Characterizing species abundance distributions across taxa and ecosystems using a simple maximum entropy model

The species abundance distribution (SAD) is one of themost studied patterns in ecology due to its potential insights into commonness and rarity, community assembly, and patterns of biodiversity. It is well established that communities are composed of a few common and many rare species, and numerous theoretical models have been proposed to explain this pattern. However, no attempt has been made to determine how well these theoretical characterizations capture observed taxonomic and global-scale spatial variation in the general form of the distribution. Here, using data of a scope unprecedented in community ecology, we show that a simple maximum entropy model produces a truncated log-series distribution that can predict between 83% and 93% of the observed variation in the rank abundance of species across 15 848 globally distributed communities including birds, mammals, plants, and butterflies. This model requires knowledge of only the species richness and total abundance of the community to predict the full abundance distribution, which suggests that these factors are sufficient to understand the distribution for most purposes. Since geographic patterns in richness and abundance can often be successfully modeled, this approach should allow the distribution of commonness and rarity to be characterized, even in locations where empirical data are unavailable.     

Estimating species richness and accumulation by modeling species occurrence and detectability

A statistical model is developed for estimating species richness and accumulation by formulating these community-level attributes as functions of model-based estimators of species occurrence while accounting for imperfect detection of individual species. The model requires a sampling protocol wherein repeated observations are made at a collection of sample locations selected to be representative of the community. This temporal replication provides the data needed to resolve the ambiguity between species absence and nondetection when species are unobserved at sample locations. Estimates of species richness and accumulation are computed for two communities, an avian community and a butterfly community. Our model-based estimates suggest that detection failures in many bird species were attributed to low rates of occurrence, as opposed to simply low rates of detection. We estimate that the avian community contains a substantial number of uncommon species and that species richness greatly exceeds the number of species actually observed in the sample. In fact, predictions of species accumulation suggest that even doubling the number of sample locations would not have revealed all of the species in the community. In contrast, our analysis of the butterfly community suggests that many species are relatively common and that the estimated richness of species in the community is nearly equal to the number of species actually detected in the sample. Our predictions of species accumulation suggest that the number of sample locations actually used in the butterfly survey could have been cut in half and the asymptotic richness of species still would have been attained. Our approach of developing occurrence-based summaries of communities while allowing for imperfect detection of species is broadly applicable and should prove useful in the design and analysis of surveys of biodiversity.     

Estimating dyad association probability under imperfect and heterogeneous detection

In animal behaviour studies, association indices estimate the proportion of time two individuals (i.e. a dyad) spend in association. In terms of dyads, all association indices can be interpreted as estimators of the probability that a dyad is associated. However, traditional indices rely on the assumptions that the probability to detect a particular individual (p) is either approximately one and/or homogeneous between associated and not associated individuals. Based on marked individuals we develop a likelihood based model to estimate the probability a dyad is associated (ψ) accounting for p < 1 and possibly varying between associated and not associated individuals. The proposed likelihood based model allows for both individual and dyadic missing observations. In addition, the model can easily be extended to incorporate covariate information for modeling p and ψ. A simulation study showed that the likelihood based model approach yield reasonably unbiased estimates, even for low and heterogeneous individual detection probabilities, while, in contrast, traditional indices showed moderate to strong biases. The application of the proposed approach is illustrated using a real data set collected from a population of Commerson's dolphin (Cephalorhynchus commersonii) in Patagonia Argentina. Finally, we discuss possible extensions of the proposed model and its applicability in animal behaviour and ecological studies.     

Hierarchical analysis of species distributions and abundance across environmental gradients

Abiotic and biotic processes operate at multiple spatial and temporal scales to shape many ecological processes, including species distributions and demography. Current debate about the relative roles of niche-based and stochastic processes in shaping species distributions and community composition reflects, in part, the challenge of understanding how these processes interact across scales. Traditional statistical models that ignore autocorrelation and spatial hierarchies can result in misidentification of important ecological covariates. Here, we demonstrate the utility of a hierarchical modeling framework for testing hypotheses about the importance of abiotic factors at different spatial scales and local spatial autocorrelation for shaping species distributions and abundances. For the two orchid species studied, understory light availability and soil moisture helped to explain patterns of presence and abundance at a microsite scale (<4 m2), while soil organic content was important at a population scale (<400 m2). The inclusion of spatial autocorrelation is shown to alter the magnitude and certainty of estimated relationships between abundance and abiotic variables, and we suggest that such analysis be used more often to explore the relationships between species life histories and distributions. The hierarchical modeling framework is shown to have great potential for elucidating ecological relationships involving abiotic and biotic processes simultaneously at multiple scales.     

