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.     

A comparative analysis of alternative approaches to fitting species-abundance models

Aims Fits of species-abundance distributions to empirical data are increasingly used to evaluate models of diversity maintenance and community structure and to infer properties of communities, such as species richness. Two distributions predicted by several models are the Poisson lognormal (PLN) and the negative binomial (NB) distribution; however, at least three different ways to parameterize the PLN have been proposed, which differ in whether unobserved species contribute to the likelihood and in whether the likelihood is conditional upon the total number of individuals in the sample. Each of these has an analogue for the NB. Here, we propose a new formulation of the PLN and NB that includes the number of unobserved species as one of the estimated parameters. We investigate the performance of parameter estimates obtained from this reformulation, as well as the existing alternatives, for drawing inferences about the shape of species abundance distributions and estimation of species richness.Methods We simulate the random sampling of a fixed number of individuals from lognormal and gamma community relative abundance distributions, using a previously developed 'individual-based' bootstrap algorithm. We use a range of sample sizes, community species richness levels and shape parameters for the species abundance distributions that span much of the realistic range for empirical data, generating 1?000 simulated data sets for each parameter combination. We then fit each of the alternative likelihoods to each of the simulated data sets, and we assess the bias, sampling variance and estimation error for each method.Important findings Parameter estimates behave reasonably well for most parameter values, exhibiting modest levels of median error. However, for the NB, median error becomes extremely large as the NB approaches either of two limiting cases. For both the NB and PLN,>90% of the variation in the error in model parameters across parameter sets is explained by three quantities that corresponded to the proportion of species not observed in the sample, the expected number of species observed in the sample and the discrepancy between the true NB or PLN distribution and a Poisson distribution with the same mean. There are relatively few systematic differences between the four alternative likelihoods. In particular, failing to condition the likelihood on the total sample sizes does not appear to systematically increase the bias in parameter estimates. Indeed, overall, the classical likelihood performs slightly better than the alternatives. However, our reparameterized likelihood, for which species richness is a fitted parameter, has important advantages over existing approaches for estimating species richness from fitted species-abundance models.     

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。     

Analytical evidence for scale-invariance in the shape of species abundance distributions

The distribution of species abundances within an ecological community provides a window into ecological processes and has important applications in conservation biology as an indicator of disturbance. Previous work indicates that species abundance distributions might be independent of the scales at which they are measured which has implications for data interpretation. Here we formulate an analytically tractable model for the species abundance distribution at different scales and discuss the biological relevance of its assumptions. Our model shows that as scale increases, the shape of the species abundance distribution converges to a particular shape given uniquely by the Jaccard index of spatial species turnover and by a parameter for the spatial correlation of abundances. Our model indicates that the shape of the species abundance distribution is taxon specific but does not depend on sample area, provided this area is large. We conclude that the species abundance distribution may indeed serve as an indicator of disturbances affecting species spatial turnover and that the assumption of conservation of energy in ecosystems, which is part of the Maximum Entropy approach, should be re-evaluated.     

Artifactions in the Log-Transformation of Species Abundance Distributions

One of the most frequently studied pattern in ecology is the Species Abundance Distribution (SAD) that represents the frequency distribution of species abundances in an assemblage. Two main approaches to displaying such information have been employed: histograms constructed using exponentially increasing bin widths as pioneered by Preston (1948), and plots of ranked species abundances. While both techniques have been extensively used in the investigation of community ecology hypotheses, the Preston-style species-abundance histogram has become central to current debates concerning appropriate characterization of the SAD and the processes generating it. Here we point out an important issue in the Preston approach that has profound implications to this debate: by employing bins of exponentially increasing size, the resultant histogram may display a hump-shaped pattern that is not congruent with the shape of the untransformed distribution. Moreover, any distribution constructed from log-transformed abundances will necessarily reveal at least one internal mode, even when the non-transformed probability density function is strictly decreasing. We warn against misinterpretation of such transformed datasets, and suggest that rank-abundance plots, which are equivalent to the cumulative distribution functions extensively used in other branches of science, represent a more informative approach as they allow for better discrimination between a number of probability distributions. Ecologists should be aware that logarithmic transformation often generates a log-normal-like shape, and are encouraged to use rank abundance curves to visualize and analyze species-abundance patterns.     

