Nothing is irrelevant: Strong inferences, race differences, and causal g

One of the more arcane arguments in the race-IQ debate, concerns the correlation between the Black-White mean difference and heritability estimates within both Black and White populations. The argument from the hereditarian side goes something like this: Aptitude tests differ in their heritabilities; some tests are more environmentally influenced and other tests are more genetically influenced. A genetic hypothesis would predict that tests found to be more heritable for Blacks would also be more heritable for Whites and that the Black-White difference would correlate positively with indexes of heritability (and negatively with indexes of environmentality). In contrast, most formulations of the environmental hypothesis predict that the Black-White difference would correlate negatively with indexes of heritability (and positively with indexes of environmentality). A number of studies, using sibling correlations (Jensen, 1973 pg. 107-117; Jensen, 1998) and inbreeding depression (Jensen and Rushton, 2010) as indexes of heritability, have borne out the genetic hypothesis’ prediction. Just as the highly heritable differences within populations correlate with genes (the correlation being the square root of the heritability estimate), the between population difference also correlates with genes within populations. This argument has been made a number of times. Jensen spent several pages on it in his 1973 book, Educability and Group differences (pg. 113-177) and mentioned it briefly in The G-factor (pg. 471-472). Michael Levin elaborated on it in Why Race Matters and mentioned it elsewhere. For example, in “The Race concept: a Defense,” he argued:

There are also apparent heritable differences in psychological functioning, particularly in phenotypic IQ, a valid, unbiased proxy for intelligence (Neisser et al., 1996)…. While systematic review of the question of genetic factors in these discrepancies is inappropriate here (see Hocutt & Levin, 1999; Levin, 1997), two lines of evidence support genetic involvement firmly enough to warrant retaining broad racial categories pending further inquiry. The first is the correlation of the size of white/African-American mean differences on IQ subtests with (within-group) subtest heritability, a result difficult to explain by means of environmental variables, for these variables would have to produce larger effects as sensitivity to environment dwindles.

More recently, Rushton has brought this argument to the fore in The rise and fall of the Flynn Effect as a reason to expect a narrowing of the Black–White IQ gaps. Previously, Rushton and his co-authors extended the argument globally. In Genetic and environmental contributions to population group differences on the Raven’s Progressive Matrices estimated from twins reared together and apart, they reason:

In 55 comparisons, group differences were more pronounced on the more heritable and on the more environmental items (mean rs=0.40 and 0.47, respectively; Ns=58; ps<0.05). After controlling for measurement reliability and variance in item pass rates, the heritabilities still correlated with the group differences, although the environmentalities did not. Puzzles found relatively difficult (or easy) by the twins were those found relatively difficult (or easy) by the others (mean r=0.87). These results suggest that population group differences are part of the normal variation expected within a universal human cognition.” (Rushton et al., 2007.)

The environmentalist response has been varying. Some, like Flynn and Nisbett, tried to create a Reductio ad absurdum by showing that heritability estimates were also positively correlated with the secular increase. But this attempt has met with failure (Rusthon and Jensen, 2010; see Flynn’s concession in The spectacles through which I see the race and IQ debate). More recently, it has been argued that the positive correlation is a function of multi-collinearity. The reasoning goes: Within populations, g and heritability correlate, so between population differences in g necessarily also lead to a correlation with heritability. Revelle et al (2011), for example, make this case:

Related to this is the so – called “ Spearman hypothesis, ” which claims that, if factor loadings on a variable are correlated with heritability and also with between – group
differences, then the between – group differences must be genetic. A simple thought
experiment shows why this is not true. Consider variables measuring overall height.
Of these, some will be better measures of height than others, perhaps because of
reliability issues, perhaps because the others are less valid. In this case the factor loadings on the general factor of height will be correlated with their heritability values. In addition, those measures that represent the better measure of height will show the biggest between – group differences in height. Indeed factor loadings, heritabilities, and between – group differences will be highly correlated, even though the between group difference is due to nutrition.” (Revelle et al., 2011. Individual differences: An up to date historical and methodological overview)

In A genetic origin of Black-White mean IQ differences? Weak inferences based on ambiguous results, Kan (et al.) makes this same case, just more elaborately. As he illustrates, a environmentally induced g difference would lead to the found correlation just as a genetically induced differences would.

Naturally, for this explanation to hold, one must posit g differences. Now, one would think that the existence of g differences was established. The evidence for them is rather strong. It’s difficult to explain the consistent correlations between IQ differences and g-loadings, without positing them (1). Yet, not infrequently, their existence is challenged; for example, Malda et al. (2010) recently conclude:

Our study fits in a series of studies that have given arguments to question the validity of [Spearman’s hypothesis]. The first type of argument focuses on the statistical analyses applied to test SH that are said to be too lenient (see Dolan et al., 2004). The second type of argument concerns the confounding of cognitive complexity with cultural complexity in current tests of SH. A high loading on a general cognitive ability factor does not merely imply a high cognitive complexity, but usually goes together with a high cultural complexity. Confirmations of SH that have been reported in the literature (e.g., Hartmann et al., 2007; Lynn & Owen, 1994; Te Nijenhuis & Van der Flier, 1997) may be based on this confounding in the data. We confirmed findings by Helms- Lorenz et al. (2003) which indicated that SH can only be tested when cultural complexity and cognitive complexity are both varied independently. Data from the present study and from Helms-Lorenz et al. show that when these types of complexity are unconfounded, SH is not supported. (Rugby versus Soccer in South Africa: Content familiarity contributes to cross-cultural differences in cognitive test scores.)

