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.     

Assessment of species diversity from species abundance distributions at different localities

We show how the spatial structure of species diversity can be analyzed using the correlation between the log abundances of the species in the communities, assuming that two communities at different localities can be described by a bivariate lognormal species abundance distribution. A useful property of this approach is that the log abundances of the species at two localities can be considered as samples from a bivariate normal distribution defined by only five parameters. The variances and the correlation can be estimated by maximum likelihood methods even if there is no information about the sampling intensity and the number of unobserved species. This method also enables estimation of over-dispersion in the sampling relative to a Poisson distribution that allows sampling adjustment of the estimate of β-diversity. Furthermore, we also obtain a partitioning of species diversity into additive components of α-, β- and γ-diversity. For instance, if the correlation between the log abundances of the species is close to one, the same species will be common and rare in the two communities and the β-diversity will be low. We illustrate this approach by analysing similarities of communities of rare and endangered species of oak-living beetles in south-eastern Norway. The number of recorded species was estimated to be only 48.1% of the total number of species actually present in these communities. The correlations among communities dropped rather quickly with distance with a scaling of order 200 km. This illustrates large spatial heterogeneity in species composition, which should be accounted for in the design of schemes of such devices for assessing species diversity in these habitat-types.     

Relating species abundance distributions to species-area curves in two Mediterranean-type shrublands

Abstract. Based on both theoretical and empirical studies there is evidence that different species abundance distributions underlie different species‐area relationships. Here I show that Australian and Californian shrubland communities (at the scale from 1 to 1000 m²) exhibit different species‐area relationships and different species abundance patterns. The species‐area relationship in Australian heathlands best fits an exponential model and species abundance (based on both density and cover) follows a narrow log normal distribution. In contrast, the species‐area relationship in Californian shrublands is best fit with the power model and, although species abundance appears to fit a log normal distribution, the distribution is much broader than in Australian heathlands. I hypothesize that the primary driver of these differences is the abundance of small‐stature annual species in California and the lack of annuals in Australian heathlands. Species‐area is best fit by an exponential model in Australian heathlands because the bulk of the species are common and thus the species‐area curves initially rise rapidly between 1 and 100 m². Annuals in Californian shrublands generate very broad species abundance distributions with many uncommon or rare species. The power function is a better model in these communities because richness increases slowly from 1 to 100 m² but more rapidly between 100 and 1000 m² due to the abundance of rare or uncommon species that are more likely to be encountered at coarser spatial scales. The implications of this study are that both the exponential and power function models are legitimate representations of species‐area relationships in different plant communities. Also, structural differences in community organization, arising from different species abundance distributions, may lead to different species‐area curves, and this may be tied to patterns of life form distribution.     

Using species abundance distribution models and diversity indices for biogeographical analyses

We examine whether Species Abundance Distribution models (SADs) and diversity indices can describe how species colonization status influences species community assembly on oceanic islands. Our hypothesis is that, because of the lack of source-sink dynamics at the archipelago scale, Single Island Endemics (SIEs), i.e. endemic species restricted to only one island, should be represented by few rare species and consequently have abundance patterns that differ from those of more widespread species. To test our hypothesis, we used arthropod data from the Azorean archipelago (North Atlantic). We divided the species into three colonization categories: SIEs, archipelagic endemics (AZEs, present in at least two islands) and native non-endemics (NATs). For each category, we modelled rank-abundance plots using both the geometric series and the Gambin model, a measure of distributional amplitude. We also calculated Shannon entropy and Buzas and Gibson's evenness. We show that the slopes of the regression lines modelling SADs were significantly higher for SIEs, which indicates a relative predominance of a few highly abundant species and a lack of rare species, which also depresses diversity indices. This may be a consequence of two factors: (i) some forest specialist SIEs may be at advantage over other, less adapted species; (ii) the entire populations of SIEs are by definition concentrated on a single island, without possibility for inter-island source-sink dynamics; hence all populations must have a minimum number of individuals to survive natural, often unpredictable, fluctuations. These findings are supported by higher values of the α parameter of the Gambin mode for SIEs. In contrast, AZEs and NATs had lower regression slopes, lower α but higher diversity indices, resulting from their widespread distribution over several islands. We conclude that these differences in the SAD models and diversity indices demonstrate that the study of these metrics is useful for biogeographical purposes.     

Marine sponges of the Dampier Archipelago, Western Australia: patterns of species distributions, abundance and diversity

Quantitative surveys revealed high diversity (species richness) of sponges (150 species) in the previously little explored Dampier Archipelago, northwestern Australia. Classification analyses disclosed 11 station groups with high internal heterogeneity in species composition, however some spatial patterns were evident. The composition of sponge assemblages varied with environmental factors such as substrate type (coral, igneous rock, limestone rock), aspect (exposed, protected), substrate configuration (limestone platform, dissected reef) and depth. Most of the species (61%) reported from the Dampier Archipelago were rare (found at one or two stations). The number of species found at only one location was high (48%), supporting previous findings that northwestern Australia has high sponge endemism. As a result of all sponge surveys undertaken in the archipelago (qualitative and quantitative, subtidal and intertidal), 275 sponge species have now been reported from the area. This number indicates high species diversity in the region. Estimations of diversity based on non-parametric modelling suggests that there are potentially more species (range 245–346) than presently recorded in the archipelago.     

