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.     

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.     

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.     

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.     

A General and Dynamic Species Abundance Model, Embracing the Lognormal and the Gamma Models

One aspect of community ecology that has been given particular attention is the pattern of species abundances in a community. The species may have a wide range of abundances; some are very common and others rare. When species abundance models are fitted to observations, the lognormal model and one of the gamma models (e.g., the log-series model) are usually applied. The model that gives the best fit according to some goodness-of-fit test is then chosen. By applying a diffusion approximation for each species' dynamics with density regulation of the straight theta-logistic type, we here present a general species abundance model that embraces the two most widely applied species abundance models, the lognormal and the gamma. Our general model will, therefore, provide a better fit than the two special cases, except when it corresponds to one of them. In contrast to the classical models, ours is also dynamic, making it possible to evaluate the fluctuations in species abundance over time through both biotic and abiotic factors. The model is fitted to several species abundance data sets and our results compared to previous attempts to fit a model, usually either the lognormal or the log-series.     

亚热带喀斯特地区不同地形植物群落物种多度分布格局

为探究亚热带喀斯特地区不同地形下植物群落物种多度分布格局,揭示不同地形下群落的物种多度格局形成的作用机制,丰富该地区植物群落构建理论,该文以贵州茂兰喀斯特地区山脊、槽谷、鞍部、洼地4种典型地形下植物群落的乔木层与灌木层为对象,统计物种多度,采用累计经验分布曲线(ECDF)表征多度分布格局,采取Wilcoxon秩和检验探究不同地形之间物种多度的差异性。采用不同生态学模型进行多度拟合,利用Kolmogorov-Smirnov(K-S)检验与赤池信息量准则(AIC)检验模型接受与拟合优度。结果表明:(1)不同地形下植物群落的个体数量与物种数存在差异,鞍部个体数最多,洼地的物种数最多,山脊的个体数、物种数均最少。(2)不同地形下植物群落的乔木层物种多度格局无显著差异,灌木层之间出现显著差异,山脊与鞍部、洼部,鞍部与槽谷、洼部都存在显著差异。(3)不同地形下乔木层物种多度对中性模型接受较好,其中山脊拟合最优,对生态位模型接受较差,仅山脊与鞍部通过两种生态位模型,拟合优度不及中性模型。灌木层对中性模型接受也较好,鞍部拟合最优,对生态位模型接受较差,仅洼地通过断棍模型。整体而言,乔木层比灌木层能更好地接受两种生态学模型,可能乔木层物种多度格局有更明显生态过程的印记,但不同地形下灌木层拟合优度差异更大,可能与灌木层物种对环境变化更剧烈有关。不同地形会引起群落构建不同程度的生态学过程,物种多度分布格局会逐渐适应地形。     

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.     

塔里木荒漠河岸林不同生境群落物种多度分布格局

为解释塔里木荒漠河岸林群落构建和物种多度分布格局形成的机理, 本文以塔里木荒漠河岸林2个不同生境(沙地、河漫滩) 4 ha固定监测样地为研究对象, 基于两样地物种调查数据, 采用统计模型(对数级数模型、对数正态模型、泊松对数正态分布模型、Weibull分布模型)、生态位模型(生态位优先占领模型、断棍模型)和中性理论模型(复合群落零和多项式模型、Volkov模型)拟合荒漠河岸林群落物种多度分布, 并用K-S检验与赤池信息准则(AIC)筛选最优拟合模型。结果表明: (1)随生境恶化(土壤水分降低), 植物物种多度分布曲线变化减小, 群落物种多样性、多度和群落盖度降低, 常见种数减少。(2)选用的3类模型均可拟合荒漠河岸林不同生境群落物种多度分布格局, 统计模型和中性理论模型拟合效果均优于生态位模型。复合群落零和多项式模型对远离河岸的干旱沙地生境拟合效果最好; 对数正态模型和泊松对数正态模型对洪水漫溢的河漫滩生境拟合效果最优; 中性理论模型与统计模型无显著差异。初步推断中性过程在荒漠河岸林群落构建中发挥着主导作用, 但模型拟合结果只能作为推断群落构建过程的必要非充分条件, 不能排除生态位过程的潜在作用。     

