The implicit assumption of symmetry and the species abundance distribution

Species abundance distributions (SADs) have played a historical role in the development of community ecology. They summarize information about the number and the relative abundance of the species encountered in a sample from a given community. For years ecologists have developed theory to characterize species abundance patterns, and the study of these patterns has received special attention in recent years. In particular, ecologists have developed statistical sampling theories to predict the SAD expected in a sample taken from a region. Here, we emphasize an important limitation of all current sampling theories: they ignore species identity. We present an alternative formulation of statistical sampling theory that incorporates species asymmetries in sampling and dynamics, and relate, in a general way, the community-level SAD to the distribution of population abundances of the species integrating the community. We illustrate the theory on a stochastic community model that can accommodate species asymmetry. Finally, we discuss the potentially important role of species asymmetries in shaping recently observed multi-humped SADs and in comparisons of the relative success of niche and neutral theories at predicting SADs.     

天童常绿阔叶林中常绿与落叶物种的物种多度分布格局

物种多度分布是对群落内不同物种多度情况的数量描述, 作为理解群落性质的基石, 其形成机制受到广泛关注。常绿与落叶物种是两类有着不同物候性状与生长策略的物种集合, 它们普遍共存于常绿阔叶林中。在天童20 ha常绿阔叶林动态监测样地内, 虽然常绿物种在物种多度和胸高断面积等指标上占有绝对优势, 但其在物种丰富度上却不及落叶物种。分析两者在常绿阔叶林中的物种多度分布特征, 能够为理解常绿阔叶林内物种多样性的维持机制提供一个全新的视角。为此, 我们基于天童样地的植被调查数据, 一方面利用累积经验分布函数对两类生活型植物的物种多度分布进行描述, 使用Kolmogorov-Smirnov检验(K-S检验)判断其差异性; 另一方面, 采用纯统计模型、生态位模型和中性理论模型对二者的物种多度分布曲线进行拟合, 并基于K-S检验的结果以及AIC值进行最优模型的筛选。结果显示: (1)常绿与落叶物种的物种多度分布曲线间并无显著差异。(2)在选用的3类模型中, 中性理论模型对于两类物种多度分布曲线的拟合效果都最好, 而生态位模型的拟合效果则一般。从上述结果可以看出, 尽管常绿与落叶物种在物种数量和多度等方面均存在差异, 但它们却有着近似的物种多度分布格局以及相近的多样性维持机制。然而, 鉴于模型拟合的结果只能作为理解群落多样性构建机制的必要非充分条件, 故而只能初步判定中性过程对于常绿与落叶物种的物种多样性格局影响更大, 却不能排除或衡量诸如生态位分化等其他过程在两类生活型多样性格局形成中的贡献。     

Responses of species abundance distribution patterns to spatial scaling in subtropical secondary forests

To quantify and assess the processes underlying community assembly and driving tree species abundance distributions(SADs) with spatial scale variation in two typical subtropical secondary forests in Dashanchong state‐owned forest farm, two 1‐ha permanent study plots (100‐m × 100‐m) were established. We selected four diversity indices including species richness, Shannon–Wiener, Simpson and Pielou, and relative importance values to quantify community assembly and biodiversity. Empirical cumulative distribution and species accumulation curves were utilized to describe the SADs of two forests communities trees. Three types of models, including statistic model (lognormal and logseries model), niche model (broken‐stick, niche preemption, and Zipf‐Mandelbrodt model), and neutral theory model, were estimated by the fitted SADs. Simulation effects were tested by Akaike's information criterion (AIC) and Kolmogorov–Smirnov test. Results found that the Fagaceae and Anacardiaceae families were their respective dominance family in the evergreen broad‐leaved and deciduous mixed communities. According to original data and random sampling predictions, the SADs were hump‐shaped for intermediate abundance classes, peaking between 8 and 32 in the evergreen broad‐leaved community, but this maximum increased with size of total sampled area size in the deciduous mixed community. All niche models could only explain SADs patterns at smaller spatial scales. However, both the neutral theory and purely statistical models were suitable for explaining the SADs for secondary forest communities when the sampling plot exceeded 40 m. The results showed the SADs indicated a clear directional trend toward convergence and similar predominating ecological processes in two typical subtropical secondary forests. The neutral process gradually replaced the niche process in importance and become the main mechanism for determining SADs of forest trees as the sampling scale expanded. Thus, we can preliminarily conclude that neutral processes had a major effect on biodiversity patterns in these two subtropical secondary forests but exclude possible contributions of other processes.     

