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.     

A statistical theory for sampling species abundances

The pattern of species abundances is central to ecology. But direct measurements of species abundances at ecologically relevant scales are typically unfeasible. This limitation has motivated a long-standing interest in the relationship between the abundance distribution in a large, regional community and the distribution observed in a small sample from the community. Here, we develop a statistical sampling theory to describe how observed patterns of species abundances are influenced by the spatial distributions of populations. For a wide range of regional-scale abundance distributions we derive exact expressions for the sampled abundance distributions, as a function of sample size and the degree of conspecific spatial aggregation. We show that if populations are randomly distributed in space then the sampled and regional-scale species-abundance distribution typically have the same functional form: sampling can be expressed by a simple scaling relationship. In the case of aggregated spatial distributions, however, the shape of a sampled species-abundance distribution diverges from the regional-scale distribution. Conspecific aggregation results in sampled distributions that are skewed towards both rare and common species. We discuss our findings in light of recent results from neutral community theory, and in the context of estimating biodiversity.     

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.     

Inferring species abundance distribution across spatial scales

A long-standing problem in ecology is to understand how the species–abundance distribution (SAD) varies with sampling scale. The problem was first characterized by Preston as the veil line problem. Although theoretical and empirical studies have now shown the nonexistence of the veil line, this problem has generated much interest in scaling biodiversity patterns. However, research on scaling SAD has so far exclusively focused on the relationship between the SAD in a smaller sampling area and a known SAD assumed for a larger area. An unsolved challenge is how one may predict species–abundance distribution in a large area from that of a smaller area. Although upscaling biodiversity patterns (e.g. species–area curve) is a major focus of macroecological research, upscaling of SAD across scale is, with few exceptions, ignored in the literature. Methods that directly predict SAD in a larger area from that of a smaller area have just started being developed. Here we propose a Bayesian method that directly answers this question. Examples using empirical data from tropical forests of Malaysia and Panama are employed to demonstrate the use of the method and to examine its performance with increasing sampling area. The results indicate that only 10-15% of the total census area is needed to adequately predict species abundance distribution of a region. In addition to species abundance distributions, the method also predicts well the regional species richness.     

长白山不同演替阶段针阔混交林群落物种多度分布格局

为解释长白山温带森林群落构建和物种多度格局的形成过程, 该文以不同演替阶段的针阔混交林监测样地数据为基础, 采用中性理论模型、生物统计模型(对数正态分布模型)和生态位模型(Zifp模型、分割线段模型、生态位优先模型)拟合森林群落物种多度分布, 并用χ ²检验、Kolmogorov-Smirnov (K-S)检验和赤池信息准则(AIC)选择最佳拟合模型。结果显示: 中性模型能很好地预测长白山温带森林不同演替阶段植物群落的物种多度分布。在10 m × 10 m尺度上, 5种模型均可被χ ²检验和K-S检验接受, 但中性模型拟合效果不如对数正态分布模型、Zifp模型、分割线段模型和生态位优先模型, 表明小尺度上中性过程和生态位过程均能解释群落物种多度分布, 但生态位过程的解释能力相对较大。而在中大尺度上(30 m × 30 m、60 m × 60 m和90 m × 90 m), 中性模型为最优拟合模型, 并且随着研究尺度增加, 生态位模型和生物统计模型逐渐被χ ²检验拒绝, 表明中性过程在长白山针阔混交林群落物种多度分布格局形成中的作用随着研究尺度增加而逐渐增大。该文证实了中性过程在长白山温带针阔混交林群落结构形成中具有重要作用, 但未否认生态位机制在群落构建中的贡献。因此, 温带森林群落构建过程中中性理论和生态位理论并非相互矛盾, 而是相互融合的。在研究森林群落物种多度分布时, 应重视取样尺度和演替阶段的影响, 并采用多种模型进行拟合。     

