How and how much does RAD-seq bias genetic diversity estimates?

Abstract

Background: RAD-seq is a powerful tool, increasingly used in population genomics. However, earlier studies have raised red flags regarding possible biases associated with this technique. In particular, polymorphism on restriction sites results in preferential sampling of closely related haplotypes, so that RAD data tends to underestimate genetic diversity.

Results: Here we (1) clarify the theoretical basis of this bias, highlighting the potential confounding effects of population structure and selection, (2) confront predictions to real data from in silico digestion of full genomes and (3) provide a proof of concept toward an ABC-based correction of the RAD-seq bias. Under a neutral and panmictic model, we confirm the previously established relationship between the true polymorphism and its RAD-based estimation, showing a more pronounced bias when polymorphism is high. Using more elaborate models, we show that selection, resulting in heterogeneous levels of polymorphism along the genome, exacerbates the bias and leads to a more pronounced underestimation. On the contrary, spatial genetic structure tends to reduce the bias. We confront the neutral and panmictic model to "ideal" empirical data (in silico RAD-sequencing) using full genomes from natural populations of the fruit fly Drosophila melanogaster and the fungus Shizophyllum commune, harbouring respectively moderate and high genetic diversity. In D. melanogaster, predictions fit the model, but the small difference between the true and RAD polymorphism makes this comparison insensitive to deviations from the model. In the highly polymorphic fungus, the model captures a large part of the bias but makes inaccurate predictions. Accordingly, ABC corrections based on this model improve the estimations, albeit with some imprecisions.

Conclusion: The RAD-seq underestimation of genetic diversity associated with polymorphism in restriction sites becomes more pronounced when polymorphism is high. In practice, this means that in many systems where polymorphism does not exceed 2 %, the bias is of minor importance in the face of other sources of uncertainty, such as heterogeneous bases composition or technical artefacts. The neutral panmictic model provides a practical mean to correct the bias through ABC, albeit with some imprecisions. More elaborate ABC methods might integrate additional parameters, such as population structure and selection, but their opposite effects could hinder accurate corrections.

Keywords: ABC; Allele drop-out; Non-neutral model; Population genomics; Population structure; Reduced representation genomics.

Fig. 1

a The relation between π_true, the nucleotidic diversity measured using all individuals at RAD loci, and π_RAD, measured using only loci associated with an intact restriction site, simulated under a neutral and panmictic model. b The relation between the amplitude of the RAD polymorphism bias (π_RAD / π_true) and the level of polymorphism. Solid lines represent local linear regressions

Fig. 2

The relation between π_true and π_RAD in a non neutral model. Black open dots: homogeneous θ values (neutral model, equivalent to Fig. 1). Solid coloured dots: heterogeneous θ values along the genome. Each simulation was run by randomly choosing a reference θ value (θ_ref), which was used to assign different θ values to different genomic regions, with increasing heterogeneity in the three models. Blue dots: Model 1: 70 % of loci with θ₁ = θ_ref, 20 % with θ₂ = θ_ref /2 and 10 % with θ₃ = θ_ref /10; orange dots: Model 2: 70 % of loci with θ₁ = θ_ref, 20 % with θ₂ = θ_ref /10 and 10 % with θ₃ = θ_ref /100; red dots: Model 3: 50 % of loci with θ₁ = θ_ref, 40 % with θ₂ = θ_ref /10 and 10 % with θ₃ = θ_ref /100. Solid lines represent local linear regressions. The figure shows that the underestimation of genetic diversity is stronger when polymorphism is more heterogeneous along the genome

Fig. 3

The relation between π_true and π_RAD in a spatially structured model. Colours indicate divergence time between sub-populations (t), measured in 4*Ne units (that is, the ratio between the divergence time and the average coalescence time). Solid lines represent local linear regressions. The figure shows that the underestimation of genetic diversity is less strong when sub-populations are more divergent

Fig. 4

A comparison between simulations and empirical data in highly diverse populations. Distributions show the π_RAD values expected under the neutral panmictic model with θ = 9.7 % (American population, on the left) and θ = 7.4 % (Russian population, on the right). The black arrows indicate the true polymorphism values (π_true) in the two populations. The grey arrows indicate the observed π_RAD values. Each distribution was computed from 400 simulations

Fig. 5

ABC corrections of the RAD-seq bias. The figure shows the relation between π_true and the corrected π_RAD values, that is, the θ parameter estimated by ABC. Black dots correspond to simulated data (cross-validation). Green dots represent Drosophila melanogaster populations. Blue and red dots represent American and Russian populations of Schizophyllum commune, respectively