Inferring local competition intensity from patch size distributions: a test using biological soil crusts

Dryland vegetation is inherently patchy. This patchiness goes on to impact ecology, hydrology, and biogeochemistry. Recently, researchers have proposed that dryland vegetation patch sizes follow a power law which is due to local plant facilitation. It is unknown what patch size distribution prevails when competition predominates over facilitation, or if such a pattern could be used to detect competition. We investigated this question in an alternative vegetation type, mosses and lichens of biological soil crusts, which exhibit a smaller scale patch‐interpatch configuration. This micro‐vegetation is characterized by competition for space. We proposed that multiplicative effects of genetics, environment and competition should result in a log‐normal patch size distribution. When testing the prevalence of log‐normal versus power law patch size distributions, we found that the log‐normal was the better distribution in 53% of cases and a reasonable fit in 83%. In contrast, the power law was better in 39% of cases, and in 8% of instances both distributions fit equally well. We further hypothesized that the log‐normal distribution parameters would be predictably influenced by competition strength. There was qualitative agreement between one of the distribution's parameters (μ) and a novel intransitive (lacking a ‘best’ competitor) competition index, suggesting that as intransitivity increases, patch sizes decrease. The correlation of μ with other competition indicators based on spatial segregation of species (the C‐score) depended on aridity. In less arid sites, μ was negatively correlated with the C‐score (suggesting smaller patches under stronger competition), while positive correlations (suggesting larger patches under stronger competition) were observed at more arid sites. We propose that this is due to an increasing prevalence of competition transitivity as aridity increases. These findings broaden the emerging theory surrounding dryland patch size distributions and, with refinement, may help us infer cryptic ecological processes from easily observed spatial patterns in the field.     

基于无人机影像的阿拉善东南部荒漠灌丛植被空间格局研究

干旱区灌丛植被空间格局受多种物理和生态过程影响,能够指示生态系统的状态。研究通过量化灌丛斑块大小的空间分布来评估阿拉善高原东南部覆沙荒漠植被生态系统的状态,采用点格局分析法分析灌木种群的相互关系,以阐明不同灌木种在斑块格局形成中的作用,并结合土壤条件及下垫面粗糙度等指标验证评估的准确性,探讨灌丛空间格局差异的内在机理。结果表明,研究区样方2灌丛斑块大小符合截尾幂律分布,其他样方符合对数正态分布,前者的空间结构及生境条件均优于后者,说明植被空间格局可以准确表征生态系统状态。在局地尺度上灌木种内和种间呈现不同的相互关系,以竞争关系为主导是导致斑块破碎化的主要驱动机制。小灌木（如猫头刺）的种内互利关系有利于促进多样化斑块形态的形成,而大灌木（如沙冬青和蒙古扁桃）种间的互利作用则有利于形成异质性更强的复杂空间格局。基于灌丛斑块的空间格局评估生态系统状态,可为保护和恢复生态脆弱区受损植被提供重要的借鉴。     

Vegetation Pattern Formation Due to Interactions Between Water Availability and Toxicity in Plant–Soil Feedback

Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model’s parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.     

Exogenous disturbances and endogenous self-organized processes are not mutually exclusive drivers of spatial patterns in macroalgal assemblages

Complex spatial patterns are common in coastal marine systems, but mechanisms underlying their formation are disputed. Most empirical work has focused on exogenous spatially structured disturbances as the leading cause of pattern formation in species assemblages. However, theoretical and observational studies suggest that complex spatial patterns, such as power laws in gap-size distribution, may result from endogenous self-organized processes involving local-scale interactions. The lack of studies simultaneously assessing the influence of spatially variable disturbances and local-scale interactions has fuelled the idea that exogenous and endogenous processes are mutually exclusive explanations of spatial patterns in marine ecosystems. To assess the relative contribution of endogenous and exogenous processes in the emergence of spatial patterns, an intertidal assemblage of algae was exposed for two years to various combinations of intensity and spatial patterns of disturbance. Localized disturbances impinging at the margins of previously disturbed clearings and homogenous disturbances without any spatial pattern generated heterogeneous distributions of disturbed gaps and macroalgal patches, characterized by a power-law scaling. Spatially varying disturbances produced a spatial gradient in the distribution of algal patches and, to a lesser extent, also a power-law scaling in both patch- and gap-size distributions. These results suggest that exogenous and endogenous processes are not mutually exclusive forces that can lead to the formation of similar spatial patterns in species assemblages.     

