Species coexistence by permanent spatial heterogeneity in a lottery model

We studied the effect of permanent spatial heterogeneity in promoting species coexistence in a lottery model. The system consisted of multiple habitats, each composed of a number of sites occupied by adults of two species. Larvae produced from different habitats were mixed in a common pool. When an adult died, the vacant site became occupied by an individual randomly chosen from the larval pool. If there were n habitats, there could be up to n-1 internal equilibria with both species in addition to two single-species equilibria. These equilibria and their local stability can be calculated from a single function, indicating the difference among species in their average lifetime reproductive success. Our main result is that between-habitat variation in the ratio of mortalities of two species promotes coexistence, while that of reproductive rates does not. This conclusion is the opposite of the role of temporal variation in the standard lottery model, in which between-year variation in the reproductive rate, but not that in the mortalities, promotes coexistence.     

Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity

Abstract In the presence of permanent spatial heterogeneity, local dispersal, especially short‐range dispersal, can facilitate coexistence by concentrating low‐density species in the areas where their rates of increase are higher. We present a framework for predicting the effects of local dispersal on coexistence for arbitrary forms of dispersal and arbitrary spatial patterns of environmental variation. Using the lottery model as an example, we find that local dispersal contributes to coexistence by enhancing the effects of environmental variation on scales longer than typical dispersal distances, which can be characterized solely by the variance of the dispersal kernel. Higher moments of the dispersal kernel are not important.     

Dispersal network heterogeneity promotes species coexistence in hierarchical competitive communities

Understanding the mechanisms of biodiversity maintenance is a fundamental issue in ecology. The possibility that species disperse within the landscape along differing paths presents a relatively unexplored mechanism by which diversity could emerge. By embedding a classical metapopulation model within a network framework, we explore how access to different dispersal networks can promote species coexistence. While it is clear that species with the same demography cannot coexist stably on shared dispersal networks, we find that coexistence is possible on unshared networks, as species can surprisingly form self‐organised clusters of occupied patches with the most connected patches at the core. Furthermore, a unimodal biodiversity response to an increase in species colonisation rates or average patch connectivity emerges in unshared networks. Increasing network size also increases species richness monotonically, producing characteristic species–area curves. This suggests that, in contrast to previous predictions, many more species can co‐occur than the number of limiting resources.     

Reduction of species coexistence through mixing in a spatial competition model

Many ecological systems exhibit self-organized spatial patterns due to local interactions. Such patterns can promote species diversity and therefore serve as an important mechanism for biodiversity maintenance. Previous work has shown that when species interactions occurred at local spatial scales, species diversity was greatest when robust mosaic spatial patterns formed. Also, intransitive interactions led to the emergence of spiral patterns, frequently resulting in multispecies coexistence. In some instances, intransitive interactions reduced species diversity as the consequence of competitive hierarchies. Here, we extend and broaden this line of investigation and examine the role of global competition along a continuum ranging from spatial mosaics to spiral patterns. While previous models have predicted that species diversity is reduced when interactions occur over larger spatial scales, our model considers the effects of various levels of mixing on species diversity, in the context of various network structures as measured by the covariance of row and column sums of the competition matrix. First, we compare local competition (unmixed system) versus global competition (mixed systems) and show that greater species diversity is maintained under a positive covariance. Second, we show that under various levels of mixing, species diversity declines more rapidly under a negative covariance. Lastly, we demonstrate that time to extinction in our model occurs much more rapidly under a negative covariance.     

Spatial heterogeneity and plant species richness at different spatial scales under rabbit grazing

