Applications of species accumulation curves in large-scale biological data analysis

Abstract

The species accumulation curve, or collector's curve, of a population gives the expected number of observed species or distinct classes as a function of sampling effort. Species accumulation curves allow researchers to assess and compare diversity across populations or to evaluate the benefits of additional sampling. Traditional applications have focused on ecological populations but emerging large-scale applications, for example in DNA sequencing, are orders of magnitude larger and present new challenges. We developed a method to estimate accumulation curves for predicting the complexity of DNA sequencing libraries. This method uses rational function approximations to a classical non-parametric empirical Bayes estimator due to Good and Toulmin [Biometrika, 1956, 43, 45-63]. Here we demonstrate how the same approach can be highly effective in other large-scale applications involving biological data sets. These include estimating microbial species richness, immune repertoire size, and k-mer diversity for genome assembly applications. We show how the method can be modified to address populations containing an effectively infinite number of species where saturation cannot practically be attained. We also introduce a flexible suite of tools implemented as an R package that make these methods broadly accessible.

Keywords: accumulation region; immune repertoire; microbiome diversity; rational function approximation; species accumulation curve; species richness.

Figure 1. Predicting the number of unique words as a function of the size of the sample

The observed curve is the accumulation curve of the total word counts of Shakespeare’s known works compared to the predicted curve (A) when the size of the initial sample is 5% of the total words from Shakespeare’s known works; (B) when the size of the initial sample is 10%; and (C) when the size of the initial sample is 100% and comparing the RFA-GT lower bound to the lower bound of Efron and Thisted (E & T).

Figure 2. Annotated species as a function of the sample abundance using (A) a 5% subsample and (B) the full observed experiment

The x-axis is the sample abundance and the y-axis is the expected number of unique annotated species. Note that the original curve provided by MG-RAST uses the number of sequences as its x-axis. We convert it to the sample abundance by rescaling.

Figure 3. Age-related decrease in TCR repertoire

(A) Interpolation of the accumulation region of TCR β CDR3 clonotypes for each group. (B) Extrapolation of the accumulation region of TCR β CDR3 clonotypes for each group using the observed data in A. (C) Predicting the total number of unique TCR β CDR3 clonotypes as a function of the total number of TCR β cDNA molecules by combining all groups.

Figure 4. The number of distinct 31-mers as a function of sequenced 31-mers with extrapolations using 1% and 10% subsamples

(A) Extrapolations from the subsamples using default preseqR, with the rational function approximations to the Good-Toulmin power series behaving like a constant asymptotically. (B) Extrapolations from the subsample using rational function approximations to the Good-Toulmin power series behaving like a linear function asymptotically.