I see a lot of studies on GWAS not filter out for linkage disequilibrium or even make the slightest mention of it. Why is this the case? I would imagine that you want to keep SNPs that are only in linkage equilibrium to promote independence (and besides, without it an additive model makes no sense)
One possible reason to not filter for linkage disequilibrium is to produce peaks/hits with multiple SNPs, thereby clearly indicating a region of a causal genotype. For example, in the manhattan plot below, each point represents a SNP, the higher it is in the plot the more it relates to the phenotype. We see that in each of the peaks multiple points are significant due to linkage disequilibrium. If instead we had pre-filtered all of these points out then a peak has a greater choice of representing some type of error in data collection, since there is some probability that there is some error in each SNP, but not much chance of the error occurring in all the SNPs of one peak.
I am unclear why not pruning for linkage equilibrium would prevent an additive, or any model from working. After all a GWAS is just a series of regressions between the genotypes of one SNP and one phenotype. In this single SNP frame of reference the LD does not affect the calculation of the betas. Zooming out, all of the significant SNPs should group together because of the LD, thereby indicating only a few regions and not causing an increase in the false error rate.