Herbivores influence spatial heterogeneity in soil resources and vegetation in ecosystems. Despite increasing recognition that spatial heterogeneity can drive species richness at different spatial scales, few studies have quantified the effect of grazing on spatial heterogeneity and species richness simultaneously. Here we document both these variables in a rabbit-grazed grassland. We measured mean values and spatial patterns of grazing intensity, rabbit droppings, plant height, plant biomass, soil water content, ammonia and nitrate in sites grazed by rabbits and in matched, ungrazed exclosures in a grassland in southern England. Plant species richness was recorded at spatial scales ranging between 0.0001 and 150 m(2). Grazing reduced plant height and plant biomass but increased levels of ammonia and nitrate in the soil. Spatial statistics revealed that rabbit-grazed sites consisted of a mixture of heavily grazed patches with low vegetation and nutrient-rich soils (lawns) surrounded by patches of high vegetation with nutrient-poor soils (tussocks). The mean patch size (range) in the grazed controls was 2.1 +/- 0.3 m for vegetation height, 3.8 +/- 1.8 m for soil water content and 2.8 +/- 0.9 m for ammonia. This is in line with the patch sizes of grazing (2.4 +/- 0.5 m) and dropping deposition (3.7 +/- 0.6 m) by rabbits. In contrast, patchiness in the ungrazed exclosures had a larger patch size and was not present for all variables. Rabbit grazing increased plant species richness at all spatial scales. Species richness was negatively correlated with plant height, but positively correlated to the coefficient of variation of plant height at all plot sizes. Species richness in large plots (<25 m(2)) was also correlated to patch size. This study indicates that the abundance of strong competitors and the nutrient availability in the soil, as well as the heterogeneity and spatial pattern of these factors may influence species richness, but the importance of these factors can differ across spatial scales.     

The effects of spatial heterogeneity in population dynamics

The dynamics of a population inhabiting a heterogeneous environment are modelled by a diffusive logistic equation with spatially varying growth rate. The overall suitability of an environment is characterized by the principal eigenvalue of the corresponding linearized equation. The dependence of the eigenvalue on the spatial arrangement of regions of favorable and unfavorable habitat and on boundary conditions is analyzed in a number of cases.Research supported by National Science Foundation grant #DMS 88-02346     

Environmental heterogeneity,species diversity and co‐existence at different spatial scales

The positive relationship between spatial environmental heterogeneity and species diversity is a widely accepted concept, generally associated with niche limitation. However, niche limitation cannot account for negative heterogeneity–diversity relationships (HDR) revealed in several case studies. Here we explore how HDR varies at different spatial scales and provide novel theories for small‐scale species co‐existence that explain both positive and negative HDR. At large spatial scales of heterogeneity (e.g. landscape level), different communities co‐exist, promoting large regional species pool size and resulting in positive HDR. At smaller scales within communities, species co‐existence can be enhanced by increasing the number of different patches, as predicted by the niche limitation theory, or alternatively, restrained by heterogeneity. We conducted meta‐regressions for experimental and observational HDR studies, and found that negative HDRs are significantly more common at smaller spatial scales. We propose three theories to account for niche limitation at small spatial scales. (1) Microfragmentation theory: with increasing spatial heterogeneity, large homogeneous patches lose area and become isolated, which in turn restrains the establishment of new plant individuals and populations, thus reducing species richness. (2) Heterogeneity confounded by mean: when heterogeneity occurs at spatial scales smaller than the size of individual plants, which forage through the patches, species diversity can be either positively or negatively affected by a change in the mean of an environmental factor. (3) Heterogeneity as a separate niche axis: the ability of species to tolerate heterogeneity at spatial scales smaller than plant size varies, affecting HDR. We conclude that processes other than niche limitation can affect the relationship between heterogeneity and diversity.     

Spatial heterogeneity of mortality and temporal fluctuation in fertility promote coexistence but not vice versa: a random-community approach

Both spatial heterogeneity and temporal fluctuation of the environment are important mechanisms promoting species coexistence, but they work in different manners. We consider many pairs of species with randomly generated survivorship and fertility in the lottery model, and examine how the variability in demographic processes affects the outcome of competition. The results are: [1] Coexistence is easier if habitat difference in mortality is greater, or if year-to-year variation in reproductive rate is larger. But neither habitat-difference in fertility nor temporal variation in mortality promotes coexistence. [2] Mean fertility does not affect the outcome if CV remains constant. In contrast, enhanced mean mortality decreases the fraction of coexisting pairs if the environment fluctuates temporally. [3] We also investigate the effect of limited dispersal of propagules between habitats. Compared with the complete mixing case, the fraction of coexisting pairs is clearly enhanced if the spatial heterogeneity is the major source of environmental variation, but shows slight increase if the temporal fluctuation is dominant. We conclude that spatial heterogeneity is likely to work more effectively in promoting species coexistence than temporal fluctuation, especially when the species suffer relatively high mortality, and disperse their propagules in a limited spatial scale.     

