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.     

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.     

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.     

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.     

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.     

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.     

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.     

甘蔗绵蚜不同地理种群异柠檬酸脱氢酶（IDH）的多样性

用等位酶分析方法对三个用药背景不同的甘蔗绵蚜地理种群在9种酶（EST,G3PD,HEX,IDH,LDH,MDH,ME,PGI和PCM）上的遗传组成进行检测。结果显示：甘蔗绵蚜在9种酶共检测到9个等位酶位点,仅IDH位点具有多态性。在多态性的IDH位点共检测到3个等位基因,其中连续两年未曾用药的两院种群和用药较少的木棠种群均具有三个等位基因（a,b和c）,而用药次数最多的临高种群仅存在两个等位基因（a和b）。等位基因a的频率从两院种群到临高种群逐渐升高,而等位基因b的频率却逐渐降低。说明IDH在甘蔗绵蚜的种群遗传进化过程中起着重要作用,杀虫剂的选择压力可能对甘蔗绵蚜地理种群的遗传结构具有分化作用,同时也说明IDH在甘蔗绵蚜对杀虫剂的抗性产生中具有重要作用。IDH-a频率的升高,可能导致甘蔗绵蚜对杀虫剂产生抗性,可通过检测IDH位点等位基因频率的变化来监测甘蔗绵蚜对杀虫剂的抗性。     

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.     

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.     

Displacement in two invasive species of leafminer fly in different localities

Liriomyza sativae was displaced by L. trifolii in the USA probably due to the lower insecticide susceptibility of L. trifolii, but L. trifolii was displaced by L. sativae in Japan. To know the possible causes of the species displacement observed in Japan, differences in the insecticide susceptibility, fecundity, effects of natural enemies, and reproductive interference between L. trifolii and L. sativae were evaluated. As a result, the higher fecundity of L. sativae and differential effects of parasitoids on the two Liriomyza species are considered to be contributing factors.     

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.     

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.     

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.     

Comparison of pistachio hull essential oils from different Tunisian localities

Pistachio (Pistacia vera L.) fruit is well known for its oleaginous and edible seed. Less information is available about the hull constituted by the epicarp and the mesocarp. This part of the fruit contains an essential oil that can be valorized. Tunisia is one of the countries cultivating pistachio trees. This work presents essential oil composition of pistachio hulls (Mateur variety) from different geographical localities: Grombalia (North-East), Kairouan (Middle) and Sfax (Middle-East). Yields were more important in Sfax samples (0.53% on a dry weight basis). Alpha-terpinolene was the major compound for Grombalia fruits (35.7%), whereas Kairouan and Sfax samples where characterized by alpha-pinene (42.5 and 43.8% respectively). For all samples, monoterpene hydrocarbons predominated (more than 79.8% of the essential oil).     

Effects of stand tree species composition and diversity on abundance of predatory arthropods

Diverse plant communities are predicted to have higher abundance of predators as compared to species-poor ones. In this study we explored whether this prediction holds true for the abundance of predatory arthropods in forest ecosystems, which have been poorly studied in this respect. We collected ground-dwelling arthropods using pitfall traps from six long-term forest diversity experiments in Finland, Sweden and UK. The effects of tree species diversity on abundance of five main groups of predatory arthropods (ants, spiders, carabids, staphylinids and opilionids) were examined by means of meta-analysis. Overall, the diversity of tree species did not affect abundances of predators with the exception of staphylinids, which were more abundant in mixed stands than in monocultures. However, the effects of stand diversity on predator abundance became apparent when analyses were conducted on tree species basis. Preference for stands containing particular tree species was clear in the case of opilionids, carabids and staphylinids, and these preferences overruled the effects of tree species diversity in comparisons between monocultures and mixed stands containing the same tree species. Tree species diversity effects on predator abundance were furthermore mediated by the tree age, plot size and planting density used in the experiment. Overall, our results show that predator abundance does not increase uniformly with increase in tree species diversity, but rather suggest that predators have distinct preferences for stands composed of particular tree species and that these species preferences may overrule the effects of diversity.     

Environmental heterogeneity,species diversity and co‐existence at different spatial scales

The positive relationship between spatial environmental heterogeneity and species diversity is a widely accepted concept, generally associated with niche limitation. However, niche limitation cannot account for negative heterogeneity–diversity relationships (HDR) revealed in several case studies. Here we explore how HDR varies at different spatial scales and provide novel theories for small‐scale species co‐existence that explain both positive and negative HDR. At large spatial scales of heterogeneity (e.g. landscape level), different communities co‐exist, promoting large regional species pool size and resulting in positive HDR. At smaller scales within communities, species co‐existence can be enhanced by increasing the number of different patches, as predicted by the niche limitation theory, or alternatively, restrained by heterogeneity. We conducted meta‐regressions for experimental and observational HDR studies, and found that negative HDRs are significantly more common at smaller spatial scales. We propose three theories to account for niche limitation at small spatial scales. (1) Microfragmentation theory: with increasing spatial heterogeneity, large homogeneous patches lose area and become isolated, which in turn restrains the establishment of new plant individuals and populations, thus reducing species richness. (2) Heterogeneity confounded by mean: when heterogeneity occurs at spatial scales smaller than the size of individual plants, which forage through the patches, species diversity can be either positively or negatively affected by a change in the mean of an environmental factor. (3) Heterogeneity as a separate niche axis: the ability of species to tolerate heterogeneity at spatial scales smaller than plant size varies, affecting HDR. We conclude that processes other than niche limitation can affect the relationship between heterogeneity and diversity.