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.     

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.     

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.     

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.     

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。     

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.     

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.     

Butterfly (Order: Lepidoptera) species Richness,diversity and distribution in different localities of Battagram,Pakistan

Butterflies are the beautiful creatures and need to be conserved. The present survey was conducted to explore the biodiversity of butterflies of District Battagram Khyber Pakhtunkhwa Pakistan, from March to September 2021. During this study the butterflies were collected from 2 Tehsil including 12 localities using line transect method. A total of 572 specimens were collected from all localities. Species identified were belonging to 3 families and 7 genera. The species were Cynthia cardui. Danaus chrysippus, Junonia orithya, Papilio demoleus, Papilio polytes, Colias croceus, Pieris ajaka, Pontia daplidice and Pieris napi. In the recorded 9 species Papilo demoleus was the most common species of the district Battagram and the most rear specie was Pieris ajaka during this study. The current study is new detailed work on the butterflies from district Battagram . It is concluded from the present study that district Battagram is rich in flora and provide a much suitable environment and place for biodiversity to insects. As this study is the first survey of butterflies population in the district and recorded rich diversity, so more explorative work is needed for its population estimation and specie abundance.     

The effects of intraspecific density dependence on species richness and species abundance distributions

Species richness and patterns of abundance result from the interplay between niche differences, realized as intraspecific density dependence (IDD), and so-called neutral processes that arise when species fitnesses are similar. This paper presents an extension of neutral models that incorporates delays in IDD that could result from resource-mediated competition or through a pathogen pool. These delays reduce standing species richness and qualitatively change the shape of species abundance distributions and render them consistent with the hollow curve shape even in the presence of strong IDD.     

From plots to islands: species diversity at different scales

Aim To investigate how plant diversity of whole islands (‘gamma’) is related to alpha and beta diversity patterns among sampling plots within each island, thus exploring aspects of diversity patterns across scales. Location Nineteen islands of the Aegean Sea, Greece. Methods Plant species were recorded at both the whole‐island scale and in small 100 m² plots on each island. Mean plot species richness was considered as a measure of alpha diversity, and six indices of the ‘variation’‐type beta diversity were also applied. In addition, we partitioned beta diversity into a ‘nestedness’ and a ‘replacement’ component, using the total species richness recorded in all plots of each island as a measure of ‘gamma’ diversity. We also applied 10 species–area models to predict the total observed richness of each island from accumulated plot species richness. Results Mean alpha diversity was not significantly correlated with the overall island species richness or island area. The range of plot species richness for each island was significantly correlated with both overall species richness and area. Alpha diversity was not correlated with most indices of beta diversity. The majority of beta diversity indices were correlated with whole‐island species richness, and this was also true for the ‘replacement’ component of beta diversity. The rational function model provided the best prediction of observed island species richness, with Monod’s and the exponential models following closely. Inaccuracy of predictions was positively correlated with the number of plots and with most indices of beta diversity. Main conclusions Diversity at the broader scale (whole islands) is shaped mainly by variation among small local samples (beta diversity), while local alpha diversity is not a good predictor of species diversity at broader scales. In this system, all results support the crucial role of habitat diversity in determining the species–area relationship.     

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.