In light of the objections to the existence of g-differences, the correlation between heritability and group differences is not without meaning. From them we can infer g-differences in a way that we can not from the correlation between g-loadedness and group differences. Now, elsewhere Kan (2011) shows that the correlation between g-loadedness and heritability implies that g, within populations, is partially causally genetic. This is illustrated in the figure below:

A statistical model of g, within groups, predicts no correlation between heritability and g-loadedness. It follows that a statistical model of g, between groups, predicts no correlation between heritability and g-loadedness. So the correlation between heritability and group differences in IQ implies that there must be differences in causal g. The correlation would occur if:

1) there is, within groups, a causal g, which is partially genetic
and
2) groups differences are, in part, differences in this causal g, whether this difference arose due to genetic or environmental factors or a combination thereof

Of course, one would think that the existence of causal g differences was established. The evidence for them is rather strong, too. But… So, what does all this mean? While the correlation between the Black-White mean difference and heritability estimates does not allow for a strong inference about genetic differences, it does allow for one about causal g differences. Which is important in its own right.

1) Dolan (2000), Lubke et al. (2001), Dolan et al. (2004), Ashton and Lee (2005), maintain that the method of correlated vectors (MCV) can produce spurious results. As Dolan et al. note, while MCV established Spearman’s correlation, spearman’s correlations is necessary but not sufficient to establish g-differences, let alone that most of the differences between groups are due to g-differences (i.e. Spearman’s hypothesis). Alternatively, te Nijenhuis et al. (2007) state:

“The fact that our meta-analytical value of r=−1.06 is virtually identical to the theoretically expected correlation between g and d of −1.00 holds some promise that a psychometric meta-analysis of studies using MCV is a powerful way of reducing some of the limitations of MCV…Additional meta-analyses of studies employing MCV are necessary to establish the validity of the combination of MCV and psychometric meta-analysis. Most likely, many would agree that a high positive meta-analytical correlation between measures of g and measures of another construct implies that g plays a major role, and that a meta-analytical correlation of −1.00 implies that g plays no role. However, it is not clear what value of the meta-analytical correlation to expect from MCV when g plays only a modest role.” (Score gains on g-loaded tests: No g, 2007)”

In the case of the Black-White difference in the US, the meta-analytic correlation is approximately 0.6, so, going with te Nijenhuis et al. it seems reasonable to infer that g plays some role in the difference.

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41 Responses to Nothing is irrelevant: Strong inferences, race differences, and causal g

  1. Kees-Jan Kan says:

    Hey Chuck,

    Thanks for bringing my dissertation under attention! 🙂 Also thanks for the nice discussions here on the blog!

    One remark here. You write “While the correlation between the Black-White mean difference and heritability estimates does not allow for a strong inference about genetic differences, it does allow for one about causal g differences.” I don’t fully agree with the latter part. I would say that it is the vector correlation is consistent with causal g differences, but that one cannot draw inferences from it. One can only draw conclusions by comparing different models using structural equation modeling (which allows you to test the models statistically). Also, one must consider other (counter) evidence. g theory does not explain the positive relation between heritability coeffients and cultural load, for example.

    In the simulations in my dissertation (Chapter 7) there is also a correlation between g loadings and heritabilty, wheres there is no causal g. A mean group difference on g (the statistical one) would not be caused by g, because there is no causal g!

    Thanks again and kind regards,
    Kees-Jan

    • Chuck says:

      Kees-Jan,

      Thanks for the comment. Your dissertation was excellent by the way.

      1) As for biological g theory and cultural loadings, it seems to me that you are making a “weak inference based on ambiguous results.” For one, it has not been consistently found that “cultural loaded” tests are more heritable than “culturally reduced” tests. Take, for example, Davies et al. (2011) who found a heritability of 0.4 for crystal tests and a heritability of 0.51 for fluid tests based on matrix wide SNP similarity (N = 3511 versus your combined N = 7852 in section 3.2.1.). More importantly, it’s not clear that the correlation between g, heritability, and cultural loadedness is actually a problem for g-theory. G-theory, as you note, proposes that individual differences in IQ are largely due to differences in causal g which are largely due to (additive) genetic differences. Here was Jensen’s most recent statement on his version:

      “Each individual comes into the world possessing all of the de facto and potential behavioral variance that exists in any large population in the world. This latent matrix consists entirely of the genetic and extra genetic material composing the still developing organism, i.e., the individual human being. Included in this developmental process are the roots of the behavior that becomes recognized as psychometrc intelligence, specifically the g factor. Information gained through sensory contact with the environment is processed and brought to bear on further sensorimotor exploration of the surrounding environmental stimulation. The rate and asymptote of mental development are conditioned by genetic factors which account for an estimated 70 to 80% of the total population variance in psychometric g. (Jensen, 2011. The theory of intelligence and its measurement)”

