Kolmogorov-type competition model with finitely supported allocation profiles and its applications to plant competition for sunlight

A Kolmogorov-type competition model featuring allocation profiles, gain functions, and cost parameters is examined. For plant species that compete for sunlight according to the canopy partitioning model [R.R. Vance and A.L. Nevai, Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning, J. Theor. Biol. 245 (2007), pp. 210–219] the allocation profiles describe vertical leaf placement, the gain functions represent rates of leaf photosynthesis at different heights, and the cost parameters signify the energetic expense of maintaining tall stems necessary for gaining a competitive advantage in the light gradient. The allocation profiles studied here, being supported on three alternating intervals, determine “interior” and “exterior” species. When the allocation profile of the interior species is a delta function (a big leaf) then either competitive exclusion or coexistence at a single globally attracting equilibrium point occurs. However, if the allocation profile of the interior species is piecewise continuous or a weighted sum of delta functions (multiple big leaves) then multiple coexistence states may also occur.     

Kolmogorov-type competition model with finitely supported allocation profiles and its applications to plant competition for sunlight

A Kolmogorov-type competition model featuring allocation profiles, gain functions, and cost parameters is examined. For plant species that compete for sunlight according to the canopy partitioning model [R.R. Vance and A.L. Nevai, Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning, J. Theor. Biol. 245 (2007), pp. 210-219] the allocation profiles describe vertical leaf placement, the gain functions represent rates of leaf photosynthesis at different heights, and the cost parameters signify the energetic expense of maintaining tall stems necessary for gaining a competitive advantage in the light gradient. The allocation profiles studied here, being supported on three alternating intervals, determine "interior" and "exterior" species. When the allocation profile of the interior species is a delta function (a big leaf) then either competitive exclusion or coexistence at a single globally attracting equilibrium point occurs. However, if the allocation profile of the interior species is piecewise continuous or a weighted sum of delta functions (multiple big leaves) then multiple coexistence states may also occur.     

Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning

Can a difference in the heights at which plants place their leaves, a pattern we call canopy partitioning, make it possible for two competing plant species to coexist? To find out, we examine a model of clonal plants living in a nonseasonal environment that relates the dynamical behavior and competitive abilities of plant populations to the structural and functional features of the plants that form them. This examination emphasizes whole plant performance in the vertical light gradient caused by self-shading. This first of three related papers formulates a prototype single species Canopy Structure Model from biological first principles and shows how all plant properties work together to determine population persistence and equilibrium abundance. Population persistence is favored, and equilibrium abundance is increased, by high irradiance, high maximum photosynthesis rate, rapid saturation of the photosynthetic response to increased irradiance, low tissue respiration rate, small amounts of stem and root tissue necessary to support the needs of leaves, and low density of leaf, stem, and root tissues. In particular, equilibrium abundance decreases as mean leaf height increases because of the increased cost of manufacturing and maintaining stem tissue. All conclusions arise from this formulation by straightforward analysis. The argument concludes by stating this formulation's straightforward extension, called a Canopy Partitioning Model, to two competing species.     

An expanded modern coexistence theory for empirical applications

Understanding long‐term coexistence of numerous competing species is a longstanding challenge in ecology. Progress requires determining which processes and species differences are most important for coexistence when multiple processes operate and species differ in many ways. Modern coexistence theory (MCT), formalised by Chesson, holds out the promise of doing that, but empirical applications remain scarce. We argue that MCT's mathematical complexity and subtlety have obscured the simplicity and power of its underlying ideas and hindered applications. We present a general computational approach that extends our previous solution for the storage effect to all of standard MCT's spatial and temporal coexistence mechanisms, and also process‐defined mechanisms amenable to direct study such as resource partitioning, indirect competition, and life history trade‐offs. The main components are a method to partition population growth rates into contributions from different mechanisms and their interactions, and numerical calculations in which some mechanisms are removed and others retained. We illustrate how our approach handles features that have not been analysed in the standard framework through several case studies: competing diatom species under fluctuating temperature, plant–soil feedbacks in grasslands, facilitation in a beach grass community, and niche differences with independent effects on recruitment, survival and growth in sagebrush steppe.     

Signs of stabilisation and stable coexistence

Many empirical studies motivated by an interest in stable coexistence have quantified negative density dependence, negative frequency dependence, or negative plant–soil feedback, but the links between these empirical results and ecological theory are not straightforward. Here, we relate these analyses to theoretical conditions for stabilisation and stable coexistence in classical competition models. By stabilisation, we mean an excess of intraspecific competition relative to interspecific competition that inherently slows or even prevents competitive exclusion. We show that most, though not all, tests demonstrating negative density dependence, negative frequency dependence, and negative plant–soil feedback constitute sufficient conditions for stabilisation of two‐species interactions if applied to data for per capita population growth rates of pairs of species, but none are necessary or sufficient conditions for stable coexistence of two species. Potential inferences are even more limited when communities involve more than two species, and when performance is measured at a single life stage or vital rate. We then discuss two approaches that enable stronger tests for stable coexistence‐invasibility experiments and model parameterisation. The model parameterisation approach can be applied to typical density‐dependence, frequency‐dependence, and plant–soil feedback data sets, and generally enables better links with mechanisms and greater insights, as demonstrated by recent studies.     