A dynamical model of communities and a new species-abundance distribution

It is known to many field biologists that biosurveys of natural communities tend to produce a J-shaped curve when the numbers of species are plotted against abundance. In other words, when the number of species of abundance k is plotted against k (running from 1 to some large number), the resulting distribution peaks at the lowest abundance, then forms a concave ramp as it approaches zero at the far end of the abundance axis. Does this distribution represent a single formula operating behind the scenes, or does it represent several formulas, appropriate for different types of community? Or does it represent no particular formula at all? The research reported here has three components: (1) The analysis of a new dynamical system that simulates multispecies communities (producing J-curves in the process) and the derivation of the "logistic-J" distribution, as the underlying community equilibrium curve; (2) the summary of a general theory of sampling as a bridge between natural communities and samples of them; (3) the evaluation of extant proposals for species-abundance distributions by application of a general theory of sampling or by cross-comparison via 100 biosurveys randomly selected from the literature.     

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.     

The shape of abundance distributions across temperature gradients in reef fishes

Improving predictions of ecological responses to climate change requires understanding how local abundance relates to temperature gradients, yet many factors influence local abundance in wild populations. We evaluated the shape of thermal‐abundance distributions using 98 422 abundance estimates of 702 reef fish species worldwide. We found that curved ceilings in local abundance related to sea temperatures for most species, where local abundance declined from realised thermal ‘optima’ towards warmer and cooler environments. Although generally supporting the abundant‐centre hypothesis, many species also displayed asymmetrical thermal‐abundance distributions. For many tropical species, abundances did not decline at warm distribution edges due to an unavailability of warmer environments at the equator. Habitat transitions from coral to macroalgal dominance in subtropical zones also influenced abundance distribution shapes. By quantifying the factors constraining species’ abundance, we provide an important empirical basis for improving predictions of community re‐structuring in a warmer world.     

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.     

Frequent and occasional species and the shape of relative-abundance distributions

Recently, three different models have been proposed to explain the distribution of abundances in natural communities: the self‐similarity model; the zero‐sum ecological drift model; and the occasional–frequent species model of Magurran and Henderson. Here we study patterns of relative abundance in a large community of forest Hymenoptera and show that it is indeed possible to divide the community into a group of frequent species and a group of occasional species. In accordance with the third model, frequent species followed a lognormal distribution. Relative abundances of the occasional species could be described by the self‐similarity model, but did not follow a log‐series as proposed by the occasional–frequent model. The zero‐sum ecological drift model makes no explicit predictions about frequent and occasional species but the abundance distributions of the hymenopteran species did not show the excess of rare species predicted by this model. Separate fits of this model to the frequent and to the occasional species were worse than the respective fits of the lognormal and the self‐similarity model.     

Microbial community analysis in incompletely or destructively sampled systems

Analyses of microbial community dynamics are often constrained by the destructive, indirect, and incomplete nature of most sampling techniques. These methodological constraints compel assumptions that are rarely verified about the relationships among separate communities. We evaluated the consequences for community analysis of the common assumption that separate microbial communities are described by the same species abundance distribution. Sample data were generated from simulated communities in which the species abundance distributions were the same or were different. Samples from communities that had the same number of species or were described by the same species abundance distribution sometimes had significantly different numbers of species. Samples from simulated communities that had different species number-species abundance distribution combinations sometimes contained indistinguishable numbers of species. When sampling from independent communities described by unknown distributions (e.g., microbial communities on plant surfaces), the simulations showed that standardization of sample size (number of individuals or colony-forming units) does not guarantee samples of equal proportions of the total species in a community. Sample sizes that are logistically feasible for many microbial systems will provide only limited information for differentiating species numbers or species abundance distributions among separate communities over time. For ecologists studying destructively or incompletely sampled communities this seriously influences both the sample designs that are reasonable and the questions that can be addressed in such systems. Send offprint requests to: L. Kinkel.     

Palms as rainforest resources: how evenly are they distributed in Peruvian Amazonia?

The distribution and the abundance of a species define the limits of itspotential use. Despite this simple fact, there are only a few studies thathave quantified the actual abundance and the distribution of species/resourcesin Amazonian rainforests, especially within unflooded (tierra firme) forests.The present study focused on the distributions and the abundances of palms,since they are both structurally important and widely utilized in the forests ofAmazonia. The similarity of the palm communities at eight different sites intierra firme forests of Peruvian Amazonia were examined, and the eighteconomically most important palm species were selected for more detailed studieson abundance and population structure. The results showed that both the overallpalm community composition and the abundances of the eight focal palm speciesvaried among the sites, and that these differences in abundances were related tothe amount of exchangeable cations in the soils. Population structure differedbetween growth forms: large, solitary palm species were mainly represented byseedlings and juveniles, whereas small, clonal palm species had very fewseedlings. The great variability in abundance of palm species should be takeninto account when estimating the availability of palm resources, as well as inconservation planning of the palm species in an area of interest.     