      Now, in terms of “cultural loadedbess” and heritability what would Jensen’s model predict? Conceptualizing cultural loadedness as rarity of information (Jensen, 1973, 1976), and assuming that our population is heterogeneous with respect to exposure to this information, we would predict, controlling for task complexity of course, that cultural loadedness is negatively correlated with heritability, as heterogeneity of exposure introduces environmental variance. Granted. But rarity of information, and cultural loaded in this sense, correlates with “information loadedness” or the amount of prior information that a task requires. In terms of “cultural loadedness” qua informational loadedness, what would this model predict? One might expect no correlation or a slight negative correlation (as you suggested when discussing investment theory), but Jensen’s model above has a compounding aspect (” Information gained through sensory contact with the environment is processed and brought to bear on further sensorimotor exploration”) that mimics from the inside out the effect one would get from an active g-e correlational model. It does this, because it’s a genetic amplification model. Robert Plomin characterized these models accordingly:

      “Genes that affect IQ make only a small contribution to phenotypic variance at first, but their effects are amplified throughout development. Suppose, for example, that genetic differences among infants are responsible for differences among them in the formation of dendritic spines during the first few years of life and that the complexity of dendritic spines is related to information processing capabilities. At first, these structural differences do not have a chance to cause function differences because so little information has been processed at this point. Gradually, the functional differences are amplified as more and more information is processed by children. If we were to measure differences in categorizing ability early in childhood, the genetic differences among children due to the complexity of dendritic spines would contribute a negligible amount of variance to observed variability among children in categorization ability. The differences snowball as development proceeds, so that a study of the children when they are older will show more genetic variance.. (Plomin, 1987. Development, genetics, and psychology)”

      Now, if we argue that heritability increases due to genetic amplification our expectations change. Exposure to information would be directly related heritability. Cultural loadedness qua Information-loadedness then would be correlated with heritability (and, in Jensen’s model, if I’m reading it correctly, the ability to acquire new information). Now, this positive correlation between heritability and cultural loadedbess” qua informational loadedness would be attenuated by the negative one between heritability and rarity. But finding an overall positive correlation might not be surprising and until rarity and informationality (my neologism) are disentangled, it would be difficult to interpret the results.

      What about “cultural loadedbess” and g-loadedness? Well, since we are proposing an (endogenous) amplificatory effect, we might expect more informationally loaded tests to be more g-loaded, controlling for rarity. Consider Plomin’s statement: “Gradually, the functional differences are amplified as more and more information is processed.” If g differences were due to differences in “the complexity of dendritic spines” or “neural connectivity” or “neural Oscillation” or whatever exotic entity biological g-amplification-theorists propose, we might expect more informationally loaded tests to be more g-loaded, as the differences are amplified with information.

      So, again, it’s not clear that the correlation between g, heritability, and cultural loadedness is actually a problem for g-theory, or at least a g-amp-theory. But you could convince me otherwise with one of your fancy models, if you get around to it.

      2) As for g-e correlational models in general, Davies et al (2011) concluded that their estimate represents a lower bounds estimate of g’s narrow heritability; to the extent that that inference, specifically about additive genetic variance, is correct, any model which rests on active g-e correlations is disconfirmed. Do you disagree with Davies et al (2011)’s conclusion? See also: “A commentary on “Common SNPs explain a large proportion of the heritability for human height” by Yang et al. (2010): What about G×G and G×E interactions?” The estimates derived from Vissher’s methodology is clearly thought to be in exclusion of g-e correlations.

      3) As for heritability and group differences. Ok. I didn’t read fully your 7th chapter. I’ll have to think about that some more.

      • JL says:

        I came across the following in Jason Major’s master’s thesis:

        In addition to the overestimation of how much variance g accounts for in cognitive test batteries, it has been found that the use of single-factor models for general cognitive ability (with PCA or otherwise) gives undue weight to crystallized ability subtests (Ashton & Lee, 2005; Kvist & Gustafsson, 2008). These two research groups concluded that the high g loadings of crystallized subtests in batteries such as the Multidimentional Aptitude Battery (MAB) and Wechsler Adult Intelligence Scale-III (WAIS-III), are not due so much to the overrepresentation of verbal subtests, as the fact that fluid ability subtests are more narrowly-defined tasks with more unique variance, leaving crystallized subtests to represent most of the common variance attributed to g.

        So, if the more culturally loaded Gc subtests are more highly g-loaded than the Gf subtests and thus display a higher heritability, the reason may be that Gc tests are overrepresented in the test battery, or that Gf tests have more unique variance, or that PCA or other inadequate methods have caused the g-loadings of the Gc subtests to be overestimated.

      • JL says:

        Many studies suggest that PCA is not a good method for estimating g, but both the original Davies et al. study and the Chabris et al. study that replicated their results used PCA. As a lack of statistical power is a big problem in genomic studies of massively multigenic traits like intelligence, it seems a bit stupid to piss away some of that power by using PCA.

        • Chuck says:

          JL, by your reading, does Visscher’s method allow for a true estimate of narrow heritability? Or are we still “lost in correlations”? Maybe I’m falsely assuming that there’s a conflict between A and COVGE. In principle, COVGE could take on a negative value and so wouldn’t be, in effect, squeezed out by high A + E. I don’t know. Maybe I’m not making sense here. Let me know your thoughts on this.

      • Kees-Jan Kan says:

        Hey Chuck,

        You wrote; “Again, it’s not clear that the correlation between g, heritability, and cultural loadedness is actually a problem for g-theory, or at least a g-amp-theory.” Yes, that’s what I also concluded (see Discussion and Appendix B) (not infrred ;). It’s not a problem for a g-theory per se; it’s a problem because current g theories are not specific enough. That’s why I advance explicit (preferably longitudinal) GxE covariance modeling. ‘Amplification theory’ in itself is also not specific enough; we need to model how this amplification occurs.

