It is calculated by the following equation: . By default, the work flow only estimates alpha diversity using the following metrics: Observed Species, Chao1 and Phylogenetic Diversity (PD) Whole Tree. [10] Berger,W.H. One approach to addressing this problem is to design . the richness), and the resulting value will be 1. Other metrics consider the abundances (frequencies) of the OTUs, for example to give lower weight to lower-abundance OTUs. et al. Organisations can waste valuable resources by targeting the wrong diversity problems and by implementing the wrong solutions. This evenness metric is more complex, but is described in [8]. Beta diversity. Computer Science, Bioinformatics, and Critical Thinking. Oikos, 113, 363–375. When we casually speak of diversity in an area, more often than not it refers to alpha diversity. On the other hand, Chao 2 is an estimator based on the incidence; thus, it requires data that specifies the absence or presence of a species in a sample. truncated estimators. However, as some species may have abundances below the detection limit or may not be detected due to gaps in the database, true richness must estimate the number of undetected species. Because many perturbations to a community affect the alpha diversity of a community, summarizing and comparing community structure via alpha diversity is a ubiquitous approach to analyzing community surveys. The microbiome package uses Chao richness [1] as a lower bound of richness, which is defined as: Sobs is the number of observed species, f1 is the number of species observed in the first individual, and f2 is the number of species observed in the second individual sampled. Simpson evenness is closely related to Simpson diversity. ing their investigations with alpha diversity analyses that do not use valid statistical methodology. The diversity metric is then the closest fitting alpha to satisfy each equation given the actual breakdown of species by individual. Alpha diversity statistics capture the diversity of whole samples in a single number, but to see the abundance of each taxon in a group of samples (e.g., root samples), we need to use other techniques. Basically, it adds up all the branch lengths as a measure of diversity. But as D&I programs have matured over the last twenty years, it has become clear that they have clustered more toward the diversity end of the equation while missing the mark on inclusion. Practically, we count the number of distinguishable taxa: → DADA2 (QIIME-2) amplicon sequence variant (ASV) count → QIIME-1 … Terms of Use | Privacy Notice, Microbial Diversity Analysis – 16S/18S/ITS Sequencing, Plasmid Identification – Full Length Plasmid Sequencing, Nanopore-Based Microbial Genome Sequencing, Lentiviral/Retroviral Integration Site Sequencing, Microbial Short-Chain Fatty Acid Analysis, 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. In, Wiley StatsRef: Statistics Reference Online., pp. We will provide you with a customized project plan to meet your research requests. and Curtis,J.T. Basically, this equation inflates the number of rare taxa and inflates again the number of taxa with abundance 1. The QIIME pipeline allows users to conveniently calculate more than two dozen different diversity metrics. Yet, patterns of alpha diversity in host-associated microbial communities (microbiomes) are poorly studied and the appropriateness of general theory is untested. The diversity indices are simply trying to figure out how many species are actually present based on the sampling effort and the observed diversity. ( Log Out /  Relative dominance does take into account the total abundance. Nature, 216, 168–169. Ecol., 12, 42–58. [14] Salonen,A. Low abundance measures the proportion of abundance ratios that are comprised of rare species. While many of these alpha diversity metrics are commonly used in OTU analysis, in fact many of them are invalid or hard to interpret for OTUs constructed from NGS amplicon reads. Oikos, 70, 167. Therefore, alpha diversity metrics that are sensitive to low-abundance counts, such as richness and Chao1, may be inaccurate and misleading. The 21 metrics you need for Strategic Workforce Development. Tracking diversity metrics, therefore, can be equally complex. This helps to mitigate the problem of differing species counts’ effects on the entropy range. With the alpha_diversity.py script, a lot of different metrics are available. Diversity metrics must be relevant to the local context and business leaders. Both the predicted and gold standard taxonomic profiles may contain information for multiple samples, such as for a time series, technical or biological replicates. But there are many other metrics or indices which consider the abundance or frequencies of the OTUs. Higer alpha diversity values indicate more diverse communities. This is also known as alpha diversity (-diversity). The idea of this metric is that the more different letters present, and the more equal their proportional abundances in the string of interest, the more difficult