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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

On the statistical mechanics of species abundance distributions

A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of  [Volkov et?al., 2003] and [Volkov et?al., 2005] and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure.     

Palm species richness,abundance and diversity in the Yucatan Peninsula,in a neotropical context

Species richness, abundance and diversity patterns in palm communities in the Yucatan Peninsula were compared at three sites with different forest types (semi‐deciduous, semi‐evergreen and evergreen), as well as different precipitation, geomorphology and soil depth. All individual palms, including seedlings, juveniles and adults, were identified and counted in forty‐five (0.25 ha) transects. A total of 46 000 individual palms belonging to 11 species from nine genera and two subfamilies were recorded. Palm richness, diversity and abundance were highest in the evergreen forest. Species from the subfamily Coryphoideae dominated the semi‐deciduous and semi‐evergreen forests while species from the subfamily Arecoideae dominated the evergreen forest. Seven species were found only in the evergreen forest. Chamaedorea seifrizii and Sabal yapa were found in all three forest types, while Thrinax radiata was found in the semi‐deciduous and semi‐ evergreen forests and Cocothrinax readii only in the semi‐evergreen forest. Compared to other neotropical palm communities, the richness and diversity in the Yucatan Peninsula are lower than in the western Amazon basin. Although palm richness and diversity on the Yucatan Peninsula were positively associated with precipitation, other variables, in particular soil depth and fertility as well as habitat heterogeneity (microtopography and canopy cover), need to be considered to better understand the observed patterns.     

Multimodal species abundance distributions: a deconstruction approach reveals the processes behind the pattern

It is becoming increasingly apparent that the species abundance distribution of many ecological communities contains multiple modes, a phenomenon that has been largely overlooked. Here, we test for multiple modes in the species abundance distribution using a combination of one, two and three mode Poisson lognormal distributions and an extensive arthropod dataset from the Azores. We consider the abundance distribution of twelve native laurisilva forest fragments and the combination of fragments within five islands, allowing us to detect whether patterns are consistent across scales. An information theoretic approach is employed to determine the best model in each case. To explore the processes driving multimodal abundance distributions we tested various potential mechanisms. We classified species as core if they are present in over half the fragments in our study, and as satellite if they are sampled in fewer than half the fragments. Furthermore, species are classified based on body size, whether they are indigenous (i.e. endemic or native non‐endemic) or introduced to the Azores, abundance in land uses other than native forest, and dispersal ability. We find that models incorporating multiple modes perform best for most fragments and islands. A large number of communities are bimodal, comprising a mode of very rare species and a mode of relatively common species. Deconstructing the full assemblages into their constituent subsets reveals that the combination of ecologically different groups of species into a single sample underpins the multimodal pattern. Specifically, the rarer mode prevailingly contains a higher proportion of satellite taxa, introduced species and species that are more adapted to anthropogenic land uses that surround the native forest.     

Parametric scaling from species to growth-form diversity: an interesting analogy with multifractal functions

We propose a measure of divergence from species to life-form diversity aimed at summarizing the ecological similarity among different plant communities without losing information on traditional taxonomic diversity. First, species and life-form relative abundances within a given plant community are determined. Next, using Rényi's generalized entropy, the diversity profiles of the analyzed community are computed both from species and life-form relative abundances. Finally, the speed of decrease from species to life-form diversity is obtained by combining the outcome of both profiles. Interestingly, the proposed measure shows some formal analogies with multifractal functions developed in statistical physics for the analysis of spatial patterns. As an application for demonstration, a small data set from a plant community sampled in the archaeological site of Paestum (southern Italy) is used.     

Estimating bacterial diversity from clone libraries with flat rank abundance distributions

There are a number of parametric and non-parametric methods for estimating diversity. However all such methods employ either the proportional abundance of the most abundant taxon in a sample or require that a specific taxon is sampled more than once. Consequently, the available methods for estimating diversity cannot be applied to samples consisting entirely of singletons, which might be characteristic of some hyperdiverse communities. Here we present a non-parametric method that estimates the probability that a given number of unique taxa would be sampled from a community with a particular diversity. We have applied this approach to a well known data set of 100 unique clones from a sample of Amazonian soil (Borneman and Triplett (1997) Appl Environ Microbiol 63: 2647-2653) and determine the probability that this observation would be made from an environment of a given diversity. On this basis we can state this observation would be very unlikely (P = 0.006) if the soil diversity was less than 10(3), and quite unlikely (P = 0.6) if the diversity was less than 10(4), and probable (P = 0.95) if the diversity was about 10(5). There are essentially no contestable assumptions in our method. Thus we are able to offer almost unequivocal evidence that the bacterial diversity, of at least soils, is very large and a method that may be used to interpret samples consisting entirely of singletons from other hyperdiverse communities.     

Partitioning species diversity across landscapes and regions: a hierarchical analysis of alpha, beta, and gamma diversity

Species diversity may be additively partitioned within and among samples (alpha and beta diversity) from hierarchically scaled studies to assess the proportion of the total diversity (gamma) found in different habitats, landscapes, or regions. We developed a statistical approach for testing null hypotheses that observed partitions of species richness or diversity indices differed from those expected by chance, and we illustrate these tests using data from a hierarchical study of forest-canopy beetles. Two null hypotheses were implemented using individual- and sample-based randomization tests to generate null distributions for alpha and beta components of diversity at multiple sampling scales. The two tests differed in their null distributions and power to detect statistically significant diversity components. Individual-based randomization was more powerful at all hierarchical levels and was sensitive to departures between observed and null partitions due to intraspecific aggregation of individuals. Sample-based randomization had less power but still may be useful for determining whether different habitats show a higher degree of differentiation in species diversity compared with random samples from the landscape. Null hypothesis tests provide a basis for inferences on partitions of species richness or diversity indices at multiple sampling levels, thereby increasing our understanding of how alpha and beta diversity change across spatial scales.     

Combining richness and abundance into a single diversity index using matrix analogues of Shannon's and Simpson's indices

Shannon's and Simpson's indices have been the most widely accepted measures of ecological diversity for the past fifty years, even though neither statistic accounts for species abundances across geographic locales ("patches"). An abundant species that is endemic to a single patch can be as much of a conservation concern as a rare cosmopolitan species. I extend Shannon's and Simpson's indices to simultaneously account for species richness and relative abundances – i.e. extend them to multispecies metacommunities – by making the inputs to each index a matrix, rather than a vector. The Shannon's index analogue of diversity is mutual entropy of species and patches divided by marginal entropy of the individual geographic patches. The Simpson's index analogue of diversity is a modification of mutual entropy, with the logarithm moved to the outside of the summation, divided by Simpson's index of the patches. Both indices are normalized for number of patches, with the result being inversely proportional to biodiversity. These methods can be extended to account for time-series of such matrices and average age-classes of each species within each patch, as well as provide a measure of spatial coherence of communities.