Estimating population abundance using counts from an auxiliary population

Environmental and Ecological Statistics - We develop a new method for estimating population abundance for notoriously difficult to count populations. This is made possible using an easy to count...     

Grassland root communities: species distributions and how they are linked to aboveground abundance

There is little comprehensive information on the distribution of root systems among coexisting species, despite the expected importance of those distributions in determining the composition and diversity of plant communities. This gap in knowledge is particularly acute for grasslands, which possess large numbers of species with morphologically indistinguishable roots. In this study we adapted a molecular method, fluorescent fragment length polymorphism, to identify root fragments and determine species root distributions in two grasslands in Yellowstone National Park (YNP). Aboveground biomass was measured, and soil cores (2 cm in diameter) were collected to depths of 40 cm and 90 cm in an upland, dry grassland and a mesic, slope-bottom grassland, respectively, at peak foliar expansion. Cores were subdivided, and species that occurred in each 10-cm interval were identified. The results indicated that the average number of species in 10-cm intervals (31 cm3) throughout the sampled soil profile was 3.9 and 2.8 species at a dry grassland and a mesic grassland, respectively. By contrast, there was an average of 6.7 and 14.1 species per 0.5 m2, determined by the presence of shoot material, at dry and mesic sites, respectively. There was no relationship between soil depth and number of species per 10-cm interval in either grassland, despite the exponential decline of root biomass with soil depth at both sites. There also was no relationship between root frequency (i.e., the percentage of samples in which a species occurred) and soil depth for the vast majority of species at both sites. The preponderance of species were distributed throughout the soil profile at both sites. Assembly analyses indicated that species root occurrences were randomly assorted in all soil intervals at both sites, with the exception that Festuca idahoensis segregated from Artemisia tridentata and Pseudoroegnaria spicata in 10-20 cm soil at the dry grassland. Root frequency throughout the entire sampled soil profile was positively associated with shoot biomass among species. Together these results indicated the importance of large, well-proliferated root systems in establishing aboveground dominance. The findings suggest that spatial belowground segregation of species probably plays a minor role in fostering resource partitioning and species coexistence in these YNP grasslands.     

Estimating total abundance of a large temperate-reef fish using visual strip-transects

Total abundance estimates for the large, common, reef fish Cheilodactylus spectabilis (Hutton) were obtained for a marine reserve and adjacent section of coast in north-eastern New Zealand during 1985. Visual strip-transects were used to estimate abundance and size structure in both areas. The accuracy, precision and cost efficiency of five transect sizes (500, 375, 250, 100, 75 m²) were examined over three times per day (dawn, midday and dusk), by simulating transects over mapped C. spectabilis populations. Two transect sizes showed similarly high efficiency. The smaller of the two (20x5 m) was chosen for the survey because of the general advantages attributable to small sampling units. Biases related to strip-transect size are discussed. Preliminary sampling indicated that C. spectabilis was distributed heterogeneously, and that density was habitat-related. An optimal stratified-random design was employed in both locations, to obtain total abundance and size-structure estimates. This reduced the between-habitat source of variability in density. The total number of sampling units used was governed by the time available. The resulting total abundance estimates obtained were 18 338±2 886 (95% confidence limit) for the 5 km marine reserve, compared to 3 987±1 117 for an adjacent, heavily fished 4 km section of coast. When corrected for total area and habitat area sampled, this represented a 2.3-fold difference in abundance. If sampling had been designed to detect an arbitrary 10% difference in abundance within each habitat, an infeasible 440 h of sampling would have been required. Size-frequency distributions of C. spectabilis at the reserve had a larger model size class than distributions from the adjacent area. The data suggest that reserve status is causal in these differing abundance and size structure estimates.     

