Modeling the genetic components of variance. (a, b) The idea of the multifactorial liability-threshold model is, first, that the actual discontinuous distribution of risk (a) (estimates given for schizophrenia risk to monozygotic twins (MZ) and first and second degree relatives of affected people) can be modeled as a continuous distribution of 'liability' (b). Second, at the extreme end of the normal distribution of 'liability', the cumulative genetic burden of risk alleles suddenly passes a tipping point (from n alleles to n + 1 alleles), triggering pathogenicity (b). (c) Increased risk to relatives can be modeled with a distribution of risk allele load that is shifted to the right. If n is small (0 or 1, for example), then the idea of a threshold of burden makes sense (for example, when there are dominant or recessive alleles). If n is supposed to be in the hundreds or even the thousands, this scenario becomes rather fanciful.

Interpreting positive GWAS signals. (a) GWAS can point to chromosomal loci that may harbor causal variants. (b) The associated SNP will act as a marker of multiple additional common variants in an LD block. The marker SNP or any of these other common variants could be the causal variant. The very low odds ratio across the population might represent a tiny effect of one of these variants in every individual or a large effect that arises only in the context of some rare mutation. (c) Alternatively, at least some common SNP signals could actually be tagging rare variants of large effect in the population, which are in strong LD with it (stars). If these occur, by chance, more prevalently on one haplotype than on another, this will lead to a slightly increased frequency of one allele in cases when compared to controls (that is, an association signal).