低覆盖度固沙林的乔木分布格局与防风效果

低覆盖度植被是我国干旱、半干旱区经过漫长的自然演替过程逐步发育形成且广泛分布的植被类型。前人研究认为,植被覆盖度达到40%为固定沙地,40%-20%为半固定-半流动沙地。但在实践观察中发现:在低密度(或覆盖度)时,灌丛的水平分布格局对固定流沙和阻止风沙流的作用差异显著。在干旱区、半干旱区,存在着大量天然的乔木疏林,其覆盖度均在低于40%,地表处于半流动状态,而配置成行带式后,即使覆盖度降低到20%时,地面也不会出现风蚀现象。因此,在内蒙古浑善达克沙地,针对覆盖度在20%左右的乔木疏林,同时测定了随机与行带式两种分布格局的防风阻沙效果。结果表明:(1)在不同的对照风速下,行带式配置的林内的相对风速均低于随机分布,其中在200 cm高度处行带式配置的平均相对风速比随机分布的低53.89%,在50 cm高度处低36.82%;(2)行带式林内的水平风速流场变化有一定规律,而随机分布林内风速流场变化主要受树冠在空间的分布影响,变化非常复杂;(3)随机分布的疏林内出现风速超过旷野对照的现象,在50 cm和200 cm的两个观测高度上分别有约27.45%和22.55%的风速测定值超过对照风速,说明出现明显的局部风速"抬升"现象,形成了强的涡流;(4)行带式配置林内的平均地表粗糙度达到1.01 cm,比随机分布的疏林内增大约5倍之多;(5)总体而论,行带式分布格局第1带降低风速的作用最显著,第2带及其以后各带间的风速均比第1带后的风速小,但逐带降低的叠加效益不明显;(6)由于乔木基本(枝下高)没有枝条对风的阻碍,乔木行带式固沙林在迎风面的第1林带的基部有一定的风力"抬升"作用,对林带基部地面产生较强的侵蚀作用,多数第1带树木的根系被侵蚀裸露,过境的风沙流只能在林带后树冠外侧堆积;(7)随机分布林内在许多位置出现了非常低的地表粗糙度,地表粗糙度低的位置基本与风速"抬升"区相吻合,这种"抬升"区形成的强的涡流是疏林内出现风蚀坑的重要因素,这也是浑善达克沙地出现榆树与风蚀坑相间分布的主要原因。     

干旱半干旱区灌丛斑块与降水量响应关系的熵模型模拟

灌丛斑块分布格局是灌木在干旱缺水条件下对生存环境的自我调节和适应的具体表现。应用熵理论和Klausmier模型,解释了灌丛斑块水分聚集原理并模拟了不同年降水条件下灌丛斑块的最佳面积比值(即最佳灌丛盖度)。研究结果表明:灌丛斑块生物量与其土壤含水量呈反比例函数关系,当生态系统处于稳定状态时(即熵最大状况下),年降水量与灌丛斑块面积比值符合一定的线性关系。研究采用内蒙古草原地区的野外调查数据,获得模型所需参数,进而模拟了不同年降水量条件下灌丛斑块最佳面积比值,研究结果可为半干旱地区植被保护与恢复提供参考。     

Detection of two-component mixtures of lognormal distributions in grouped, doubly truncated data: analysis of red blood cell volume distributions

We have examined the statistical requirements for the detection of mixtures of two lognormal distributions in doubly truncated data when the sample size is large. The expectation-maximization algorithm was used for parameter estimation. A bootstrap approach was used to test for a mixture of distributions using the likelihood ratio statistic. Analysis of computer simulated mixtures showed that as the ratio of the difference between the means to the minimum standard deviation increases, the power for detection also increases and the accuracy of parameter estimates improves. These procedures were used to examine the distribution of red blood cell volume in blood samples. Each distribution was doubly truncated to eliminate artifactual frequency counts and tested for best fit to a single lognormal distribution or a mixture of two lognormal distributions. A single population was found in samples obtained from 60 healthy individuals. Two subpopulations of cells were detected in 25 of 27 mixtures of blood prepared in vitro. Analyses of mixtures of blood from 40 patients treated for iron-deficiency anemia showed that subpopulations could be detected in all by 6 weeks after onset of treatment. To determine if two-component mixtures could be detected, distributions were examined from untransfused patients with refractory anemia. In two patients with inherited sideroblastic anemia a mixture of microcytic and normocytic cells was found, while in the third patient a single population of microcytic cells was identified. In two family members previously identified as carriers of inherited sideroblastic anemia, mixtures of microcytic and normocytic subpopulations were found. Twenty-five patients with acquired myelodysplastic anemia were examined. A good fit to a mixture of subpopulations containing abnormal microcytic or macrocytic cells was found in two. We have demonstrated that with large sample sizes, mixtures of distributions can be detected even when distributions appear to be unimodal. These statistical techniques provide a means to characterize and quantify alterations in erythrocyte subpopulations in anemia but could also be applied to any set of grouped, doubly truncated data to test for the presence of a mixture of two lognormal distributions.     

