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.     

Sampling species abundance distributions: resolving the veil-line debate

Preston's classic work on the theory of species abundance distributions (SADs) in ecology has been challenged by Dewdney. Dewdney contends that Preston's veil-line concept, relating to the shape of sample SADs, is flawed. Here, I show that Preston's and Dewdney's theories can be reconciled by considering the differing mathematical properties of the sampling process on logarithmic (Preston) versus linear (Dewdney) abundance scales. I also derive several related results and show, importantly, that one cannot reject the log-normal distribution as a plausible SAD based only on sampling arguments, as Dewdney and others have done.     

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.     

Self-organizing map and species abundance distribution of stream benthic macroinvertebrates in revealing community patterns in different seasons

Benthic macroinvertebrates are considered to be one of the most representative taxa in assessing the ecological integrity of aquatic ecosystems. Data for benthic macroinvertebrates collected using the Surber sampler were used for analysis at different sampling sites across different levels of pollution. Species Abundance Distribution (SAD) and Self-Organizing Map (SOM) were utilized in combination to reveal both consistency and variability in community compositions under natural and anthropogenic conditions. According to the SOM benthic macroinvertebrates were clustered in different season groups (e.g., “summer”, “autumn–winter”) at the less polluted site. SADs of the sampled communities, however, were overall stable across different seasons except the period from late spring to summer (i.e., low level of abundance for the mid-ranked species in SADs) due to heavy rainfall in the Monsoon climate. Along with increase in degree of pollution, seasonality deceased for both SOMs and SADs. In all seasons, the SAD curves were fitted to a lognormal distribution for the less polluted site while the polluted site was in accordance with a geometric series. The parameters in the SAD models were not significantly different across different seasons. Species in the highest ranks in the SADs were persistently dominant regardless of seasons, while densities of the mid-ranked species were variable in different seasons at the less and intermediately polluted sites. At the severely polluted site a few selected tolerant species showed high densities persistently and variability of densities in different seasons was minimized. Species groups clustered using the SOM also presented stronger persistence in SADs, and were feasible in addressing diverse patterns of species composition and in outlining species associations presented in different sampling sites through ordination and clustering. The combined use of SOM and SAD is highly be suitable in presenting community properties and ecological integrity in stream ecosystems in response to natural variability and anthropogenic disturbances.     

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。     

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.     

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.     

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.     

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。     

Self-similarity in species–area relationship and in species abundance distribution

In an influential paper, Harte et al. highlighted the scaling or 'self-similar' character of the power law species–area relationship (SAR), and used this feature to derive a species abundance distribution (SAD) and an endemics–area relationship. Here I show that their analysis was incorrect and leads to unrealistic results. I develop a different approach and obtain different results, both for SAD and for endemism. In particular, I show that the power law SAR is naturally associated with the power law statistical distribution, which is the only self-similar distribution and closely matches empirical SADs. The results in this paper shed light on some of the main issues that have been discussed with regard to SARs: their relationship with the lognormal and with the neutral theory, the relative importance of sampling effects vs other mechanisms, and the deviations from a power law. The equations that I develop are simple and easy to apply to field studies.     

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.     

Neutral theory and the species abundance distribution: recent developments and prospects for unifying niche and neutral perspectives

Published in 2001, The Unified Neutral Theory of Biodiversity and Biogeography (UNTB) emphasizes the importance of stochastic processes in ecological community structure, and has challenged the traditional niche‐based view of ecology. While neutral models have since been applied to a broad range of ecological and macroecological phenomena, the majority of research relating to neutral theory has focused exclusively on the species abundance distribution (SAD). Here, we synthesize the large body of work on neutral theory in the context of the species abundance distribution, with a particular focus on integrating ideas from neutral theory with traditional niche theory. First, we summarize the basic tenets of neutral theory; both in general and in the context of SADs. Second, we explore the issues associated with neutral theory and the SAD, such as complications with fitting and model comparison, the underlying assumptions of neutral models, and the difficultly of linking pattern to process. Third, we highlight the advances in understanding of SADs that have resulted from neutral theory and models. Finally, we focus consideration on recent developments aimed at unifying neutral‐ and niche‐based approaches to ecology, with a particular emphasis on what this means for SAD theory, embracing, for instance, ideas of emergent neutrality and stochastic niche theory. We put forward the argument that the prospect of the unification of niche and neutral perspectives represents one of the most promising future avenues of neutral theory research.     

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.     

