Optimizing performance of nonparametric species richness estimators under constrained sampling

Understanding the functional relationship between the sample size and the performance of species richness estimators is necessary to optimize limited sampling resources against estimation error. Nonparametric estimators such as Chao and Jackknife demonstrate strong performances, but consensus is lacking as to which estimator performs better under constrained sampling. We explore a method to improve the estimators under such scenario. The method we propose involves randomly splitting species‐abundance data from a single sample into two equally sized samples, and using an appropriate incidence‐based estimator to estimate richness. To test this method, we assume a lognormal species‐abundance distribution (SAD) with varying coefficients of variation (CV), generate samples using MCMC simulations, and use the expected mean‐squared error as the performance criterion of the estimators. We test this method for Chao, Jackknife, ICE, and ACE estimators. Between abundance‐based estimators with the single sample, and incidence‐based estimators with the split‐in‐two samples, Chao2 performed the best when CV < 0.65, and incidence‐based Jackknife performed the best when CV > 0.65, given that the ratio of sample size to observed species richness is greater than a critical value given by a power function of CV with respect to abundance of the sampled population. The proposed method increases the performance of the estimators substantially and is more effective when more rare species are in an assemblage. We also show that the splitting method works qualitatively similarly well when the SADs are log series, geometric series, and negative binomial. We demonstrate an application of the proposed method by estimating richness of zooplankton communities in samples of ballast water. The proposed splitting method is an alternative to sampling a large number of individuals to increase the accuracy of richness estimations; therefore, it is appropriate for a wide range of resource‐limited sampling scenarios in ecology.     

Efficient sampling of plant diversity in arid deserts using non-parametric estimators

Surveying plant diversity in arid desert areas is extremely difficult because of the harsh climate, hostile terrain, lack of roads, and insecurity, which is why it is particularly important to improve the sampling efficiency, but few relevant studies have been done. The performance of non-parametric estimators was assessed with first-hand field data to determine (a) the threshold of the proportion of uniques (number of species that occur in exactly one plot divided by the number of species sampled) that involves the least sampling effort and (b) the method of locating plots to obtain a more reliable estimate of species richness. The study area (Gurbantunggut desert, China) was divided into five sub-regions based on variation in physical environment and vegetation. The following common correction factors were selected: ACE, Chao1, Bootstrap, Chao2, ICE, Jack1, and Jack2. The estimates for each sub-region (partition) and for the entire region (without partition), the threshold of proportion of uniques, and the method of determining sampling locations (including prior sampling of plots that show large differences in habitats) were compared in terms of their ability to predict the number of species more accurately. We found that ACE and Chao1 (which use abundance data) showed more biased estimates than the other factors (incidence data), and best estimator is Jack1. Species richness was significantly underestimated for the region, but the non-parametric estimators could estimate the species richness for each sub-region reliably. Sampling locations affected the performance of non-parametric estimators significantly. The threshold of minimum sampling was 15% and that of uniques was 30%; the two were able to limit the bias within 5 and 10%, respectively. It is concluded that the non-parametric estimators can estimate the plant diversity of arid deserts reliably from the data on incidence. The study area (on the scale of a region) should be partitioned to improve the performance of the non-parametric estimators. The plots with larger differences in habitats should be sampled more extensively based on the threshold of the proportion of uniques.     

Could we obtain better estimates of plot species richness from multiple‐observer plant censuses?

Question: Could we better estimate plot species richness by asking several botanists to survey the same plots and using non‐parametric estimators of richness? Location: Two French deciduous forests. Methods: Using replicated, independent censuses made by 11 professional botanists on the same eight 100‐m² forest plots, the relative performance of different richness estimators (Lincoln‐Petersen, Jackknife 1&2, Chao 1&2, Bootstrap, Chao Mth, Darroch) and the variation in their performance with the number of botanists involved (teams with two to eight botanists) were investigated. The sensitivity of these estimators to the presence of misidentifications in the data was also assessed. Results: When misidentifications are removed, Chao Mth estimators converged fastest to true richness, but none of the tested estimators correctly accounted for differences in exhaustiveness between the teams. Finally, all estimators were highly sensitive to misidentifications. Conclusions: Richness estimators are of little help in the presence of misidentifications and are ineffective at removing between‐team discrepancies, thus strongly limiting their usefulness in practice. Methods are presented to show how surveys can be designed to remove misidentifications and limit between‐team discrepancies. A sensible sampling design for 100‐m² plots in temperate forests would involve triplets of botanists and correcting data with the Chao N1. Pairs of botanists would already significantly improve the richness estimates, but such estimates would still be biased low. However, further research is needed to design new richness estimators that are more robust to observer effects.     

