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.     

Universal scaling of species‐abundance distributions across multiple scales

The scale‐dependent species abundance distribution (SAD) is fundamental in ecology, but few spatially explicit models of this pattern have thus far been studied. Here we show spatially explicit neutral model predictions for SADs over a wide range of spatial scales, which appear to match empirical patterns qualitatively. We find that the assumption of a log‐series SAD in the metacommunity made by spatially implicit neutral models can be justified with a spatially explicit model in the large area limit. Furthermore, our model predicts that SADs on multiple scales are characterized by a single, compound parameter that represents the ratio of the survey area to the species’ average biogeographic range (which is in turn set by the speciation rate and the dispersal distance). This intriguing prediction is in line with recent empirical evidence for a universal scaling of the species‐area curve. Hence we hypothesize that empirical SAD patterns will show a similar universal scaling for many different taxa and across multiple spatial scales.     

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.     

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.     

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.     

Measures, perceptions and scaling patterns of aggregated species distributions

Non-random (aggregated) species distributions arise from habitat heterogeneity and nonlinear biotic processes. A comprehensive understanding of the concept of aggregation, as well as its measurement, is pivotal to our understanding of species distributions and macroecological patterns. Here, using an individual-based model, we analyzed opinions on the concept of aggregation from the public and experts (trained ecologists), in addition to those calculated from a variety of aggregation indices. Three forms of scaling patterns (logarithmic, power-law and lognormal) and four groups of scaling trajectories emerged. The experts showed no significant difference from the public, although with a much lower deviation. The public opinion was partially influenced by the abundance of individuals in the spatial map, which was not found in the experts. With the increase of resolution (decrease of grain), aggregation indices showed a general trend from significantly different to significantly similar to the expert opinion. The over-dispersion index (i.e. the clumping parameter k in the negative binomial distribution) performed, at certain scales, as the closest index to the expert opinion. Examining performance of aggregation measures from different groups of scaling patterns was proposed as a practical way of analyzing spatial structures. The categorization of the scaling patterns of aggregation measures, as well as their over- and in-sensitivity towards spatial structures, thus not only provides a potential solution to the modifiable areal unit problem, but also unveils the interrelationship among the concept, measures and perceptions of aggregated species distributions.     

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

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

Spatial patterns of species distributions in grazed subalpine grasslands

Spatial patterns of species diversity have important influences on the functioning of ecosystems, and the effect of livestock grazing on spatial heterogeneity can differ depending on the scale of the analysis. This study examined the effects of grazing on the spatial patterns of species distributions and whether the effects of grazing on the spatial distributions of a species vary with the scale of the analysis. Data were collected at three locations in the subalpine grasslands of Ordesa-Monte Perdido National Park and Aísa Valley, Central Pyrenees, Spain, which differed in mean stocking rates. Aspect explained about one-third of the environmental variation in species distributions. In flat areas, spatial variation in species composition varied with grazing intensity at two scales. At a coarse scale (among vegetation patches), grazing promoted patchiness, and among-transect variation in species diversity and grazing intensity were positively correlated. At a fine scale (within vegetation patches), the disruption of the self-organizing processes of the species spatial distributions resulted in a reduction in the long-range spatial autocorrelations of some of the characteristic species and in the homogenization of species spatial distributions. The presence of encroaching Echinospartum horridum had a significant influence on the effect of grazing on south-facing grassland slopes.     

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.     

Moving beyond assumptions to understand abundance distributions across the ranges of species

The assumption that species are most abundant in the center of their range and decline in abundance toward the range edges has a long history in the ecological literature. This assumption has driven basic and applied ecological and evolutionary hypotheses about the causes of species range limits and their responses to climate change. Here, we review recent studies that are taking biogeographical ecology beyond previously held assumptions by observing populations in the field across large parts of the species range. When these studies combine data on abundance, demographics, organismal physiology, genetics and physical factors, they provide a promising approach for teasing out ecological and evolutionary mechanisms of the patterns and processes underlying species ranges.     