Multiple modes in a coral species abundance distribution

Species abundance distributions are an important measure of biodiversity and community structure. These distributions are affected by sampling, and alternative species-abundance models often make similar predictions for small sample sizes. Very large samples reveal the relative abundances of rare species, and thus provide information about species relative abundances that small samples cannot. Here, we present the species-abundance distribution for a sample of > 40,000 coral colonies at a single site, exceeding existing samples of coral local assemblages by over an order of magnitude. This abundance distribution is multimodal when examined on a logarithmic scale. Four different model selection procedures all indicate that the underlying community abundance distribution has at least three modes. We show that the multiple modes are not caused by mixtures of species with different habitat preferences. However, spatial aggregation partially explains our results. We inspect published work on species abundance distributions, and suggest that multimodality may be a common feature of large samples.     

The wealth of species: ecological communities, complex systems and the legacy of Frank Preston

General statistical patterns in community ecology have attracted considerable recent debate. Difficulties in discriminating among mathematical models and the ecological mechanisms underlying them are likely related to a phenomenon first described by Frank Preston. He noted that the frequency distribution of abundances among species was uncannily similar to the Boltzmann distribution of kinetic energies among gas molecules and the Pareto distribution of incomes among wage earners. We provide additional examples to show that four different 'distributions of wealth' (species abundance distributions, species–area and species–time relations, and distance decay of compositional similarity) are not unique to ecology, but have analogues in other physical, geological, economic and cultural systems. Because these appear to be general statistical patterns characteristic of many complex dynamical systems they are likely not generated by uniquely ecological mechanistic processes.     

Links between the species abundance distribution and the shape of the corresponding rank abundance curve

Species abundance distribution (SAD) is a classic topic of multispecies ecology. Different types of SAD may indicate specific environmental conditions. A possible way to present some properties of a theoretical or empirical SAD is the construction of a rank-abundance curve (RAC). With regard to the applicability of the RAC as a widely used indicator of the structure of a multispecies community and of the ecological status of its habitat, a basic question is the link between the type of SAD and the shape of the associated RAC. One of the simplest ways to characterize a RAC is to determine its concave and convex segments. However, none of ecological textbooks does give a clear-cut guideline concerning this issue. In the paper a connection is presented between some types of SAD and the convex and concave segments of the related RAC: including among others linearity for the geometric SAD (e.g. with communities in early stage of succession), convexity for the Zipf-Mandelbrot SAD (e.g. with communities with slow successional process), and convexity and then concavity with an inflexion point at approximately the mode of the associated histogram for the lognormal SAD (e.g. with climax, equilibrium communities). Our approach has the potential to improve and justify the use of RACs when searching for the determinants of community structure, initiating further studies in this field.     

The form of species-abundance distributions

Small, isolated communities in harsh environments are sometimes found to contain many, very rare species together with a few, extremely abundant ones. The species-abundance distribution (frequencies of species vs. abundance levels) drops rapidly from an initial peak to an elongated tail. A distribution with similar form is also predicted by a model of resource apportioning. This concurrence has been viewed by some as evidence of the accuracy of the model. However, it is shown here that such a form is to be expected whenever species abundances are not influenced greatly by either immigration or density-dependent regulation.The species-abundance distribution in larger communities is often found to increase initially to a mode, and then decrease to an elongated tail. This form is also to be expected whenever each species in the larger “community” consists of a substantial number of roughly independent populations.     

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.     

A general framework for the distance-decay of similarity in ecological communities

Species spatial turnover, or β -diversity, induces a decay of community similarity with geographic distance known as the distance–decay relationship. Although this relationship is central to biodiversity and biogeography, its theoretical underpinnings remain poorly understood. Here, we develop a general framework to describe how the distance–decay relationship is influenced by population aggregation and the landscape-scale species-abundance distribution. We utilize this general framework and data from three tropical forests to show that rare species have a weak influence on distance–decay curves, and that overall similarity and rates of decay are primarily influenced by species abundances and population aggregation respectively. We illustrate the utility of the framework by deriving an exact analytical expression of the distance–decay relationship when population aggregation is characterized by the Poisson Cluster Process. Our study provides a foundation for understanding the distance–decay relationship, and for predicting and testing patterns of beta-diversity under competing theories in ecology.     