Null model analysis of species associations using abundance data

The influence of negative species interactions has dominated much of the literature on community assembly rules. Patterns of negative covariation among species are typically documented through null model analyses of binary presence/absence matrices in which rows designate species, columns designate sites, and the matrix entries indicate the presence (1) or absence (0) of a particular species in a particular site. However, the outcome of species interactions ultimately depends on population-level processes. Therefore, patterns of species segregation and aggregation might be more clearly expressed in abundance matrices, in which the matrix entries indicate the abundance or density of a species in a particular site. We conducted a series of benchmark tests to evaluate the performance of 14 candidate null model algorithms and six covariation metrics that can be used with abundance matrices. We first created a series of random test matrices by sampling a metacommunity from a lognormal species abundance distribution. We also created a series of structured matrices by altering the random matrices to incorporate patterns of pairwise species segregation and aggregation. We next screened each algorithm-index combination with the random and structured matrices to determine which tests had low Type I error rates and good power for detecting segregated and aggregated species distributions. In our benchmark tests, the best-performing null model does not constrain species richness, but assigns individuals to matrix cells proportional to the observed row and column marginal distributions until, for each row and column, total abundances are reached. Using this null model algorithm with a set of four covariance metrics, we tested for patterns of species segregation and aggregation in a collection of 149 empirical abundance matrices and 36 interaction matrices collated from published papers and posted data sets. More than 80% of the matrices were significantly segregated, which reinforces a previous meta-analysis of presence/absence matrices. However, using two of the metrics we detected a significant pattern of aggregation for plants and for the interaction matrices (which include plant-pollinator data sets). These results suggest that abundance matrices, analyzed with an appropriate null model, may be a powerful tool for quantifying patterns of species segregation and aggregation.     

Weighted distributions and estimation of resource selection probability functions

Understanding how organisms selectively use resources is essential for designing wildlife management strategies. The probability that an individual uses a given resource, as characterized by environmental factors, can be quantified in terms of the resource selection probability function (RSPF). The present literature on the topic has claimed that, except when both used and unused sites are known, the RSPF is non-estimable and that only a function proportional to RSPF, namely, the resource selection function (RSF) can be estimated. This paper describes a close connection between the estimation of the RSPF and the estimation of the weight function in the theory of weighted distributions. This connection can be used to obtain fully efficient, maximum likelihood estimators of the resource selection probability function under commonly used survey designs in wildlife management. The method is illustrated using GPS collar data for mountain goats (Oreamnos americanus de Blainville 1816) in northwest British Columbia, Canada.     

Annual occurrence,abundance and diversity of fish in a South Carolina intertidal creek

An intertidal creek in North Inlet Estuary, South Carolina, USA, was sampled monthly for 1 year to determine the occurrence, abundance and diversity of fish species. Sampling was so conducted as to reduce sampling bias to a minimum and all individuals caught were weighed and measured. A total of 16,611 individuals weighing 202.45 kg and comprising 51 species and 25 families of fish was collected. Three diversity indices were calculated for species number. Analysis of variance revealed that season had a highly significant effect on all indices and the number of species, but had no effect on the number of individuals caught.This work was supported by the Belle W. Baruch Foundation and the South Carolina State Development Board, and is Contribution No. 71 of the Belle W. Baruch Institute for Marine Biology and Coastal Research.     

Drivers of euphausiid species abundance and numerical abundance in the Atlantic Ocean

Mid-ocean ridges are common features of the world’s oceans but there is a lack of understanding as to how their presence affects overlying pelagic biota. The Mid-Atlantic Ridge (MAR) is a dominant feature of the Atlantic Ocean. Here, we examined data on euphausiid distribution and abundance arising from several international research programmes and from the continuous plankton recorder. We used a generalized additive model (GAM) framework to explore spatial patterns of variability in euphausiid distribution on, and at either side of, the MAR from 60°N to 55°S in conjunction with variability in a suite of biological, physical and environmental parameters. Euphausiid species abundance peaked in mid-latitudes and was significantly higher on the ridge than in adjacent waters, but the ridge did not influence numerical abundance significantly. Sea surface temperature (SST) was the most important single factor influencing both euphausiid numerical abundance and species abundance. Increases in sea surface height variance, a proxy for mixing, increased the numerical abundance of euphausiids. GAM predictions of variability in species abundance as a function of SST and depth of the mixed layer were consistent with present theories, which suggest that pelagic niche availability is related to the thermal structure of the near surface water: more deeply-mixed water contained higher euphausiid biodiversity. In addition to exposing present distributional patterns, the GAM framework enables responses to potential future and past environmental variability including temperature change to be explored.     