Effects of spatial heterogeneity on butterfly species richness in Rocky Mountain National Park, CO, USA

We investigated butterfly responses to plot-level characteristics (plant species richness, vegetation height, and range in NDVI [normalized difference vegetation index]) and spatial heterogeneity in topography and landscape patterns (composition and configuration) at multiple spatial scales. Stratified random sampling was used to collect data on butterfly species richness from seventy-six 20 × 50 m plots. The plant species richness and average vegetation height data were collected from 76 modified-Whittaker plots overlaid on 76 butterfly plots. Spatial heterogeneity around sample plots was quantified by measuring topographic variables and landscape metrics at eight spatial extents (radii of 300, 600 to 2,400 m). The number of butterfly species recorded was strongly positively correlated with plant species richness, proportion of shrubland and mean patch size of shrubland. Patterns in butterfly species richness were negatively correlated with other variables including mean patch size, average vegetation height, elevation, and range in NDVI. The best predictive model selected using Akaike’s Information Criterion corrected for small sample size (AIC_c), explained 62% of the variation in butterfly species richness at the 2,100 m spatial extent. Average vegetation height and mean patch size were among the best predictors of butterfly species richness. The models that included plot-level information and topographic variables explained relatively less variation in butterfly species richness, and were improved significantly after including landscape metrics. Our results suggest that spatial heterogeneity greatly influences patterns in butterfly species richness, and that it should be explicitly considered in conservation and management actions.     

Small-scale spatial heterogeneity of arbuscular mycorrhizal fungal abundance and community composition in a wetland plant community

Although it has become increasingly clear that arbuscular mycorrhizal fungi (AMF) play important roles in population, community, and ecosystem ecology, there is limited information on the spatial structure of the community composition of AMF in the field. We assessed small-scale spatial variation in the abundance and molecular diversity of AMF in a calcareous fen, where strong underlying environmental gradients such as depth to water table may influence AMF. Throughout an intensively sampled 2 × 2 m plot, we assessed AMF inoculum potential at a depth of 0–6 and 6–12 cm and molecular diversity of the AMF community using terminal restriction fragment length polymorphism of 18S rDNA. Inoculum potential was only significantly spatially autocorrelated at a depth of 6–12 cm and was significantly positively correlated with depth to water table at both depths. Molecular diversity of the AMF community was highly variable within the plot, ranging from 2–14 terminal restriction fragments (T-RFs) per core, but the number of T-RFs did not relate to water table or plant species richness. Plant community composition was spatially autocorrelated at small scales, but AMF community composition showed no significant spatial autocorrelation. Saturated soils of calcareous fens contain many infective AMF propagules and the abundance and diversity of AMF inoculum is patchy over small spatial scales. An erratum to this article can be found at     

东海带鱼和小型鱼类空间异质性及其空间关系

根据2001年秋季东海区121个调查站位的调查资料,以变异函数为工具,分析带鱼和7种小型鱼类(黄鲫、棘头梅童鱼、鳄齿鱼、六丝钝尾虎鱼、发光鲷、七星底灯鱼和细条天竺鲷)的空间异质性及其空间关系.结果表明,带鱼的变异函数曲线与细条天竺鲷、六丝钝尾虎鱼和发光鲷的曲线极为相似,对不同距离的变异函数值进行相关分析,带鱼与上述3种小型鱼类均达到极显著相关水平(P<0.01).黄鲫和棘头梅童鱼的变异函数表现出纯金块效应,而其它几种鱼都可拟合为球状或指数模型,并且都具有较强的空间自相关特性,其中细条天竺鲷、六丝钝尾虎鱼和发光鲷的变程也都接近或超过带鱼265km的变程,带鱼与这3种小型鱼类之间具有较强的空间追随关系,因此它们是带鱼的主要摄食对象.     

Soil phosphorus heterogeneity promotes tree species diversity and phylogenetic clustering in a tropical seasonal rainforest

The niche theory predicts that environmental heterogeneity and species diversity are positively correlated in tropical forests, whereas the neutral theory suggests that stochastic processes are more important in determining species diversity. This study sought to investigate the effects of soil nutrient (nitrogen and phosphorus) heterogeneity on tree species diversity in the Xishuangbanna tropical seasonal rainforest in southwestern China. Thirty‐nine plots of 400 m² (20 × 20 m) were randomly located in the Xishuangbanna tropical seasonal rainforest. Within each plot, soil nutrient (nitrogen and phosphorus) availability and heterogeneity, tree species diversity, and community phylogenetic structure were measured. Soil phosphorus heterogeneity and tree species diversity in each plot were positively correlated, while phosphorus availability and tree species diversity were not. The trees in plots with low soil phosphorus heterogeneity were phylogenetically overdispersed, while the phylogenetic structure of trees within the plots became clustered as heterogeneity increased. Neither nitrogen availability nor its heterogeneity was correlated to tree species diversity or the phylogenetic structure of trees within the plots. The interspecific competition in the forest plots with low soil phosphorus heterogeneity could lead to an overdispersed community. However, as heterogeneity increase, more closely related species may be able to coexist together and lead to a clustered community. Our results indicate that soil phosphorus heterogeneity significantly affects tree diversity in the Xishuangbanna tropical seasonal rainforest, suggesting that deterministic processes are dominant in this tropical forest assembly.     