Estimating species richness: still a long way off!

Xu et al., in this issue of the Journal of Vegetation Science, compare several species richness estimators. All the non‐parametric estimators, such as Chao and jackknife estimators, underestimated the true number, whereas all the area‐based models, based on species–area curves, overestimated it. No reliable method yet exists to predict the number of species in an area that is appreciably larger than the one(s) sampled.     

Limited sampling hampers “big data” estimation of species richness in a tropical biodiversity hotspot

Macro‐scale species richness studies often use museum specimens as their main source of information. However, such datasets are often strongly biased due to variation in sampling effort in space and time. These biases may strongly affect diversity estimates and may, thereby, obstruct solid inference on the underlying diversity drivers, as well as mislead conservation prioritization. In recent years, this has resulted in an increased focus on developing methods to correct for sampling bias. In this study, we use sample‐size‐correcting methods to examine patterns of tropical plant diversity in Ecuador, one of the most species‐rich and climatically heterogeneous biodiversity hotspots. Species richness estimates were calculated based on 205,735 georeferenced specimens of 15,788 species using the Margalef diversity index, the Chao estimator, the second‐order Jackknife and Bootstrapping resampling methods, and Hill numbers and rarefaction. Species richness was heavily correlated with sampling effort, and only rarefaction was able to remove this effect, and we recommend this method for estimation of species richness with “big data” collections.     

Evaluating the performance of species richness estimators: sensitivity to sample grain size

1. Fifteen species richness estimators (three asymptotic based on species accumulation curves, 11 nonparametric, and one based in the species-area relationship) were compared by examining their performance in estimating the total species richness of epigean arthropods in the Azorean Laurisilva forests. Data obtained with standardized sampling of 78 transects in natural forest remnants of five islands were aggregated in seven different grains (i.e. ways of defining a single sample): islands, natural areas, transects, pairs of traps, traps, database records and individuals to assess the effect of using different sampling units on species richness estimations. 2. Estimated species richness scores depended both on the estimator considered and on the grain size used to aggregate data. However, several estimators (ACE, Chao 1, Jackknifel and 2 and Bootstrap) were precise in spite of grain variations. Weibull and several recent estimators [proposed by Rosenzweig et al. (Conservation Biology, 2003, 17, 864-874), and Ugland et al. (Journal of Animal Ecology, 2003, 72, 888-897)] performed poorly. 3. Estimations developed using the smaller grain sizes (pair of traps, traps, records and individuals) presented similar scores in a number of estimators (the above-mentioned plus ICE, Chao2, Michaelis-Menten, Negative Exponential and Clench). The estimations from those four sample sizes were also highly correlated. 4. Contrary to other studies, we conclude that most species richness estimators may be useful in biodiversity studies. Owing to their inherent formulas, several nonparametric and asymptotic estimators present insensitivity to differences in the way the samples are aggregated. Thus, they could be used to compare species richness scores obtained from different sampling strategies. Our results also point out that species richness estimations coming from small grain sizes can be directly compared and other estimators could give more precise results in those cases. We propose a decision framework based on our results and on the literature to assess which estimator should be used to compare species richness scores of different sites, depending on the grain size of the original data, and of the kind of data available (species occurrence or abundance data).     

Temporal Patterns of Species Accumulation in a Survey of Lepidoptera in a Beech-Maple Forest

One of the most significant challenges to insect conservation is lack of information concerning species diversity and distribution. Because a complete inventory of all species in an area is virtually impossible, interest has turned to developing statistical techniques to guide sampling design and to estimate total species richness within a site. We used two such techniques, diversity partitioning and non-parametric richness estimation, to determine how variation in sampling effort over time affected species accumulation for a survey of Lepidoptera in an old-growth beech-maple forest. Temporal scaling of sampling effort had significant effects on two measures of species diversity. Increases in species richness were primarily driven by changes in species occurrences with season, while Shannon diversity was largely determined at the scale of individual sampling units (i.e. by spatial effects). Variation in sampling effort affected the values of the two most widely regarded richness estimators (ICE and Chao 2); neither diversity estimator achieved stable values across a range of sampling efforts. Even after 52 trap-nights and accounting for seasonality, rare species (singletons and uniques) remained a significant component of the moth community. To the extent that moth communities in other forest systems are similarly comprised of many rare species, non-parametric richness estimators should be expected to yield variable estimates with increased effort and should only be used to provide a minimum benchmark for predicting the number of species remaining to be sampled. Our results suggest the best strategy for a short-term survey of forest Lepidoptera should emphasize spreading sampling intervals throughout a given year rather than focusing on intensive sampling during a short time period or prolonged sampling over many years.     

