Effect of species richness and relative abundance on the shape of the species accumulation curve

Abstract We explain how species accumulation curves are influenced by species richness (total number of species), relative abundance and diversity using computer‐generated simulations. Species richness defines the boundary of the horizontal asymptote value for a species accumulation curve, and the shape of the curve is influenced by both relative abundance and diversity. Simulations with a high proportion of rare species and a few abundant species have a species accumulation curve with a low ‘shoulder’ (inflection point on the ordinate axis) and a long upward slope to the asymptote. Simulations with a high proportion of relatively abundant species have a steeply rising initial slope to the species accumulation curve and plateau early. Diversity (as measured by Simpson's and Shannon–Weaver indices) for simulations is positively correlated with the initial slope of the species accumulation curve. Species accumulation curves cross when one simulation has a high proportion of both rare and abundant species compared with another that has a more even distribution of abundance among species.     

An approach based on the total‐species accumulation curve and higher taxon richness to estimate realistic upper limits in regional species richness

Most of accumulation curves tend to underestimate species richness, as they do not consider spatial heterogeneity in species distribution, or are structured to provide lower bound estimates and limited extrapolations. The total‐species (T–S) curve allows extrapolations over large areas while taking into account spatial heterogeneity, making this estimator more prone to attempt upper bound estimates of regional species richness. However, the T–S curve may overestimate species richness due to (1) the mismatch among the spatial units used in the accumulation model and the actual units of variation in β‐diversity across the region, (2) small‐scale patchiness, and/or (3) patterns of rarity of species. We propose a new framework allowing the T–S curve to limit overestimation and give an application to a large dataset of marine mollusks spanning over 11 km² of subtidal bottom (W Mediterranean). As accumulation patterns are closely related across the taxonomic hierarchy up to family level, improvements of the T–S curve leading to more realistic estimates of family richness, that is, not exceeding the maximum number of known families potentially present in the area, can be considered as conducive to more realistic estimates of species richness. Results on real data showed that improvements of the T–S curve to accounts for true variations in β‐diversity within the sampled areas, small‐scale patchiness, and rarity of families led to the most plausible richness when all aspects were considered in the model. Data on simulated communities indicated that in the presence of high heterogeneity, and when the proportion of rare species was not excessive (>2/3), the procedure led to almost unbiased estimates. Our findings highlighted the central role of variations in β‐diversity within the region when attempting to estimate species richness, providing a general framework exploiting the properties of the T–S curve and known family richness to estimate plausible upper bounds in γ‐diversity.     

Using species accumulation curves to estimate trapping effort in fauna surveys and species richness

Abstract The shape of species accumulation curves is influenced by the relative abundance and diversity of the fauna being sampled, and the order in which individuals are caught. We use resampling to show the variation in species accumulation curves caused by the order of trapping periods. Averaged species accumulation curves calculated by randomly assigning the order of trapping periods are smooth curves that are a better estimate of species richness and a more useful tool for determining the trapping effort required to adequately survey a site. We extend this concept of randomly resampling the trapping period to show that randomizing the number of individuals caught for each species over the number of collection periods (e.g. days) can provide an accurate estimate of the averaged species accumulation curve. This is particularly useful as it enables an accurate estimation of the proportion of the total number of species caught in an area during a survey from information on the number of individuals caught for each species and the number of trapping periods, and is not dependent on having knowledge of the trapping period in which each individual was caught. This calculation also enables an assessment to be made of the adequacy of fauna surveys to report a species inventory in environmental impact assessments when only a species list and relative abundance data are provided.     

Determining adequate trapping effort and species richness using species accumulation curves for environmental impact assessments

Abstract Environmental impact assessments (EIA) require that the proponent indicates the potential impact that a development will have on the biodiversity of the area. As part of this assessment it is normal practice to inventory the vertebrate species in the area. We show here how species accumulation curves can be used as a tool by environmental consultants to indicate the adequacy of their trapping effort and predict species richness for a disturbance site. The shape of a species accumulation curve is influenced by the number of species in an assemblage and the proportional number of singletons (rarely caught species) in the survey sample. We provide guidelines for the number of individuals that need to be caught in a trapping program to achieve 80% and 90% of the species in a habitat, and we indicate how this number can be adjusted to accommodate variations in relative species abundance.     