Extracting abundance information from DNA-based data

The accurate extraction of species-abundance information from DNA-based data (metabarcoding, metagenomics) could contribute usefully to diet analysis and food-web reconstruction, the inference of species interactions, the modelling of population dynamics and species distributions, the biomonitoring of environmental state and change, and the inference of false positives and negatives. However, multiple sources of bias and noise in sampling and processing combine to inject error into DNA-based data sets. To understand how to extract abundance information, it is useful to distinguish two concepts. (i) Within-sample across-species quantification describes relative species abundances in one sample. (ii) Across-sample within-species quantification describes how the abundance of each individual species varies from sample to sample, such as over a time series, an environmental gradient or different experimental treatments. First, we review the literature on methods to recover across-species abundance information (by removing what we call “species pipeline biases”) and within-species abundance information (by removing what we call “pipeline noise”). We argue that many ecological questions can be answered with just within-species quantification, and we therefore demonstrate how to use a “DNA spike-in” to correct for pipeline noise and recover within-species abundance information. We also introduce a model-based estimator that can be used on data sets without a physical spike-in to approximate and correct for pipeline noise.     

Fish and Phytoplankton Exhibit Contrasting Temporal Species Abundance Patterns in a Dynamic North Temperate Lake

Temporal patterns of species abundance, although less well-studied than spatial patterns, provide valuable insight to the processes governing community assembly. We compared temporal abundance distributions of two communities, phytoplankton and fish, in a north temperate lake. We used both 17 years of observed relative abundance data as well as resampled data from Monte Carlo simulations to account for the possible effects of non-detection of rare species. Similar to what has been found in other communities, phytoplankton and fish species that appeared more frequently were generally more abundant than rare species. However, neither community exhibited two distinct groups of “core” (common occurrence and high abundance) and “occasional” (rare occurrence and low abundance) species. Both observed and resampled data show that the phytoplankton community was dominated by occasional species appearing in only one year that exhibited large variation in their abundances, while the fish community was dominated by core species occurring in all 17 years at high abundances. We hypothesize that the life-history traits that enable phytoplankton to persist in highly dynamic environments may result in communities dominated by occasional species capable of reaching high abundances when conditions allow. Conversely, longer turnover times and broad environmental tolerances of fish may result in communities dominated by core species structured primarily by competitive interactions.     

On the use of measures of structure and diversity in applied diatom ecology

Water managers ask for simple ecological indices as a tool for measuring the effectiveness of their activities. Diversity indices are often used as such tools. The concept of diversity is closely related to the nature of species-abundance distributions. There is empirical and theoretical evidence that diatom-assemblages have a species-abundance distribution of log-series type. Then the most appropriate diversity index is the dominance,i.e. the relative abundance of the commonest species. The number of species in a sample of fixed size of the assemblage is a useful additional index. It appears from some examples that these indices have no consistent relationships with the degree of water pollution. This in contrast to the species composition of the assemblages. (Complete paper published in: HAKANSSON, H. and J.GERLOFF, Eds., (1982). Festschrift Niels Foged. Diatomaceae III. Beiheft zur Nova Hedwigia     

Grenadier abundance examined at varying spatial scales in deep waters off Newfoundland, Canada, with special focus on the influence of corals

There is a growing body of research examining the effects of corals on fish communities, species abundances, and biodiversity. Yet, few studies have quantitatively examined what factors are influencing the distribution of individual fish species. In general, many researchers believe they know what influences the distribution of grenadiers on large spatial scales, but numerous studies have shown the distributions of organisms are often determined by various factors that change in relative importance when viewed at differing scales. Our study used video collected from three deep canyons off Newfoundland, Canada (North west Atlantic) to examine how the factors apparently influencing the distribution of four grenadiers (Macrouridae: Coryphaenoides rupestris, Coryphaenoides carapinus, Nezumia bairdii, and Macrourus berglax) change when assessed at varying spatial scales. We paid special attention to the influence of deep-water corals found in the study area (large gorgonians/antipatharians, small gorgonians, sea pens, soft corals, and cup corals). The factors that influenced grenadier presence and/or abundance (and the magnitude of this effect) varied as different sampling resolutions were examined. We found C. rupestris abundance was positively related to cup coral abundance in transects longer than 10 m, likely as a result of similar habitat preferences between both taxa. When significant relationships between depth and C. rupestris presence and/or abundance were found, they were always negative. Depth was a significant predictor of C. carapinus abundance in transects longer than 10 m. Very few predictors of M. berglax abundance or presence could be found. Depth and the number of small gorgonians were consistent predictors of N. bairdii abundance.     