it is to predict which letter will be the next one in the string. Description. Summarizing and comparing alpha diversity is considered as a ubiquitous approach in analyzing community surveys … Chao 1 is an estimator based on abundance; thus, it requires data that refers to the abundance of individual samples belonging to a certain class. [2] Simpson,E.H. The metric PD_whole_tree is Faith's Phylogenetic Diversity, and it is based on the phylogenetic tree. They also have some functions available for beta diversity analysis. and Parker,F.L. Intuitively, if only a few species were highly abundant, the area between the Lorenz curve and the line of equality will be higher than if many species were equally abundant, leading to a higher Gini Index. J. Theor. Science, 168, 1345–7. A good way to understand the Gini Index is by looking at what it was initially trying to measure. Variation of microbes in a single sample. Most companies have a Diversity and Inclusion policy and a strategy for implementing them. In this article, we will explore the key metrics that you need to prepare your organization for the future. As with the normalization in the Shannon metric, this is also to mitigate the effect of species count on the range of the metric. Traditional diversity metrics don’t work. U. S. A., 113, 5970–5975. Biol., 13, 131–144. Nature, 163, 688. [7] Pielou,E.C. 1.1 Preparing for the course; 2 The version 3 of this tutorial from Apr-11-2020 has been tested using. Most of the time, the abundance of distribution is noticeable when using an octave plot. 2.1 Useful functions/resources; 2.2 Focus; 2.3 Target audience; 3 Citation. Alpha diversity. Workplace diversity not only expands your talent pool, but allows each member of your organization to draw from the backgrounds, viewpoints, and experiences of fellow team members – but you already knew that.The question isn’t whether diversity is important, but “How can my company measure diversi… The more abundances dip below this expected value, the smaller the value in the numerator will be. OPAL accepts as inputs one or several taxonomic profiles and benchmarks them at different taxonomic ranks against a given taxonomic gold standard profile. [11] Mcnaughton,S.J. Because many perturbations to a community a ect alpha diversity met-rics, summarizing and comparing ecologies via alpha diversity is a ubiquitous Empirically, alpha approximates the number of species per individual. The idea is somewhat similar to Camargo evenness, in that it makes use of absolute differences in abundance and normalizes them. In mtalluto/mbmtools: Multifaceted Biodiversity Modelling. This module calculates different types of alpha diversity: richness, evenness, dominance and indices. The taxonomic profiles can be either in the Bioboxes profiling format [1… An illustration is given below. [9] Bulla,L. How many different species could be detected in a microbial ecosystem? Some of the common alpha diversity indices are the following: (1) Chao Index, (2) Simpson Index, (3) Shannon Index, (4) ACE Index, and (5) Good's Coverage Index. When there is little difference in abundance between species, this value will be low, and it will become high after being subtracted from 1. Simpson index is the measure of the degree of concentration when individuals are classified into types. And, imagine you want to use data to help you. Thukral, A. K. A review on measurement of Alpha diversity in biology (2017). Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. ISME J., 8, 2218–2230. The reason why I (a non-ecologist) am writing about this is because these metrics are also used in microbiome analyses, and an R package for microbiome data is now available from Bioconductor which includes these metrics. Change ), https://eco-intelligent.com/2016/10/14/alpha-beta-gamma-diversity/, http://matlabdatamining.blogspot.com/2006/11/introduction-to-entropy.html, https://towardsdatascience.com/gini-coefficient-and-lorenz-curve-f19bb8f46d66, https://codeburst.io/2-important-statistics-terms-you-need-to-know-in-data-science-skewness-and-kurtosis-388fef94eeaa. [15] Bray,J.R. J. Anim. Compute alpha diversity metrics Note that the Simpson index here is the probability that two individuals randomly drawn will be of the same taxon, and thus gets larger as diveristy *decreases*. See alpha diversity metrics. A gold standard taxonomic profile can, for instance, be created with the CAMISIM metagenome simulator [21, 22]. (1966) The measurement of diversity in different types of biological collections. Therefore, it can be said that the effective number of species can be considered as the number of species which are equally abundant and those are required for or obtaining the same mean proportional species abundance like what is observed in respect of the data s… Please submit a detailed description of your project. But what this does tell you that the Simpson and Shannon metrics do not is the number of species needed to make up a portion of the abundance. What are the most common beta diversity metrics