Effects of community structure on the species–area relationship in China's forests

The species–area relationship (SAR) is the oldest and most frequently documented law in ecology. In a community, the SAR is regulated by the abiotic environment and biotic interactions and depends on the individual–spatial distribution of species (ISD) and the species–abundance distribution (SAD). In this study, we explored the effects of aggregation of ISDs and unevenness of SADs on SARs in forests of China by comparing the empirical and simulated SARs of 32 nested plots distributed along an extensive latitudinal gradient. Both aggregation and unevenness affected the shape of SARs significantly: ISDs accounted for 12.6 ± 4.0% of the incremental increase in species richness with area, and SADs accounted for 18.7 ± 3.8 and 23.5 ± 3.9% under the broken‐stick model and even abundance model, respectively. Effects of both aggregation and unevenness decreased as temperature increased, suggesting that individuals of a species were spatially more aggregated than random, and the individuals among species were more discrepant from the null distribution (broken‐stick model and even abundance model in this study), in the cold than in the warm areas. Taken together, our results demonstrate that ISDs and SADs within communities can shape SARs, but these effects vary along latitudinal gradients, and are likely mediated by temperature.     

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.     

Distribution-abundance relationship for passerines breeding in Tunisian oases: test of the sampling hypothesis

The positive relationship between local abundance and distribution of species is a widely recognized pattern in community ecology. However, it has been suggested that this relationship can simply be an artefact of sampling because locally rare species are less detectable then locally abundant ones, and hence their distribution can easily be underestimated. Here, we use count data to investigate the relationship between distribution and abundance of passerines breeding in a sample of oases from southern Tunisia, and we provide a test of the sampling artefact hypothesis. In particular, we checked for a difference in detection probability between localized and widespread species, and we tested if increasing the sampling effort affects the significance of the relationship. A significant positive relationship between the average local abundance of passerine species and the proportion of occupied oases was found. The use of a capture-recapture approach allowed us to estimate and to compare the detection probabilities of localized and widespread species subsets. We found that localized species were locally less detectable than widespread species, which is consistent with the main assumption of the sampling artefact hypothesis. However, increasing the detection probability of species by conducting more counts did not affect the significance of the relationship, which did not give support to the sampling artefact hypothesis. Our work implies that sampling contributed to the distribution-abundance relationship we found, but that it is unlikely that such a relationship could entirely be explained by an artefact of sampling. It also underlines the insight that can be gained by using probabilistic approaches of estimating species number and detection probability when attempting to disentangle sampling from ecological effects in community ecology studies.     

Accounting for dispersal and biotic interactions to disentangle the drivers of species distributions and their abundances

Although abiotic factors, together with dispersal and biotic interactions, are often suggested to explain the distribution of species and their abundances, species distribution models usually focus on abiotic factors only. We propose an integrative framework linking ecological theory, empirical data and statistical models to understand the distribution of species and their abundances together with the underlying community assembly dynamics. We illustrate our approach with 21 plant species in the French Alps. We show that a spatially nested modelling framework significantly improves the model's performance and that the spatial variations of species presence-absence and abundances are predominantly explained by different factors. We also show that incorporating abiotic, dispersal and biotic factors into the same model bring new insights to our understanding of community assembly. This approach, at the crossroads between community ecology and biogeography, is a promising avenue for a better understanding of species co-existence and biodiversity distribution.     

A General Theory of the Sampling Process with Applications to the “Veil Line”

When a community of species is sampled, nonappearing species are not those with abundances that fall shy of some arbitrary mark, the “veil line” proposed by E. F. Preston in 1948 (Ecology29, 254–283). Instead, they follow a hypergeometric distribution, which has no resemblance to the veil line. There is therefore no justification for the truncation of distributions proposed to describe the abundances of species in natural communities. The mistake of the veil line points to the need for a general theory of sampling. If a community has a distributiongof species abundances and if samples taken of the community tend to follow distributionf, what is the relationship offtog? The seeds of such a theory are available in the work of E. C. Pielou. Using the Poisson distribution as a close approximation to the hypergeometric, one may immediately write and (in most cases) solve the transformation fromgtof. The transformation appears to preserve distribution formulas to within constants and parameters, providing yet another reason to rule out the use of truncation. Well beyond this application, the theory provides a foundation for rethinking the sampling process and its implications for ecology.     