Inside‐container effects drive mosquito community structure in Brazilian Atlantic forest

Metacommunity theory is a convenient framework in which to investigate how local communities linked by dispersal influence patterns of species distribution and abundance across large spatial scales. For organisms with complex life cycles, such as mosquitoes, different pressures are expected to act on communities due to behavioral and ecological partitioning of life stages. Adult females select habitats for oviposition, and resulting offspring are confined to that habitat until reaching adult stages capable of flight; outside‐container effects (OCE) (i.e., spatial factors) are thus expected to act more strongly on species distributions as a function of adult dispersal capability, which should be limited by geographic distances between sites. However, larval community dynamics within a habitat are influenced by inside‐container effects (ICE), mainly interactions with conspecifics and heterospecifics (e.g., through effects of competition and predation). We used a field experiment in a mainland‐island scenario to assess whether environmental, spatial, and temporal factors influence mosquito prey and predator distributions and abundances across spatial scales: within‐site, between‐site, and mainland‐island. We also evaluated whether predator abundances inside containers play a stronger role in shaping mosquito prey community structure than do OCE (e.g., spatial and environmental factors). Temporal influence was more important for predators than for prey mosquito community structure, and the changes in prey mosquito species composition over time appear to be driven by changes in predator abundances. There was a negligible effect of spatial and environmental factors on mosquito community structure, and temporal effects on mosquito abundances and distributions appear to be driven by changes in abundance of the dominant predator, perhaps because ICE are stronger than OCE due to larval habitat restriction, or because adult dispersal is not limited at the chosen spatial scales.     

Confronting different models of community structure to species-abundance data: a Bayesian model comparison

Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species‐abundance data that yields a full joint probability distribution of each model's parameters plus a relatively parameter‐independent criterion, the posterior Bayes factor, to compare these models. We illustrate our approach by comparing three classical distributions: the zero‐sum multinomial (ZSM) distribution, based on Hubbell's neutral model, the multivariate Poisson lognormal distribution (MPLN), based on niche arguments, and the discrete broken stick (DBS) distribution, based on MacArthur's broken stick model. We give explicit formulas for the probability of observing a particular species‐abundance data set in each model, and argue that conditioning on both sample size and species count is needed to allow comparisons between the two distributions. We apply our approach to two neotropical communities (trees, fish). We find that DBS is largely inferior to ZSM and MPLN for both communities. The tree data do not allow discrimination between ZSM and MPLN, but for the fish data ZSM (neutral model) overwhelmingly outperforms MPLN (niche model), suggesting that dispersal plays a previously underestimated role in structuring tropical freshwater fish communities. We advocate this approach for identifying the relative importance of dispersal and niche‐partitioning in determining diversity of different ecological groups of species under different environmental conditions.     

Connections between ecology,biogeography, and paleobiology: Relationship between local abundance and geographic distribution in fossil and recent molluscs

Summary We used data on Contemporary and Pleistocene molluscs at one site in the Gulf of California to evaluate and extend earlier ideas about the relationship between local abundance and geographic distribution. For each species whose shells occurred in one Recent and two Pleistocene deposits, we measured its abundance in the sample and relative latitudinal position within its contemporary geographic range. Species near the edges of their ranges showed uniformly low abundances, whereas those near the centres exhibited a wide range of abundances. Species near the edges of their ranges also appear to have exhibited greater changes in abundance, including more colonization and extinction events, between the Pleistocene interglacial sample and the Recent one. The constraint of location in the geographic range on maximal local and regional abundance appears to offer an example of a connection between patterns and processes on local, regional, and geographical scales. Characteristics of community structure, such as relative abundance of individual species and frequency of local co-existence of multiple species, may be influenced by the location of the sample site with respect to the geographic ranges of the constituent species. These results demonstrate emergent, statistical features of population ecology and community organization that are manifest over geographic space and evolutionary time.     

Limits to the estimation of species richness: The use of relative abundance distributions

The present study demonstrates the possibility of estimating species numbers of animal or plant communities from samples using relative abundance distributions. We use log‐abundance–species‐rank order plots and derive two new estimators that are based on log‐series and lognormal distributions. At small to moderate sample sizes these estimators appear to be more precise than previous parametric and nonparametric estimators. We test our estimators using samples from 171 published medium‐sized to large animal and plant communities taken from the literature. By this we show that our new estimators define also limits of precision.