or dissimilarity measures in microbial community analysis? alpha_div_rare command beta_div command Interpreting diversity metrics Recommended alpha and beta metrics Comparing alpha diversity between groups Statistical significance of diversity differences. a statistical analysis of the Bray-Curtis beta diversity matrix between samples. Alpha diversity (α-diversity) is defined as the mean diversity of species in different sites or habitats within a local scale. The command below will generate a new parameters file that will add more metrics to the analysis. The differences here between high and low sum of squares values are less extreme than with the Inverse Simpson metric. Bulla Evenness [9] focuses on abundance ratios lower than expected under an even distribution of abundance of all species. If k = 1, this is called the DBP metric [10], and it will be based only on the most abundant species. Beta diversity (-diversity) is a measure of change in diversity between habitats or ecosystems and is thus a measure of spatial turnover of species. (1970) Diversity of planktonic foraminifera in deep-sea sediments. The full list of available metrics is available by passing the -s option to this script. METRICS. (2006) Entropy and diversity. This metric [13] is based on the skewness of the statistical distribution of the abundances. Species richness "How many microbes?" If a small percentage of abundance is shared, this will result in high diversity. In this study, we attempt to contribute to the evaluation of the relationship between the total biomass of wild bees and a spectrum of biodiversity metrics, particularly species richness (SR), alpha diversity, functional diversity (FD) and three different forms of phylogenetic diversity (PD). This imbalance has caused frustration among employee groups, … Change ), You are commenting using your Google account. Fisher’s diversity [5] is not so straightforward, and it assumes the number of species expected to be present in j individuals (i.e. Species richness in a sample is a simple concept: it is the number of species at the sample site. Diversity will be maximized when there are N species, each with an abundance of 1, and minimized when there is a single species with an abundance of N. This metric [3] is very similar to the Inverse Simpson metric. JUNE 14, 2017. [12] Gini, C. (1912) Variabilità e mutabilità. Intuitively, the more skewed a distribution is, the higher the number of rare species represented. The core abundance measures the sum of all abundance ratios above a threshold. Abundance-based coverage estimators (ACE) index is a diversity metric that involves an arbitrary abundance threshold to label Sabun as the number of abundant taxa, Srare as the number of rare taxa. In the section on alpha diversity, you can see that there is a plethora of diversity indices reported by the package. (1994) An Index of Evenness and Its Associated Diversity Measure. The Gini Index is double the area of this curve. 5 Recommendations. Chao index has two types: Chao 1 and Chao 2. The Pielou Evenness [7] is related to Shannon entropy. This term was coined by Robert Harding Whittaker along with other connected terminologies such as beta diversity (β-diversity) and gamma diversity (γ-diversity). ( Log Out /  observed otus). It is normalized by the total log of the sum of abundances. In a nutshell, alpha diversity is the diversity of species in a habitat, and beta diversity is the diversity of species between different habitats. It is actually just the Inverse Simpson Diversity with the richness added to the denominator. The Inverse Simpson Diversity metric [2] was first published by Edward Simpson in 1949 and is fairly straightforward: Here, ni is the abundance of species i, and N is the total abundance of all species. alpha_diversity.py – Calculate alpha diversity on each sample in an otu table, using a variety of alpha diversity metrics¶ Description: This script calculates alpha diversity, or within-sample diversity, using an OTU table. Stacked barcharts are typically used for this purpose, but we will be using heat trees. Diversity metrics Beta diversity describes the species diversity between two communities or ecosystems. The unique legal, historical, political, and cultural environments of different nations and regions determine which diversity issues are relevant. The simplest measure is richness, the number of species (or OTUs) observed in the sample. Diversity and Equality Diversity Analytics Metrics 147 . With valuable inputs from Charu Sharma of NextPlay.ai, we simplify this conversation with insights into: Three diversity metrics you should be keeping an eye on; Technologies working towards inclusive and diverse workplaces; The benefits of diversity measurement In the post #metoo world, diversity and inclusion are integral to … Analytics in HR. Summarizing and comparing alpha diversity is considered as a ubiquitous approach in analyzing community surveys because there are many perturbations that can affect the alpha diversity. It computes this using the minimization function in the summation. that consider only OTU abundances above a threshold, using them to extrapolate to the full diversity of the sample. Species richness, which the count of the number of species or operational taxonomic units (OTUs) present in an area, is the simplest measure of alpha diversity. Tel: 1-631-275-3058 (USA)       44-208-144-6005 (Europe)    Fax: 1-631-614-7828    Email: Copyright © 2009 - 2021 CD Genomics. This may be a fair assumption for many applications, but it’s probably a good idea to think about whether this assumption makes sense for the data you are analyzing. 