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.     

Heterogeneous communities with lognormal species abundance distribution: Species-area curves and sustainability

Heterogeneous species abundance models are models in which the dynamics differ between species, described by variation among parameters defining the dynamics. Using a dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution it is first shown that different degrees of heterogeneity may result in equivalent species abundance distributions. An alternative to Preston's canonical lognormal model is defined by assuming that reduction in resources, for example reduction in available area, increases the density regulation of each species. This leads to species-individual curves and species-area curves that are approximately linear in a double logarithmic plot. Preston's canonical parameter gamma varies little along these curves and takes values in the neighborhood of one. Quite remarkably, the curves, which define the sensitivity of the community to area reductions, are independent of the heterogeneity among species for this model. As a consequence, the curves can be estimated from a single sample from the community using the Poisson lognormal distribution. It is shown how to perform sensitivity analysis with respect to over-dispersion in sampling relative to the Poisson distribution as well as sampling intensity, that is, the fraction of the community sampled. The method is exemplified by analyzing three simulated data sets.     

A novel genealogical approach to neutral biodiversity theory

Current neutral theory in community ecology views local biodiversity as a result of the interplay between speciation, extinction and immigration. Simulations and a mean‐field approximation have been used to study this neutral theory. As simulations have limitations of convergence and the mean‐field approximation ignores dependencies between species’ abundances when applied to species‐abundance data, there is still no final conclusion whether the neutral theory or the traditional lognormal model describes community structure best. We present a novel analytical framework, based on the genealogy of individuals in the local community, to overcome the problems of previous approaches, and show, using Bayesian statistics, that the lognormal model provides a slightly better fit to the species‐abundance distribution of a much‐discussed tropical tree community. A key feature of our approach is that it shows the tight link between genetic and species diversity, which creates important perspectives to future integration of evolutionary and community ecological theory.     

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.     

Analyzing spatial structure of communities using the two-dimensional poisson lognormal species abundance model

The joint spatial and temporal fluctuations in the community structure of tropical butterflies are analyzed by fitting the bivariate Poisson lognormal distribution to a large number of observations in space and time. By applying multivariate dependent diffusions for describing the fluctuations in the abundances, the environmental variance is estimated to be very large and so is the strength of local density regulation. The variance in the lognormal species abundance distribution is partitioned into components expressing the heterogeneity between the species, independent noise components for the different species, a demographic stochastic component, and a component due to overdispersion in the sampling. In disagreement with the neutral theory, the estimates show that the heterogeneity component is the dominating one, representing 81% of the total variance in the lognormal model. Different spatial components of diversity, the alpha, beta, and gamma diversity, are also estimated. The spatial scale of the autocorrelation function for the community is of order 1 km, while sampling of a quadrat would need to be 10 km on a side to yield the total diversity for the community.     

A metacommunity-scale comparison of species-abundance distribution models for plant communities of eastern Australia

Various models of the species-abundance distribution (SAD) have been proposed to fit empirically derived data however there is no general consensus as to which model provides the best fit. Further, the zero-sum multinomial SAD model (ZSM) was proposed as a metacommunity model, yet it has not previously been fitted at the metacommunity scale. We note that SAD models based on compound lognormal distributions (such as the Poisson-lognormal, PLN, and the negative binomial-lognormal models, NBLN) can also be thought of as metacommunity models, and we compare these with the ZSM when fitted as metacommunity models to SADs of related communities.
We collected five datasets in the Sydney Basin, eastern Australia, representing five different types of subtropical/temperate plant communities ranging from closed warm-temperate rainforest to open wet sclerophyll forest to dry sclerophyll woodland. For each type of plant community, five local communities were identified across the Sydney Basin, and SAD data collected in five randomly placed 0.2-ha quadrats at each local community. Analysis was performed at two levels: all abundance data from each local community were pooled across each metacommunity and analysed as a single pooled community; and a metacommunity model was fitted to all five local communities of a community type, simultaneously. For the pooled data, we considered the negative-binomial (NB) and the log-series (LS) models in addition to ZSM, PLN and NBLN. All five models performed similarly, however the LS had a better fit to three pooled communities and the ZSM and PLN to the remaining two communities. By contrast, the ZSM performed statistically better against the PLN and NBLN when considered as a metacommunity model. We conclude that the ZSM generally provides a more reliable null model for metacommunity abundance data than the lognormal model.     