Relationships between species richness, evenness, and abundance in a southwestern savanna

Species richness and evenness are components of biological diversity that may or may not be correlated with one another and with patterns of species abundance. We compared these attributes among flowering plants, grasshoppers, butterflies, lizards, summer birds, winter birds, and rodents across 48 plots in the grasslands and mesquite-oak savannas of southeastern Arizona. Species richness and evenness were uncorrelated or weakly negatively correlated for each taxonomic group, supporting the conclusion that richness alone is an incomplete measure of diversity. In each case, richness was positively correlated with one or more measures of abundance. By contrast, evenness usually was negatively correlated with the abundance variables, reflecting the fact that plots with high evenness generally were those where all species present were about equally uncommon. Therefore richness, but not evenness, usually was a positive predictor of places of conservation value, if these are defined as places where species of interest are especially abundant. Species diversity was more positively correlated with evenness than with richness among grasshoppers and flowering plants, in contrast to the other taxonomic groups, and the positive correlations between richness and abundance were comparatively weak for grasshoppers and plants as well. Both of these differences can be attributed to the fact that assemblages of plants and grasshoppers were numerically dominated by small subsets of common species (grasses and certain spur-throated grasshoppers) whose abundances differed greatly among plots in ways unrelated to species richness of the groups as a whole.     

Resident mysids: community structure,abundance and small-scale distributions in a coral reef lagoon

Seasonal and diel variations in community structure and abundance of coral-reef lagoon mysids were examined at Davies Reef in the central region of the Great Barrier Reef (GBR) between June 1980 and May 1981. Twenty-five mysid species belonging to three subfamilies of the family Mysidae were captured during the study, with six new records for the GBR. The epibenthic mysid community differed from that in the overlying water, was faunistically uniform, but formed characteristic seasonal and diel groupings. The dominant epibenthic species were Erythrops sp., Anisomysis pelewensis, Doxomysis littoralis, A. laticauda, Prionomysis stenolepis, A. lamellicauda, and A. australis, five of which formed schools. Total mysid abundances ranged between 110 and 790 m^-3 with peak abundance in October. Schooling species occurred at local densities of up to 500 000 m^-3. Mysids were absent from shallow and midwater depths during the day, but were distributed throughout all depths at night with peak abundances in mid-water and deep layers. The dominant species in the water column at night were Pseudanchialina inermis, A. laticauda and Gastrosaccus indicus, in descending order of abundance. Lagoonal mysids contribute little to the food of sessile reef planktivores, as all but three species remain concentrated near or on the lagoon floor both day and night. The contribution of resident lagoon mysids to reef trophodynamics is probably through remineralization of lagoon detritus. Given the vast reef areas comprised of sandy lagoons, the large populations and relatively large size of lagoon mysids, this trophodynamic role may be of considerable importance.A.I.M.S. Contribution No. 477     

Estimating total species using a weighted combination of expected mixture distribution component counts

Environmental and Ecological Statistics - In this paper we present a weighted mixture distribution component counts (MDCC) approach for estimating total number of species. The proposed method...     

A study on abundance and distribution of mangrove species in Indian Sundarban using remote sensing technique

Conservation and management of Sundarban mangrove forest is difficult chiefly due to inaccessibility and hostile condition. Remote sensing serves as an important tool to provide up-to date baseline information which is the primary requirement for the conservation planning of mangroves. In this study, supervised classification by maximum likelihood classifier (MLC) has been used to classify LANDSAT TM and LANDSAT ETM satellite data. This algorithm is used for computing likelihood of unknown measurement vector belonging to unknown classes based on Bayesian equation. Image spectra for various mangrove species were also generated from hyperspectral image. During field visits, GPS locations of five dominant mangrove species with appreciable distribution were taken and image spectra were generated for the same points from hyperion image. The result of this classification shows that, in 1999 total mangrove forest accounted for 55.01 % of the study area which has been reduced to 50.63 % in the year 2010. Avicennia sp. is found as most dominating species followed by Excoecaria sp. and Phoenix sp. but the aerial distribution of Avicennia sp., Bruguiera sp. and Ceriops sp. has reduced. In this classification technique the overall accuracy and Kappa value for 1999 and 2010 are 80 % and 0.77, 85.71 % and 0.81 respectively.     