        Greets and thanks for your quick and thorough response,
        Kees-Jan

  2. Kees-Jan Kan says:

    Oh and g loadings maybe affected by the kind of tests you put in your analysis to some extent, but subtests’ heritabilities should not.

    KJ

    • Chuck says:

      Re: “It’s not a problem for a g-theory per se; it’s a problem because current g theories are not specific enough.”

      In replying, I was just trying to come up with a semi-plausible scenario for correlations which do seem rather counter-intuitive from a g-theory perspective. (I’m a dilettante, here, so proposing semi-plausible scenarios that reconcile contradicting results with my pet models is as far as I go.) Anyways, my statement above — concerning g, heritability, and cultural loadedness — wasn’t too clear. Let me restate it for my future reference — to see how far off I was (below).

      Anyways, thanks for commenting.

      ……
      a) Let’s define biological g models as all models which propose that statistical g is a result of some latent biological variable, which we will call “biological g.” Jensen (2011), for example, offers his theory of biological g:

      “Intelligence is the periodicity of neural oscillation in the action potentials of the brain and central nervous system (CNS)

      Operationally this hypothesizes that the typical standard psychometric measures of g are correlated with the oscillation rates of the brain and CNS as measured by various Reaction Time (RT) and Inspection Time (IT) paradigms. (See Jensen, 2006). But first a caution about possibly misleading inferences that could result from the seeming simplicity of this definitional theory, in which the term periodicity is absolutely more basic than any of the usual definitions of ‘intelligence.’ It decidedly should not be confused with Mental Age, IQ, the g factor, either fluid or crystallized intelligence, or any other psychometric test score, principal component, or factor score. Rather, the periodicity of the CNS is hypothesized as a psychophysically-derived measure….”

      b) Biological g models tend to propose that differences in biological (and with it statistical) g are due to mostly additive genetic effects. Let’s call the genetic effects underlying our theoretical biological g, “true genetic g” and differentiate this from the genetic effects underlying statistical g.

      c) When it comes to additive genetic models, the most plausible explanation for the age related increase in the heritability of statistical g is genetic amplification. So (by b) biological g models tend to involve genetic amplification models. They tend to involve some mechanism by which “true genetic g” can explain little variance in early childhood and a great deal of variance by adulthood.

      d) As you note, Biological g models tend to explain g-loadedness by both complexity theory and investment theory. These theories can’t explain well the g-loadeness and heritability of informationally loaded subtests (e.g., vocabulary). But Jensen’s theory above seems to be, what we might call, an investment model with compounding interest. The compounding aspect — or how “Information gained through sensory contact … is processed and brought to bear on further sensorimotor exploration” — can be seen as a “multiplier effect” on the neural level. The richer the neural network, the more they can absorb. The more they absorb, the richer.

      e) To be honest, I’m not sure what to make of Jensen’s statement in (d). But imagine if we did propose some type of neural multiplier effect to account for genetic amplification. If so: information amplifies the effects of true genetic g differences, resulting in the increase in heritability of statistical g with age and in a neural multiplier effect, which would work similarly to a social one; tests that are more informationally loaded tap into neural networks for which there has been more neural multiplier effect; unsurprisingly, these are found to be more g loaded and heritable.

    • JL says:

      Oh and g loadings maybe affected by the kind of tests you put in your analysis to some extent, but subtests’ heritabilities should not.

      That makes sense, but what if the g-loadings are lower for Gf tests because they have more test-specific variance than Gc tests? Couldn’t that cause Gf tests to be less heritable? Wouldn’t it make more sense to look at the heritabilities of Gc and Gf rather than individual tests? As Chuck pointed out, Davies et al. 2011 estimated that Gf is more heritable than Gc.

      Then again, “cultural loadedness” seems to be a somewhat arbitrary concept. Raven’s matrices, for example, is supposedly “culture-reduced”, yet it’s been influenced by the Flynn effect more than most Gc tests.

  3. Kees-Jan Kan says:

    Hey, thanks for the further discussion (I really appreciate it!)

    In the scenario above, you would expect that “the periodicity of neural oscillation in the action potentials of the brain and central nervous system (CNS)” is higher g-loaded (actually you expect the standardized g-loadings to approach 1) and higher heritable than crystallized abilities. If this periodicity is intelligence the heritability estimate of this periodicity would be the heritability of intelligence. Personally, I have strong doubts whether this heritability is as high as the heritability of crystallized abilities, even if one would correct for differences in reliability.

    Amplification of genetic effects does not (necessarily mean) heritability goes up (because the magnitude of environmental variance or changes therein is not made explicit). As you know, heritability is a relative measure. Amplification of genetic effects results in heritability going up if environmental variance 1) stays the same, 2) diminishes or 3) increases less than the genetic variance. Again, hypotheses about genetic AND environmental effects should be modeled explicitly (using results from the method of correlated vectors doesn’t help in the discussion, for example). Van der Maas’ mutualism model provides an excellent tool to do this this formally: one cannot only model mutualistic interactions in the model but also general effects and in many ways, also without hypothesizing any mutual relationships.

