N 2004, their Equation 6) that are used to construct the 95% confidence intervals shown in Fig. Today, rarefaction has grown as a technique not just for measuring species diversity, but of understanding diversity at higher taxonomic levels as well. Thus, Q1 represents the number of unique species (those that are detected in only one sample) and Q2 represents the number of duplicate species (those that are detected in only two samples), in the terminology of Colwell and Coddington (1994), while Q0 denotes the number of species among the S species in the assemblage that were not detected in any of the T sampling units. = i The species frequency counts appear in Table 1. beetle species abundance frequency counts from two sites on the Osa Peninsula in southwestern Costa Rica (Janzen 1973a, 1973b). = Colwell et al. Longino and Colwell 1997). 2003) and the Poisson model (Chao and Shen 2004), as well as to methods for predicting the number of additional individuals (multinomial model, Chao et al. For the Osa second-growth site (Table 2b; Fig. j The statistical technique or method used to evaluate species richness from the results of sampling is rarefaction. Generally, it initially grows rapidly (as the most common species are found) and then slightly flattens (as the rarest species remain to be sampled). ) is an indicator function that equals 1 when true and 0 otherwise, so that k=1nkfk=n, Sobs=k=1nfk. The number of species present in the assemblage but not detected in the reference sample is thus represented as f0. As with any extrapolation, the estimate becomes more uncertain the further it is extended away from the reference sample. Table 6) retains any information on the spatial structure of the biological populations sampled. Version 9, User's Guide and application published at, Estimating terrestrial biodiversity through extrapolation, Interpolating, extrapolating, and comparing incidence-based species accumulation curves, The number of new species, and the increase in population coverage, when a sample is increased, Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness, Counting ants (Hymenoptera: Formicidae): biodiversity sampling and statistical analysis for myrmecologists, Explicit calculation of the rarefaction diversity measurement and the determination of sufficient sample size, The nonconcept of species diversity: a critique and alternative parameters, Sweep samples of tropical foliage insects: description of study sites, with data on species abundances and size distributions, Sweep samples of tropical foliage insects: effects of seasons, vegetation types, elevation, time of day, and insularity, The rarefaction diversity measurement and the spatial distribution of individuals, Another calculation for the rarefaction diversity measurement for different spatial distributions, Biodiversity inventories, indicator taxa and effects of habitat modification in tropical forest, Estimating population size via sample coverage for closed capture-recapture models, The importance of protected areas for the forest and endemic avifauna of Sulawesi (Indonesia), Biodiversity assessment using structured inventory: capturing the ant fauna of a lowland tropical rainforest, Density compensation, species composition, and richness of ants on a Neotropical elevational gradient, Estimation of species richness: mixture models, the role of rare species, and inferential challenges, Estimating species accumulation curves using mixtures, Estimating species accumulation curves and diversity indices, Comparing species assemblages via species accumulation curves, Resilience of tropical rain forests: tree community reassembly in secondary forests, Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance, http://insectscience.org/3.34 (13 November 2011, date last accessed), Marine benthic diversity: a comparative study, Predicting the number of new species in further taxonomic sampling, Rarefaction as a distribution-free method of expressing and estimating diversity, Ecological Diversity in Theory and Practice, International Cooperative Publishing House, Sampling properties of a family of diversity measures, The speciesaccumulation curve and estimation of species richness, The Author 2012. 2, with the Poisson variables in Fig. Species diversity is a measure of biological diversity in a specific ecological community. (Each incidence is the occurrence of one species in one sampling unit.). 4b) (Longino and Colwell 2011), which spans an elevation gradient from lowland rainforest at 50-m elevation to montane cloud forest at 2000 m, is an excellent example. All our examples (Tables 2, 3, 5 and 7; Figs 2 and 4) reveal that the unconditional variance increases sharply with sample size for extrapolated curves, and thus, the confidence interval expands accordingly. For extrapolation, the SE values are relatively small up to a doubling of the reference sample, signifying quite accurate extrapolation in this range. j Unfortunately, the statisticians among us (A.C., C.X.M. Rarefaction does not provide an estimate of asymptotic richness, so it cannot be used to extrapolate species richness trends in larger samples.