Bryophyte and vascular plant species richness in boreo-nemoral moist forests and mires

We compare species richness of bryophytes and vascular plants in Estonian moist forests and mires. The material was collected from two wetland nature reserves. Bryophyte and vascular plant species were recorded in 338 homogeneous stands of approximately 1 ha in nine forest and two mire types. Regional species pools for bryophytes and vascular plants were significantly correlated. The correlations between the species richnesses of bryophytes and vascular plants per stand were positive in all community types. The relative richnesses (local richness divided by the regional species pool size) were similar for bryophyte species and for vascular plant species. This shows that on larger scales, conservation of the communities rich in species of one taxonomic plant group, maintains also the species richness of the other. The minimum number of stands needed for the maintenance of the regional species pool of typical species for the every community type was calculated using the species richness accumulation curves. Less stands are needed to maintain the bryophyte species pools (300–5300 for bryophytes and 400–35 000 for vascular plants).     

Energy availability, abundance, energy-use and species richness in forest bird communities: a test of the species–energy theory

Aim To test the ‘more individuals hypothesis’ as a mechanism for the positive association between energy availability and species richness. This hypothesis predicts that total density and energy use in communities is linearly related to energy availability, and that species richness is a positive function of increased density. We also evaluate whether similar energy–density patterns apply to different migratory groups (residents, short‐distance migrants and tropical migrants) separately. Location European and North American forest bird communities. Methods We collected published breeding bird census data from Europe and North America (n = 187). From each census data we calculated bird density (pairs 10 ha^?1), energy use by the community (the sum of metabolic needs of individuals, Watts 10 ha^?1) and geographical location with an accuracy of 0.5°. For each bird census data coordinate we extracted the corresponding monthly values of actual evapotranspiration (AET). From these values we calculated corresponding AET values that we expected to explain the density energy use of forest birds: total annual, breeding season (June) and winter AET. We used general linear modelling to analyse these data controlling for the area of census plots, forest type and census method. Results Total density and energy use in European and North American forest bird communities were linear functions of annual productivity, and increased density and energy use then translated into more species. Also resident bird density and energy consumption were positive functions of annual productivity, but the relationship between productivity and density as well as between productivity and energy use was weaker for migrants. Main conclusions Our results are consistent with the more individuals hypothesis that density and energy use in breeding forest bird communities is coupled tightly with the productivity of the environment, and that increased density and energy consumption results in more species. However, not all community members (migratory groups) are limited by productivity on the breeding grounds.     

On the estimation of species richness based on the accumulation of previously unrecorded species

Estimation of species richness of local communities has become an important topic in community ecology and monitoring. Investigators can seldom enumerate all the species present in the area of interest during sampling sessions. If the location of interest is sampled repeatedly within a short time period, the number of new species recorded is typically largest in the initial sample and decreases as sampling proceeds, but new species may be detected if sampling sessions are added. The question is how to estimate the total number of species. The data collected by sampling the area of interest repeatedly can be used to build species accumulation curves: the cumulative number of species recorded as a function of the number of sampling sessions (which we refer to as “species accumulation data”). A classic approach used to compute total species richness is to fit curves to the data on species accumulation with sampling effort. This approach does not rest on direct estimation of the probability of detecting species during sampling sessions and has no underlying basis regarding the sampling process that gave rise to the data. Here we recommend a probabilistic, nonparametric estimator for species richness for use with species accumulation data. We use estimators of population size that were developed for capture‐recapture data, but that can be used to estimate the size of species assemblages using species accumulation data. Models of detection probability account for the underlying sampling process. They permit variation in detection probability among species. We illustrate this approach using data from the North American Breeding Bird Survey (BBS). We describe other situations where species accumulation data are collected under different designs (e.g., over longer periods of time, or over spatial replicates) and that lend themselves to of use capture‐recapture models for estimating the size of the community of interest. We discuss the assumptions and interpretations corresponding to each situation.     