Light partitioning in experimental grass communities

Through complementary use of canopy space in mixtures, aboveground niche separation has the potential to promote species coexistence and increase productivity of mixtures as compared to monocultures. We set up an experiment with five perennial grass species which differed in height and their ability to compete for light to test whether plants partition light under conditions where it is a limiting resource, and if this resource partitioning leads to increased biomass production in mixtures (using relative yield-based methods). Further, we present the first application of a new model of light competition in plant communities. We show that under conditions where biomass production was high and light a limiting resource, only a minority of mixtures outperformed monocultures and overyielding was slight. The observed overyielding could not be explained by species differences in canopy structure and height in monoculture and was also not related to changes in the canopy traits of species when grown in mixture rather than monoculture. However, where overyielding occurred, it was associated with higher biomass density and light interception. In the new model of competition for light, greater light use complementarity was related to increased total energy absorption. Future work should address whether greater canopy space-filling is a cause or consequence of overyielding.     

Canopy ergodicity: can a single leaf represent an entire plant canopy?

While leaves typically emerge near shoot apices around the outer surface of a plant canopy, their relative position “moves” deeper into the canopy as additional leaves emerge. The photosynthetic capacity (A _max) of a given leaf can be expected to decline over time as its relative position (P _r) in the canopy becomes progressively deeper; this can be observed as a spatial gradient with the A _max of leaves declining distally from the shoot apex. As a consequence, we propose that the photosynthetic capacity averaged over a single leaf’s lifespan is equivalent to the average photosynthetic capacity of the entire plant canopy at a given time; in other words, there is an ergodic time to space averaging in the organization and development of plant canopies. We tested this “canopy ergodic hypothesis” in two woody (Alnus sieboldiana and Mallotus japonica) and two herbaceous (Polygonum sachalinensis and Helianthus tuberosus) species by following the photosynthetic capacity in 100 individual leaves from the time of their emergence until their death. We compared the average photosynthetic capacity of individual leaves through time (time-average) to the average photosynthetic capacity of all the leaves along a shoot at the time of emergence of the focal leaf (space-average). We found that A _max and P _r were positively correlated and that the time-averages of three plant species (Alnus, Mallotus, and Helianthus) were not significantly different from the corresponding space-averages, although the averages differed among individual plants. Polygonum, however, did show significant differences between time and space averages. Ergodicity appears to apply to the leaf–canopy relationship, at least approximately—the average photosynthetic capacity of a single leaf through time (time-average) can represent the average photosynthetic capacity of the entire canopy.     

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

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

Competitive exclusion through reproductive interference

A simple differential equation model was developed to describe the competitive interaction that may occur between species through reproductive interference. The model has the form comparable to Volterra's competition equations, and the graphical analysis of the outcome of the two-species interaction based on its zero-growth isoclines proved that: (1) The possible outcome in this model, as in usual models of resource competition, is either stable coexistence of both species or gradual exclusion of one species by the other, depending critically upon the values of the activity overlapping coefficient c_ij; (2) but, for the same c_ij-values, competitive exclusion is much more ready to occur here than in resource competition; (3) and moreover, the final result of the competition is always dependent on the initial-condition due to its non-linear isoclines, i.e., even under the parameter condition that generally allows both species to coexist, an extreme bias in intial density to one species can readily cause subsequent complete exclusion of its counterparts. Thus, it may follow that the reproductive interference is likely to be working in nature as an efficient mechanism to bring about habitat partitioning in either time or space between some closely related species in insect communities, even though they inhabit heterogeneous habitats where resource competition rarely occurs so that they could otherwise attain steady coexistence.     