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。     

Ecological consequences of evolution in plant defenses in a metacommunity

Dispersal can affect the assembly of local communities in a metacommunity as well as evolution of local populations in a metapopulation. These two processes may also affect each other in ways that have not yet been well studied and that may have novel effects on community structure. Here, we illustrate the interaction of these two processes on community structure with a model of adaptive evolutionary dynamics of plant defenses in a metacommunity food web involving multiple patches along a productivity gradient. We find an enhanced suite of adaptive plant types in our metacommunity model than is predicted in the absence of dispersal. We also find that this, and the movement of nutrients among patches via dispersal, alters patterns of food web architecture, trophic structure and diversity along the productivity gradient. Overall, our model illustrates that evolutionary and metacommunity dynamics may influence communities in complex interactive ways that may not be predicted by models that ignore either of these types of processes.     

Species abundance distribution and dynamics in two locally coupled communities

This study considered a model for species abundance dynamics in two local community (or islands) connected to a regional metacommunity. The model was analyzed using continuous probabilistic technique that employs Kolmogorov-Fokker-Planck forward equation to derive the probability density of the species abundance in the two local communities. Using this technique, we proposed a classification for the species abundance dynamics in the local communities. This classification was made based on such characteristics as immigration intensity, species representation in the metacommunity and the size of local communities. We further distinguished several different scenarios for species abundance dynamics using different ecological characteristics such as species persistence, extinction and monodominance in one or both local communities. The similarity of the species abundance distributions between the two local communities was studied using the correlation coefficient between species abundances in two local communities. The correlation is a function of migration rates between local communities and between local and metacommunity. Immigration between local communities drives the homogenization of the local communities, while immigration from the metacommunity will differentiate them. This community subdivision model provides useful insights for studying the effect of landscape fragmentation on species diversity.     

Disentangling the role of connectivity,environmental filtering,and spatial structure on metacommunity dynamics

Dispersal is a key process in metacommunity dynamics, allowing the maintenance of diversity in complex community networks. Geographic distance is usually used as a surrogate for connectivity implying that communities that are closely located are considered more prone to exchange individuals than distant communities. However, in some natural systems, organisms may be subjected to directional dispersal (air or water flows, particular landscape configuration), possibly leading close communities to be isolated from each other and distant communities to be connected. Using geographic distance as a proxy for realised connectivity may then yield misleading results regarding the role of dispersal in structuring communities in such systems. Here, we quantified the relative importance of flow connectivity, geographic distance, and environmental gradients to explain polychaete metacommunity structure along the coasts of the Gulf of Lions (northwest Mediterranean Sea). Flow connectivity was estimated by Lagrangian particle dispersal simulations. Our results revealed that this metacommunity is strongly structured by the environment at large spatial scales, and that both flow connectivity and geographic distance play an important role within homogeneous environments at smaller spatial scales. We thus strongly advocate for a wider use of connectivity measures, in addition to geographic distance, to study spatial patterns of biological diversity (e.g. distance decay) and to infer the processes behind these patterns at different spatial scales. Synthesis Everything is connected, but connections are seldom accurately quantified. Biological communities are often studied separately, using observations, experiments and models to unravel local dynamics of organisms interacting with each other. However, regional processes such as dispersal through ocean and air circulation, likely to connect distant communities and influence their local dynamics, are not always accounted for, or, at best, used as an homogeneous and distance‐related factor. Ocean models have being extensively developed and validated during the past decades with the increasing availability of accurate meteorological data. Using such model outputs, precise quantifi cation of exchange rates of organisms between communities was performed in a marine Mediterranean coastal area. Jointly with local environmental and biological data, these results were used to quantify the effects of realistic connectivity on local and regional polychaete community structure, and revealed that the environmental gradient, geographic distance, and connectivity were responsible for community structure at different spatial scales.     