    I managed to establish positive relationships among g-loading, heritability coefficients and cultural load using a general effects model (which leads to amplification of genetic effects over time), but only by making additional assumptions. For example, I always needed at least 2 latent variables (capacities; g and another one), and in which there were direct and indirect genetic effects on the second factor. The reason why tests that estimate the second variable had higher estimated narrow sense heritability coefficients than tests that estimate the first variable (hence g), was that this coefficient was overestimated, because it included the indirect effects. That is, h2 was actually h2+covariance-effects. Therefore, in order to estimate the additive genetic effects of the variables of intelligence the pathways should be modeled correctly in the statistical behavior genetic (SEM) model.

    For the future: I think there is even a more important question than the question ‘what is g?’ and this question is: What is (the realist interpretation of) a g-loading of each intelligence subtest (or even each regression coefficient in the model)? You rightly discuss this under e)

    In any case, a developmental perspective is more than welcome!

    Greetz,
    Kees-Jan

    • Chuck says:

      “The reason why tests that estimate the second variable had higher estimated narrow sense heritability coefficients than tests that estimate the first variable (hence g), was that this coefficient was overestimated, because it included the indirect effects. That is, h2 was actually h2+covariance-effects. Therefore, in order to estimate the additive genetic effects of the variables of intelligence the pathways should be modeled correctly in the statistical behavior genetic (SEM) model.”

      Kees-Jan,

      You never directly addressed one of my questions above:

      “As for g-e correlational models in general, Davies et al. (2011) concluded that their estimate represents a lower bounds estimate of g’s narrow heritability; to the extent that that inference, specifically about additive genetic variance, is correct, any model which [largely] rests on active g-e correlations is disconfirmed. Do you disagree with Davies et al (2011)’s conclusion?”

      But maybe you’re answering it here. Would you say that Visscher’s method doesn’t allow for a (true) lower bounds narrow estimate (of statistical g) and that SEM or some other method is needed for this? I guess I’m more interested in the heritable of g (G, not covGE) than in its biological reality; though, the two issues are related.

  4. Kees-Jan Kan says:

    Hey Chuck,

    Sorry I didn’t answer your question directly. I agree nor disagree with Davies et al. I believe they actually discuss GxC correlation. I don’t think the paper disconfirms GxE models; these models naturally include additive effects. Models that (also) include GxE covariance can explain how genetic variance can amplify and how heritability coefficients can increase over time. GxE covariance is also how the biological g theorists explain this increase. Here the result is also that h2 is overestimated due to GxE correlation. The only difference between a model like that of Dickens (in fact a mutualism model) and a g model with GxE, is that the former doesn’t posit the existence of an (extra!) latent variable ( biological or psychological).

  5. Kees-Jan Kan says:

    My impression is that Davies estimated h2 of intelligence of 0.4-0.5 is indeed about the magnitude of additive genetic effects. The 0.8 later in life likely includes a lot of GxE effects.

    • Chuck says:

      Kees-Jan,

      Thanks for replying. As for Davies and Chabris’s estimates (.45, .47), they are supposedly lower bounds ones. Presumably, including more genetic indexes would raise them. The estimated adult additive genetic effect, based on kinship studies, is as we know 0.6, so not much raising is needed. As for the difference between narrow and broad estimates, one would think that dominance, epistasis, and assortative counted for something. My reasoning is: if the narrow heritability is found to be .45 based on current indices (e.g., 1/2 million SNPS), it’s bound to be higher (i.e., around the .6 estimated from kinship studies). If the narrow heritability is .6, the broad heritability is likely to, in fact, be around .7-.8. Which leaves .3-.2 to be explained by some mix of error, environment, CovG-E, etc. I’m not sure about your model, but this does not fit with the Flynn and Dickens’ 2001 one. Flynn and Dickens argue that the genetic effect (minus CovGE) is well below 0.8. That was the whole point of Flynn’s IQ paradox which he restated in his most recent article:

      “Reconciling IQ Gains and Heritability

      The discovery of IQ gains over time created a seeming paradox. Identical twin studies (and other kinship studies) indicated that genetic influence on IQ is strong and the effects of environment on IQ are weak. But Dutch males gained 20 IQ points on a test composed of 40 items from Raven’s Progressive Matrices between 1952 and 1982, which seems to imply environmental factors of enormous potency. How can environment be so weak and so potent at the same time? Dickens and Flynn (2001a, 2001b) offered a model that distinguishes the dynamics of a situation in which two separated twins develop highly similar IQs and of a situation in which a whole society shows a huge IQ gain over time” (2012, January 2). Intelligence: New Findings and Theoretical Developments)”

      Refer also to, “The spectacles through which I see the race and IQ debate.” Flynn’s model or more precisely, his account for the secular rise, requires that the total genetic effect be well below 0.7.