Partitioning of \alpha and \beta diversity using hierarchical Bayesian modeling of species distribution and abundance

Diversity partitioning is becoming widely used to decompose the total number of species recorded in an area or region \((\gamma )\) into the average number of species within samples \((\alpha )\) and the average difference in species composition \((\beta )\) among samples. Single-value metrics of \(\alpha \) and \(\beta \) diversity are popular because they may be applied at multiple scales and because of their ease in computation and interpretation. Studies thus far, however, have emphasized observed diversity components or comparisons to randomized, null distributions. In addition, prediction of \(\alpha \) and \(\beta \) components using environmental or spatial variables has been limited to more extensive data sets because multiple samples are required to estimate single \(\alpha \) and \(\beta \) components. Lastly, observed diversity components do not incorporate variation in detection probabilities among species or samples. In this study, we used hierarchical Bayesian models of species abundances to provide predictions of \(\alpha \) and \(\beta \) components in species richness and composition using environmental and spatial variables. We illustrate our approach using butterfly data collected from 26 grassland remnants to predict spatially nested patterns of \(\alpha \) and \(\beta \) based on the predicted counts of butterflies. Diversity partitioning using a Bayesian hierarchical model incorporated variation in detection probabilities by butterfly species and habitat patches, and provided prediction intervals for \(\alpha \) and \(\beta \) components using environmental and spatial variables.     

Wet and dry epoch durations of spatially averaged rain rate,their probability distributions and scaling properties

This article is concerned with the notion of duration of wet and dry epochs in stochastic processes of spatially averaged (instantaneous) rain rate over a given region. Gamma, Lognormal, and Inverse Gaussian parametric families of probability distributions have been considered as candidate models for the distribution of such durations. Goodness of these model's fit to data of dry and wet epoch durations obtained from real time series of spatially averaged rain rate, has been tested with Pearson's -test. The parameters of each of these models have been estimated by maximum likelihood and method of moments, based on TOGA-COARE measurements of tropical rainfall. The hypotheses of independence and identical distribution (i.i.d.) among durations of dry or wet epochs have also been tested using a certain version of the Wald-Wolfowitz test. Finally, the effect of spatial scale on the moments of dry and wet epoch durations has also been investigated, pointing to self-similarity of the underlying random structures over space. The main result of this study is that among the three candidate models, Inverse Gaussian is the one conforming most adequately with all the classical testing criteria implemented here, and also with the newly established scaling behavior of both dry and wet epoch duration processes over space. This is a remarkable finding, considering that the Inverse Gaussian family has recently been also justified from a theoretical viewpoint as a reasonable model for the probability distributions of dry and wet epoch durations.     

Estimating abundance of killer whales in the nearshore waters of the Gulf of Alaska and Aleutian Islands using line-transect sampling