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.     

Which Models Are Appropriate for Six Subtropical Forests: Species-Area and Species-Abundance Models

The species-area relationship is one of the most important topic in the study of species diversity, conservation biology and landscape ecology. The species-area relationship curves describe the increase of species number with increasing area, and have been modeled by various equations. In this paper, we used detailed data from six 1-ha subtropical forest communities to fit three species-area relationship models. The coefficient of determination and F ratio of ANOVA showed all the three models fitted well to the species-area relationship data in the subtropical communities, with the logarithm model performing better than the other two models. We also used the three species-abundance distributions, namely the lognormal, logcauchy and logseries model, to fit them to the species-abundance data of six communities. In this case, the logcauchy model had the better fit based on the coefficient of determination. Our research reveals that the rare species always exist in the six communities, corroborating the neutral theory of Hubbell. Furthermore, we explained why all species-abundance figures appeared to be left-side truncated. This was due to subtropical forests have high diversity, and their large species number includes many rare species.     

太白山锐齿栎林物种-多度分布格局

以太白山1.5 hm²的锐齿栎原始林和次生林样地中环境因子和胸径≥1 cm的木本植物调查数据为基础,采用统计模型(对数正态模型)、生态位模型(Zipf模型、断棍模型、生态位优先模型)和中性模型,拟合了锐齿栎群落的物种多度分布。结果表明: 太白山锐齿栎林物种多度分布格局受到生境异质性的影响。其中,地形因子对原始林物种分布影响较大,在凹凸度较大的生境中,物种分布同时受到中性过程和生态位过程的影响,但中性过程发挥的作用较小;而在凹凸度较小的生境中,中性模型被拒绝,物种的多度分布符合生态位理论的假设。在群落坡度大的区域,群落中生态位过程和中性过程同等重要;而在坡度较小的平缓区域,生态位分化对群落物种分布的影响较大。在次生林中,影响物种分布的因素主要是土壤养分。在次生林土壤速效磷含量高的生境中,生态位过程是影响群落物种分布的主要生态学过程;而在土壤速效磷含量低的生境中,中性过程和生态位过程在群落物种分布中同时存在。太白山锐齿栎林物种多度分布格局存在明显的尺度效应。原始林在20 m×20 m尺度上,生态位模型和中性模型都能预测物种多度分布,而在40 m×40 m和70 m×70 m尺度上,生态位过程可解释物种多度分布格局。在次生林样地20 m×20 m、40 m×40 m、70 m×70 m尺度上,生态位过程和中性过程共同作用于物种的分布,但是生态位过程更为重要。可见,除了尺度和生境异质性外,原始林与受干扰的次生林中的物种多度分布也存在明显的差异。     

闽北地区森林群落物种多样性的测定

采用8个物种多样性指数对闽北地区的8个森林群落类型物种多样性进行测定,并选用4个种一多度关系模型(对数正态分布、Weibull分布、对数级数分布、生态位优先占领模型)分析其物种-多度关系,把多样性指数与对数正态分布、Weibull分布和生态位优先占领模型的有关参数进行线性回归,以分析多度模型参数描述物种多样性的可行性。结果表明：(1)多数物种多样性指数对群落的测度是一致的,(2)对数正态分布、Weibull分布和生态位优先占领模型对8个群落的物种多度拟合效果很好;(3)对数正态分布、Weibull分布和生态位优先占领模型有关模型参数与部分物种多样性指数的线性关系达显著或极显著水平。通过闽北地区8个类型森林群落物种多样性指数测定,使生物多样性较准确地数量化,同时还说明采用改进单纯形法进行非线性分布函数的拟合是简单有效的,可推广应用。