      As for your prior comment,

      “I don’t think the paper disconfirms GxE models; these models naturally include additive effects. Models that (also) include GxE covariance can explain how genetic variance can amplify and how heritability coefficients can increase over time. GxE covariance is also how the biological g theorists explain this increase. Here the result is also that h2 is overestimated due to GxE correlation. The only difference between a model like that of Dickens (in fact a mutualism model) and a g model with GxE, is that the former doesn’t posit the existence of an (extra!) latent variable ( biological or psychological)”

      1) Unless, I’m missing something, a high narrow heritability (let’s say .6) is inconsistent with a model that proposes strong G-E (let’s say more than 10% of variance explained), since it leaves no room (see my reasoning above). 2) As for the interaction between age and heritability, two explanations are genetic amplification and active G-E correlations. Obviously there are others (e.g., new genes coming into play during development, a decrease in environmental variance, etc.) but these two seem to be the most promising — to me at any rate. Biological g theorists like Jensen and Rushton obviously would not support the latter, as they argue that the (unconfounded or true) adult broad heritability of g is around .75 or so. I briefly commented on this issue last year: http://occidentalascent.wordpress.com/?s=genetic+amplification But that was before I had an appreciation of the mutualism model.

  6. Kees-Jan Kan says:

    The 0.6 includes the G-E cor effects. That’s the problem. These effects ascribed to A in standard behavior genetic modeling. See ‘Variance Components Models for Gene–Environment Interaction in Twin Analysis by Purcell.’

    • Chuck says:

      Here is what I said:

      “Thanks for replying. As for Davies and Chabris’s estimates (.45, .47), they are supposedly lower bounds ones. Presumably, including more genetic indexes would raise them. The estimated adult additive genetic effect, based on kinship studies, is as we know 0.6, so not much raising is needed. As for the difference between narrow and broad estimates, one would think that dominance, epistasis, and assortative counted for something”

      This was to be read: “In kinship studies, the narrow heritability is found to be 0.6; but this estimate is plausibly confounded with CovGE. Davies and Chabris estimated .46 comparing
      random individuals. Davies held that that estimate represents a true lower bounds estimate of narrow heritability. If we accept that, it seems that the .6 found in kinship studies is vindicated, i.e., not confounded. Since if the narrow heritability is found to be .46 based on current indices (e.g., 1/2 -3/4th million SNPS), it’s bound to be higher when additional indices are added. It’s bound to approach the kinship estimate. ….now, if the narrow heritability is .6, the broad heritability is likely to, in fact, be around .7-.8, since dominance, epistasis, and assortative mating should count for something.”

      I just want to know whether in your opinion Davies estimate represents a true lower bounds estimate of narrow heritability. If it does, It seems to follow the the true genetic effect is >.7.

  7. Kees-Jan Kan says:

    I think also Davies narrow heritability estimate contains G-E cor effects (unless he modeled G-e explicitly in his analysis)

    • Chuck says:

      Ok, this is what I wanted to hear.

      Visscher et al’s method does not explicitly model covGE. Rather it is assumed that the estimate captures only additive G. See: “A commentary on “Common SNPs explain a large proportion of the heritability for human height” by Yang et al. (2010): What about G×G and G×E interactions?”

      I’ve been trying to find out if others agree with this. It seems to be a relatively important point deserving clarification.

      ……

  8. Kees-Jan Kan says:

    “We implement this analysis by an equivalent model in which y = g + e where g = Wb is a vector of genetic values calculated from the SNP alleles each individual carries, and var(g) = WW’σb2. WW’ is a matrix of the relationships between all the individuals calculated from the SNPs (Goddard 2009; Hayes et al. 2009). The variance of the genetic effects (the effects in vector g) in this model is the same as the variance explained by all the SNPs together in the original model that fits SNP effects directly. In the twin (or behaviour genetics) literature the fitted model y = g + e would be called an AE model (with g a vector of latent additive genetic values), but with the difference that the additive relationships between individuals do not come from pedigree data but are estimated from marker data. The statistical equivalence of the two models (fitting SNP effects or fitting whole genome additive genetic effects) means that the inference (and, for example, likelihood) of the two models is identical.”

    So, Visscher’s model is equivalent to a standard AE-model (in which A and E are modeled as uncorrelated). If A and E are correlated in reality, the estimated A (or g as they call it) contains the effects of G-E cov.

    • JL says:

      At the very least, the Visscher method rules out some sources of G-E covariance that have been proposed to confound twin and other family correlations, because there are only unrelated people in the sample. There is no “equal environments” assumption, for example.

      I’d guess the Visscher estimate of narrow heritability could include G-E covariance effects, but those would pretty much have to be effects that amplify, in a very linear fashion, already manifest genetic propensities — in particular, individuals selecting environments that match their genetic propensities. Some have argued that that kind of “active” G-E correlations should be regarded as genetic variance to the extent they’re about “self-realization”. Neven Sesardic wrote about this:

      Namely, the influences of those environments that are chosen on the basis of genotype are typically difficult to keep apart from the influence of genotype itself. In many instances the selection of these environmental influences can be plausibly regarded as just a way a genotype is expressed, and hence as “a more or less inevitable result of genotype” (Jinks & Fulker 1970, 323). Therefore, phenotypic effects of such environments are indeed sometimes classified as heritable, on the grounds that they are practically inseparable from direct genetic effects and that they merely represent the self-realization of genotype (Jinks & Fulker 1970, 323; Jensen 1969, 39; Jensen 1973, 54, 368; Jensen 1976, 92-93; Rowe 1994, 90-92).