Seed size,establishment sites and species coexistence in a Chilean rain forest

Abstract. Seedling densities on the forest floor and on elevated microsites (logs and stumps) were compared for eight woody species in a temperate rain forest in southern Chile. Degree of association with elevated microsites varied significantly between species, showed no systematic relationship with reported shade tolerance, but was significantly negatively correlated with seed mass. Large-seeded Podocarpus nubigena established preferentially on undisturbed forest floor sites, whereas seedlings of small-seeded species such as Nothofagus nitida and Laurelia philippiana were found mainly on fallen logs and stumps. The abundance of large seedlings and saplings of N. nitida on logs/stumps, and the growth forms of canopy trees, confirm that recruitment of this species occurs mainly on decaying wood. The relationship between seed size and microsite preferences may be caused by effects of seed size on (1) ability to establish in forest floor litter and (2) retention of seeds on logs. Seedling occupancy of logs and stumps varied with state of decay. Few seedlings of any species were present on logs in the early stages of decay. N. nitida established earlier than the other species, attaining maximum abundance on wood in the middle decay classes. Species richness and overall seedling abundance were highest on wood in advanced stages of decay. Seed size differences are suggested as a determinant of differential utilization of forest floor heterogeneity, and hence of plant species coexistence.     

On the effects of spatial heterogeneity on the persistence of interacting species

 The dynamics of two interacting theoretical populations inhabiting a heterogeneous environment are modelled by a system of two weakly coupled reaction–diffusion equations having spatially dependent reaction terms. Longterm persistence of both populations is guaranteed by an invasibility condition, which is itself expressed via the signs of certain eigenvalues of related linear elliptic operators with spatially dependent lowest order coefficients. The effects of change in these coefficients upon the eigenvalues are here exploited to study the effects of spatial heterogeneity on the persistence of interacting species through two particular ecological topics of interest. The first concerns when the location of favorable hunting grounds within the overall environment does or does not affect the success of a predator in predator–prey models, while the second concerns cases of competition models in which the outcome of competition in a spatially varying environment differs from that which would be expected in a spatially homogeneous environment. Received: 9 June 1997     

Measures of spatial heterogeneity for species occurrence or disease incidence with finite-counts

We propose two types of indices with finite-count correction to measure the spatial heterogeneity of binary characteristics of organisms, such as occurrence or non-occurrence of organisms and infected or non-infected plants. We consider the following two examples: plant occurrence in a grassland community, and yellow dwarf disease infection in a rice field. For the grassland community, N quadrats comprising n cells of equal area, were set at random sites in a grassland, and the occurrence of a given species A in each of n cells was recorded. For disease infection, N quadrats, each consisting of n rice plants, were set at random sites in a paddy field, and the number of plants infected with yellow dwarf virus in each quadrat were counted. In these examples, since the number of cells in a quadrat is finite, neither occurrence nor incidence increase infinitely, unlike the number of aphids on a maize leaf. The first category of index belongs to the mean : variance ratio type. The estimated index value for occurrence (or incidence) is the same as that for non-occurrence (or non-incidence). The second category belongs to the k-type of a negative binomial distribution. If some random plants die or recover from the disease then the expected value of the second type of index does not change. For n, the current indices approach the mean : variance ratio and the inverse of k in a negative binomial distribution, respectively. This indicates that these indices are suitable for binary data sets.     