Spatial distributions of multiple plant species affect herbivore foraging selectivity

Spatial distribution of food resources is an important factor determining herbivore foraging. Previous studies have demonstrated that clumped distribution of preferred species increases its consumption by herbivores in single‐ or two‐species systems. However, the potential impact of distribution pattern of less preferred species on foraging was ignored. In natural grasslands with high species diversity and complexity, the spatial distribution of preferred species impacts on herbivore foraging may be strongly correlated with the distribution of less preferred species. Our aims were to determine the effect of distribution of both preferred and other plant species on herbivore foraging under conditions close to a native, multi‐species foraging environment, and conceptualize the relationships between spatial distribution of food resources and herbivore consumption. We hypothesized that random distribution of non‐preferred species reduces herbivore consumption of preferred species because the dispersion of less preferred species likely disturbs herbivore foraging. We conducted an experiment using three species with five combinations of clumped and random distribution patterns. Three species Lathyrus quinquenervius, Phragmites australis and Leymus chinensis, were of high, intermediate and low preferences by sheep, respectively. Results showed that distribution of low preferred species, but not that of high preferred one, affected the consumption of preferred species. Sheep obtained higher consumption of high preferred species when low preferred species followed a clumped distribution than a random distribution. Distance between aggregations of high and low preferred species did not affect sheep foraging. It was concluded that the effects of spatial distribution of preferred species on its consumption are dependent on herbivore foraging strategy, and sheep can consume more preferred species when there is a consistent spatial pattern between preferred species and the entire food resource, and that the random dispersion of low preferred species in grassland may reduce herbivore consumption of high preferred species, thus minimizing selective grazing.     

Spatial distributions of tree species in a subtropical forest of China

The spatial dispersion of individuals in a species is an important pattern that is controlled by many mechanisms. In this study we analyzed spatial distributions of tree species in a large-scale (20 ha) stem-mapping plot in a species-rich subtropical forest of China. O-ring statistic was used to measure spatial patterns of species with abundance >10. Ω_0–10, the mean conspecific density within 10 m of a tree, was used as a measure of the intensity of aggregation of a species. Our results showed: (1) aggregated distribution was the dominant pattern in the plot. The percentage of aggregated species decreased with increased spatial scale. (2) The percentages of significantly aggregated species decreased from abundant to intermediate and to rare species. Rare species was more strongly aggregated than common species. Aggregation was weaker in larger diameter classes. (3) Seed traits determined the spatial patterns of trees. Seed dispersal mode can influence spatial patterns of species, with species dispersed by both modes being less clumped than species dispersed by animal or wind, respectively. Considering these results, we concluded that seed dispersal limitation, self-thinning and habitat heterogeneity primarily contributed to spatial patterns and species coexistence in the forest.     

Species abundance distributions over time

It has been known for 50 years that the time period over which data are collected affects the shape of empirical species abundance distributions. However, despite a recent resurgence of interest in characterizing and explaining these patterns the temporal component of species abundance distributions has been largely ignored. I argue that it is essential to take account of time, and not only because sampling duration can have a profound influence on the perceived shape of the distribution. Partitions of species abundance distributions based on temporal occurrence in the record will facilitate tests of both biological and neutral models and may lead to a better understanding of rarity. These temporal partitions also have interesting, but as yet barely explored, parallels with spatial ones such as the core-satellite division. Moreover, changes in abundance distributions across all three of Preston's temporal scales (sampling time, ecological time and evolutionary time) present rich opportunities for ecological research.     

Species-area curves, diversity indices, and species abundance distributions: a multifractal analysis

Although fractals have been applied in ecology for some time, multifractals have, in contrast, received little attention. In this article, we apply multifractals to the species-area relationship and species abundance distributions. We highlight two results: first, species abundance distributions collected at different spatial scales may collapse into a single curve after appropriate renormalization, and second, the power-law form of the species-area relationship and the Shannon, Simpson, and Berger-Parker diversity indices belong to a family of equations relating the species number, species abundance, and area through the moments of the species abundance-probability density function. Explicit formulas for these diversity indices, as a function of area, are derived. Methods to obtain the multifractal spectra from a data set are discussed, and an example is shown with data on tree and shrub species collected in a 50-ha plot on Barro Colorado Island, Panama. Finally, we discuss the implications of the multifractal formalism to the relationship between species range and abundance and the relation between the shape of the species abundance distribution and area.     

