Evaluation of the evenness score in next-generation sequencing

Area of Science:

• Bioinformatics
• Genomics
• Computational Biology

Background:

• Next-generation sequencing (NGS) generates vast amounts of data requiring robust quality assessment.
• Coverage evenness is a critical metric for evaluating the reliability of NGS results.
• Existing measures like the coefficient of variation have limitations in characterizing coverage homogeneity.

Purpose of the Study:

• To mathematically clarify and derive a more computationally efficient formula for the evenness score (E) in NGS.
• To compare the evenness score (E) with the coefficient of variation (σ) for various coverage distributions.
• To provide practical R scripts for calculating E from empirical NGS data.

Main Methods:

• Mathematical derivation of a new formula for the evenness score (E) based on the probability density function.
• Analysis of E for symmetrical (Gaussian) and skewed (log-normal) distributions.
• Development of R command line scripts for empirical data analysis.

Main Results:

• A computationally efficient formula for E is derived: 1 minus the integral of f(x)*(1-x) dx.
• For symmetrical distributions, E is closely related to σ (e.g., 1-σ²/2).
• For log-normal distributions, E approximates exp(-σ*/2) or 1-F(exp(-1)) depending on σ, offering insights into well-covered targets.

Conclusions:

• The new formula for E enhances the analysis of NGS coverage evenness.
• E provides complementary information to the coefficient of variation, especially for skewed biological data.
• The score exp(-σ) may offer a broader evaluation range for realistic NGS outputs compared to E.