水分驱动半干旱区河流沉积物/土壤厌氧绳菌群落的空间异质性

【背景】厌氧绳菌纲、目、科及属是海洋沉积物和湿地土壤中优势的微生物类群,但关于特定水分梯度下河流沉积物/土壤厌氧绳菌群落是否存在空间异质性及核心环境驱动力等问题尚不明晰。【目的】阐明蒙古高原半干旱区河流系统水生、湿生、旱生环境梯度下厌氧绳菌群落的空间异质性及环境驱动力,探明干旱胁迫下萎缩型河流湿地复湿过程中厌氧绳菌群落的指示作用。【方法】利用16S rRNA基因高通量测序及相关性和变异权重分析等方法研究河流系统水分梯度下沉积物/土壤厌氧绳菌群落不同种群的组成、丰度、分布及其环境驱动力。【结果】厌氧绳菌群落15个种群主要分布在水生及湿生环境,由水分、氨氮、砂粒及pH正向驱动,由盐度、全氮、全磷、粉粒和黏粒等负向驱动(Uncultured_us15由砂粒和氨氮负向驱动及粉粒和盐度正向驱动除外);9个和6个厌氧绳菌种群分别由总有机碳正向和负向驱动。变异权重分析表明水分、氨氮、盐度、有机碳、pH分别解释了厌氧绳菌群落空间变异的64.8%、8.9%、7.5%、2.2%、1.7%。【结论】蒙古高原半干旱区厌氧绳菌群落存在明显的空间异质性,偏好高水砂、高氨、高pH等水生和湿生环境,不耐受盐度和营养偏高的旱生环境,由水分核心驱动,可能为自养异养混合的游离型氨氧化细菌,是干旱胁迫下萎缩型河流湿地水分恢复过程的重要指示生物。     

Coexistence through spatio-temporal heterogeneity and species sorting in grassland plant communities

The effect of spatial heterogeneity on species coexistence relies on the degree of niche heterogeneity in the habitat and the ability of species to exploit the available niche opportunities. We studied species coexistence in a perennial grassland, and tested whether small-scale disturbances create environmental heterogeneity that affects coexistence and whether the functional diversity of species in the species pool affects the ability of community composition to reflect heterogeneity through species sorting. We manipulated the spatio-temporal heterogeneity of disturbance and the functional diversity of species added as seed and measured their impact on the spatial turnover of species composition. Disturbance increased environmental heterogeneity and spatial turnover, and the effect of heterogeneity on turnover was greatest in the presence of a functionally diverse species pool, showing the importance of trait variation among species for exploiting environmental heterogeneity, and suggesting that coexistence occurred due to species sorting among heterogeneous niches.     

The nature of zooplankton spatial heterogeneity in a nonriverine impoundment

Knowledge of spatial heterogeneity characteristic of reservoir plankton communities is fundamental to a variety of ecological studies. Degree of spatial heterogeneity in the zooplankton community of Center Hill Reservoir, with water residence times of 50–250 days, was positively correlated with rate of water influx. Important spatial differences resulted from the contrast between zooplankton associated with new and longer-impounded water. The nature of spatial heterogeneity differed fundamentally from the more riverine impoundments where spatial differences are often persistent and characterized by gradual change (as opposed to contrast) in plankton assemblages with respect to location. Magnitude of plankton spatial heterogeneity in nonriverine impoundments may be predictable from inflow rates. Areas, between which major differences in plankton communities exist, may also be definable from knowledge of inflow dispersal patterns in these impoundments.     

采伐干扰对帽儿山地区天然次生林土壤表层温度空间异质性的影响

研究了不同强度采伐干扰对土壤表层（3～5 cm）温度空间异质性和空间格局的影响.在帽儿山地区天然次生林内,设置3块不同强度采伐干扰处理样地: A（对照）、B（按基面积的50%随机采伐）和C（皆伐）,分别布设不同空间距离 (0.5～56 m)的取样点160、154和154个,比较了干扰以后2年内春季和夏季（共4次）土壤表层温度的空间异质性和空间格局特征.结果表明,森林采伐后,土壤表层平均温度显著增加（相差0.6～4.2 ℃,P＜0.001）,与干扰强度存在一定程度正相关,温度波动范围加大.采伐干扰导致土壤表层温度空间异质性程度和变异尺度增加,并随干扰强度加大而增大,小尺度上的空间异质性也出现增加现象,但土壤温度空间变异尺度主要体现在＜20 m范围内,空间异质性组成受干扰影响较小.经Kriging法对土壤表层温度空间格局模拟,发现采伐干扰样地土壤表层温度的空间格局强度较对照林地大,温度等值线密集,其差异春季比夏季明显.采伐干扰样地的年际间相同季节土壤表层温度格局较相似,而对照样地则呈较均匀的分布格局.