# Construction of relatedness matrices using genotyping-by-sequencing data

## TL;DR

This paper introduces a new method for calculating relatedness from genotyping-by-sequencing data, even at low sequencing depths, and provides a way to filter problematic SNPs.

## Contribution

The novel contribution is the KGD method for unbiased relatedness estimation using GBS data, adjusted for sequencing depth and SNP filtering.

## Key findings

- Unbiased relatedness estimates can be obtained using SNPs with genotype calls in both individuals, independent of sequencing depth.
- A modified estimator for self-relatedness corrects for sequencing depth bias.
- A graphical 'fin plot' helps identify and filter SNPs with non-Mendelian inheritance patterns.

## Abstract

Genotyping-by-sequencing (GBS) is becoming an attractive alternative to array-based methods for genotyping individuals for a large number of single nucleotide polymorphisms (SNPs). Costs can be lowered by reducing the mean sequencing depth, but this results in genotype calls of lower quality. A common analysis strategy is to filter SNPs to just those with sufficient depth, thereby greatly reducing the number of SNPs available. We investigate methods for estimating relatedness using GBS data, including results of low depth, using theoretical calculation, simulation and application to a real data set.

We show that unbiased estimates of relatedness can be obtained by using only those SNPs with genotype calls in both individuals. The expected value of this estimator is independent of the SNP depth in each individual, under a model of genotype calling that includes the special case of the two alleles being read at random. In contrast, the estimator of self-relatedness does depend on the SNP depth, and we provide a modification to provide unbiased estimates of self-relatedness. We refer to these methods of estimation as kinship using GBS with depth adjustment (KGD). The estimators can be calculated using matrix methods, which allow efficient computation. Simulation results were consistent with the methods being unbiased, and suggest that the optimal sequencing depth is around 2-4 for relatedness between individuals and 5-10 for self-relatedness. Application to a real data set revealed that some SNP filtering may still be necessary, for the exclusion of SNPs which did not behave in a Mendelian fashion. A simple graphical method (a ‘fin plot’) is given to illustrate this issue and to guide filtering parameters.

We provide a method which gives unbiased estimates of relatedness, based on SNPs assayed by GBS, which accounts for the depth (including zero depth) of the genotype calls. This allows GBS to be applied at read depths which can be chosen to optimise the information obtained. SNPs with excess heterozygosity, often due to (partial) polyploidy or other duplications can be filtered based on a simple graphical method.