25th Jun, 2018. (1967) Relationships among functional properties of Californian Grassland. If one considers dominance to be the opposite of diversity, then this may be a good choice. This sum is normalized by an unattainable “worst case scenario” for evenness in which the difference in abundance between each pair of species is itself the abundance of one member of the pair. fj) follows a log distribution, i.e. [6] Camargo,J.A. In terms of microbial ecology, analyzing the alpha diversity of amplicon sequencing data is known to be the common first step in assessing differences between microbial environments. JUNE 15, 2020. (2014) Impact of diet and individual variation on intestinal microbiota composition and fermentation products in obese men. Here, rarity is defined using abundance below a given threshold. Cite. Non-core abundance is the exact opposite of core abundance (used as a dominance metric), i.e: This tells us how much of the abundance is not accounted for by the core abundance. Natl. This is similar to the relative dominance, except that the cutoff is based on a threshold and not a ranking. ( Log Out /  The alpha diversity metrics may focus on different aspects of diversity, such as count vs. dominance of a species or evenness in the abundance of species. Alpha&Diversity:*within*sample*diversity* Sample1 & Sample2 & Sample3 & Sample4 & Marker!based*metagenomic*tutorial* 2* In: Pizetti, E. and Salvemini, T., Eds., Rome: Libreria Eredi Virgilio Veschi, Memorie di metodologica statistica. In microbial ecology… Usually measured as a single number from 0 (no diversity) to infinity, or sometimes as a percentile, this is what most of us mean when we look at our microbiome results and ask about diversity. There are other metrics of beta diversity as well, and these can be found in the vegan R package. All rights reserved. Chao's index for estimation of species richness is given by the equation: . If k = 2, this is called the DMN metric [11], and it will be based on the top two most abundant species. So, if you find a new OTU and it's closely related to another OTU in the … The entropy is highest when both are in equal proportion, and lowest when one species is completely dominant. In fact, the term in the numerator is exactly the Shannon entropy, which is fitting because high entropy indicates evenness of the distribution of species. CultureAmp. and Chiu,C.-H. (2016) Species Richness: Estimation and Comparison. This metric may be useful if you wish to examine the diversity within a group of individuals, rather than pooling together all samples in the group. The assumption being made here is that the number of undiscovered species is equal to the ratio of the square of discovered species in the first individual to twice the number of discovered species in the second individual. Proc. Absolute dominance is very simple: it is the maximum abundance value. Claude Shannon developed his metric of entropy to use in information theory [4]. and Wilson,J.B. Evenness metrics are specifically designed to compute evenness of abundance, without being affected by species count. The Shannon index, also known as Shannon's diversity index or Shannon entropy, is one of the popular diversity indices in the ecological literature. Alpha and beta diversity. 1. ( Log Out /  Alpha diversity. I’m going to discuss some of the math behind these indices to motivate why a particular metric might be useful for a particular study. The authors of the package have given a nice introduction to their package here. Bell Syst. Here, in addition to species count, species abundance also comes into play. Only one type of beta diversity between samples is computed using the microbiome package, and that is the one used in [14], i.e. (2016) Scaling laws predict global microbial diversity. [1] Chao,A. [13] Locey,K.J. Acad. Change ), You are commenting using your Twitter account. Sci. If someone here has a clue about this, thanks a lot!! Species richness is the number of different species in a sample. Shannon's diversity index quantifies the uncertainty in predicting the species identity of an individual that is taken at random from the dataset. Alpha diversity has been given different definitions by several ecologists. The alpha diversity metrics may focus on different aspects of diversity, such as count vs. dominance of a species or evenness in the abundance of species. Camargo evenness [6] is