[9]. Rescaling to incidences can also be useful for any organisms that, like ants, live colonially or that cannot be counted individually (e.g. individual-based interpolation, extrapolation and prediction of additional individuals required to reach gSest, under the multinomial model, for beetle samples from two sites on the Osa Peninsula in southwestern Costa Rica (Janzen 1973a, 1973b). A sample-by-species incidence matrix was therefore produced for each of the five sites. {\displaystyle \sum _{j=1}^{\infty }M_{j}=K} The relevance of a rarefied sample is that some groups may now be necessarily absent from this subsample. K Confidence intervals for those estimates have always been based on conditional variances because unconditional variances for individual-based classical rarefaction and Coleman curves have until now remained elusive. (b) Osa second-growth forest sample (c) Comparison of the curves from the samples in (a) and (b). 1975), but in practice the two probability distributions differ little if sample size (n) is small relative to assemblage size (N). 4b. n "Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness", 10.1666/0094-8373(2004)030<0666:RBFDCT>2.0.CO;2, https://en.wikipedia.org/w/index.php?title=Rarefaction_(ecology)&oldid=1090157810, Articles with dead external links from June 2021, Articles with unsourced statements from March 2021, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 27 May 2022, at 19:44. Copyright 2022 CD Genomics. 4b plots on the species axis are actually estimates of species density, the number of species in multiples of a 1-m2 area. This long-range extrapolation (>3 the original sample size) inevitably yields very wide confidence intervals. Rarefaction allows the calculation of species richness for a given number of individual samples, based on the construction of so-called rarefaction curves. 2009). (2009) compared species composition of trees, saplings and seedlings in six 1-ha forest plots spanning three successional stages in lowland forests of northeastern Costa Rica. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. 0 An example of this phenomenon can be seen in the lower two curves of Fig. For the Osa old-growth site (Table 2a; Fig. The sampling unit consisted of all worker ants extracted from a 1-m2 forest floor plot, applying a method called mini-Winkler extraction. On the other hand, beta diversity is the ratio between alpha diversity and regional diversity. n We compared three statistically distinct models, one based on the multinomial distribution, for counts of individuals (Fig. 2b), the extrapolation is extended only to double the reference sample size (not fully shown in Fig. For the Poisson model, the summation in the denominator should be replaced by (k=1Rkfk)2. 2009). The ant dataset (Fig. Alpha diversity gives an overview of the structure of an ecological community with respect to its species richness, species evenness, or both. For interpolation to samples smaller than the reference sample, these correspond to classical rarefaction (Hurlbert 1971), Coleman rarefaction (Coleman 1981) and sample-based rarefaction (Colwell et al. Figure 3 shows just how close the results based on the two models are for this example. Because ants are colonial and the colony is the unit of reproduction, scoring each sampling unit for presence or absence of each species makes more sense than using abundance data (Gotelli et al. Under all three of the models we discuss, all our estimators for extrapolated richness, as well as all our unconditional variance estimators, require an estimate of asymptotic species richness for the assemblage sampled. Clearly the number of species at any plotted sample size (beyond very small samples) is significantly greater for LEP old growth than in either of the two samples from second-growth forest. E ) n n Here, we apply individual-based rarefaction and extrapolation to the same reference sample for the first time. It is true that This curve is created by randomly re-sampling the pool of N samples several times and then plotting the average number of species found on each sample. N = total number of items Despite being defined at discrete values of n, these curves are most frequently displayed as continuous functions.[7]. From, If we assume that individuals are randomly and independently distributed in space, then, For the multinomial model, the extrapolation problem is to estimate the expected number of species, For the Poisson model, the objective is to estimate the expected number of species, Several estimators in the previous two sections require either an estimate of. This curve is a plot of the number of species as a function of the number of samples. Ni = the number of items in group i (i = 1, , K). 1 Rarefaction involves the selection of a certain number of samples which is either equal or less than to the number of samples (in the smallest sample), and then randomly discarding reads from the larger samples until the number of remaining samples is equal to the threshold. The multinomial model assumes that the sampling procedure itself does not substantially alter relative abundances of species (p1,p2,,pS). 