for the low AMF treatment without salinity, but the effect of AMF level on the self-thinning exponent was not significant under the two higher salinity levels. The effect of AMF treatments on the intercept of the self-thinning line was not significant at 0.2% salinity but was significant at 0.5% salinity, higher elevation for high AMF treatment. In self-thinning populations, AMF decreased the survival rate without salinity, but increased the survival rate at the highest salinity level. Our results support the hypothesis that salinity and AMF interact to influence plant neighbour effects and self-thinning. Under no-salinity conditions, AMF increased competition, steepened the self-thinning line and decreased survival rate, but these effects of AMF were not significant in the presence of salinity.     

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     

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.     

The ecological effect of phenotypic plasticity — Analyzing complex interaction networks (COIN) with agent-based models

Analyzing complex dynamics of ecological systems is complicated by two important facts: First, phenotypic plasticity allows individual organisms to adapt their reaction norms in terms of morphology, anatomy, physiology and behavior to changing local environmental conditions and trophic relationships. Secondly, individual reactions and ecological dynamics are often determined by indirect interactions through reaction chains and networks involving feedback processes.

We present an agent-based modeling framework which allows to represent and analyze ecological systems that include phenotypic changes in individual performances and indirect interactions within heterogeneous and temporal changing environments. We denote this structure of interacting components as COmplex Interaction Network (COIN).

Three examples illustrate the potential of the system to analyze complex ecological processes that incorporate changing phenotypes on the individual level:

• A model on fish population dynamics of roach (Rutilus rutilus) leads to a differentiation in fish length resulting in a conspicuous distribution that influences reproduction capability and thus indirectly the fitness.

• Modeling the reproduction phase of the passerine bird Erithacus rubecula (European Robin) illustrates variation in the behavior of higher organisms in dependence of environmental factors. Changes in reproduction success and in the proportion of different activities are the results.

• The morphological reaction of plants to changes in fundamental environmental parameters is illustrated by the black alder (Alnus glutinosa) model. Specification of physiological processes and the interaction structure on the level of modules allow to represent the reaction to changes in irradiance and temperature accurately.

Applying the COIN-approach, individual plasticity emerges as a structural and functional implication in a self-organized manner. The examples illustrate the potential to integrate existing approaches to represent detailed and complex traits for higher order organisms and to combine ecological and evolutionary aspects.

Shedding light on plant competition: modelling the influence of plant morphology on light capture (and vice versa)

A plant's morphology is both strongly influenced by local light availability and, simultaneously, strongly influences this local light availability. This reciprocal relationship is complex, but lies at the heart of understanding plant growth and competition. Here, we develop a sub-individual-based simulation model, cast at the level of interacting plant components. The model explicitly simulates growth, development and competition for light at the level of leaves, branches, etc., located in 3D space. In this way, we are able to explore the manner in which the low-level processes governing plant growth and development give rise to individual-, cohort-, and community-level phenomena. In particular, we show that individual-level trade-offs between growing up and growing out arise naturally in the model, and robustly give rise to cohort-level phenomena such as self-thinning, and community processes such as the effect of ecological disturbance on the maintenance of biodiversity. We conclude with a note on our methodology and how to interpret the results of simulation models such as this one.     

Ecological consequences of phenotypic plasticity

Phenotypic plasticity is widespread in nature, and often involves ecologically relevant behavioral, physiological, morphological and life-historical traits. As a result, plasticity alters numerous interactions between organisms and their abiotic and biotic environments. Although much work on plasticity has focused on its patterns of expression and evolution, researchers are increasingly interested in understanding how plasticity can affect ecological patterns and processes at various levels. Here, we highlight an expanding body of work that examines how plasticity can affect all levels of ecological organization through effects on demographic parameters, direct and indirect species interactions, such as competition, predation, and coexistence, and ultimately carbon and nutrient cycles.