[Paper Review] Species richness estimation with high diversity but spurious singletons

Amy D. Willis|arXiv (Cornell University)|Apr 9, 2016

Species Distribution and Climate Change7 references5 citations

TL;DR

This paper introduces a statistical method, implemented in the R package breakaway, to estimate species richness in high-diversity microbial communities by predicting unobserved and true singleton taxa from non-singleton frequency counts. It demonstrates that traditional richness estimation is highly unstable when singleton counts are unreliable, and shows that breakaway_nof1 provides more robust estimates under measurement error, though the author cautions against overinterpreting such estimates without reporting large standard errors.

ABSTRACT

The presence of uncommon taxa in high-throughput sequenced ecological samples pose challenges to the microbial ecologist, bioinformatician and statistician. It is rarely certain whether these taxa are truly present in the sample or the result of sequencing errors. Unfortunately, alpha-diversity quantification relies on accurate frequency counts, which can rarely be guaranteed. We present a species richness estimation tool which predicts both the number of unobserved taxa and the number of true singletons based on the non-singleton frequency counts. This method can be treated as either inferential (for formally estimating richness) or exploratory (for assessing robustness of the richness estimate to the singleton count). If the estimate, called breakaway_nof1, is comparable to other richness estimators, this provides evidence that the richness estimate is robust to the level of quality control (eg. chimera-checking) employed in pre-processing. The function breakaway_nof1 is freely available from CRAN via the R package breakaway.

Motivation & Objective

• To address the instability of species richness estimation when singleton counts are unreliable due to sequencing errors.
• To develop a method that predicts both unobserved taxa and true singleton counts using only non-singleton frequency counts.
• To provide a statistically rigorous alternative to standard richness estimators that are sensitive to measurement error in singleton frequencies.
• To highlight the critical impact of singleton uncertainty on diversity estimation and advocate for transparent reporting of standard errors.

Proposed method

• The method models the ratio of consecutive frequency counts using a rational function of the form $ \frac{f_{j+1}}{f_j} = \frac{\beta_0 + \beta_1 j + \dots + \beta_p j^p}{1 + \alpha_1 j + \dots + \alpha_q j^q} + \varepsilon_j $, where $ f_j $ is the number of taxa observed $ j $ times.
• Nonlinear least squares is used to estimate the model parameters, enabling prediction of the unobserved frequency $ \hat{f}_0 $ and the true singleton count $ \hat{f}_1 $.
• The total richness is estimated as $ \hat{C} = \hat{f}_0 + \sum_{j \geq 1} f_j $, with standard errors and fit diagnostics provided.
• The approach treats the singleton count as a latent variable to be predicted, reducing dependence on potentially erroneous observed singleton counts.
• The method is implemented as the function `breakaway_nof1` in the R package `breakaway`, freely available on CRAN.
• The method is evaluated via simulations under varying levels of singleton deflation and inflation, and applied to real soil microbiome datasets.

Experimental results

Research questions

• RQ1 How does uncertainty in singleton counts affect the reliability of species richness estimation in high-throughput sequencing data?
• RQ2 Can a statistical model predict the true number of singletons and unobserved taxa using only non-singleton frequency counts?
• RQ3 How does the performance of the proposed method compare to existing richness estimators under realistic levels of sequencing error and singleton inflation?
• RQ4 To what extent does the method improve robustness to pre-processing choices such as chimera-checking and clustering thresholds?
• RQ5 What is the impact of sampling variability on standard errors when singleton counts are unstable?

Key findings

• The method `breakaway_nof1` provides a statistically rigorous way to estimate species richness while accounting for measurement error in singleton counts, which are often unreliable in microbial sequencing data.
• Under high singleton inflation (e.g., 100%), `breakaway_nof1` converges to the true richness from below, while other estimators converge from above, indicating better stability under error.
• The method shows comparable runtime to `breakaway` (0.08–0.21 seconds) and is significantly faster than `CatchAll` (0.44 seconds), though `Chao1` remains the fastest due to its simplicity.
• In simulations with 5000 true taxa, `breakaway_nof1` demonstrated stable convergence and lower error compared to competitors under singleton deflation and inflation.
• The method's performance is robust across varying levels of singleton uncertainty, and it provides standard errors that reflect the high sampling variability inherent in richness estimation.
• The authors caution that even with this method, large standard errors should be reported, as failing to do so constitutes sloppy science, and recommend against drawing firm conclusions about diversity without such uncertainty quantification.