1a. 4a, we plot the multinomial rarefaction curves and extrapolation curves up to a sample size of 2400 individuals. 2011). N N Clearly the old-growth assemblage is richer, based on these samples. 1 It is a measure of microbiome diversity applicable to a single sample. K K [4], Following initial development by Sanders, the technique of rarefaction has undergone a number of revisions. (b) Sample-based interpolation (rarefaction) and extrapolation for reference samples (filled black circles) for ground-dwelling ants from five elevations on the Barva Transect in northeastern Costa Rica (Longino and Colwell 2011) under the Bernoulli product model, with 95% unconditional confidence intervals. 1a for the multinomial model, with 95% unconditional confidence intervals. Extra parameters that describe spatial aggregation would need to be introduced in the generalized model, and thus, statistical inference would become more complicated. Richness in LEP (green) significantly exceeds richness in Lindero Sur (blue) for sample sizes between 500 and 1600 individuals, based conservatively on non-overlapping confidence intervals. Then, differences in density (the number of individuals per sampling unit) among datasets can be accounted for by rescaling the X-axis of sample-based rarefaction and extrapolation curves to individuals (Chazdon et al. This novel integration of mathematically distinct approaches allowed us to link interpolated (rarefaction) curves and extrapolated curves to plot a unified species accumulation curve for empirical examples (Figs 2 and 4). In a sample-based study of the same assemblage, however, the aggregated species will generally have a lower incidence frequency (since many individuals will end up some samples and none in others) than the randomly distributed species. ); the US Department of Energy (022821 to N.J.G. None declared. = All rights reserved. We postpone specification of an estimator for Q0 for the next section. The species frequency counts for the three plots appear in Table 4. Rarefaction curves generally grow rapidly at first, as the most common species are found, but the curves plateau as only the rarest species remain to be sampled. We define the incidence frequency count Qk as the number of species each represented exactly Yi = k times in the incidence matrix sample, 0 k T. Formally, Qk=i=1SI(Yi=k), so that k=1TkQk=i=1SYi, Sobs=k=1TQk. = {\displaystyle \sum _{i=1}^{K}N_{i}=N} In other words, we assume in this paper that the assemblage is the effectively infinite sampling universe from which the reference sample has been collected. 2a, we plot the multinomial rarefaction curve and extrapolation curve up to a sample size of 1200 individuals and show the predicted number of individuals need to reach for g = 0.6. Rarefaction can be used to determine whether a specific sample has been sufficiently sequenced to represent its identity. multiple stems of stem-sprouting plants or cover-based vegetation data). We assume that, in most biological applications, the biological populations in the assemblage being sampled are sufficiently large that this assumption is met. 128-131. A true measure of diversity accounts for both the number of species present and the relative abundance of each. (c) Lindero Sur younger (21 years) second growth, Copyright 2022 IBCAS and the Botanical Society of China, Copyright 2022 Oxford University Press. Moreover, the similarity applies not only to rarefaction (as previously noted by Brewer and Williamson 1994) but also to extrapolation. Applying the multinomial model (Equation 9) to the Janzen dataset to increase the sample size (number of individuals) in each site yields the extrapolated curves (broken line curves) for each site is shown in Fig. K When the sample size in the second-growth site is rarefied down to 237 individuals to match the size of the old-growth sample (Fig. Individual-based rarefaction of abundance data, like the interpolation analysis above, has been carried out in this way for decades. 1985), although sampling designs are nonetheless critical to avoiding bias from spatial structure (Collins and Simberloff 2009; Chiarucci et al. Individual-based interpolation and extrapolation, under the multinomial model, for tree samples from three forest sites in northeastern Costa Rica (Norden et al. n Maximum species density is found at the 500-m elevation site, consistently exceeding the species density at both higher and lower elevations. The conditional variance of the larger sample Y is appropriate for answering the question: Is the number of species recorded in the smaller sample, X, statistically different from the richness of a random sample of the same size drawn from the larger reference sample, Y ? From this it follows that 0 f(n) K. 1 Terms of Use | Privacy Notice, Microbial Diversity Analysis 16S/18S/ITS Sequencing, PCR-based Antibiotic Resistance Gene Analysis, Plasmid Identification Full Length Plasmid Sequencing, Microbial Functional Gene Analysis Service, Nanopore-Based Microbial Genome Sequencing, Lentiviral/Retroviral Integration Site Sequencing, Microbial Short-Chain Fatty Acid Analysis, Blood (Whole Blood, Plasma, and