The impact of neutrality, niche differentiation and species input on diversity and abundance distributions

We present a spatially-explicit generalization of Hubbell's model of community dynamics in which the assumption of neutrality is relaxed by incorporating dispersal limitation and habitat preference. In simulations, diversity and species abundances were governed by the rate at which new species were introduced (usually called 'speciation') and nearly unaffected by dispersal limitation and habitat preference. Of course, in the absence of species input, diversity is maintained solely by niche differences. We conclude that the success of the neutral model in predicting the abundance distribution has nothing to do with neutrality, but rather with the species-introduction process: when new species enter a community regularly as singletons, the typical J-shaped abundance distribution, with a long tail of rare species, is always observed, whether species differ in habitat preferences or not. We suggest that many communities are indeed driven by the introduction process, accounting for high diversity and rarity, and that species differences may be largely irrelevant for either.     

Species-area curves and estimates of total species richness in an old-field chronosequence

Average species-area curves were generated for vascular plants in 20 old-fields that were sampled in 1983, 1989, and 1994. These curves were fit with a saturating function to estimate total species richness for each old-field. Additional estimates of total species richness were generated by fitting the same saturating function to subsets of the species area curves and with a first-order jackknife procedure. Estimates of total species richness were strongly correlated with observed species richness. There was limited evidence suggesting that greater sampling was necessary to identify the same proportion of species in older, more species-rich old-fields.     

On plotting species abundance distributions

1. There has been a revival of interest in species abundance distribution (SAD) models, stimulated by the claim that the log-normal distribution gave an underestimate of the observed numbers of rare species in species-rich assemblages. This led to the development of the neutral Zero Sum Multinomial distribution (ZSM) to better fit the observed data. 2. Yet plots of SADs, purportedly of the same data, showed differences in frequencies of species and of statistical fits to the ZSM and log-normal models due to the use of different binning methods. 3. We plot six different binning methods for the Barro Colorado Island (BCI) tropical tree data. The appearances of the curves are very different for the different binning methods. Consequently, the fits to different models may vary depending on the binning system used. 4. There is no agreed binning method for SAD plots. Our analysis suggests that a simple doubling of the number of individuals per species in each bin is perhaps the most practical one for illustrative purposes. Alternatively rank-abundance plots should be used. 5. For fitting and testing models exact methods have been developed and application of these does not require binning of data. Errors are introduced unnecessarily if data are binned before testing goodness-of-fit to models.     

How selection structures species abundance distributions

How do species divide resources to produce the characteristic species abundance distributions seen in nature? One way to resolve this problem is to examine how the biomass (or capacity) of the spatial guilds that combine to produce an abundance distribution is allocated among species. Here we argue that selection on body size varies across guilds occupying spatially distinct habitats. Using an exceptionally well-characterized estuarine fish community, we show that biomass is concentrated in large bodied species in guilds where habitat structure provides protection from predators, but not in those guilds associated with open habitats and where safety in numbers is a mechanism for reducing predation risk. We further demonstrate that while there is temporal turnover in the abundances and identities of species that comprise these guilds, guild rank order is conserved across our 30-year time series. These results demonstrate that ecological communities are not randomly assembled but can be decomposed into guilds where capacity is predictably allocated among species.     

Taking species abundance distributions beyond individuals

The species abundance distribution (SAD) is one of the few universal patterns in ecology. Research on this fundamental distribution has primarily focused on the study of numerical counts, irrespective of the traits of individuals. Here we show that considering a set of Generalized Species Abundance Distributions (GSADs) encompassing several abundance measures, such as numerical abundance, biomass and resource use, can provide novel insights into the structure of ecological communities and the forces that organize them. We use a taxonomically diverse combination of macroecological data sets to investigate the similarities and differences between GSADs. We then use probability theory to explore, under parsimonious assumptions, theoretical linkages among them. Our study suggests that examining different GSADs simultaneously in natural systems may help with assessing determinants of community structure. Broadening SADs to encompass multiple abundance measures opens novel perspectives in biodiversity research and warrants future empirical and theoretical developments.     

Spatial scaling of species abundance distributions

Species abundance distributions are an essential tool in describing the biodiversity of ecological communities. We now know that their shape changes as a function of the size of area sampled. Here we analyze the scaling properties of species abundance distributions by using the moments of the logarithmically transformed number of individuals. We find that the moments as a function of area size are well fitted by power laws and we use this pattern to estimate the species abundance distribution for areas larger than those sampled. To reconstruct the species abundance distribution from its moments, we use discrete Tchebichef polynomials. We exemplify the method with data on tree and shrub species from a 50 ha plot of tropical rain forest on Barro Colorado Island, Panama. We test the method within the 50 ha plot, and then we extrapolate the species abundance distribution for areas up to 5 km². Our results project that for areas above 50 ha the species abundance distributions have a bimodal shape with a local maximum occurring for the singleton classes and that this maximum increases with sampled area size.     

