Unveiling the species‐rank abundance distribution by generalizing the Good‐Turing sample coverage theory

Abstract

Based on a sample of individuals, we focus on inferring the vector of species relative abundance of an entire assemblage and propose a novel estimator of the complete species-rank abundance distribution (RAD). Nearly all previous estimators of the RAD use the conventional "plug-in" estimator Pi (sample relative abundance) of the true relative abundance pi of species i. Because most biodiversity samples are incomplete, the plug-in estimators are applied only to the subset of species that are detected in the sample. Using the concept of sample coverage and its generalization, we propose a new statistical framework to estimate the complete RAD by separately adjusting the sample relative abundances for the set of species detected in the sample and estimating the relative abundances for the set of species undetected in the sample but inferred to be present in the assemblage. We first show that P, is a positively biased estimator of pi for species detected in the sample, and that the degree of bias increases with increasing relative rarity of each species. We next derive a method to adjust the sample relative abundance to reduce the positive bias inherent in j. The adjustment method provides a nonparametric resolution to the longstanding challenge of characterizing the relationship between the true relative abundance in the entire assemblage and the observed relative abundance in a sample. Finally, we propose a method to estimate the true relative abundances of the undetected species based on a lower bound of the number of undetected species. We then combine the adjusted RAD for the detected species and the estimated RAD for the undetected species to obtain the complete RAD estimator. Simulation results show that the proposed RAD curve can unveil the true RAD and is more accurate than the empirical RAD. We also extend our method to incidence data. Our formulas and estimators are illustrated using empirical data sets from surveys of forest spiders (for abundance data) and soil ciliates (for incidence data). The proposed RAD estimator is also applicable to estimating various diversity measures and should be widely useful to analyses of biodiversity and community structure.

Dysregulation of B Cell Repertoire Formation in Myasthenia Gravis Patients Revealed through Deep Sequencing

“…A minimum bound on the estimate of unseen clones was determined using the Chao1 estimator (37). The complete clonal abundance distribution was inferred using the one-parameter variant of the Chao et al, 2015 method (38), with confidence intervals derived via bootstrapping (resampling with replacement) from the inferred complete distribution using 2,000 realizations. Repertoire diversity and evenness was characterized using the generalized diversity index proposed by Hill (39).…”

Evidence for Trait-Based Dominance in Occupancy among Fossil Taxa and the Decoupling of Macroecological and Macroevolutionary Success

“…Therefore, we estimated average species richness per genus after sampling standardization. We employed shareholder quorum subsampling (SQS; Alroy 2010; Chao and Jost 2012), which uses coverage statistics (Good 1953;Chao et al 2015) to approximate comparable levels of sampling among intervals. Thus, genera are species rich only if they have many frequently subsampled species.…”

The Number and Abundance of Ichneumonidae (Hymenoptera, Apocrita) Subfamilies Occurring in Apple Orchards and on Their Edges

“…Values of ACE (Abundance Coverage-based Estimator of species richness), Jack1 (First-order jackknife estimator of species richness), Jack2 (Secondorder jackknife estimator of species richness), Chao1 and Chao2 (Chao richness estimators) and the dominance index (D) [Colwell et al 2004, Magurran 2004, Chao et al 2005, Colwell et al 2012, Chao et al 2015 are also calculated. The dominance index for subfamilies was determined as a percentage of specimens of a particular subfamily in the total of specimens caught.…”