长白山阔叶红松林草本层物种多度分布格局及其季节动态

草本层是森林生态系统的重要组成部分, 对维持森林生物多样性具有重要意义。本文以长白山阔叶红松(Pinus koraiensis)林25 ha固定监测样地为研究平台, 运用不同的统计模型(对数正态模型和对数级数模型)及机理模型(包括生态位模型: 断棍模型和生态位优先占领模型; 中性模型: 复合群落零和多项式模型和Volkov模型), 对不同季节草本物种多度分布进行拟合。采用Kolmogorov-Smirnov和AIC检验确定最优模型, 以揭示草本层物种多度分布格局随季节的变化规律, 探讨草本层物种组成与结构背后的生态学过程。结果表明: (1)草本层物种多度分布季节差异明显。春季各多度级物种数差异不大, 夏季中间种较多, 秋季则是稀有种较多; (2)模型拟合结果显示, 不同季节草本层物种多度分布的最优拟合模型相近。统计模型中对数级数模型表现最优, 机理模型中中性模型的拟合效果优于生态位模型。复合群落零和多项式模型较好地拟合了春夏季草本物种多度分布, Volkov模型较好地拟合了秋季草本物种多度分布。综上所述, 尽管长白山阔叶红松林草本植物不同季节的物种多度分布格局不尽一致, 但其背后的构建机制相似, 中性随机过程在草本层物种多样性维持过程中显得更为重要。     

Evaluating the performance of neutrality tests of a local community using a niche‐structured simulation model

Understanding the processes that underlie species diversity and abundance in a community is a fundamental issue in community ecology. While the species abundance distributions (SADs) of various natural communities may be well explained by Hubbell's neutral model, it has been repeatedly pointed out that Hubbell's SAD‐fitting approach lacks the ability to detect the effects of non‐neutral factors such as niche differentiation; however, our understanding of its quantitative effect is limited. Herein, we conducted extensive simulations to quantitatively evaluate the performance of the SAD‐fitting method and other recently developed tests. For simulations, we developed a niche model that incorporates the random stochastic demography of individuals and the nonrandom replacements of those individuals, i.e. niche differentiation. It therefore allows us to explore situations with various degrees of niche differentiation. We found that niche differentiation has strong effects on SADs and the number of species in the community under this model. We then examined the performance of these neutrality tests, including Hubbell's SAD‐fitting method, using extensive simulations. It was demonstrated that all these tests have relatively poor performance except for the cases with very strong niche structure, which is in accordance with previous studies. This is likely because two important parameters in Hubbell's model are usually unknown and are commonly estimated from the data to be tested. To demonstrate this point, we showed that the precise estimation of the two parameters substantially improved the performance of these neutrality tests, indicating that poor performance can be owed to overfitting Hubbell's neutral model with unrealistic parameters. Our results therefore emphasize the importance of accurate parameter estimation, which should be obtained from data independent of the local community to be tested.     

Separating the effect of mechanisms shaping species‐abundance distributions at multiple scales in a subtropical forest

Species abundance distributions (SADs) play an important role in the current dispute over mechanisms shaping community assembly. Niche theory assumes differential occurrence of species in different habitats while neutral theory emphasizes stochastic events and dispersal. The previous tests of niche and neutral models shaping SADs lead to the claim that SADs are not informative for inferring underlying processes. Using spatial statistical models in a fully mapped 24‐ha subtropical forest in China, we first demonstrate that one can not distinguish between the effect of habitat heterogeneity and dispersal limitation on SADs by inspecting whether the observed SADs fall within 95% confidence intervals of the simulated SADs. Subsequently, we demonstrate that SADs can be used to detect mechanisms shaping SADS by comparing alternative process‐based models using model selection techniques. We found that dispersal limitation explain SADs at smaller spatial scales, while the combination of niche and dispersal limitation explain SADs at larger scales. These processes are linked with the degree of conspecific aggregation, informing further attempts to refine and parameterize the statistical theory of sampling SADs.     