Instantaneous canopy photosynthesis: analytical expressions for sun and shade leaves based on exponential light decay down the canopy and an acclimated non-rectangular hyperbola for leaf photosynthesis

Analytical expressions for the contributions of sun and shade leaves to instantaneous canopy photosynthesis are derived. The analysis is based on four assumptions. First, that the canopy is closed in the sense that it is horizontally uniform. Secondly, that there is an exponential profile of light down the canopy with the same decay constant for light from different parts of the sky. Thirdly, that the leaf photosynthetic response to incident irradiance can be described by a three-parameter non-rectangular hyperbola (NRH). And lastly, that light acclimation at the leaf level occurs in only one parameter of the NRH, that describing the light-saturated photosynthetic rate, which is assumed to be proportional to the local averaged leaf irradiance. These assumptions have been extensively researched empirically and theoretically and their limitations are quite well understood. They have been widely used when appropriate. Combining these four assumptions permits the derivation of algebraic expressions for instantaneous canopy photosynthesis which are computationally efficient because they avoid the necessity for numerical integration down the canopy. These are valuable for modelling plant and crop ecosystems, for which canopy photosynthesis is the primary driver. Ignoring the sun/shade dichotomy can result in overestimates of canopy photosynthesis of up to 20 %, but using a rectangular hyperbola instead of a non-rectangular hyperbola to estimate canopy photosynthesis taking account of sun and shade leaves can lead to a similarly sized underestimate.     

How flocculation can explain coexistence in the chemostat

We study a chemostat model in which two microbial species grow on a single resource. We show that species coexistence is possible when the species which would normally win the exclusive competition aggregates in flocs. Our mathematical analysis exploits the fact that flocculation is fast compared to biological growth, a common hypothesis in floc models. A numerical study shows the validity of this approach in a large parameter range. We indicate how our model yields a mechanistic justification for the so-called density-dependent growth.     

Winning and losing with microbes: how microbially mediated fitness differences influence plant diversity

Interactions between plants and soil microbes can strongly influence plant diversity and community dynamics. Soil microbes may promote plant diversity by driving negative frequency‐dependent plant population dynamics, or may favor species exclusion by providing one species an average fitness advantage over others. However, past empirical research has focused overwhelmingly on the consequences of frequency‐dependent feedbacks for plant species coexistence and has generally neglected the consequences of microbially mediated average fitness differences. Here we use theory to develop metrics that quantify microbially mediated plant fitness differences, and show that accounting for these effects can profoundly change our understanding of how microbes influence plant diversity. We show that soil microbes can generate fitness differences that favour plant species exclusion when they disproportionately harm (or favour) one plant species over another, but these fitness differences may also favor coexistence if they trade off with competition for other resources or generate intransitive dominance hierarchies among plants. We also show how the metrics we present can quantify microbially mediated fitness differences in empirical studies, and explore how microbial control over coexistence varies along productivity gradients. In all, our analysis provides a more complete theoretical foundation for understanding how plant–microbe interactions influence plant diversity.     

Colourful coexistence of red and green picocyanobacteria in lakes and seas

Hutchinson's paradox of the plankton inspired many studies on the mechanisms of species coexistence. Recent laboratory experiments showed that partitioning of white light allows stable coexistence of red and green picocyanobacteria. Here, we investigate to what extent these laboratory findings can be extrapolated to natural waters. We predict from a parameterized competition model that the underwater light colour of lakes and seas provides ample opportunities for coexistence of red and green phytoplankton species. To test this prediction, we sampled picocyanobacteria of 70 aquatic ecosystems, ranging from clear blue oceans to turbid brown peat lakes. As predicted, red picocyanobacteria dominated in clear waters, whereas green picocyanobacteria dominated in turbid waters. We found widespread coexistence of red and green picocyanobacteria in waters of intermediate turbidity. These field data support the hypothesis that niche differentiation along the light spectrum promotes phytoplankton biodiversity, thus providing a colourful solution to the paradox of the plankton.     

围封与放牧管理对高寒草甸植物功能性状和功能多样性的影响

植物功能性状能够响应生存环境的变化并直接决定着生态系统功能。为了揭示围封与放牧管理对物种共存和驱动群落构建的影响机理,该研究以青藏高原东缘高寒草甸为对象,分析了围封与放牧处理对植物功能性状和功能多样性的影响。结果显示:(1)在群落水平,放牧显著降低了比叶面积和植物高度;在物种水平,放牧群落中多数杂类草比叶面积减小,而莎草类和禾草类的比叶面积在处理间无显著差异。(2)叶干物质含量与比叶面积在围封和放牧处理中均呈显著负相关关系,在放牧处理中,叶干物质含量与植物高度呈显著的二次函数关系,即随着叶干物质含量的增大,植物高度先减小后增大;在同等比叶面积的情况下,与围封相比,放牧降低了叶干物质含量;在相同叶干物质含量的情况下,与围封相比,放牧降低了植物高度。(3)放牧在总体上降低了种间性状的平均差异,植物性状表现出趋同响应,具体表现为放牧减小了叶干物质含量和植物高度的种间差异;与围封相比,放牧显著提高了功能均匀度,减小了功能分离度。研究表明,不同植物种对放牧的响应模式存在差异,放牧降低了种间对光资源的竞争,可能增加了对土壤养分的竞争,放牧驱动群落构建的过程中,土壤养分是非常重要的作用因子,说明放牧影响物种共存依赖于对多种资源的竞争。     