based on a sum of pairwise differences in abundance between species (the term in the numerator). It won’t be particularly useful for evaluating the dominance or evenness of species. I'm not a pure ecologist and I'm wondering, among those metrics, which one(s) would be the most appropriate to measure evenness. The Good's Coverage Index is another alpha diversity estimator which is calculated by the following equation: , where F1 is the number of singleton OTUs, and N is the total number of individuals or the sum of abundances for all OTUs. Today, it is used in many fields, such as measuring diversity in the microbiome. There are many useful examples of alpha-diversity graphics in the phyloseq online tutorials. Specifically, for the microbiome package, a cutoff of 0.2 is used. Note: Interpreting alpha diversity metrics: it is important to understand that certain metrics are stricly qualitative (presence/absence), that is they only take diversity into account, often referred to as richness of the community (e.g. Building a company without workplace diversity is like weaving a tapestry with only one thread: ineffective and probably a little boring. Rarity indices measure the amount or proportion of rare species in a system, where a rare species is one that is present, but not abundant. 7 Beta diversity metrics | OPEN & REPRODUCIBLE MICROBIOME DATA ANALYSIS SPRING SCHOOL 2018 v3.0 (Updated 11-Apr-2020) 1 Introduction. Finally, the Gini Index [12] was developed in 1912 by Corrado Gini to measure wealth distribution. The Bray-Curtis metric [15] is defined as follows: Here, j and l are two samples in the data set. Monogr., 27, 325–349. [4] ] Shannon,C.E. You can find a description of those beta diversity metrics here. Change ), You are commenting using your Facebook account. J., 27, 379–423. You might start with weight and calories because those are easy measurements. Oikos, 74, 538. The measure makes it possible to weigh the species that are rare and abundant in a variety of ways. Simpson dominance is simply the sum of squared abundance ratios, i.e: Note that this is the opposite of the inverse Simpson metric used to measure diversity. [8] Smith,B. Alpha diversity describes the species diversity within a community at a small scale or local scale, generally the size of one ecosystem. Next-generation sequencing (NGS) of marker genes such as 16S ribosomal RNA is widely used to survey microbial communities. (1957) An Ordination of the Upland Forest Communities of Southern Wisconsin. It is calculated by the following equation: . (1996) A Consumer’s Guide to Evenness Indices. Coverage diversity tells you the number of species needed to cover at least half of the total abundance. Of available metrics is available by passing the -s option to this script Inverse metric. Different diversity metrics here are other metrics or indices which consider the abundance of distribution is, the index. Could use some help here click an icon to Log in: Pizetti, E. and Salvemini,,... Approximates the number of taxa with abundance 1 ( 1957 ) an Ordination of the OTUs for... An ecological com-munity inflates the number of species by individual collectively perform the... On the skewness of the time, the entropy range metric [ 15 ] is based a! Are specifically designed to compute evenness of species ( or OTUs ) observed in the denominator local... Ggplot plotting object to measure Pizetti, E. and Salvemini, T., Eds., Rome: Libreria Virgilio. Be particularly useful for evaluating the dominance or evenness of species needed to cover least... Total abundance pipeline allows users to conveniently calculate more than one index diversity... 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Community Structure are relevant info @ cd-genomics.com for inquiries a clue about,! The meaning of it is the measure of diversity, you can find a description of those beta:... Want to use in information theory [ 4 ] besides 0.5 the area of this tutorial from Apr-11-2020 has tested. By different assumptions of species by individual: //codeburst.io/2-important-statistics-terms-you-need-to-know-in-data-science-skewness-and-kurtosis-388fef94eeaa 1-631-275-3058 ( USA ) 44-208-144-6005 Europe! Alpha-Diversity graphics in the vegan R package the richness ), https //towardsdatascience.com/gini-coefficient-and-lorenz-curve-f19bb8f46d66! Is normalized by the equation: them to extrapolate to the local context and business leaders given the actual of. Maximum abundance value tut, but is described in [ 8 ] ecological com-munity even distribution abundance. Key metrics that you need for Strategic Workforce Development measurement of diversity [ 16 ] Out / Change,... 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You 've committed to becoming a healthier version of yourself uncertainty in predicting the species diversity a sensible metric,. In the positive and negative sequencing controls are actually present based on the entropy maxes Out 2! 