Ecological response hides behind the species abundance distribution: Community response to low‐intensity disturbance in managed grasslands

Land‐use and management are disturbance factors that have diverse effects on community composition and structure. In traditional rural grasslands, such as meadows and pastures, low‐intensity management is maintained to enhance biodiversity. Maintenance of road verges, in turn, creates habitat, which may complement traditional rural grasslands. To evaluate the effect of low‐intensity disturbance on insect communities, we characterized species abundance distributions (SAD) for Carabidae, Formicidae, and Heteroptera in three grassland types, which differed in management: meadows, pastures, and road verges. The shape of SAD was estimated with three parameters: abundance decay rate, dominance, and rarity. We compared the SAD shape among the grassland types and tested the effect of environmental heterogeneity (plant species richness) and disturbance intensity (trampling in pastures) on SADs. The shape of SADs did not differ among the grassland types but among the taxonomic groups instead. Abundance decay rate and dominance were larger for Formicidae, and rarity smaller, than for Carabidae and Heteroptera. For Carabidae and window‐trapped Heteroptera, rarity increased with increasing plant species richness. For Formicidae, dominance increased with trampling intensity in pastures. Although the SAD shape remained largely unchanged, the identity of the dominant species tended to vary within and among grassland types. Our study shows that for a given taxonomic group, the SAD shape is similar across habitat types with low‐intensity disturbances resulting from different management. This suggests that SADs respond primarily to the intensity of disturbance and thus could be best used in monitoring communities across strong disturbance and environmental gradients. Because taxonomic groups can inherently have different SADs, taxon‐specific SADs for undisturbed communities must be empirically documented before the SAD shape can be used as an indicator of environmental change. Because the identity of the dominant species changes from management type to another, the SAD shape alone is not an adequate monitoring tool.     

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.     

Universal ecological patterns in college basketball communities

The rank abundance of common and rare species within ecological communities is remarkably consistent from the tropics to the tundra. This invariant patterning provides one of ecology's most enduring and unified tenets: most species rare and a few very common. Increasingly, attention is focused upon elucidating biological mechanisms that explain these species abundance distributions (SADs), but these evaluations remain controversial. We show that college basketball wins generate SADs just like those observed in ecological communities. Whereas college basketball wins are structured by competitive interactions, the result produces a SAD pattern indistinguishable from random wins. We also show that species abundance data for tropical trees exhibits a significant-digit pattern consistent with data derived from complex structuring forces. These results cast doubt upon the ability of SAD analysis to resolve ecological mechanism, and their patterning may reflect statistical artifact as much as biological processes.     

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.     

Taking species abundance distributions beyond individuals

The species abundance distribution (SAD) is one of the few universal patterns in ecology. Research on this fundamental distribution has primarily focused on the study of numerical counts, irrespective of the traits of individuals. Here we show that considering a set of Generalized Species Abundance Distributions (GSADs) encompassing several abundance measures, such as numerical abundance, biomass and resource use, can provide novel insights into the structure of ecological communities and the forces that organize them. We use a taxonomically diverse combination of macroecological data sets to investigate the similarities and differences between GSADs. We then use probability theory to explore, under parsimonious assumptions, theoretical linkages among them. Our study suggests that examining different GSADs simultaneously in natural systems may help with assessing determinants of community structure. Broadening SADs to encompass multiple abundance measures opens novel perspectives in biodiversity research and warrants future empirical and theoretical developments.     

亚高寒草甸不同生境植物群落物种多度分布格局的拟合

物种多度分布是群落生态学研究的核心内容。通过对青藏高原东部亚高寒草甸3种不同生境草本植物群落的抽样调查,结合16个物种多度分布模型的两种曲线拟合优度检验得出如下结果：多种不同模型可以拟合同一生境的物种多度分布。相比于其他可拟合模型,几何级数模型在3种生境中两种拟合优度检验方法下的平均拟合效果是最好的,拟合优度值均在最优拟合优度值10左右波动。次优模型鉴于不同生境不同的检验方法表现不一。除了几何级数模型外,Sugihara分数模型在最小二乘法的拟合方法下,也可以拟合3种生境的物种多度分布。研究结果表明,仅用拟合优度检验区分产生不同物种分布格局的模型和机制是不可靠的,需要做进一步的检验性实验研究。     

The contribution of common and rare species to species abundance patterns in alpine meadows: The effect of elevation gradients

Ecological niche modeling uses environmental variables associated with species distribution points to simulate species distribution and its importance in biodiversity conservation. This study aimed to quantify plant community composition and species abundance distribution (SAD) in alpine meadows at different elevations and to assess the contribution of rare and common species to SAD. We established a permanent study plot of 210 hm² in Gannan Tibetan Autonomous Prefecture, China, surveyed 315 sample squares (0.5 m × 0.5 m), and calculated the Hill numbers. The results showed that (1) a total of 72 species were surveyed at different altitudes, with Kobresia humilis and Kobresia macrantha as the main dominant species; (2) the SADs of overall and common species fit the ecological niche model (GSM (Geometric Sequence Model)), indicating that ecological niche differentiation is the main factor influencing SAD. The fitted model for rare species SAD varied with elevation, suggesting that various ecological processes influence rare species SAD. (3) Hill numbers showed a “single peak” pattern with increasing elevation. The number of rare species was higher than that of common species. Still, the distribution frequency of common species was significantly higher than rare species. The correlation between common-rare species sequences and cumulative species distribution was high. This indicates that common species dominate the species diversity pattern of the community, are the main contributors to the SAD pattern, and should be protected first. Rare species are also important carriers of community function and include much spatial information. Rare and common species work together in different ways to influence and maintain the species diversity patterns of alpine meadow plant communities.