0: Unrelated individuals
In a previous post we talked about how GRM is calcuated in Proferssor Yang Jian’s landmark 2010 NG paper. It is for unrelated individuals, where it is assumed that the average relationship between all pairs of individuals in 0 and the average relationships of an individual with itself is 1 (see the last paragraph of the Statistical framework of the ONLINE METHODS section). The relationship of an individual with itself provides an unbiased estimate of the inbreeding coefficient (F)， with a mean of 1+F and variance of 1 when F=0. F for each locus is one minus the observed frequency of heterozygotes over that expected from Hardy–Weinberg equilibrium. When more He is observed than expected, F<0, outbreeding; when less He is observed than expected, 0<F<1, inbreed. Then the observed equals the expected, F=0, thus E(1+F)=1. Therefore the higher number in GRM on the diagnols for an individual, the higher degree of heterozygosity.
There is a slightly differen flavor for this version:
–make-grm-alg 0 The default value is 0, and the GRM is calculated using the equation sum{[(xij - 2pi)(xik - 2pi)] / [2pi(1-pi)]} as described in Yang et al. 2010 Nat Genet. If the value = 1, the GRM will be calculated using the equation sum[(xij - 2pi)(xik - 2pi)] / sum[2pi(1-pi)].
For my data it does not make a big difference.
1: Inbred data
On the same page as the usual --make-grm, there is an option called --make-grm-inbred Make a GRM for an inbred population such as inbred mice or inbred crops. Note the difference between inbred data and family data. Inbred data is usually referring to low, very low degree of heterozygosity, which is usually a result of generations of inbred. Whereas family data still have a good amount of heterozygosity. This definition focus on the pedigree. In the Citation part, two papers were mentioned, Yang 2010 NG and Yang 2011 AJHG (the GCTA paper). However when I searched for the word inbred in both papers, no hits. Therefore theoretically, I do not know what happens when you use this option. However, I did compapred the two GRMs resulted from the two options with the same input data, let’s call them GRM and GRM_inbred, and at least for my data, GRM = GRM_inbred * 2.
2: Family data.
GCTA offers an implementation of this method proposed by Zaitlen et al. 2013 PLoS Genetics. This is their description of this method:
…estimate pedigree-based and SNP-based h2 simultaneously in one model using family data. The main advantage of this method is that it allows us to estimate SNP-based h2 in family data without having to remove related individuals.
Their documentation is great. Basically you make a grm with --make-grm, and then you create another grm based on this grm using --make-bK. This sets the off-diagnals (relationships) that are lower than user-defined threshold (i.e. unrelated) to 0. Then this GRM is about related individuals only. You can inclulde both matrices in your model as random effect if you have a mixed of unrelated (the first GRM) and related (the second GRM). For family data where everyone is related, you could just use the second GRM.