Universal scaling of species‐abundance distributions across multiple scales

The scale‐dependent species abundance distribution (SAD) is fundamental in ecology, but few spatially explicit models of this pattern have thus far been studied. Here we show spatially explicit neutral model predictions for SADs over a wide range of spatial scales, which appear to match empirical patterns qualitatively. We find that the assumption of a log‐series SAD in the metacommunity made by spatially implicit neutral models can be justified with a spatially explicit model in the large area limit. Furthermore, our model predicts that SADs on multiple scales are characterized by a single, compound parameter that represents the ratio of the survey area to the species’ average biogeographic range (which is in turn set by the speciation rate and the dispersal distance). This intriguing prediction is in line with recent empirical evidence for a universal scaling of the species‐area curve. Hence we hypothesize that empirical SAD patterns will show a similar universal scaling for many different taxa and across multiple spatial scales.     

On the statistical mechanics of species abundance distributions

A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of  [Volkov et?al., 2003] and [Volkov et?al., 2005] and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure.     

Diversity: between neutrality and structure

Here I present an integrated framework for species abundance distributions (SADs) that goes beyond the neutral theory without relying on complex mechanistic models. I give some general mathematical results on the relationship between SADs and their underlying dynamics, and analyse an extensive set of marine phytoplankton data in order to test the neutral theory against this broader framework.
The main theoretical and empirical results are: (i) the logseries, which is the SAD produced by simple neutral models without migration, is quite robust in response to additional factors, including some forms of niche segregation; (ii) when there is a small but significant deviation from a logseries, the SAD will generally have the form of a power law, regardless of the specific mechanisms; (iii) when the deviation is moderate, the SAD will generally have the form of a lognormal, regardless of the specific mechanisms; (iv) although in a wide range of situations neutral and non-neutral dynamics cannot be distinguished from the SAD alone, some empirical SADs do have the fingerprint of non-neutrality: this is the case of marine dinoflagellates, in contrast to marine diatoms, which adjust to neutral theory predictions. The results for marine phytoplankton illustrate that both neutral and non-neutral mechanisms coexist in nature, and seem to have different weights in different groups of organisms.
In addition to the above findings, I discuss several related contributions and point out some important pitfalls in the literature.     

Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework

Species abundance distributions (SADs) follow one of ecology's oldest and most universal laws – every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science.     

Cryptic diversity in a fig wasp community—morphologically differentiated species are sympatric but cryptic species are parapatric

A key debate in ecology centres on the relative importance of niche and neutral processes in determining patterns of community assembly with particular focus on whether ecologically similar species with similar functional traits are able to coexist. Meanwhile, molecular studies are increasingly revealing morphologically indistinguishable cryptic species with presumably similar ecological roles. Determining the geographic distribution of such cryptic species provides opportunities to contrast predictions of niche vs. neutral models. Discovery of sympatric cryptic species increases alpha diversity and supports neutral models, while documentation of allopatric/parapatric cryptic species increases beta diversity and supports niche models. We tested these predictions using morphological and molecular data, coupled with environmental niche modelling analyses, of a fig wasp community along its 2700‐km latitudinal range. Molecular methods increased previous species diversity estimates from eight to eleven species, revealing morphologically cryptic species in each of the four wasp genera studied. Congeneric species pairs that were differentiated by a key morphological functional trait (ovipositor length) coexisted sympatrically over large areas. In contrast, morphologically similar species, with similar ovipositor lengths, typically showed parapatric ranges with very little overlap. Despite parapatric ranges, environmental niche models of cryptic congeneric pairs indicate large regions of potential sympatry, suggesting that competitive processes are important in determining the distributions of ecologically similar species. Niche processes appear to structure this insect community, and cryptic diversity may typically contribute mostly to beta rather than alpha diversity.     

How species richness and total abundance constrain the distribution of abundance

The species abundance distribution (SAD) is one of the most intensively studied distributions in ecology and its hollow‐curve shape is one of ecology's most general patterns. We examine the SAD in the context of all possible forms having the same richness (S) and total abundance (N), i.e. the feasible set. We find that feasible sets are dominated by similarly shaped hollow curves, most of which are highly correlated with empirical SADs (most R² values > 75%), revealing a strong influence of N and S on the form of the SAD and an a priori explanation for the ubiquitous hollow curve. Empirical SADs are often more hollow and less variable than the majority of the feasible set, revealing exceptional unevenness and relatively low natural variability among ecological communities. We discuss the importance of the feasible set in understanding how general constraints determine observable variation and influence the forms of predicted and empirical patterns.     