      [I]n certain specific situations researchers may wish to include the G-E covariance into genetic variance, but when they do that, they are typically guided by common-sense notions about causal attributions, rather than going against them. Namely, in some cases of active G-E covariance, G leads to E, which in turn leads to P, and all this unfolds in such a way that the genotype-environment correlation strikes us as just a self-actualization (or natural manifestation) of the genotype. Consequently, some behavior geneticists do tend to interpret phenotypic differences arising in this manner as resulting from genetic differences (that is, as being heritable) simply because they think that in that type of situation the role of the environment degenerates into its being a mere reflection of the genotype, or the way the genotype expresses itself: “To what extent could we ever get a dull person to select for himself an intellectually stimulating environment to the same extent as a bright person might?” (Jinks & Fulker 1970, 323)

  9. Kees-Jan Kan says:

    “Some have argued that that kind of “active” G-E correlations should be regarded as genetic variance to the extent they’re about “self-realization”.”

    Yes, as a source of interdividual differences one can regard G-E correlation as similar to G effects. But as a source of intraindividual differences it is similar to E effects. If this occurs a trait is highly heritable but also highly malleable.

    • Chuck says:

      Kees-Jan

      Sorry, I got lost on a tangent. Ok, I see what you’re saying about G-E correlations.

      I agree that were intra-individual differences due to G-E correlations, inter-individual differences would be highly environmentally malleable. That is, an individual’s IQ, relative to others in the population, would not be constrained by their genotype. This malleability would, of course, show up, in degree, as a lowered correlation between genes and IQ.

      Why then has the correlation repeatedly been found to be high for adults? This is inductive evidence against a G-E correlational model. It was plausible, before Davies, that the high correlation was an artifact of kinship studies, but now no more. So now a correlational model has to explain why, in spite of the prediction that adult IQ is highly environmentally malleable (i.e., genotype is loosely bound to phenotype), it’s repeatedly not found to be.

  10. Kees-Jan Kan says:

    “This malleability would, of course, show up, in degree, as a lowered correlation between genes and IQ.” I don’t agree on this. Actually, it is the opposite. If there is A by E covariance, its effects will be attributed to A in a standard behavior genetic model (and also with Davies method), and heritability will be higher. I cannot repeat this often enough.

    • Chuck says:

      Hmmm….

      I agree that “If there is A by E covariance, its effects will be attributed to A in a standard behavior genetic model.” This doesn’t contradict my point.

      To say something is highly environmentally malleable, is to say that the phenotype can readily depart from the genotype.

      If intra-individual differences were due largely to g-e correlations, as you say, difference could be highly malleable. And this malleability should from time to time in some circumstances show up.

      But, by adulthood, differences are consistently found not to be highly malleable. So this is inductive evidence against a G-E correlational model.

  11. Kees-Jan Kan says:

    No, it does not, and it is certainly not evidence against g-e correlation! The high heritability estimate in adulthood is very likely DUE to those correlations!

    The high heritability means that dynamical gene-environment interaction, which results in GxE correlation (genetic across people, environmental within people), has (or has had) its effect. Intelligence was/is still malleable (although perhaps not upwards for people who train their cognitive skills a lot, like academics).

    Make a comparison with sports: You will see that differences across people are largely genetic if the environment allows and stimulate people to practice sports a lot (so that within people effects of the environment are huge) and when people who are ‘talented’ (do relatively well compared to other people of the same age) get selected to receive even more practice (so that environmental effects across people are attributed to genetic effects). If people would quit practicing that much, their sport skills and physical condition would drop dramatically.The rankorder between people can change dramatically.

    That differences in intelligence among adults seem not malleable is probably due to the fact that intelligent adults (people who became intelligent) still practice their cognitive abilities in their jobs, while less intelligent adults (people who became less intelligent) practice less.

    By the way, that the between people rankordering of cognitive abilities is or is not malleable is a different question than the question whether cognitive abilities are malleable.This makes the discussion very complex. Malleability within people can be very large, while the rankordering among same aged people can be very stable. This will especially be the case if G by E covariance is large. Imagine for example that G is fixed and E modifies the trait and that E correlates 1 with G. The stable rankordering among people of the same age reflects then genetic differences, while the malleability of the trait is caused by the environment. Taking the entire population however, shows that the rankorder among all people changes throughout development (caused by environmental influences!).

    The larger G-E correlation the bigger the stability within same aged people!

    • Chuck says:

      Kees-Jan,

      Are you aware of any studies/meta-analyses that estimate effect size (i.e., decompose variance into an A + E + COVGE model?

      Generally,

      1. I see no evidence that the “the high heritability estimates in adulthood are very likely DUE to those correlations.” On what grounds are you deducing “very likely”? As an alternative model, I offered “pure” genetic amplification (GA). (I’m conceptualizing CovGE as Genotype –> Trait –> Environment –> IQ and GA as Environment –> Genotype –> IQ.)

      GA could involve GE in the sense that:

      (a) Environment –>Genotype–>IQ–>Environment –>Genotype–>IQ

      But it doesn’t necessarily, in the sense that:

      (b) Environment –> Genotype –> IQ

      As it see it, the increasing heritability with age could be due to (b).

      (The practical difference between GA and GE is that, were IQ related environments identical, with GE there would be no inter-indivudal differences (because individuals have the same genetic potential with respect to IQ), with GA, were IQ related environment identical, there would be differences (because individuals don’t have the same genetic potential with respect to IQ.) (i.e., genes cause environmental differences, which cause IQ differences vrs. genes cause differences, environment amplifies these, environmental differences amplifies these even more.)

