So, if these traits are in our genes, how come we can't find them there?
The article does a great job at identifying the possible ways to find the "hidden heritability". Here they are, in my own words:
1. Look at more DNA spots
There is a long way between the million or so DNA bases covered by current microarray chips and the whole human genome. Because of linkage disequilibrium, i.e., DNA's propensity to be cut and inherited in large chunks, and not small pieces, you can often tell the value of a marker by looking at nearby markers. But, still, you don't really know until you look. So, denser microarrays, or even whole genome sequences may uncover some of the hidden heritability.
2. Look at more people
Associations between traits and genes are established by statistics. To find a weak association, or an association between a not-so-common variant and the trait in question, you need a large sample. So, if the hidden heredity is hidden away in markers that are beyond your statistical power, you can simply increase this power: sample more people.
3. Look at copy-number variations (CNVs)
Any two individuals don't just have single-letter differences, but also structural changes, where an individual may have more or fewer copies of entire chunks of DNA. So, by looking at single nucleotides you are examining one source of human variation, but missing another chunk of it that may as important.
3. Study gene-gene interactions
Genes form complex networks of interaction. If you flip a SNP from C to T, you don't always get the same effect on the phenotype. This flip may increase, decrease, or leave unaffected, your risk for a disease, depending on what other genes you have. This epistatic interaction of genes makes it difficult to detect associations. It's a lot easier to study the individual effects of 2N alleles at N genes than it is to study the effects of 2N possible combinations.
4. Don't trust heritability estimates
What if inherited conditions thought to be genetic aren't really genetic, because of epigenetic modifications of gene expression, or shared environments (e.g., in the womb) that aren't accounted for?
5. Don't trust diagnoses of conditions
If you want to find a correlation between a gene G and a trait T, you'd better be sure what T actually is. If it's a whole set of different behaviors, conveniently bundled into a condition T (such as schizophrenia), then you're in trouble, since each of these conditions may have its own causative agent. Many major diseases may be caused by more than one underlying condition, with a different genetic background. So, if you are seeking to find the common thread between people with trait T, you might not find it because there is no common thread!
My guess is that the bulk of the missing heritability is to be found in three sources:
- Epistasis. Humans are makeshift accidents of evolution, and not well-engineered machines where the effects of individual components have been designed to work well in isolation, shielding other components from their effects. Most things in the human body affects most other things, either directly or indirectly. There are, of course, some master switches which do have individual pronounced effects (e.g., giving you lactose tolerance or breast cancer), but these are the exception. Normal variation is due to how well-put together the individual is, and not so much in the individual components.
- Gene-Environment interactions. Just as the effect of genes depends on the joint presence of other genes (epistasis), so it depends on the presence of particular environmental influences. Imagine an allele that shows zero association with a particular trait. Does this mean that it has no influence on that trait? No, since zero association is perfectly compatible with even a huge influence, provided that a positive influence under one type of genomic or environmental background is balanced by a negative influence under another.
- Very low frequency (family) alleles. Natural selection faces a constant battle against the continuing re-emergence of less-than-optimal alleles. Children are almost certainly on average genetically worse than their parents, since parents have survived and reproduced, while children's ability to do so is yet to be tested (*) While human variation is -in part- due to long-lived alleles that have braved the generations, quite a lot of it is due to recent alleles that arose in families, and have not had the time to spread to many bodies. It is these extremely rare family alleles and allele combinations that population studies can't quite capture.
Some related posts on the limits of genome-wide association studies: on intelligence, on height and body mass index, and on CNVs.
(*) Incidentally, this is why the population replacement rate is more than 2 children per woman.