Species abundance distributions as a proxy for the niche-neutrality continuum

Aims Species abundance distributions (SADs) are often used to verify mechanistic theories underlying community assembly. However, it is now accepted that SADs alone are not sufficient to reveal biological mechanisms. Recent attention focuses on the relative importance of stochastic dispersal processes versus deterministic processes such as interspecific competition and environmental filtering. Here, we combine a study of the commonness and rarity of species (i.e. the SAD) with mechanistic processes underlying community composition. By comparing the occurrence frequencies of each and every species with its abundance, we quantify the relative contributions of common and rare species to the maintenance of community structure. Essentially, we relate the continuum between commonness and rarity with that of niches and neutrality.Methods An individual-based, spatially explicit model was used to simulate local communities in niche spaces with the same parameters. We generated sets of assemblages from which species were eliminated in opposing sequences: from common to rare and from rare to common, and investigated the relationship between the abundance and frequency of species. We tested the predictions of our model with empirical data from a field experiment in the environmentally homogeneous alpine meadows of the Qinghai–Tibetan plateau.Important findings Our simulations support the widespread notion that common species maintain community structure, while rare species maintain species diversity, in both local and regional communities. Our results, both from theoretical simulations and from empirical observations, revealed positive correlations between the abundance of a particular species and its occurrence frequency. SAD curves describe a continuum between commonness and rarity. Removing species from the 'rare' end of this continuum has little effect on the similarity of communities, but removing species from the 'common' end of the continuum causes significant increases in beta diversity, or species turnover, between communities. In local communities distributed in a homogenous habitat, species located at the 'common' end of the continuum should be selected by environmental filtering, with niche space partitioning governed by interspecific competition. Conversely, species located at the 'rare' end of the continuum are most likely subject to stochastic dispersal processes. Species situated at intermediate locations on this continuum are therefore determined by niche and neutral processes acting together. Our results suggest that, in homogeneous habitats, SAD curves describing the common-rare continuum may also be used to describe the continuum between niches and neutrality.     

生态位模型的理论基础、发展方向与挑战

生态位模型是一个以生态位理论为基础的新兴研究领域.它通过采集研究对象的已知分布点及其相关的环境数据组成训练样本,利用数理统计或机器学习理论分析数据,构建特征函数表示物种在生态位空间的实际生态位.以生态位模型预测物种潜在分布地或计算物种间的生态位重叠等研究,在生态学、生物地理学和进化生物学研究中显得越来越重要.本文从生态位概念出发,详细解析了生态位模型的理论基础、相关的焦点争论、使用时的注意点以及可能的发展方向与面临的挑战,指出模型中要考虑人类活动对物种生态位的影响.希望本文所探讨的本领域最新的争论焦点能引起相关学者的关注与深入思考.     

Neutral theory in community ecology

One of the central goals of community ecology is to understand the forces that maintain species diversity within communities. The traditional niche-assembly theory asserts that species live together in a community only when they differ from one another in resource uses. But this theory has some difficulties in explaining the diversity often observed in specie-rich communities such as tropical forests. As an alternative to the niche theory, Hubbell and other ecologists introduced a neutral model. Hubbell argues that the number of species in a community is controlled by species extinction and immigration or speciation of new species. Assuming that all individuals of all species in a trophically similar com-munity are ecologically equivalent, Hubbell's neutral theory predicts two important statistical distributions. One is the asymptotic log-series distribution for the metacommunities under point mutation speciation, and the other is the zero-sum multinomial distribution for both local communities under dispersal limitation and metacommunities under random fission speciation. Unlike the niche-assembly theory, the neutral theory takes similarity in species and individuals as a starting point for investigating species diversity. Based on the fundamental processes of birth, death, dispersal and spe-ciation, the neutral theory provided the first mechanistic explanation of species abundance distribution commonly observed in natural communities. Since the publication of the neutral theory, there has been much discussion about it, pro and con. In this paper, we summarize recent progress in the assumption, prediction and speciation mode of the neutral theory, including progress in the theory itself, tests about the assumption of the theory, prediction and speciation mode at the metacommunity level. We also suggest that the most important task in the future is to bridge the niche-assembly theory and the neutral theory, and to add species differences to the neutral theory and more stochasticity to the niche theory.     

