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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Are there differences in structure between marine and terrestrial assemblages?

Recently, interest in species abundance (SAD) distributions has been revived by introduction of a new model, the zero-sum multinomial (ZSM). Yet detailed statistical analyses show that the model does not differ from the lognormal distribution proposed in the 1940s. These analyses were based on data from tropical trees where all individuals in a defined area were identified to species. For many ecological data sets it is not possible to identify and count all individuals in a given area. Here we compare data on marine benthos and fish assemblages with data on terrestrial microfauna and ants. We show that these assemblages show similar SAD patterns and that the SADs are best described by a two-group lognormal model. Whereas the 2-group model fitted all data sets the single group model fitted all except the tropical rainforest ants. However, tests comparing the fits to the 2-group versus the single lognormal model showed that the 2-group model was a significantly better fit to the fish and insect data. The two groups are of rare and common species and the rare group dominates in all four data sets. We suggest that the reason for this is that rare species are continuously immigrating from outside the sampled area. Data on tropical tree assemblages where complete accounts were made do not show such high dominance of rare species where the sampled area is large. We conclude that SAD patterns are similar in marine and terrestrial systems that are open to immigration and that the lognormal distribution is still a valid model for SADs.     

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。     

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.     

Evidence from GC-TRFLP that bacterial communities in soil are lognormally distributed

The Species Abundance Distribution (SAD) is a fundamental property of ecological communities and the form and formation of SADs have been examined for a wide range of communities including those of microorganisms. Progress in understanding microbial SADs, however, has been limited by the remarkable diversity and vast size of microbial communities. As a result, few microbial systems have been sampled with sufficient depth to generate reliable estimates of the community SAD. We have used a novel approach to characterize the SAD of bacterial communities by coupling genomic DNA fractionation with analysis of terminal restriction fragment length polymorphisms (GC-TRFLP). Examination of a soil microbial community through GC-TRFLP revealed 731 bacterial operational taxonomic units (OTUs) that followed a lognormal distribution. To recover the same 731 OTUs through analysis of DNA sequence data is estimated to require analysis of 86,264 16S rRNA sequences. The approach is examined and validated through construction and analysis of simulated microbial communities in silico. Additional simulations performed to assess the potential effects of PCR bias show that biased amplification can cause a community whose distribution follows a power-law function to appear lognormally distributed. We also show that TRFLP analysis, in contrast to GC-TRFLP, is not able to effectively distinguish between competing SAD models. Our analysis supports use of the lognormal as the null distribution for studying the SAD of bacterial communities as for plant and animal communities.     

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.     

The gambin model provides a superior fit to species abundance distributions with a single free parameter: evidence,implementation and interpretation

The species abundance distribution (SAD) has been a central focus of community ecology for over fifty years, and is currently the subject of widespread renewed interest. The gambin model has recently been proposed as a model that provides a superior fit to commonly preferred SAD models. It has also been argued that the model's single parameter (α) presents a potentially informative ecological diversity metric, because it summarises the shape of the SAD in a single number. Despite this potential, few empirical tests of the model have been undertaken, perhaps because the necessary methods and software for fitting the model have not existed. Here, we derive a maximum likelihood method to fit the model, and use it to undertake a comprehensive comparative analysis of the fit of the gambin model. The functions and computational code to fit the model are incorporated in a newly developed free‐to‐download R package (gambin). We test the gambin model using a variety of datasets and compare the fit of the gambin model to fits obtained using the Poisson lognormal, logseries and zero‐sum multinomial distributions. We found that gambin almost universally provided a better fit to the data and that the fit was consistent for a variety of sample grain sizes. We demonstrate how α can be used to differentiate intelligibly between community structures of Azorean arthropods sampled in different land use types. We conclude that gambin presents a flexible model capable of fitting a wide variety of observed SAD data, while providing a useful index of SAD form in its single fitted parameter. As such, gambin has wide potential applicability in the study of SADs, and ecology more generally.     

Sampling,sequencing and the SAD

The Species Abundance Distribution (SAD) is a common metric for characterizing macroscopic ecological communities. Recently, this metric has been applied to analysis of microbial communities as well. However, as compared to macroscopic communities, sampling of microscopic communities is different. In particular, most microbial communities are studied using sequencing techniques. These techniques have known biases that result in certain taxa being detected more often than others, even if the taxa are present in the sample at equivalent abundances. There are, for example, amplification biases that result in some sequences being amplified more than others. Likewise, differences in genome size across organisms can result in different numbers of reads from different taxa, again resulting in biased detection. A number of bioinformatics methods have been devised to account for biases in sequencing data, allowing for more accurate estimates of relative taxon abundances. However, because the sampling process itself is affected by biased detection, and because sampling (and under-sampling in particular) can influence the shape of the SAD, it is possible that, even when corrected for through re-scaling, detection biases can affect SAD predictions from sequencing data. To test this hypothesis, we construct a simulation model of the sampling process, focusing on biased detection in shotgun sequencing that arises from genome size differences across microbial taxa. Interestingly, we find that, although genome size itself does not impact SAD predictions, predictions can vary depending on the range of genome sizes that are represented in a community, as well as how genome size is distributed (i.e., whether the majority of species have small versus large genomes). Our results suggest that care should be taken when comparing SADs across environments, particularly when those environments might have taxa with different genome size distributions. Furthermore, our results indicate that relatively deep sequencing might be required to avoid drawing spurious inferences about ecological differences across microbial communities.     

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.     

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.     

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.