Diversity and Patch-Size Distributions of Biological Soil Crusts Regulate Dryland Ecosystem Multifunctionality

Recent studies report that multifunctionality—the simultaneous provision of multiple ecosystem functions—in drylands depends on biodiversity. Others report that specific size distributions of vegetation patches indicate overall ecosystem health and function. Using a biocrust (micro-vegetation of mosses, lichens, and cyanobacteria) model system, and multivariate modeling, we determined the relative importance of biodiversity, patch-size distribution, and total abundance to nutrient cycling and multifunctionality. In most cases we explained at least 20%, and up to 65%, of the variation in ecosystem functions, and 42% of the variation in multifunctionality. Species richness was the most important determinant of C cycling, constituting an uncommonly clear link between diversity and function in a non-experimental field setting. Regarding C cycling in gypsiferous soils, we found that patch size distributions with a greater frequency of small to medium patches, as opposed to very small patches, were more highly functional. Nitrogen cycling was largely a function of biocrust cover in two soil types, whereas in gypsiferous soils, more central-tending patch size distributions were less functional with regards to N cycling. All three community properties were about equally important to multifunctionality. Our results highlight the functional role of biotic attributes other than biodiversity, and indicate that high cover and diversity, together with a particular patch-size distribution, must be attained simultaneously to maximize multifunctionality. The results also agree with trends observed with other terrestrial and aquatic communities that more biodiversity is needed to sustain multifunctionality compared to single functions considered independently.     

Large herbivores maintain a two‐phase herbaceous vegetation mosaic in a semi‐arid savanna

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干旱区荒漠景观的植被自然更新机制初探

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Effects of Patch-Size on Populations of Intertidal Limpets,Siphonaria spp., in a Linear Landscape

Organisms with different life-histories and abilities to disperse often utilise habitat patches in different ways. We investigated the influence of the size of patches of rock (separated by stretches of sand) on the density of pulmonate limpets (Siphonaria spp.) along 1500 km of the linear landscape of the South African coastline. We compared the influence of patch-size on two congeneric species with different modes of development, S. serrata a direct developer, and S. concinna a planktonic developer. We tested the spatial and temporal consistency of the effects of patch-size by sampling 7 independent regions spanning the distributional range of both species of limpets, and by sampling one region at monthly intervals for 1 year. Within each region or month, 4 small patches (<20 m in length) interspersed with the 4 large patches (>60 m in length) were sampled. Across the entire geographic range and throughout the year, there were more of both species of limpets in large patches than in small patches. In most regions, there was greater variability in large patches than small patches. Variability within patches in a single region was similar throughout the year, with greater variability of both species in large than in small patches. We found little influence of the mode of development on the response of limpets to patch-size. Our findings highlight the importance of understanding patterns of distribution of species with respect to habitat heterogeneity in linear landscapes, and contradict the idea that organism mobility at an early ontogenetic stage directly affects habitat use.     

塔里木荒漠河岸林不同生境群落物种多度分布格局

为解释塔里木荒漠河岸林群落构建和物种多度分布格局形成的机理, 本文以塔里木荒漠河岸林2个不同生境(沙地、河漫滩) 4 ha固定监测样地为研究对象, 基于两样地物种调查数据, 采用统计模型(对数级数模型、对数正态模型、泊松对数正态分布模型、Weibull分布模型)、生态位模型(生态位优先占领模型、断棍模型)和中性理论模型(复合群落零和多项式模型、Volkov模型)拟合荒漠河岸林群落物种多度分布, 并用K-S检验与赤池信息准则(AIC)筛选最优拟合模型。结果表明: (1)随生境恶化(土壤水分降低), 植物物种多度分布曲线变化减小, 群落物种多样性、多度和群落盖度降低, 常见种数减少。(2)选用的3类模型均可拟合荒漠河岸林不同生境群落物种多度分布格局, 统计模型和中性理论模型拟合效果均优于生态位模型。复合群落零和多项式模型对远离河岸的干旱沙地生境拟合效果最好; 对数正态模型和泊松对数正态模型对洪水漫溢的河漫滩生境拟合效果最优; 中性理论模型与统计模型无显著差异。初步推断中性过程在荒漠河岸林群落构建中发挥着主导作用, 但模型拟合结果只能作为推断群落构建过程的必要非充分条件, 不能排除生态位过程的潜在作用。     

Exploiting the Adaptation Dynamics to Predict the Distribution of Beneficial Fitness Effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.     