Heterogeneity in dynamic species abundance models: the selective effect of extinction processes

There is often large variation in traits across the species of a community. In particular, variation in life history traits affecting population dynamics is likely to affect the species abundance distribution. Applying a dynamic and heterogeneous species abundance model we study how differences in extinction time for species in a community act as a force changing the distribution of dynamic parameters across species. This process may generate communities that are more heterogeneous then the heterogeneity measured as the species enter the community. Analytical results for some versions of the lognormal and gamma species abundance model are given as exemplifications of this process, together with stochastic simulations demonstrating the temporal changes in number of species and community heterogeneity through time.     

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 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.     

Methods for fitting dominance/diversity curves

Abstract. Dominance/diversity curves, displaying the relative abundances of the species within a community, have often been constructed from field data. Several ecological and statistical models of dominance/diversity have been proposed, to explain the curves. Yet, rarely have curves of different models been fitted to field data. In this paper the appropriate parameters and methods of curve fitting for plant communities are described for the General Lognormal, Canonical Lognormal, Geometric, Broken Stick, Zipf and Zipf-Mandelbrot models. Distinction is made between fixed and optimised parameters, to clarify para-meterisation of the models. It is concluded that all should be fitted by minimising the deviance in a ranked-abundance plot. Statistical tests of goodness of fit are discussed. It is concluded that consistency of fit between replicate quadrats of a community provide the best test. Curves of all the models discussed are fitted to data from a species-rich Spanish hay meadow, and to data from a New Zealand intertidal algal community. The Spanish meadow data are best fitted by General Lognormal. The New Zealand algal data are best fitted by Geometric or General Lognormal. Goodness of fit for a sample is usually relatively good or poor for all models, since much of the deviance comes from steps in the curve which none of the models can fit closely.     

山东半岛潮上带沙草地的物种多度格局及其对人为干扰的响应

沿海岸线分布的潮上带沙滩是受风暴潮影响的独特生境, 蕴含着独特的植物群落与植物资源。很多沙滩已受到不同程度的人为干扰。人们尚未了解潮上带沙滩植物群落的构建方式, 也忽视了各种人为干扰对它的影响。该文以几何级数模型、分割线段模型、重叠生态位模型和中性理论模型, 剖析了山东半岛潮上带3处典型沙草地的物种多度格局, 同时研究了滩涂养殖和旅游践踏两种最重要的干扰方式对潮上带沙滩植物群落的影响。对于这3处植被, 中性理论模型的拟合效果最好, 其次是几何级数模型, 而分割线段模型和重叠生态位模型的拟合效果不够理想。旅游践踏和沙滩养殖使潮上带沙草地的植被盖度降低, 不利于珍稀特有植物的生存。在潮上带沙滩上很多植物具有不少相似的特征, 导致它们在个体水平上的空间替代有强烈的随机性, 服从群落中性理论。然而, 它们的性状毕竟存在或多或少的差异, 这些差异难免对各种植物的资源分配或竞争能力产生微弱的影响, 经过很多年的积累, 这种影响必然在群落水平上逐渐显现出来, 以至于用几何级数模型也可拟合物种的多度格局。作者建议应控制人为干扰对潮上带沙滩珍稀植物的不利影响。     

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。     

Species abundance distributions and numerical dominance in gastrointestinal helminth communities of fish hosts

