An extension of Chao’s estimator of population size based on the first three capture frequency counts

A more reliable species richness estimator based on the Gamma-Poisson model

Background

Accurately estimating the true richness of a target community is still a statistical challenge, particularly in highly diverse communities. Due to sampling limitations or limited resources, undetected species are present in many surveys and observed richness is an underestimate of true richness. In the literature, methods for estimating the undetected richness of a sample are generally divided into two categories: parametric and nonparametric estimators. Imposing no assumptions on species detection rates, nonparametric methods demonstrate robust statistical performance and are widely used in ecological studies. However, nonparametric estimators may seriously underestimate richness when species composition has a high degree of heterogeneity. Parametric approaches, which reduce the number of parameters by assuming that species-specific detection probabilities follow a given statistical distribution, use traditional statistical inference to calculate species richness estimates. When species detection rates meet the model assumption, the parametric approach could supply a nearly unbiased estimator. However, the infeasibility and inefficiency of solving maximum likelihood functions limit the application of parametric methods in ecological studies when the model assumption is violated, or the collected data is sparse.

Method

To overcome these estimating challenges associated with parametric methods, an estimator employing the moment estimation method instead of the maximum likelihood estimation method is proposed to estimate parameters based on a Gamma-Poisson mixture model. Drawing on the concept of the Good-Turing frequency formula, the proposed estimator only uses the number of singletons, doubletons, and tripletons in a sample for undetected richness estimation.

Results

The statistical behavior of the new estimator was evaluated by using real and simulated data sets from various species abundance models. Simulation results indicated that the new estimator reduces the bias presented in traditional nonparametric estimators, presents more robust statistical behavior compared to other parametric estimators, and provides confidence intervals with better coverage among the discussed estimators, especially in assemblages with high species composition heterogeneity.

GTRD: a database on gene transcription regulation-2019 update

The current version of the Gene Transcription Regulation Database (GTRD; http://gtrd.biouml.org) contains information about: (i) transcription factor binding sites (TFBSs) and transcription coactivators identified by ChIP-seq experiments for Homo sapiens, Mus musculus, Rattus norvegicus, Danio rerio, Caenorhabditis elegans, Drosophila melanogaster, Saccharomyces cerevisiae, Schizosaccharomyces pombe and Arabidopsis thaliana; (ii) regions of open chromatin and TFBSs (DNase footprints) identified by DNase-seq; (iii) unmappable regions where TFBSs cannot be identified due to repeats; (iv) potential TFBSs for both human and mouse using position weight matrices from the HOCOMOCO database. Raw ChIP-seq and DNase-seq data were obtained from ENCODE and SRA, and uniformly processed. ChIP-seq peaks were called using four different methods: MACS, SISSRs, GEM and PICS. Moreover, peaks for the same factor and peak calling method, albeit using different experiment conditions (cell line, treatment, etc.), were merged into clusters. To reduce noise, such clusters for different peak calling methods were merged into meta-clusters; these were considered to be non-redundant TFBS sets. Moreover, extended quality control was applied to all ChIP-seq data. Web interface to access GTRD was developed using the BioUML platform. It provides browsing and displaying information, advanced search possibilities and an integrated genome browser.

Upper bound estimators of the population size based on ordinal models for capture-recapture experiments

Capture-recapture studies have attracted a lot of attention over the past few decades, especially in applied disciplines where a direct estimate for the size of a population of interest is not available. Epidemiology, ecology, public health, and biodiversity are just a few examples. The estimation of the number of unseen units has been a challenge for theoretical statisticians, and considerable progress has been made in providing lower bound estimators for the population size. In fact, it is well known that consistent estimators for this cannot be provided in the very general case. Considering a case where capture-recapture studies are summarized by a frequency of frequencies distribution, we derive a simple upper bound of the population size based on the cumulative distribution function. We introduce two estimators of this bound, without any specific parametric assumption on the distribution of the observed frequency counts. The behavior of the proposed estimators is investigated using several benchmark datasets and a large-scale simulation experiment based on the scheme discussed by Pledger.

A nonparametric method of estimation of the population size in capture-recapture experiments

A recent method for estimating a lower bound of the population size in capture-recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent for count distributions having a log-convex pgf ( L C -class). This is a large family that includes mixed and compound Poisson distributions, and their independent sums and finite mixtures as well. The finite-sample performance of the lower bound estimator is assessed via simulation showing a better behavior than some close competitors. Several examples of application are also analyzed and discussed.

Population size estimation for quality control of ChIP-Seq datasets

Chromatin immunoprecipitation followed by sequencing, i.e. ChIP-Seq, is a widely used experimental technology for the identification of functional protein-DNA interactions. Nowadays, such databases as ENCODE, GTRD, ChIP-Atlas and ReMap systematically collect and annotate a large number of ChIP-Seq datasets. Comprehensive control of dataset quality is currently indispensable to select the most reliable data for further analysis. In addition to existing quality control metrics, we have developed two novel metrics that allow to control false positives and false negatives in ChIP-Seq datasets. For this purpose, we have adapted well-known population size estimate for determination of unknown number of genuine transcription factor binding regions. Determination of the proposed metrics was based on overlapping distinct binding sites derived from processing one ChIP-Seq experiment by different peak callers. Moreover, the metrics also can be useful for assessing quality of datasets obtained from processing distinct ChIP-Seq experiments by a given peak caller. We also have shown that these metrics appear to be useful not only for dataset selection but also for comparison of peak callers and identification of site motifs based on ChIP-Seq datasets. The developed algorithm for determination of the false positive control metric and false negative control metric for ChIP-Seq datasets was implemented as a plugin for a BioUML platform: https://ict.biouml.org/bioumlweb/chipseq_analysis.html.

A Truncation Model for Estimating Species Richness

We propose a truncation model for the abundance distribution in species richness estimation. This model is inherently semiparametric and incorporates an unknown truncation threshold between rare and abundant observations. Using the conditional likelihood, we derive a class of estimators for the parameters in this model by stepwise maximization. The species richness estimator is given by the integer maximizing the binomial likelihood, given all other parameters in the model. Under regularity conditions, we show that our estimators of the model parameters are asymptotically efficient. We recover Chaos lower bound estimator of species richness when the parametric part of the model is single-component Poisson. Thus our class of estimators strictly generalized the latter. We illustrate the performance of the proposed method in a simulation study, and compare it favorably to other widely-used estimators. We also give an application to estimating the number of distinct vocabulary words in French playwright Molière's Tartuffe.