Applications of species accumulation curves in large-scale biological data analysis

The species accumulation curve, or collector’s curve, of a population gives the expected number of observed species or distinct classes as a function of sampling effort. Species accumulation curves allow researchers to assess and compare diversity across populations or to evaluate the benefits of additional sampling. Traditional applications have focused on ecological populations but emerging large-scale applications, for example in DNA sequencing, are orders of magnitude larger and present new challenges. We developed a method to estimate accumulation curves for predicting the complexity of DNA sequencing libraries. This method uses rational function approximations to a classical non-parametric empirical Bayes estimator due to Good and Toulmin [Biometrika, 1956, 43, 45–63]. Here we demonstrate how the same approach can be highly effective in other large-scale applications involving biological data sets. These include estimating microbial species richness, immune repertoire size, and k-mer diversity for genome assembly applications. We show how the method can be modified to address populations containing an effectively infinite number of species where saturation cannot practically be attained. We also introduce a flexible suite of tools implemented as an R package that make these methods broadly accessible.     

Species richness estimation and determinants of species detectability in butterfly monitoring programmes

Abstract 1. Species richness is the most widely used biodiversity index, but can be hard to measure. Many species remain undetected, hence raw species counts will often underestimate true species richness. In contrast, capture–recapture methods estimate true species richness and correct for imperfect and varying detectability. 2. Detectability is a crucial quantity that provides the link between a species count and true species richness. For insects, it has hardly ever been estimated, although this is required for the interpretation of species counts. 3. In the Swiss butterfly monitoring programme about 100 transect routes are surveyed seven times a year using a highly standardised protocol. In July 2003, control observers made two additional surveys on 38 transects. Data from these 38 quadrats were analysed to see whether currently available capture–recapture models can provide quadrat‐specific estimates of species richness, and to estimate species detectability in relation to transect, observer, survey, region, and abundance. 4. Species richness over the entire season cannot be estimated using current capture–recapture methods. The species pool was open, preventing use of closed population models, and detectability varied by species, preventing use of current open population models. Assuming a closed species pool during two mid‐season (July) surveys, a Jackknife capture–recapture method was used that accounts for heterogeneity to estimate mean detectability and species richness. 5. In every case, more species were present than were counted. Mean species detectability was 0.61 (SE 0.01) with significant differences between observers (range 0.37–0.83). Species‐specific detection at time t+ 1 was then modelled for those species seen at t for three mid‐season surveys. Detectability averaged 0.50 (range 0.17–0.81) for individual species and 0.65, 0.44, and 0.42 for surveys. Abundant species were detected more easily, although this relationship explained only 5% of variation in species detectability. 6. These are important, although not entirely unexpected, results for species richness estimation of short‐lived animals. Raw counts of species may be misleading species richness indicators unless many surveys are conducted. Monitoring programmes should be calibrated, i.e. the assumption of constant detectability over dimensions of interest needs to be tested. The development of capture–recapture or similar models that can cope with both open populations and heterogeneous species detectability to estimate species richness should be a research priority.     

Multi-scale altitudinal patterns in species richness of land snail communities in south-eastern France

Aim Species richness is an important feature of communities that varies along elevational gradients. Different patterns of distribution have been described in the literature for various taxonomic groups. This study aims to distinguish between species density and species richness and to describe, for land snails in south‐eastern France, the altitudinal patterns of both at different spatial scales. Location The study was conducted on five calcareous mountains in south‐eastern France (Etoile, Sainte Baume, Sainte Victoire, Ventoux and Queyras). Methods Stratified sampling according to vegetation and altitude was undertaken on five mountains, forming a composite altitudinal gradient ranging from 100 to 3100 m. Visual searching and analysis of turf samples were undertaken to collect land snail species. Species density is defined as the number of species found within quadrats of 25 m². Species richness is defined as the number of species found within an elevation zone. Different methods involving accumulation curves are used to describe the patterns in species richness. Elevation zones of different sizes are studied. Results Eighty‐seven species of land snails were recovered from 209 samples analysed during this study. Land snail species density, which can vary between 29 and 1 species per 25 m², decreases logarithmically with increasing altitude along the full gradient. However, on each mountain separately, only a linear decrease is observable. The climatic altitudinal gradient can explain a large part of this pattern, but the great variability suggests that other factors, such as heterogeneity of ground cover, also exert an influence on species density. The altitudinal pattern of species richness varies depending on the spatial resolution of the study. At fine resolution (altitudinal zones of 100 m) land snail species richness forms a plateau at altitudes below 1000 m, before decreasing with increasing altitude. At coarse resolution (altitudinal zones of 500 and 1000 m) the relationship becomes linear. Main conclusions This study reveals that land snail species density and land snail species richness form two different altitudinal patterns. Species density exhibits strong variability between sites of comparable altitude. A large number of samples seem necessary to study altitudinal patterns of species density. Species density decreases logarithmically with increasing altitude. Above a critical altitudinal threshold, this decrease lessens below the rate seen in the first 1500 m. Different methods exist to scale‐up species density to species richness but these often produce different patterns. In this study, the use of accumulation curves has yielded a pattern of species richness showing a plateau at low altitude, whereas simple plotting of known altitudinal ranges from single mountains would have produced stronger mid‐altitudinal peaks. This study shows that not only factors such as temperatures and habitat heterogeneity, but also an ecotone effect, are responsible for the observed patterns.     