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.     

EstimateS turns 20: statistical estimation of species richness and shared species from samples,with non‐parametric extrapolation

EstimateS offers statistical tools for analyzing and comparing the diversity and composition of species assemblages, based on sampling data. The latest version computes a wide range of biodiversity statistics for both sample‐based and individual‐based data, including analytical rarefaction and non‐parametric extrapolation, estimators of asymptotic species richness, diversity indices, Hill numbers, and (for sample‐based data) measures of compositional similarity among assemblages. In the first 20 yr of its existence, EstimateS has been downloaded more than 70 000 times by users in 140 countries, who have cited it in 5000 publications in studies of taxa from microbes to mammals in every biome.     

Quantifying rotifer species richness in temperate lakes

1. Biodiversity assessments of lakes depend on the ability to identify the complement of species present, although the degree of sampling required is often uncertain. We utilise long‐term data to predict rotifer species richness in three habitats in three Polish lakes using rarefaction sampling methods. 2. Richness in littoral and psammon habitats did not saturate, even with up to 130 samples. Highest richness was observed in psammon habitat (119 species) in Lake Mikolajskie, followed by littoral habitat in Lakes ?uknajno (114 species) and Kuc (110 species). Littoral habitats in Lakes ?uknajno (56%) and Kuc (51%) had the most species not shared with other habitats in the same lake. 3. Species richness (Chao2) estimates ranged between 44 for pelagic and 135 for psammon habitat in Lake Mikolajskie, to 100 for psammon and 137 for littoral habitat in Lake Kuc, and 65 for pelagic and 162 for littoral habitat in Lake ?uknajno. Whole lake estimates were 167, 205 and 171 species, respectively, for these lakes, higher than the 150 to 160 species predicted by Dumont and Segers (Hydrobiologia, 1996, 341 , 125). 4. Using standardised sampling, richness was significantly higher in littoral than either pelagic or psammon habitats. Contrasts of standardised rarefaction curves revealed that richness in Lakes Kuc and Mikolajskie was described as well by littoral‐only or psammon‐only samples, respectively, as by those randomly drawn from across all habitats in the lake. 5. Species richness estimates for Lake Mikolajskie were highest in summer, followed by autumn and spring. Interannual estimates differed by up to 427%, nearly an order of magnitude greater than maximal seasonal variation of 70%. 6. Results indicate that much higher sampling intensity is required to establish species richness than is presently carried out in most lakes. Because many species can be detected only with very intensive sampling, conservation programmes must consider sampling intensity when designing studies.     

The diversity of insectivorous bat assemblages among habitats within a subtropical urban landscape

We investigated the bat (Microchiroptera) diversity of four major habitat types within a large Australian subtropical city (Brisbane, Australia) to determine whether species richness was affected by habitat changes associated with urbanization, as suggested from studies elsewhere. Forty sites, ten in each habitat type (remnant bushland, parkland, low‐density residential and high‐density residential) were surveyed using acoustic bat detectors on six non‐consecutive occasions. Fourteen bat species were recorded. The species accumulation curve of the entire Brisbane bat assemblage reached a plateau at 14 species. The total numbers of species in bushland, parkland, low‐density residential and high‐density residential habitats were 14, 13, 14 and 11 species, respectively. Asymptotic estimates of species richness for each habitat were close or equal to these totals. Mean asymptotic estimated species richness differed significantly among habitats, being lowest in high‐density residential sites and highest in low‐density residential sites. Evenness profiles were similar across habitats, and were not strongly dominated by a few species. Partitioning of diversity components showed that landscape (γ) diversity was mainly determined by the high species richness of low‐density residential and bushland habitats (α diversity), rather than high beta (β) diversity among habitats. These findings contradict those of other studies on bat diversity in which species richness was highest within ‘natural’ areas of the urban landscape and assemblages were dominated by one or two species. This highlights the need for caution in making generalizations based on existing information, which is dominated by studies in temperate regions.     

