Quality GL entries in vcf file

Question

I have a vcf v4.2 file with structural variants, the 8 columns describing the variant are clear, but in the genotype information I got confused by values of GL entries. In the vcf specification they mention that GL are likelihoods of the individual genotypes, but as far as I am concerned, likelihood should be a number between 0 and 1, therefore I am suprised to see negative numbers. Then I thought that it might be log-likelihood, but then it's strange that the higher the number is the better. Here is a sample of 5 variants with various called genotypes

...       GT:GL:GQ:FT:RCL:RC:RCR:CN:DR:DV:RR:RV   0/1:-22.4949,0,-4.49485:45:PASS:20:1:11:0:1:4:0:0
...       GT:GL:GQ:FT:RCL:RC:RCR:CN:DR:DV:RR:RV   0/1:-3.1888,0,-43.9892:32:PASS:16:26:13:2:9:2:0:0
...       GT:GL:GQ:FT:RCL:RC:RCR:CN:DR:DV:RR:RV   0/1:-0.190635,0,-49.2888:4:LowQual:26:51:31:2:10:1:0:0
...       GT:GL:GQ:FT:RCL:RC:RCR:CN:DR:DV:RR:RV   0/0:0,-1.01435,-75.899:10:LowQual:18:54:26:2:14:1:0:0
...       GT:GL:GQ:FT:RCL:RC:RCR:CN:DR:DV:RR:RV   1/1:-19.198,-1.5031,0:15:PASS:70:0:58:0:0:5:0:0

The vcf file was generated by delly genotyper. I followed their recommendations for germline SV calling. However, negative likelihoods are even in the vcf specification, therefore it seems that it's not something delly specific.

So, what exactly is GL in vcf files? And how do they relate to other entries GP (genotype posterior probabilities, not in the file by delly) and GQ (conditional genotype quality)?

Answer 1

The VCF spec clearly states that these are indeed log likelihood values:

• GL : genotype likelihoods comprised of comma separated floating point log10-scaled likelihoods for all possible genotypes given the set of alleles defined in the REF and ALT fields. In presence of the GT field the same ploidy is expected and the canonical order is used; without GT field, diploidy is assumed. If A is the allele in REF and B,C,... are the alleles as ordered in ALT, the ordering of genotypes for the likelihoods is given by: F(j/k) = (k*(k+1)/2)+j. In other words, for biallelic sites the ordering is: AA,AB,BB; for triallelic sites the ordering is: AA,AB,BB,AC,BC,CC, etc. For example: GT:GL 0/1:-323.03,-99.29,-802.53 (Floats)

With log-likelihood values, the higher the number, the better the value. So -2 is better than -3.