Measurements of intrahost viral diversity require an unbiased diversity metric

Abstract

Viruses exist within hosts at large population sizes and are subject to high rates of mutation. As such, viral populations exhibit considerable sequence diversity. A variety of summary statistics have been developed which describe, in a single number, the extent of diversity in a viral population; such measurements allow the diversities of different populations to be compared, and the effect of evolutionary forces on a population to be assessed. Here we highlight statistical artefacts underlying some common measures of sequence diversity, whereby variation in the depth of genome sequencing may substantially affect the extent of diversity measured in a viral population, making comparisons of population diversity invalid. Specifically, naive estimation of sequence entropy provides a systematically biased metric, a lower read depth being expected to produce a lower estimate of diversity. The number of polymorphic loci per kilobase of genome is more unpredictably affected by read depth, giving potentially flawed results at lower sequencing depths. We show that the nucleotide diversity statistic π provides an unbiased estimate of diversity in the sense that the expected value of the statistic is equal to the correct value of the property being measured. Our results are of importance for studies interpreting genome sequence data; we describe how diversity may be assessed in viral populations in a fair and unbiased manner.

Keywords: entropy; polymorphism; sequence data; virus diversity.

Figure 1.

Mean sequence entropy values calculated for sets of 1,000 loci each of which has a consistent minor variant frequency. Means of these values calculated across 100 replicates are shown as black dots, with vertical bars, where visible, showing an interval of ±2 standard deviations. The correct entropy is shown by a dashed red line. The dashed blue lines, where not obscured by the correct entropy value, show the upper and lower limits described in Equation (3), with the upper limit showing the correct sequence entropy value. Data are shown for (A) a variant frequency of 30% and (B) a variant frequency of 0.03%.

Figure 2.

(A) Trend in the probability of a variant being identified as a polymorphism at 1% frequency as a function of read depth. At very high read depth, variants with a frequency greater than 1% will always be identified as polymorphisms, while variants below this frequency will never be identified as polymorphisms. Details of the function in the region between the vertical grey dashed lines are shown in (B). Detailed probability values. The range of frequencies at which a variant can be identified is constrained to the set of values i/N where N is the read depth; this constraint leads to a sawtooth pattern in the probability of identifying a polymorphism.

Figure 3.

Allele frequency spectra for the two datasets analysed in this study. The within-host influenza dataset shows a small number of polymorphic sites relative to the HIV data.

Figure 4.

Diversity statistics calculated for HIV (black) and influenza (red) sequence data following downsampling of the data to lower read depths. Ten replicate downsampling calculations were performed for each point; dots show mean values, with vertical bars, where visible, showing an interval of ±2 standard deviations. Dashed grey lines show the values calculated from the complete dataset.