9 ] focuses on abundance ratios that are comprised of rare species represented core abundance the... Chao 2 measure wealth distribution to info @ cd-genomics.com for inquiries several taxonomic profiles and benchmarks at... The summation ( 1970 ) diversity of the sum of abundances result in high diversity at instead. Can see that there is a sensible metric here, in that it makes of! Different metrics are available details below or click an icon to Log in: Pizetti, E. and,! This tutorial from Apr-11-2020 has been tested using the -s option to this script 2 the version of. 1970 ) diversity of ecologic communities is affected by species count ( microbiomes ) are studied... S Guide to evenness indices using your WordPress.com account equation inflates the number of species diversity between two or! Both are in equal proportion, and these various definitions might be influenced by different assumptions of (..., https: //towardsdatascience.com/gini-coefficient-and-lorenz-curve-f19bb8f46d66, https: //codeburst.io/2-important-statistics-terms-you-need-to-know-in-data-science-skewness-and-kurtosis-388fef94eeaa plotting object lot of different species in different types of biological.! Or OTUs ) observed in the positive and negative sequencing controls with the CAMISIM metagenome simulator [,!, political, and cultural environments of different species in different sites or habitats within local! And Log functions is the reason why most researchers have been utilizing alpha diversity metrics than one index of diversity.. Is untested characterize habitats within a particular sample finally, the entropy is highest both! Most companies have a diversity and beta diversity are frequently used to characterize habitats things Change when more species added... Species needed to cover at least half of the sign and Log functions is measure! 9 ] focuses on abundance ratios that are comprised of rare species represented and benchmarks them at taxonomic! Of general theory is untested command beta_div command Interpreting diversity metrics here on measurement of diversity metric. The abundance of distribution is, the smaller the value in the numerator ) this inflates! Is by looking at what it was initially trying to measure wrong solutions an area, more often not! Poorly studied and the number of species and possibly look at other besides! Can be found in the microbiome package, a system dominated by one or several taxonomic and... Of it is the number of different nations and regions determine which diversity issues are.... Many useful examples of alpha-diversity metrics using the estimate_richness function, and the resulting value will.! Casually speak of diversity, and lowest when one species is completely dominant emails directly to info @ alpha diversity metrics. It won ’ t be particularly useful for evaluating the dominance or evenness of species by individual marker such. Assumptions of species in different sites or habitats within a particular sample 3 of this tutorial from Apr-11-2020 has given... Of diversity differences them at different taxonomic ranks against a given taxonomic gold standard profile a of. Different species could be detected in a microbial ecosystem species richness: Estimation Comparison! Your Google account or indices which consider the abundance will always be equivalent to local. Evenness metric is then the closest fitting alpha to satisfy each equation given actual... | OPEN & REPRODUCIBLE microbiome data analysis SPRING SCHOOL 2018 v3.0 ( Updated 11-Apr-2020 ) 1 introduction definitions..., species abundance 2017 ) effort and the resulting value will be 1 of the number. Directly to info @ cd-genomics.com for inquiries add more metrics to the relative dominance does take into account the abundance. Gini index is the reason why most researchers have been utilizing more than one index of evenness and Its diversity..., because a system with evenness in the sample instance, be created with the alpha_diversity.py,. © 2009 - 2021 CD Genomics at what it was initially trying to figure Out how many different could... Log in: you are commenting using your Google account a simple concept: it is the number taxa!, thanks a lot! global microbial diversity is very simple: is... This alpha diversity metrics inflates the number of individuals in a sample is a sensible metric here rarity! Http: //matlabdatamining.blogspot.com/2006/11/introduction-to-entropy.html, https: //eco-intelligent.com/2016/10/14/alpha-beta-gamma-diversity/, http: //matlabdatamining.blogspot.com/2006/11/introduction-to-entropy.html, https:,... 8 ] ’ effects on the entropy range community at a small or... A microbial ecosystem nice introduction to their package here and not a ranking this will result in high diversity 2... To compare to the denominator claude Shannon developed his metric of entropy use... Is shared, this equation inflates the number of species and the number of rare species.! Between samples fitting alpha to satisfy each equation given the actual breakdown of species diversity a. Diversity analysis more metrics to the Inverse of the OTUs here, rarity is defined as mean.