Limits to the estimation of species richness: The use of relative abundance distributions

The present study demonstrates the possibility of estimating species numbers of animal or plant communities from samples using relative abundance distributions. We use log‐abundance–species‐rank order plots and derive two new estimators that are based on log‐series and lognormal distributions. At small to moderate sample sizes these estimators appear to be more precise than previous parametric and nonparametric estimators. We test our estimators using samples from 171 published medium‐sized to large animal and plant communities taken from the literature. By this we show that our new estimators define also limits of precision.     

Performance of nonparametric species richness estimators in a high diversity plant community

Abstract. The efficiency of four nonparametric species richness estimators — first‐order Jackknife, second‐order Jackknife, Chao2 and Bootstrap — was tested using simulated quadrat sampling of two field data sets (a sandy ‘Dune’ and adjacent ‘Swale’) in high diversity shrublands (kwongan) in south‐western Australia. The data sets each comprised > 100 perennial plant species and > 10 000 individuals, and the explicit (x‐y co‐ordinate) location of every individual. We applied two simulated sampling strategies to these data sets based on sampling quadrats of unit sizes 1/400th and 1/100th of total plot area. For each site and sampling strategy we obtained 250 independent sample curves, of 250 quadrats each, and compared the estimators’ performances by using three indices of bias and precision: MRE (mean relative error), MSRE (mean squared relative error) and OVER (percentage overestimation). The analysis presented here is unique in providing sample estimates derived from a complete, field‐based population census for a high diversity plant community. In general the true reference value was approached faster for a comparable area sampled for the smaller quadrat size and for the swale field data set, which was characterized by smaller plant size and higher plant density. Nevertheless, at least 15–30% of the total area needed to be sampled before reasonable estimates of S_t (total species richness) were obtained. In most field surveys, typically less than 1% of the total study domain is likely to be sampled, and at this sampling intensity underestimation is a problem. Results showed that the second‐order Jackknife approached the actual value of S_t more quickly than the other estimators. All four estimators were better than S_obs (observed number of species). However, the behaviour of the tested estimators was not as good as expected, and even with large sample size (number of quadrats sampled) all of them failed to provide reliable estimates. First‐ and second‐order Jackknives were positively biased whereas Chao2 and Bootstrap were negatively biased. The observed limitations in the estimators’ performance suggests that there is still scope for new tools to be developed by statisticians to assist in the estimation of species richness from sample data, especially in communities with high species richness.     

Evaluation of methods for estimating macroinvertebrate species richness using individual stones in tropical streams

1. The most straightforward way to assess diversity in a site is the species count. However, a relatively large sample is needed for a reliable result because of the presence of many rare species in rich assemblages. The use of richness estimation methods is suggested by many authors as a solution for this problem in many cases.
2. We examined the performance of 13 methods for estimating richness of stream macroinvertebrates inhabiting riffles both at local (stream) and regional (catchment) scales. The evaluation was based on (1) the smallest sub-sample size needed to estimate total richness in the sample, (2) constancy of this size, (3) lack of erratic behaviour in curve shape and (4) similarity in curve shape through different data sets. Samples were from three single stream sites (local) and three from several streams within the same catchment basin (regional). All collections were made from protected forest areas in south-east Brazil.
3. All estimation methods were dependent on sub-sample size, producing higher estimates when using larger sub-sample sizes. The Stout and Vandermeer method estimated total richness in the samples with the smallest sub-sample size, but showed some erratic behaviour at small sub-sample sizes, and the estimated curves were not similar among the six samples. The Bootstrap method was the best estimator in relation to constancy of sub-sample sizes, but needed an unacceptably large sub-sample to estimate total richness in the samples. The second order Jackknife method was the second best estimator both for minimum sub-sample size and constancy of this size and we suggest its use in future studies of diversity in tropical streams. Despite the inferior performance of several other methods, some produced acceptable results. Comments are made on the utility of using these estimators for predicting species richness in an area and for comparative purposes in diversity studies.     