The abundances of different species in a parasite community are never similar: there is typically one or a few numerically dominant species and many species with low abundance. Here, we determine whether basic features of parasite communities are associated with strong dominance by one or a few species, among 39 component communities of gastrointestinal helminths in marine fishes from Brazil. First, we tested whether the shape of the species abundance distribution in these communities fits that predicted by several theoretical models, using a goodness-of-fit procedure. Only the canonical lognormal model could be rejected for 5 out of 39 communities; all other comparisons of observed and predicted abundance distributions showed no significant differences, although this may be due to limited statistical power. Second, we used the ratio between the abundance of the most abundant species and either the second or third most abundant species, as indices of dominance; these show, for instance, that the dominant species in a community is typically twice, but sometimes over ten times, as abundant as the next most abundant species. We found that these ratios were not influenced by either the community's species richness, the mean number of individual parasites per host, or the taxonomic identity of the dominant species. However, the abundance ratio between the first and third most abundant species in a community was significantly correlated with an independent index of species interactivity, based on the likelihood that the different parasite species in a component community co-occur in the same host individuals: the difference in abundance between the dominant and third most abundant species was greater in communities characterized by weak interactions. These findings suggest that strong interactions may lead to greater evenness in the abundance of species, and that numerical dominance is more likely to result from interspecific differences in recruitment rates.     

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.     

Assembly rules operate only in equilibrium communities: Is it true?

Very little is known of how disturbance affects community assembly rules. We examine this in three disturbance states in each of two ski areas on southern New Zealand mountains. Theory suggests that a community will become progressively more spatially organized during recovery from disturbance. Firstly, different patches of the community should become more similar through time, but this was seen in only one of the two areas and even then only examining species presence/absence. Secondly, it has been suggested that spatial autocorrelation will be stronger in less‐disturbed conditions, that is, there will be a stronger pattern of more distant patches being more dissimilar in species composition. This was generally borne out. However, the method indicated more point randomness in less‐disturbed sites. Assembly rules might be seen in species abundances. Previous work has found maximum evenness of abundances in later successional communities, but the pattern here was the opposite: high evenness in the most disturbed communities. The literature suggests that in undisturbed communities the distribution of species abundances (relative abundance distribution) will be general lognormal, and we further argue that the identity of the species across occupying rank positions in that distribution should be more consistent (rank consistency). Both predictions were borne out in one area, but neither in the other. Many workers suggest that niche‐based assembly rules will be stronger in undisturbed communities. However, there was only weak evidence of constancy in species richness. Local species assemblages tended to contain a relatively constant representation from different morphological/taxonomic guilds (guild proportionality) and this was significant in some tests, but contrary to theory this effect occurred mainly in the most disturbed sites. It is concluded that there is only limited truth in the frequent assumption that community structure is stronger in undisturbed, equilibrium communities.     

A comparison of Passalidae (Coleoptera, Lamellicornia) diversity and community structure between primary and secondary tropical forest in Los Tuxtlas, Veracruz, Mexico

Comparison of the diversity and community structure of Coleoptera (Passalidae) collected in Los Tuxtlas, Veracruz, Mexico, in primary and secondary tropical forest has been carried out. The saproxylophagous beetles studied can be differentiated according to their presence in three distinct microhabitats of rotting logs: underbark, sapwood—heartwood and microhabitat generalists. Over the 2-year study period, 12 passalid species were recorded (six Passalini and six Proculini) represented by a total of 2971 individuals, collected from 234 rotting logs. The rarefaction method, the lognormal species—abundance relationship, and the nonparametric jackknife method were used to compare species richness between the habitats. The data were also fitted to log series, truncated lognormal, geometric, and broken-stick species abundance models to detect changes in community structure. The community composition of Passalidae in Los Tuxtlas did not differ ostensibly between the primary and secondary forests. Neither the mean number of individuals nor the biomass per log differed significantly. Furthermore, there were no significant differences between the two habitats in terms of the number of underbark, sapwood/heartwood, and microhabitat generalist species. Different richness estimators indicated that the primary forest community is only slightly richer. The slight decrease in richness of the secondary forest is related to a decrease in dominance by certain species, as well as to a more balanced abundance distribution, which is adequately described by the broken-stick model. Complementary explanations for this pattern may be: (1) that logging reduces the abundance of dominant species, thus preventing competitive exclusion in the secondary forest; and (2) that passalid diversity is not regulated by the diversity of tree species.     

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.     

Statistical mechanics of relative species abundance

Statistical mechanics of relative species abundance (RSA) patterns in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka–Volterra equation, with diverse interspecies interactions. Various RSA patterns observed in nature are derived from a single parameter related to productivity or maturity of a community. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. It is also found that the “canonical hypothesis” is supported in some parameter region where the typical RSA patterns are observed. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g. gene expression.