Species abundance models and patterns in dragonfly communities: effects of fish predators

We investigated if dragonfly larvae community composition and species abundance curves are sensitive to variation in predation intensity, and whether the fit to a particular niche partitioning model could be used to make inferences about mechanisms structuring communities. The approach taken was to compare communities in lakes either having or lacking fish predation. Dragonfly species classified as active, strongly dominated the dragonfly communities in fishless lakes, and low active species dominated fishless lakes. As activity level is known to correlate with susceptibility to fish predation this indicates that these communities are structured by fish predation. Fitting relative abundance data to five niche partitioning models showed that the same model fitted data from both types of habitats (fish/no fish). This means that the observed differences in relative abundances were substitutive, i.e. the relative abundance of a rank stayed constant, even though the identity of the species having this rank changed. The best fit to data from both types of lakes was found for the random assortment model, which is usually interpreted as an indication that the community is not structured by within-guild interactions. This interpretation for fishless lakes did not seem to agree with other community measures (i.e. lowered diversity and evenness and no relationship between species richness and dragonfly biomass), which indicate that the community is structured by within-guild interactions. Moreover, a detail in the fitting procedure, the number of species included in the analysis, affected which model that fitted data best. Thus, we question if fitting niche partitioning models to data can provide mechanistic understanding of how resources are partitioned in natural communities.     

The role of metacommunity processes in shaping invertebrate rock pool communities along a dispersal gradient

Explaining the variance of local communities in a spatial‐environmental matrix is one of the core interests of ecology today. Recent progress in metacommunity theory has made a substantial contribution to this field, however good empirical data in support of available theories are still relatively scarce. In this study we sampled a cluster of 36 temporary rock pools four times during one season to assess invertebrate metacommunity structure and dynamics and to search for steering processes and variables. Both Mantel tests and redundancy models indicate that local abiotic factors were dominant over spatial factors in explaining community structure and both were acting independently. Spatial variables were only important for passive dispersers and significantly explained 11% of variation in this community component. Pools connected by temporary overflows hosted more similar communities of passive dispersers than unconnected ones while community dissimilarity significantly increased with inter‐pool distance. A negative curvilinear relation was discovered between taxon richness and isolation in passive dispersers, providing some support for existing theoretical models of Mouquet and Loreau. Of different metacommunity perspectives, a combination of species sorting and mass effects best explains the observed patterns. Additionally, priority effects and monopolization may buffer against the homogenising effects of dispersal and contribute to the distinctness of isolated communities. This is one of the first studies to present evidence for spatial patterns in aquatic communities on such a small spatial scale (a rock ledge of ±9000 m²). Bridging the gap between theory and observed patterns in natural systems is one of the main challenges for future metacommunity research. Small aquatic habitats such as pitcher plants and freshwater rock pools may well have an important role to play as model systems to study ecological processes in a natural spatially explicit environment.     

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.     

集合群落及其在河流鱼类群聚研究中的应用

集合群落(metacommunity)是指多个潜在相互作用的物种通过它们之间的扩散而连接在一起的一组局域群落,目前已成为斑块生境下生物群落结构、格局和动态的重要理论基础之一。斑块动态、物种排序、群体效应和中性模型等4种理论模型,可用于解释不同情形下集合群落内物种的迁移状况,描述集合群落的动态。可采用群落结构或生态学机制等途径,来阐述所研究的群落是属于哪一种特定的集合群落类型。集合群落可用于研究河流鱼类群聚,解释鱼类的群落结构等问题。另外本文还结合我国水域生态环境及水生生物现状,对今后集合群落的研究作了展望。     

Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series

There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed ‘pink noise’: a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.     

Community differentiation on landscapes: drift, migration and speciation

Theories of the differentiation of ecological communities on landscapes have typically not considered evolutionary dynamics. Here we analytically study the expected differentiation among local communities in a large metacommunity, undergoing speciation, ecological drift and intercommunity dispersal, in the context of neutral theory. We demonstrate that heterogeneity in species diversity and abundance arises among communities when local communities are small and intercommunity migration is infrequent. We propose a new measure to describe community differentiation, defined as the average correlation or the average probability (C_st) that two randomly sampled individuals of the same species within local communities are from the same ancestor. The effects of driving forces (migration, mutation, and ecological drift) are incorporated into the two-level hierarchical community structure in a finite island model of neutral communities. Community differentiation can increase the effective metacommunity size or the Hubbell's fundamental species diversity in the metacommunity by a factor (1−C_st)⁻¹. Significant community differentiation arises when C_st≠0. Intercommunity migration promotes species diversity in local communities but reduce species diversity in the metacommunity. In either the finite or infinite island case, one can estimate the number of intercommunity migrants by using multiple local community datasets when the speciation is negligible in the neutral local communities, or by using the metacommunity dataset when the speciation is included in the local neutral communities. These results highlight the significance of the evolutionary mechanisms in generating heterogeneous communities in the absence of complicated ecological processes on large landscapes.