Killer whale (Orcinus orca Linnaeus, 1758) abundance in the North Pacific is known only for a few populations for which extensive longitudinal data are available, with little quantitative data from more remote regions. Line-transect ship surveys were conducted in July and August of 2001–2003 in coastal waters of the western Gulf of Alaska and the Aleutian Islands. Conventional and Multiple Covariate Distance Sampling methods were used to estimate the abundance of different killer whale ecotypes, which were distinguished based upon morphological and genetic data. Abundance was calculated separately for two data sets that differed in the method by which killer whale group size data were obtained. Initial group size (IGS) data corresponded to estimates of group size at the time of first sighting, and post-encounter group size (PEGS) corresponded to estimates made after closely approaching sighted groups. ‘Resident’-type (fish-eating) killer whales were more abundant than the ‘transient’-type (mammal-eating). Abundance estimates of resident killer whales (991 [95% CI = 379–2,585] [IGS] and 1,587 [95% CI = 608–4,140] [PEGS]), were at least four times greater than those of the transient killer whales (200 [95% CI = 81–488] [IGS] and 251 [95% CI = 97–644] whales [PEGS]). The IGS estimate of abundance is preferred for resident killer whales because the estimate based on PEGS data may show an upward bias. The PEGS estimate of abundance is likely more accurate for transients. Residents were most abundant near Kodiak Island in the northern Gulf of Alaska, around Umnak and Unalaska Islands in the eastern Aleutians, and in Seguam Pass in the central Aleutians. This ecotype was not observed between 156 and 164°W, south of the Alaska Peninsula. In contrast, transient killer whale sightings were found at higher densities south of the Alaska Peninsula between the Shumagin Islands and the eastern Aleutians. Only two sightings of ‘offshore’-type killer whales were recorded during the surveys, one northeast of Unalaska Island and the other south of Kodiak Island. These are the first estimates of abundance of killer whale ecotypes in the Aleutian Islands and Alaska Peninsula area and provide a baseline for quantifying the role of these top predators in their ecosystem. Electronic Supplementary Material  Supplementary material is available in the online version of this article at and is accessible for authorized users.

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Predicting species distributions: use of climatic parameters in BIOCLIM and its impact on predictions of species’ current and future distributions

Bioclimatic models are widely used tools for assessing potential responses of species to climate change. One commonly used model is BIOCLIM, which summarises up to 35 climatic parameters throughout a species’ known range, and assesses the climatic suitability of habitat under current and future climate scenarios. A criticism of BIOCLIM is that the use of all 35 parameters may lead to over-fitting of the model, which in turn may result in misrepresentations of species’ potential ranges and to the loss of biological reality. In this study, we investigated how different methods of combining climatic parameters in BIOCLIM influenced predictions of the current distributions of 25 Australian butterflies species. Distributions were modeled using three previously used methods of selecting climatic parameters: (i) the full set of 35 parameters, (ii) a customised selection of the most relevant parameters for individual species based on analysing histograms produced by BIOCLIM, which show the values for each parameter at all of the focal species known locations, and (iii) a subset of 8 parameters that may generally influence the distributions of butterflies. We also modeled distributions based on random selections of parameters. Further, we assessed the extent to which parameter choice influenced predictions of the magnitude and direction of range changes under two climate change scenarios for 2020. We found that the size of predicted distributions was negatively correlated with the number of parameters incorporated in the model, with progressive addition of parameters resulting in progressively narrower potential distributions. There was also redundancy amongst some parameters; distributions produced using all 35 parameters were on average half the size of distributions produced using only 6 parameters. The selection of parameters via histogram analysis was influenced, to an extent, by the number of location records for the focal species. Further, species inhabiting different biogeographical zones may have different sets of climatic parameters limiting their distributions; hence, the appropriateness of applying the same subset of parameters to all species may be reduced under these situations. Under future climates, most species were predicted to suffer range reductions regardless of the scenario used and the method of parameter selection. Although the size of predicted distributions varied considerably depending on the method of selecting parameters, there were no significant differences in the proportional change in range size between the three methods: under the worst-case scenario, species’ distributions decrease by an average of 12.6, 11.4, and 15.7%, using all parameters, the ‘customised set’, and the ‘general set’ of parameters, respectively. However, depending on which method of selecting parameters was used, the direction of change was reversed for two species under the worst-case climate change scenario, and for six species under the best-case scenario (out of a total of 25 species). These results suggest that when averaged over multiple species, the proportional loss or gain of climatically suitable habitat is relatively insensitive to the number of parameters used to predict distributions with BIOCLIM. However, when measuring the response of specific species or the actual size of distributions, the number of parameters is likely to be critical.     

Chemistry,abundance, detection and treatment of per- and polyfluoroalkyl substances in water: a review

Per- and polyfluoroalkyl substances (PFAS) encompass a wide range of compounds containing carbon–fluorine bonds. Due the strength of this bond and the high electronegativity of fluorine atoms, PFAS display stability, wettability and other characteristics that are unique for industrial applications and products. However, PFAS induce adverse effects on the environment and human health. Here we review the chemistry, synthesis, properties, analysis, occurrence in water, filtration, removal and oxydation of PFAS.  We highlight emerging hybrid treatments to remove PFAS from water.