Application of species richness estimators for the assessment of fungal diversity

Species richness and distribution patterns of wood-inhabiting fungi and mycetozoans (slime moulds) were investigated in the canopy of a Central European temperate mixed deciduous forest. Species richness was described with diversity indices and species-accumulation curves. Nonmetrical multidimensional scaling was used to assess fungal species composition on different tree species. Different species richness estimators were used to extrapolate species richness beyond our own data. The reliability of the abundance-based coverage estimator, Chao, Jackknife and other estimators of species richness was evaluated for mycological surveys. While the species-accumulation curve of mycetozoans came close to saturation, that of wood-inhabiting fungi was continuously rising. The Chao 2 richness estimator was considered most appropriate to predict the number of species at the investigation site if sampling were continued. Gray's predictor of species richness should be used if statements of the number of species in larger areas are required. Multivariate analysis revealed the importance of different tree species for the conservation and maintenance of fungal diversity within forests, because each tree species possessed a characteristic fungal community. The described mathematical approaches of estimating species richness possess great potential to address fungal diversity on a regional, national, and global scale.     

Species richness patterns of obligate subterranean beetles (Insecta: Coleoptera) in a global biodiversity hotspot – effect of scale and sampling intensity

We studied species richness patterns of obligate subterranean (troglobiotic) beetles in the Dinaric karst of the western Balkans, using five grid sizes with cells of 80 × 80, 40 × 40, 20 × 20, 10 × 10, and 5 × 5 km. The same two hotspots could be recognized at all scales, although details differed. Differences in sampling intensity were not sufficient to explain these patterns. Correlations between number of species and number of sampled localities increased with increasing cell size. Additional species are expected to be found in the region, as indicated by jackknife 1, jackknife 2, Chao2, bootstrap, and incidence‐based coverage (ICE) species richness estimators. All estimates increased with increasing cell size, except Chao2, with the lowest prediction at the intermediate 20 × 20 km cell size. Jackknife 2 and ICE gave highest estimates and jackknife 1 and bootstrap the lowest. Jackknife 1 and bootstrap estimates changed least with cell size, while the number of single cell species increased. In the highly endemic subterranean fauna with many rare species, bootstrap may be most appropriate to consider. Positive autocorrelation of species numbers was highest at 20 × 20 km scale, so we used this cell size for further analyses. At this scale we added 137 localities with less positional accuracy to 1572 previously considered, and increased 254 troglobiotic species considered to 276. Previously discovered hotspots and their positions did not change, except for a new species‐rich cell which appeared in the south‐eastern region. There are two centres of troglobiotic species richness in the Dinaric karst. The one in the north‐west exhibited high species richness of Trechinae (Carabidae), while in the south‐east, the Leptodirinae (Cholevidae) were much more diverse. These centres of species richness should serve as the starting point for establishing a conservation network of important subterranean areas in Dinaric karst.     

Influences of interpolation of species ranges on elevational species richness gradients

Interpolation of species ranges has been a common approach to compensate for the unevenness or incompleteness in sampling effort in studies of geographic species richness gradients. However, potential biases introduced by this estimation method remain unclear. Here, we presented an explicit examination of the influences of one‐dimensional interpolation on elevational species richness gradients, and discussed potential causes and processes of these influences. We conducted intensive surveys of birds along the elevational gradients of the Ailao Mountains, southwestern China, and compared richness patterns based on interpolation with raw data as well as estimated data from rarefaction and Chao1 non‐parametric estimator; we also compared results of multiple linear regressions and hierarchical partitioning analyses explaining these four measures of richness. Actual evapotranspiration (AET) and the mid‐domain effect (MDE) were highly correlated and separately provided a good potential explanation for the unimodal richness pattern in the Ailao Mountains, with modifying and suppressive effects of other variables such as area. Interpolation consistently and significantly increased the effects of AET/MDE, while it reduced contributions of area and human disturbance. Our results demonstrated that while compensating for biases in sampling effort, interpolation may also spuriously fill genuine distribution gaps, and tend to underestimate the effects of the non‐monotonic or discontinuous influencing factors that are responsible for these gaps, and overestimate the effects of other factors actually suppressed by these factors. These influences were most strong for species with relatively medium elevational ranges. We conclude that at the regional scale, interpolation method is a potential source of bias in identifying and explaining species richness gradients and should be used with careful consideration. It may be advantageous to adopt other robust estimation methods besides interpolation to gain a more accurate assessment of species richness and a more objective understanding of their underlying mechanisms.     