Serum) Microbiome Research Solution, Microbial Diversity in Extreme Environments, MicroCollect Oral Sample Collection Products, MicroCollect Oral Collection and Preservation Device, MicroCollect Saliva DNA Collection Device, MicroCollect Saliva RNA Collection Device, MicroCollect Stool Sample Collection Products, MicroCollect Sterile Fecal Collection Containers, MicroCollect Stool Collection and Preservation Device, MicroCollect FDA&CE Certificated Virus Collection Swab Kit, Microecology and Cancer Research Solutions, Boussarie, Germain, Bakker, J., Wangensteen, O. S. Edgar, R. C. Accuracy of microbial community diversity estimated by closed- and open-reference OTUs. 1 ( It is often done by subsampling without replacement, which means that each read that is selected and assigned to the normalized sample will not be included in the original pool of samples. = Janzen (1973a, 1973b) tabulated many data sets on tropical foliage insects from sweep samples in southwestern Costa Rica. This implies that beetle species richness for any sample size is significantly greater in the old-growth site than that in the second-growth site for sample size up to at least 1200 individuals. ; DEB-0424767 and DEB-0639393 to R.L.C. Rarefaction is unrealistic in its assumption of random spatial distribution of individuals. 1 Consider a species assemblage consisting of S different species, each of which may or may not be found in each of T independent sampling units (quadrats, plots, traps, microbial culture plates, etc.) For these datasets, abundances can first be converted to incidences (presence or absence) before applying incidence-based rarefaction. X The row sum of the incidence matrix, Yi=j=1TWij, denotes the incidence-based frequency of species i, for i = 1,2, , S. The frequencies Yi represent the incidence reference sample to be rarefied or extrapolated. Also, an ecosystem with greater species richness has higher productivity making it more sustainable and stable and could respond to more catastrophes. 2009). A more diverse ecosystem tends to be more productive and has a greater ability to withstand environmental stresses. For permissions, please email: journals.permissions@oup.com, Orchid fruiting success is unrelated to surrounding floral resources in South Australian plant communities, Effects of land use on soil microbial community structure and diversity in the Yellow River floodplain, Leaf litter decomposition characteristics and controlling factors across two contrasting forest types, INDIVIDUAL-BASED INTERPOLATION (RAREFACTION), http://chao.stat.nthu.edu.tw/softwareCE.html, Receive exclusive offers and updates from Oxford Academic. estimators based on the Bernoulli product model), using replicated incidence data (or sample-based abundance data converted to incidence), perform better in this regard as they retain some aspects of the spatial (or temporal) structure of assemblages (Colwell et al. We will provide you with a customized project plan to meet your research requests. Moreover, the 95% confidence intervals do not overlap (Fig. 1c). We have carried out simulations to investigate the performance of the unconditional variance estimators (Equations5, 7, 10 and 13). {\displaystyle \sum _{j=1}^{\infty }jM_{j}=N} If this assumption is not met, the hypergeometric model, which describes sampling without replacement, is technically more appropriate (Heck et al. On the other hand, the distribution or evenness of the species present in that area is termed as species evenness. = We see little reason, for individual-based data, to recommend computing estimators based on one model over the other (although Coleman curves are computationally less demanding than classical rarefaction), and no reason whatsoever to compute both. Colwell and Coddington (1994) and Brewer and Williamson (1994) showed that, for most datasets, S~ is quite small because both (1 m/n)k and km approach zero as subsample size m approaches the reference sample size n, and the frequency count fk also becomes small at larger k. Thus, S~ is very small except for small values of m. In a later section, we compare the two methods using an example from tropical beetles (Janzen 1973a, 1973b). In addition to applying estimators based on the multinomial model, we also analysed the Janzen beetle dataset with estimators based on the Poisson model, including Coleman area-based rarefaction (Equations 6 and 7), area-based extrapolation (Equations 12 and 13), and estimation of the additional area required to detect proportion g of the estimated assemblage richness Sest (Equation 14). sample-based interpolation, extrapolation and prediction of number of additional sampling units required to reach gSest, under the multinomial product model, for ant samples from five elevations in northeastern Costa Rica (Longino and Colwell 2011). {\displaystyle X_{n}} f We are grateful to Fangliang He and Sun Yat-sen University for the invitation to contribute this paper to a special issue of JPE and to an anonymous reviewer for helpful comments. (2004, their Equation 6) developed an estimator for the unconditional variance in terms of the frequency counts Qk, similar to our