Assessing biodiversity with species accumulation curves; inventories of small reptiles by pit‐trapping in Western Australia

Abstract We examined 11 non‐linear regression models to determine which of them best fitted curvilinear species accumulation curves based on pit‐trapping data for reptiles in a range of heterogeneous and homogenous sites in mesic, semi‐arid and arid regions of Western Australia. A well‐defined plateau in a species accumulation curve is required for any of the models accurately to estimate species richness. Two different measures of effort (pit‐trapping days and number of individuals caught) were used to determine if the measure of effort influenced the choice of the best model(s). We used species accumulation curves to predict species richness, determined the trapping effort required to catch a nominated percentage (e.g. 95%) of the predicted number of species in an area, and examined the relationship between species accumulation curves with diversity and rarity. Species richness, diversity and the proportion of rare species in a community influenced the shape of species accumulation curves. The Beta‐P model provided the best overall fit (highest r²) for heterogeneous and homogeneous sites. For heterogeneous sites, Hill, Rational, Clench, Exponential and Weibull models were the next best. For homogeneous habitats, Hill, Weibull and Chapman–Richards were the next best models. There was very little difference between Beta‐P and Hill models in fitting the data to accumulation curves, although the Hill model generally over‐estimated species richness. Most models worked equally well for both measures of trapping effort. Because the number of individuals caught was influenced by both pit‐trapping effort and the abundance of individuals, both measures of effort must be considered if species accumulation curves are to be used as a planning tool. Trapping effort to catch a nominated percentage of the total predicted species in homogeneous and heterogeneous habitats varied among sites, but even for only 75% of the predicted number of species it was generally much higher than the typical effort currently being used for terrestrial vertebrate fauna surveys in Australia. It was not possible to provide a general indication of the effort required to predict species richness for a site, or to capture a nominated proportion of species at a site, because species accumulation curves are heavily influenced by the characteristics of particular sites.     

The effect of 50 years of landscape change on species richness and community composition

We analysed a 50-year dataset of avian species observations to determine how richness and community composition varied over a period of landscape-scale environmental change. Our study area, northern lower Michigan, has experienced substantial land-use and land-cover change over time. Like much of the northern Midwest, it has shifted from a largely unpopulated, post-logging shrubland to a moderately populated closed-canopy forest. Such changes are generally expected to influence overall richness and community composition. We found that regional richness per year remained virtually unchanged over the study period. Year-to-year variation in species number was surprisingly low. Richness totals included vastly different species groups as the composition of the regional bird community changed substantially over time. Changes in the types of species present appear to reflect deterministic changes in habitat. The number of grassland and open-habitat species decreased, for example, while species associated with older forests and urban habitats increased. Our results suggest that habitat changes at the landscape scale do not necessarily lead to changes in the number of species a region can support. Such changes, however, do appear to influence the types of species that will occupy a region, and can lead to substantial changes in community composition.     

The use of incidence-based species richness estimators,species accumulation curves and similarity measures to appraise ethnobotanical inventories from South Africa

The incorporation of suitable quantitative methods into ethnobotanical studies enhances the value of the research and the interpretation of the results. Prediction of sample species richness and the use of species accumulation functions have been addressed little in applied ethnobotany. In this paper, incidence-based species richness estimators, species accumulation curves and similarity measures are used to compare and predict species richness, evaluate sampling effort and compare the similarity of species inventories for ethnobotanical data sets derived from the trade in traditional medicine in Johannesburg and Mpumalanga, South Africa. EstimateS was used to compute estimators of species richness (e.g. Jackknife), rarefaction curves, species accumulation curves and complimentarity. Results showed that while the Michaelis–Menten Means estimator appeared to be the best estimator because the curve approached a horizontal asymptote, it was not able to accurately predict species richness for one of the data sets when two of its subsamples were individually tested. Instead, the first-order Jackknife estimator best approximated the known richness.