Assessing the performance of nonparametric estimators of species richness in meadows

To accurately measure the number of species in a biological community, a complete inventory should be performed, which is generally unfeasible; hopefully, estimators of species richness can help. Our main objectives were (i) to assess the performance of nonparametric estimators of plant species richness with real data from a small set of meadows located in the Basque campiña (northern Spain), and (ii) to apply the best estimator to a larger dataset to test the effects on plant species richness caused by environmental conditions and human practices. Two non-asymptotic and seven asymptotic accumulation functions were fitted to a randomized sample-based rarefaction curve computed with data from three well sampled meadows, and information theoretic methods were used to select the best fitting model; this was the Morgan-Mercer-Flodin, and its asymptote was taken as our best guess of true richness. Then, five nonparametric estimators were computed: ICE, Chao 2, Jackknife 1 and 2, and Bootstrap; MMRuns and MMMeans were also assessed. According to the criteria set for our performance assessment (i.e., bias, precision, and accuracy), the best estimator was Jackknife 1. Finally, Jackknife 1 was applied to assess the effects of terrain slope and soil parent material, and also fertilization, grazing, and mowing, on plant species richness from a larger dataset (20 meadows). Results suggested that grass cutting was causing a loss of richness close to 30%, as compared to unmowed meadows. It is concluded that the use of nonparametric estimators of species richness can improve the evaluation of biodiversity responses to human management practices.     

Complementarity among otter trawl,cast net,and encircling gill net improves the characterization of a subtropical subtidal fish assemblage

We investigated the combined use of cast net (CN), otter trawl (OT), and encircling gill net (EG) to characterize the richness, composition, and abundance of species and functional groups of the subtidal fish assemblage in a subtropical shallow ecosystem in Brazil. Our hypothesis, that this combination would improve faunal characterization, was supported. The CN best sampled small pelagic planktivores (e.g., juvenile sardines) and detritivores (e.g., juvenile mullets); OT, small and large demersal benthivores (e.g., mojarras and croakers); and EG, large fast‐swimming species, such as piscivores (e.g., snooks and weakfishes) and large detritivores (adult mullets). The mean and total richness were best sampled with the OT. The most accurate richness estimate using non‐parametric estimators was reached by combining all three types of gear. Our findings emphasize that the careful sampling gear selection and the use of multiple gears are indispensable for solid characterizations of coastal fish fauna, and consequently, for the success of monitoring and research programs.     

Testing species richness estimation methods using museum label data on the Danish Asilidae

Museum collections are treasure troves of biodiversity information thatcan potentially be used for species richness estimation. Using label data on theDanish Asilidae (Diptera), we test eight species richness estimation techniques(abundance-based coverage estimator (ACE), ICE, Chao1, Chao2, first and secondorder Jackknife, Bootstrap and MMMeans) by comparing the estimates to the numberof species likely to occur in Denmark based on distributional information,expert opinion, and a species–area curve. We are investigating which ofthe estimators are most suited for the task. Furthermore, through theuse of four different subsampling schemes we study which kind of label information isnecessary in order to apply these estimation procedures. The first and secondorder Jackknife estimators yield the most accurate estimate of the number ofcollectable species in Denmark, while ACE, Bootstrap and Chao1 only provideslight improvements over observed values. We find that all estimatorsunderestimate the true diversity of Danish Asilidae and speculate that thisperformance is due to a discrepancy between the total and the collectable faunain the region. Finally, we discuss the implications for species richnessestimation and emphasize that for most terrestrial arthropod taxa thesediscrepancies are of such a magnitude that estimated species richness values maybe dangerously low and of limited use in conservation decision making.     

Small‐Sample Estimation of Species Richness Applied to Forest Communities

Summary Many well‐known methods are available for estimating the number of species in a forest community. However, most existing methods result in considerable negative bias in applications, where field surveys typically represent only a small fraction of sampled communities. This article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure. The proposed estimator yields small bias and reasonably accurate interval estimation even with small samples. The performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from Panama and Malaysia.     

Effects of sample standardization on mean species detectabilities and estimates of relative differences in species richness among assemblages

Ecological surveys provide the basic information needed to estimate differences in species richness among assemblages. Comparable estimates of the differences in richness between assemblages require equal mean species detectabilities across assemblages. However, mean species detectabilities are often unknown, typically low, and potentially different from one assemblage to another. As a result, inferences regarding differences in species richness among assemblages can be biased. We evaluated how well three methods used to produce comparable estimates of species richness achieved equal mean species detectabilities across diverse assemblages: rarefaction, statistical estimators, and standardization of sampling effort on mean taxonomic similarity among replicate samples (MRS). We used simulated assemblages to mimic a wide range of species-occurrence distributions and species richness to compare the performance of these three methods. Inferences regarding differences in species richness based on rarefaction were highly biased when richness estimates were compared among assemblages with distinctly different species-occurrence distributions. Statistical estimators only marginally reduced this bias. Standardization on MRS yielded the most comparable estimates of differences in species richness. These findings have important implications for our understanding of species-richness patterns, inferences drawn from biological monitoring data, and planning for biodiversity conservation.