Equation (5), that requires an incidence-based estimator Sest for assembly richness S. We postpone specification of Sest for a later section. ) The fundamental statistics for all these estimators are the abundance frequency counts fkthe number of species each represented by exactly Xi = k individuals in a reference sample (e.g. f The numbers on the ordinate show the magnitude of the multinomial estimate minus the Poisson estimate, in ordinary arithmetic units, scaled logarithmically only to spread out the values vertically so they can be seen. In microbial ecology, a common initial approach to assess the difference between environments is through the analysis of alpha diversity of amplicon sequencing data. The ability to link rarefaction curves with their corresponding extrapolated richness curves, complete with unconditional confidence intervals, helps to solve one of most frustrating limitations of traditional rarefaction: throwing away much of the information content of larger samples, in order to standardize comparisons with the smallest sample in a group of samples being compared. However, the sample sizes (number of individual beetles) for the two samples are quite different (976 vs. 237 individuals, Fig. the number of groups still present in the subsample of "n" items To model species aggregation explicitly, the current models could be extended to a negative binomial model (a generalized form of our Poisson model; Kobayashi 1982, 1983) and to a multivariate negative binomial model (a generalized form of our multinomial) model. ) The extrapolation is extended to 1000 samples for each elevation. We plan to implement the rarefaction and extrapolation estimators discussed in this paper in the freeware applications EstimateS (Colwell 2011) and in iNEXT (http://chao.stat.nthu.edu.tw/softwareCE.html). 2c, solid points). Smith and Grassle (1977) provide an unconditional variance formula of S~ind(m), but their expression for the variance is difficult to compute. (The conditional variance of sample X is zero for the full sample.) N In Fig. Analytical methods (classical rarefaction and Coleman rarefaction) have existed for decades for estimating the number of species in a subset of samples from an individual-based dataset. 2004). Based solely on information in the reference sample of n individuals or the individuals from area A, counted and identified to species, we have these six complementary objectives for abundance-based data (Fig. But consider two equally abundant species in the same assemblage, one with a very patchy spatial distribution and the other with all individuals distributed independently and at random. N 1b), and the third based on a Bernoulli product distribution, for incidence frequencies among sampling units (Fig. Rarefaction curves produce smoother lines that facilitate point-to-point or full dataset comparisons. For this reason, we do not plot the results from the Poisson model because the figure would be identical to Fig. . Hurlbert, S. H. The Nonconcept of Species Diversity: A Critique and Alternative Parameters. Oxford, 1999. Search for other works by this author on: We consider two alternative sampling models for individual-based (abundance) data. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. and S.-Y.L.) We recommend R = 10 as rule of thumb, with exploration of other values suggested for samples with large coefficients of variation. 2009). [1], The issue that occurs when sampling various species in a community is that the larger the number of individuals sampled, the more species that will be found. Under the Poisson model, individual-based rarefaction curves and species accumulation curves, because they rely on area, assume that individuals are randomly distributed in space, within and between species. = One cannot simply divide the number of species found by the number of individuals sampled in order to correct for different sample sizes. Janzens study recorded 976 individuals representing 140 species in the Osa second-growth site and 237 individuals of 112 species in the Osa old-growth site. 2a), the extrapolation is extended to five times of the original sample size in order to compare with the Osa second-growth curve. We postpone specification of f^0, which estimates the species present in the assemblage but not observed in the reference sample, for a later section. [ The two samples may be drawn from either the same assemblage or from two different assemblages. Chao and Shen (2004) recommended R = 10 as rule of thumb, with exploration of other values suggested for samples with large coefficients of variation. 2009) under the multinomial model, with 95% unconditional confidence intervals. The incidence frequency counts for the five sites appear in Table 6. species incidence frequency counts for ant samples from five elevations in northeastern Costa Rica (Longino and Colwell 2011). = The technique does not recognize species abundance, only species richness. 2009) or the amount of additional area (Poisson model, Chao and Shen 2004) needed to reach a specified proportion of estimated asymptotic richness.

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