植物种群表观竞争机制及其研究进展

植物表观竞争既影响群落结构和组成,也与生态系统功能密切相关。目前,国内尚缺乏对植物表观竞争的实验研究和机制探索。对植物表观竞争概念和研究进展进行了系统梳理和阶段性总结,分析了草食动物为媒介的表观竞争主要通过食物和生境介导植物竞争过程,以及ELP-采食者关系对表观竞争的影响;植物参与的表观竞争通常与资源竞争共同作用;AM真菌为媒介的表观竞争不仅受到宿主植物菌根依赖性的影响,还与AM真菌对资源的需求和环境资源供给状况有密切关系。未来研究既要注重实验设计的合理性,也要考虑测定方法和评价参数的有效性;重视植物群落和生态系统水平上表观竞争的功能研究。这不仅能够为植物群落结构和物种共存提供机制性解释,而且能够丰富经典的植物竞争理论和多营养级相互作用的食物网理论。     

Leaf traits determine the growth-survival trade-off across rain forest tree species

A dominant hypothesis explaining tree species coexistence in tropical forest is that trade-offs in characters allow species to adapt to different light environments, but tests for this hypothesis are scarce. This study is the first that uses a theoretical plant growth model to link leaf trade-offs to whole-plant performances and to differential performances across species in different light environments. Using data of 50 sympatric tree species from a Bolivian rain forest, we observed that specific leaf area and photosynthetic capacity codetermined interspecific height growth variation in a forest gap; that leaf survival rate determined the variation in plant survival rate under a closed canopy; that predicted height growth and plant survival rate matched field observations; and that fast-growing species had low survival rates for both field and predicted values. These results show how leaf trade-offs influence differential tree performance and tree species' coexistence in a heterogeneous light environment.     

Spatial interplay of plant competition and consumer foraging mediate plant coexistence and drive the invasion ratchet

Indirect effects may play an important role in structuring plant communities. Using a spatially explicit model of consumer foraging and plant competition, we demonstrate how the relationship between the spatial area over which plants compete and the spatial scale of consumer behaviour can determine the outcome of competition when one plant species provides a refuge for mobile consumers (i.e. refuge-mediated apparent competition). Once an initial population of the invader is established, complete invasion may be inevitable because of an ever-advancing invasion front ratchets forward driven by a feeding front of mobile consumers. Because the spatial extent of apparent competition determines the area available for colonization, consumers may also dictate the rate at which an invasion occurs. We find that, as long as refuge-mediated apparent competition is sufficiently localized, invasion is possible even in systems characterized by low overall levels of consumer pressure. Moreover, we show that a stable equilibrium can result in which both resident and invading plants coexist, suggesting that spatial heterogeneity created by refuge-mediated apparent competition may be important in mediating coexistence in plant communities. The spatial interplay of consumer behaviour and plant competition may be an underappreciated mechanism affecting the composition, diversity and spatial pattern of plant communities.     

EVOLUTION OF THE STORAGE EFFECT

The storage effect, a mechanism that promotes species coexistence in temporally variable environments, poses a dilemma to evolutionary ecologists. Ecological studies have demonstrated its importance in natural communities, but evolutionary models have predicted that selection either impedes coexistence or diminishes the storage effect if there is coexistence. Here, we develop a lottery model of competition in which two species experience a trade‐off in competitive ability between two types of years. We use an adaptive evolution framework to determine conditions favoring the evolution of the storage effect. Storage evolves via divergence of relative performance in the two environments under a wide range of biologically realistic conditions. It evolves between two initially identical species (or lineages) when the trade‐off in performance is strong enough. It evolves for species having different initial trade‐offs for both weak and strong trade‐offs. Our simple 2‐species‐2‐environment scenario can be extended to multiple species and environmental conditions. Results indicate that the storage effect should evolve in a broad range of situations that involve a trade‐off in competitive ability among years, and are consistent with empirical observations. The findings show that storage can evolve in a manner and under conditions similar to other types of resource partitioning.     

热带森林植物多样性及其维持机制

热带森林具有地球上最丰富的植物多样性。关于热带森林植物多样性的维持机制,虽有众多假说,但均未形成完善的理论体系。不同的学者从不同的角度出发得出了许多结论,但也引起了不少争议。本文主要简述了4种经常被用来解释热带森林高植物多样性的机制：生态位分化、取食压力、生活史负相关和随机竞争,每一种机制都有大量的证据支持。热带森林植物沿微环境梯度的非随机空间分布表明其生态位分化很明显,并对其多样性起重要作用。动物的取食降低母树周围同种幼苗的生长率和存活率,为其他物种存活提供了机会,这就是取食压力假说,这是一个极有前景但仍需大量实验验证的假说。生活史负相关使得热带森林的许多植物能够共存。冠层植物的抑制使得随机性在林下植物的建立过程中起决定作用。