Analytic approaches to twin data using structural equation models by Fruhling V. Rijsdijk and Pak C. Sham in 2002:
The classical twin study is the most popular design in behavioural genetics.
After saying how widely used they are, the paper talks about how twin studies work. It's pretty up front about why they don't work. The reasons they don't work are well known (and basically ignored anyway):
Assumptions of the twin method
They know they are making some assumptions. That’s not controversial. That’s interesting because many people who discuss this with me, and favor the power of genes, try to deny those assumptions exist. They will debate that because they are ignorant and the field hasn’t highlighted these assumptions enough in their public-facing material (which is no accident).
• Gene–environment correlations and interactions are minimal for the trait.
This assumption is, broadly, false for interesting or complex traits. Gene-environment interactions are everywhere. That's a key point that ruins ~all the twin studies. (More on this below.) It's not the only big problem though.
• Matings in the population occur at random (no assortment).
This assumption stood out to me because it’s so blatantly false. Mating isn't even random for animals. However, you may be able to get approximate answers anyway, so I’m not going to focus on this.
Gene–environment interaction (or genetic control of sensitivity to the environment) refers to different genotypes responding differently to the same environment or some genotypes being more sensitive to changes in environment than others.
E.g. suppose hypothetically that genes have some control over math ability. That results in the (school) environment responding differently to those genes by e.g. giving more praise and higher test scores for people with the genes that cause better mathematical ability. So if genes were involved in math ability, there would be major gene-environment interactions.
It's the same story with ~everything else. Does height help you win at basketball? Sure. But there are plenty of gene-environment interactions, like coaches who see that you're tall, or see that you hit more shots, and thus encourage you to pursue basketball more than they do for a short person who makes fewer shots. So the environment responds to you differently according to your height genes.
Any times genes have an effect that people notice, then people will respond to it. So the "environment" (which includes other people) is responding differently based on genes. So gene-environment interactions are basically only avoided when genes don't cause any variation that anyone notices. (Non-variation would be a group of people who all have one head. Genes caused them to have one head rather than zero or two. But because there is no variation in the trait, the environment can’t respond in varied ways to that trait.)
And you can't just look at gene-environment interactions which are directly on-topic. E.g. a math anxiety paper can't only look at math and anxiety stuff. You also need to consider e.g. childhood and parenting behaviors. A gene for infant smiling would be noticed by parents and result in different treatment, which could lead to better or worse results in general later on, including regarding math. Or it could be more complicated, e.g. maybe less infant smiling could result in more alienation from the parent which could tend to result in being better at math. Maybe people who have better relationships with their parents tend to end up more social, have more friends, and do, on average, more social climbing and less intellectual stuff.
The methods used by twin studies would claim that infant smiling gene as indicating partial genetic control over mathematical ability, even though it has nothing directly to do with math, and it could have dramatically different consequences, or no consequences, in a different culture. They would then publish about how genes partially control our lives, which they have proven yet again (using the same methods as all the previous studies with the same systematic weakness shared by those studies).
Here is an example of one twin study, of many, which is false and should be retracted because of the gene-environment interaction problem:
This paper is notable for citing a hostile satire (cite 30) as if it were serious research that they got some of their claims from. By “hostile” I mean that the satire article suggests that math anxiety research is a joke which does not merit funding. The paper also uses (as is typical) very-low-quality data (including getting some of their data years apart), e.g. badly designed surveys (even well designed surveys are highly problematic!) and proxies that don’t make sense (e.g. their idea of “number sense” is dot-quantity-estimation accuracy in 0.4 second flashes done 150 times). The paper also has carelessness and imprecision throughout. I discuss that paper, and its many flaws, at length in this video.
The paper authors are aware of the gene-environment problem. Near the end they say:
The current investigation presents some limitations. As well as relying on the methodological assumptions of twin design (see Rijsdijk & Sham, 2002 for a detailed description) (47), the models employed in the current investigation do not specifically account for gene–environment interplay. One possibility is that the observed genetic association between MA, attitudes and performance may operate via environmental effects that are correlated or interact with genetic predisposition. For example, children with a genetic predisposition towards experiencing difficulties with mathematics may develop a greater vulnerability to negative social influences in the context of mathematics, such as negative feedback received from teachers or parents on their effort and performance, which in turn may lead to greater feelings of anxiety towards mathematics (56). This has the potential to generate a negative feedback loop (7) between performance, motivation and anxiety - that is potentially a product of interacting inherited and environmental factors. The present investigation, including one time point for each measure of mathematics anxiety, attitudes and performance does not allow us to establish the direction of causality between the observed associations. Longitudinal genetically informative studies, integrating multiple measures of mathematics attitudes, anxiety and performance are therefore needed.
They know perfectly well that their research is inadequate to reach the conclusions they reached. They published anyway. The whole field acts like that in general. So they conclude:
Our findings of a shared, likely domain-specific, etiology between these mathematics-related traits provide a seminal step for future genetic research aimed at identifying the specific genes implicated in variation in the cognitive and non-cognitive factors of mathematics.
Instead of carefully thinking about the gene-environment interaction problem, and what to do about it, they simply ignore it and call their paper “seminal” anyway. They have no solution to the problem but they want to be scientists who publish papers with important conclusions, so they are dishonestly evading reality and lying to the public.
The field in general is like this. There are no sophisticated analyses of why gene-environment interactions would be minimal nor any counter-arguments to my fairly simple reasoning about why they’d be ever-present. They’re just making big, false claims without serious regard for what’s true. That’s the “social sciences”.