Scaling issues of neutral theory reveal violations of ecological equivalence for dominant Amazonian tree species

Neutral models are often used as null models, testing the relative importance of niche versus neutral processes in shaping diversity. Most versions, however, focus only on regional scale predictions and neglect local level contributions. Recently, a new formulation of spatial neutral theory was published showing an incompatibility between regional and local scale fits where especially the number of rare species was dramatically under‐predicted. Using a forward in time semi‐spatially explicit neutral model and a unique large‐scale Amazonian tree inventory data set, we show that neutral theory not only underestimates the number of rare species but also fails in predicting the excessive dominance of species on both regional and local levels. We show that although there are clear relationships between species composition, spatial and environmental distances, there is also a clear differentiation between species able to attain dominance with and without restriction to specific habitats. We conclude therefore that the apparent dominance of these species is real, and that their excessive abundance can be attributed to fitness differences in different ways, a clear violation of the ecological equivalence assumption of neutral theory.     

Is there an ecological basis for species abundance distributions?

Community ecologists have attempted to explain species abundance distribution (SAD) shape for more than 80 years, but usually without relating SAD shape explicitly to ecological variables. We explored whether the scale (total assemblage abundance) and shape (assemblage evenness) of avifaunal SADs were related to ecological covariates. We used data on avifaunas, in-site habitat structure and landscape context that were assembled from previous studies; this amounted to 197 transects distributed across 16,000 km² of the box-ironbark forests of southeastern Australia. We used Bayesian conditional autoregressive models to link SAD scale and shape to these ecological covariates. Variation in SAD scale was relatable to some ecological covariates, especially to landscape vegetation cover and to tree height. We could not find any relationships between SAD shape and ecological covariates. SAD shape, the core component in SAD theory, may hold little information about how assemblages are governed ecologically and may result from statistical processes, which, if general, would indicate that SAD shape is not useful for distinguishing among theories of assemblage structure.     

A meta‐analysis of species–abundance distributions

The species–abundance distribution (SAD) describes the abundances of all species within a community. Many different models have been proposed to describe observed SADs. Best known are the logseries, the lognormal, and a variety of niche division models. They are most often visualized using either species richness – log abundance class (Preston) plots or abundance – species rank order (Whittaker) plots. Because many of the models predict very similar shapes, model distinction and testing become problematic. However, the variety of models can be classified into three basic types: one that predicts a double S‐shape in Whittaker plots and a unimodal distribution in Preston plots (the lognormal type), a second that lacks the mode in Preston plots (the logseries type), and a third that predicts power functions in both plotting types (the power law type). Despite the interest of ecologists in SADs no formal meta‐analysis of models and plotting types has been undertaken so far. Here we use a compilation of 558 species–abundance distributions from 306 published papers to infer the frequency of the three SAD shapes in dependence of environmental variables and type of plotting. Our results highlight the importance of distinguishing between fully censused and incompletely sampled communities in the study of SADs. We show that completely censused terrestrial or freshwater animal communities tend to follow lognormal type SADs more often than logseries or power law types irrespective of species richness, spatial scale, and geographic position. However, marine communities tend to follow the logseries type, while plant communities tend to follow the power law. In incomplete sets the power law fitted best in Whittaker plots, and the logseries in Preston plots. Finally our study favors the use of Whittaker over Preston plots.     

Niche versus neutrality in structuring the beta diversity of damselfly assemblages

1. Differences among communities in taxonomic composition – beta diversity – are frequently expected to result from taxon‐specific responses to spatial variation in ecological conditions, through niche partitioning. Such process‐derived patterns are in sharp contrast to arguments from neutral theory, where taxa are ecologically equivalent and beta diversity results primarily from dispersal limitation. 2. Here, we compared beta diversity among assemblages of damselflies (Odonata: Zygoptera), for which previous experiments have shown that niche differences maintain genera within a community, but patterns of relative abundance for species within each genus are shaped primarily by neutral dynamics. 3. Using null‐model and ordination‐based methods, we find that both genera and (in contrast to neutral theory) species assemblage composition vary across the landscape in a deterministic fashion, shaped by environmental and spatial factors. 4. While the observed patterns in species composition conflict with theory, we suggest that this a result of weak ecological filters acting to produce spatial variation in assemblages of ecologically similar species undergoing ecological drift within communities. Such patterns are especially likely in systems of relatively weak dispersers like damselflies.