Self‐organised patchiness and scale‐dependent bio‐geomorphic feedbacks in aquatic river vegetation

Spatial self‐organisation of ecosystems is the process by which large‐scale ordered spatial patterns emerge from disordered initial conditions through local feedbacks between organisms and their environment. Such process is considered important for ecosystem functioning, providing increased productivity, resistance and resilience against environmental change. Although spatial self‐organisation has been found for an increasing number of ecosystems, it has never been shown so far for aquatic river vegetation. Here we explore the existence of spatial self‐organisation of freshwater macrophyte patches in a typical lowland river (Belgium), showing that the underlying mechanisms for pattern formation are scale‐dependent feedbacks between plant growth, water flow and local river bed erosion and sedimentation. The mapping of vegetation patches showed that the frequency distribution of patch sizes is governed by a power‐law function, suggesting that the patches are self‐organised. Scale‐dependent feedbacks, likely to lead to this self‐organised pattern, were demonstrated with a mimic experiment. Both positive and negative feedbacks on plants were confirmed by a transplantation experiment. Placing vegetation patch mimics in the river showed experimentally that on a short range (within and behind the mimics) flow reduction and increased sedimentation occurred, while on a larger range (next to patches) the flow was accelerated and decreased sedimentation took place. By transplanting macrophytes within, next to and further away from existing patches, it was proven that the conditions within the patches favoured the survival and growth of transplants (i.e. short‐range positive feedback), while the conditions just next to patches led to decreased survival and growth (i.e. long‐range negative feedback).     

Characterization of spatial scaling relationships between vegetation pattern and topography at different directions in Gurbantunggut desert,China

Vegetation striped pattern is a common feature in semiarid and arid landscapes, which is seen as mosaics including vegetated and non-vegetated patches. Identifying scales of pattern in ecological systems and referring patterns to multi-scaled processes that create them are ongoing challenges. The aim of this paper is to study the vegetation patterns and their across-scale relationships between the vegetation and anisotropic topography (W–E and N–S) in 12 transects at Gurbantunggut desert. We used wavelet-based across-scale analysis for extracting information on scales of pattern for those transect data, evaluating their inherent structure, and inferring characteristics of the processes that imposed those patterns at across scales. The results show that, in W–E direction, the scales of vegetation pattern (C. ewersmanniana is at the scale 40 m, H. ammodendron, at 35 m) correspond to the dune ridge/dune valley sequences (appearing at distance of 40 m), and vegetation on mesoscale and large scale are significant cross-scale correlation with topography on mesoscale and large scale in all W–E transects. In N–S direction, there is an irregular pattern of vegetation along the N–S irregular topography, and no unified cross-scale relationships between topography and vegetation on different scales in different transects. Moreover, cross-scale correlation analysis between topography and vegetation provides further detail on hierarchical structure and specific scales in space that strongly influenced the larger patterns. Knowledge of the cross-scale relationships between topography and vegetation could lead to better understanding and management of biological resources in that region.     

Primary production dynamics and climate variability: ecological consequences in semiarid Chile

Increase in rainfall variability has important consequences for organisms in arid and semiarid regions around the world. In South American and Australian deserts, the El Niño/Southern Oscillation (ENSO) phenomenon greatly influences rainfall patterns, and therefore the dynamics of plant communities. However, the field data needed to assess the effect of climate change on vegetational patterns is difficult to obtain because of the large spatial scale required for such studies. Normalized Difference Vegetation Index (NDVI) characteristics allow the use of several indexes related to vegetational structure. Due to its direct relationship with primary productivity, it is possible to obtain several measures of annual productivity. These include annual plant yield, annual maximum yield, onset of 'greening-up' and senescence phases, length of the 'green' season, vegetation peak, and therefore, the periods when more or less food is available for herbivores. After verification with ground-truth measures, we used NDVI data from two semiarid localities in north-central Chile (Fray Jorge and Aucó) to determine the relationship between rainfall patterns and vegetation cover and productivity related to El Niño phenomenon. With this information we gauge the influence of climatic processes on primary productivity in western South America, an area subject to strong climate variability. We predict significant variation in Chilean semiarid regions due to climate change, affecting mainly the extent and timing of annual growth season of vegetation, and also including a shorter and delayed greening-up season. Also, we predict that important decreases in rainfall levels will not have strong effects on primary production in these semiarid ecosystems.