天目山物种多样性尺度依赖及其与空间格局关系的多重分形

以浙江省天目山国家级自然保护区为例,采用多尺度分析思想,利用多重分形分析方法,研究了不同尺度下物种多样性的变化、空间分布格局以及多样性与空间格局之间的关系。研究主要得到3方面的结论：（1）物种多样性具有尺度依赖性,随着空间尺度的增大,Shannon-Wiener多样性指数Ⅳ增大,Margalef多样性指数足和均匀度指数E减小;（2）多重分形参数αmin。多重分形谱的变化范围SR等能够定量反映物种的空间分布特征,空间大尺度越大,物种越聚集,空间分布越不均匀;（3）物种多样性与空间格局存在线性或幂函数关系。研究表明多重分形分析定量描述物种空间格局是有效性的,多重分形参数与生物多样性之间的定量关系为研究物种空间格局、生态属性与尺度之间的关系奠定了基础。因此,分形结合传统方法,在生物多样性方面的研究将有很大的潜在价值。     

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.     

Species-area curves, spatial aggregation, and habitat specialization in tropical forests

The relationship between species diversity and sampled area is fundamental to ecology. Traditionally, theories of the species-area relationship have been dominated by random-placement models. Such models were used to formulate the canonical theory of species-area curves and species abundances. In this paper, however, armed with a detailed data set from a moist tropical forest, we investigate the validity of random placement and suggest improved models based upon spatial aggregation. By accounting for intraspecific, small-scale aggregation, we develop a cluster model which reproduces empirical species-area curves with high fidelity. We find that inter-specific aggregation patterns, on the other hand, do not affect the species-area curves significantly. We demonstrate that the tendency for a tree species to aggregate, as well as its average clump size, is not significantly correlated with the species' abundance. In addition, we investigate hierarchical clumping and the extent to which aggregation is driven by topography. We conclude that small-scale phenomena such as dispersal and gap recruitment determine individual tree placement more than adaptation to larger-scale topography.     

Combining counts and incidence data: an efficient approach for estimating the log-normal species abundance distribution and diversity indices

Obtaining accurate estimates of diversity indices is difficult because the number of species encountered in a sample increases with sampling intensity. We introduce a novel method that requires that the presence of species in a sample to be assessed while the counts of the number of individuals per species are only required for just a small part of the sample. To account for species included as incidence data in the species abundance distribution, we modify the likelihood function of the classical Poisson log-normal distribution. Using simulated community assemblages, we contrast diversity estimates based on a community sample, a subsample randomly extracted from the community sample, and a mixture sample where incidence data are added to a subsample. We show that the mixture sampling approach provides more accurate estimates than the subsample and at little extra cost. Diversity indices estimated from a freshwater zooplankton community sampled using the mixture approach show the same pattern of results as the simulation study. Our method efficiently increases the accuracy of diversity estimates and comprehension of the left tail of the species abundance distribution. We show how to choose the scale of sample size needed for a compromise between information gained, accuracy of the estimates and cost expended when assessing biological diversity. The sample size estimates are obtained from key community characteristics, such as the expected number of species in the community, the expected number of individuals in a sample and the evenness of the community.     

Models for the logarithmic species abundance distributions

Three models, developed by Karlin, McGregor and Ewens to describe evolving populations of selectively neutral genotypes, are shown to lead to various versions of Fisher's logarithmic series distribution for species abundance. Statistical inference procedures and measures of diversity which have been developed in one of the two contexts are therefore also applicable in the other context, and the paper reviews and extends these links. Some work of Fisher, Good and Rao is shown to be based on a faulty version of the logarithmic distribution, which, nevertheless, is a good approximation to a consistent version.     

Demographic trade-offs determine species abundance and diversity

Aims Much recent theory has focused on the role of neutral processes in assembling communities, but the basic assumption that all species are demographically identical has found little empirical support. Here, we show that the framework of the current neutral theory can easily be generalized to incorporate species differences so long as fitness equivalence among individuals is maintained through trade-offs between birth and death.Methods Our theory development is based on a careful reformulation of the Moran model of metacommunity dynamics in terms of a non-linear one-step stochastic process, which is described by a master equation.Important findings We demonstrate how fitness equalization through demographic trade-offs can generate significant macroecological diversity patterns, leading to a very different interpretation of the relation between Fisher's α and Hubbell's fundamental biodiversity number. Our model shows that equal fitness (not equal demographics) significantly promotes species diversity through strong selective sieving of community membership against high-mortality species, resulting in a positive association between species abundance and per capita death rate. An important implication of demographic trade-off is that it can partly explain the excessively high speciation rates predicted by the neutral theory of the stronger symmetry. Fitness equalization through demographic trade-offs generalizes neutral theory by considering heterospecific demographic difference, thus representing a significant step toward integrating the neutral and niche paradigms of biodiversity.