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.     

Spatial scaling of microbial biodiversity

A central goal in ecology is to understand the spatial scaling of biodiversity. Patterns in the spatial distribution of organisms provide important clues about the underlying mechanisms that structure ecological communities and are central to setting conservation priorities. Although microorganisms comprise much of Earth's biodiversity, little is known about their biodiversity scaling relationships relative to that for plants and animals. Here, we discuss current knowledge of microbial diversity at local and global scales. We focus on three spatial patterns: the distance-decay relationship (how community composition changes with geographic distance), the taxa-area relationship, and the local:global taxa richness ratio. Recent empirical analyses of these patterns for microorganisms suggest that there are biodiversity scaling rules common to all forms of life.     

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.     

Spatial patterns and scaling behaviors of Steller sea lion (Eumetopias jubatus) distributions and their environment

Fractal geometry and other multi-scale analyses have become popular tools for investigating spatial patterns of animal distributions in heterogeneous environments. In theory, changes in patterns of animal distributions with changes in scale reflect transitions between the controlling influences of one environmental factor or process over another. In an effort to find linkages between Steller sea lions (Eumetopias jubatus) and their environment, the objective of this study was to determine if the spatial distribution of Steller sea lions at sea displayed similar scaling properties to the variation of two environmental features, including bathymetry and sea surface temperature (SST). Additionally, distributions of Steller sea lion point patterns were examined with respect to measurements of bathymetric complexity. From February 2000 to May 2004, satellite transmitters were deployed on 10 groups of juvenile Steller sea lions (n=52) at eight different locations within the Aleutian Islands and Gulf of Alaska. Indices of fractal dimension were calculated for each group of sea lions using a unit square box-counting method, whereas indices of bathymetry and SST patchiness were derived by conducting a variance ratio analysis over the same scales. Distributions of Steller sea lions at sea displayed self-similar fractal patterns, suggesting that individuals were distributed in a continuous hierarchical set of clumps within clumps across scales, and foraging behavior was likely influenced by a scale invariant mechanism. Patterns of bathymetric variability also were self-similar, whereas patterns of SST variability were scale dependent and failed to retain self-similar spatial structure at larger scales. These results indicate that the distributions of Steller sea lions at sea were more influenced by bathymetry than SST at the scales examined, but scale-dependent patterns in the distribution of Steller sea lions at sea or linkages with SST may have been apparent if analyses were conducted at finer spatial scales.     

The effect of habitat stability on benthic invertebrate communities: the utility of species abundance distributions

Spatial and temporal patterns in the species abundance distribution of benthic invertebrate communities of 11 freshwater habitats (10 streams and a wind-swept lake shore) were examined with respect to habitat stability. Abundance patterns varied markedly between seasons at most sites. However, mean abundance distributions at 4 of the 5 unstable sites and the 2 most stable sites were dominated by one or two taxa with a large number of rare species, whereas sites of intermediate stability had more equitable distributions. Both the log series and log normal distributions were statistically indistinguishable, at the 5% level, from all the observed mean abundance patterns. In contrast, graphical comparisons of the observed and fitted distributions suggested the log series may be the better fit at most of the unstable sites and the two most stable sites, whereas the more equitable distribution at sites of intermediate stability suggested the log normal distribution was the better fit. If conditions at a site favoured one or two species, either through severe physical conditions, or through competitive superiority in the absence of disturbance then the log series distribution may result. However, if no species in the community was strongly advantaged over others, a log normal distribution should result. Given the discriminating power of the appropriate statistical test it may not, however, be possible to pick up these differences without graphical comparisons as well.