      2. With regards to your statement, “You will see that differences across people are largely genetic if the environment allows and stimulate people to practice sports,” the same would be the case with genetic amplification (refer above). For example, there would be a SES X heritability interaction.

      3. The problem that I have with your statement, “The rank order between people can change dramatically,” is that I don’t see evidence of a dramatic rank order change, at least by adulthood; the age to age correlation is high and stable.

      4. With regards to your statement, “that differences in intelligence among adults seems to not be malleable is probably due to the fact that intelligent adults still practice their cognitive abilities in their jobs, while less intelligent adults practice less,” what I want to know is why don’t “social amplifiers” lead intelligent people to become more intelligent relative to their genotype or lead unintelligent people to become less intelligent relative to their genotype.

      Of course, you say “The larger G-E correlation the bigger the stability within same aged people!” This statement just baffles me. Genes contribute to the age to age stability; environment to plasticity. COVGE only contributes to stability under the condition the COVGE is stable across age. My question is: why is COVGE stable across ages? I would expect pervasive “social amplifiers” to decrease the cross age stability in COVGE.

      You argue that people “get selected to receive even more practice” and that this increases IQ. Based on this, I would expect (a) Genotype –> Trait –> Environment –> IQ –> Environment –> IQ. And a decreasing correlation being genes and IQ as the amplification process goes on. Of course, perhaps people “get selected” in exact proportion to their genes (b) Genotype –> Trait –> Environment –> IQ –> Environment –> Genotype –> Trait –> Environment –> IQ….). But I see no reason why “social multipliers” would work through (b) more than (a). And (a) should have an increasingly larger effect on IQ as the correlations are less attenuated, (i.e., the causal pathway doesn’t have to go through genes and other traits).

      • Chuck says:

        To clarify the last point — You are arguing that there are pervasive social multipliers. Social multipliers (e.g., “get selected to receive even more practice”) can both decrease and increase genotype-phenotype correlations.

        (a) In the first case, imagine someone who had a small genetic edge that resulted in a small phenotypic edge. Introduce social multipliers that work net of genotype. The small phenotypic edge could magnify. (Genotype –> Trait –> Environment –> IQ –> Environment –> IQ.)

        (b) In the second case, imagine someone who had a large genetic edge but initially only a small phenotypic edge. Introduce social multipliers that work through genotype. The small phenotypic edge could magnify and comes in line with the genotypic edge. (Genotype –> Trait –> Environment –> IQ –> Environment –> Genotype –> Trait –> Environment –> IQ.)

        I see no reason to assume that social multipliers, per se, would result in an increased correlation. And it seems that social multipliers that work net of genotype should have a larger overall impact than those that work though genotype as there is less attenuation in the former case. (Ceteriss paribus, the effect of environment in “E –> IQ –> E –> IQ” — (a) above — would be stronger than environment in “E –> IQ –> E –> G –> T–> E –> IQ, — (b) above –since the latter introduces more variables and none of the correlations will be at unity.)

        So…were (a) and (b) to occur in equal amounts the overall correlation between genotype and phenotype should decrease. Your model then has to explain why (b) occurs more frequently than (a) such to increase the genotype-phenotype correlation.

  12. Kees-Jan Kan says:

    I don’t understand anything of what you are saying above.
    Let’s look at this: “Environment –>Genotype–>IQ–>Environment –>Genotype–>IQ.”. The first part: ” Environment –>Genotype”

    What do you mean by this? That environment causes genotype? That differences in environment give rise to differences in genotype? Both do not make sense (unless you talk about assortative mating, but that is not what we were considering). Genotype is virtually entirely fixed.

    Furthermore, you appear to interpret CE correlations as if they say something on the level of the individual (‘imagine someone…’). That would be incorrect. The G-E correlations say something about the population. Social multipliers are the dynamical mechanisms that amplify genetic variance. These dynamical mechanisms also cause environmental variables (e.g. education) to become correlated with genetic variables. That’s why the environmental variable education itself is heritable (though not genetically inherited of course).

    Multiplier:
    (individuel differences in genotype + individual differences in environment [whether related to differences in genotype or not]) > individual differences in phenotype -> individual differences in environment -> individual differences in phenotype -> individual differences in environment … etc, etc.

    So, the interindvidual variable genotype predicts the interindividual variable environment (that is, they are eventually correlated)

    Note about point 3:
    I was talking about the rank order in the entire population, not in same aged people. Compare to adults newborns (even the smartest newborns among the newborns) are incredibly unintelligent. Once they have been grown up even the less intelligent among the now adults are uncredibly smart compared to newborns.

    • Chuck says:

      “I don’t understand anything of what you are saying above…What do you mean by this?”

      Your original statement was:

      “The high heritability estimate in adulthood is very likely DUE to those correlations!”

      You provided no evidence for this. My guess was that you think that the rise in heritability during development is evidence of GE correlations. I’m guessing this because I have heard this argument before. For example:

      “Why, despite life’s ‘slings and arrows of outrageous fortune’, do genetically driven differences increasingly account for differences in general cognitive ability during the school years? It is possible that heritability increases as more genes come into play as the brain undergoes its major transitions from infancy to childhood and again during adolescence. However, longitudinal genetic research indicates that genes largely contribute to continuity rather than change in g during the school years. We suggest that the developmental increase in the heritability of g lies with genotype–environment correlation: as children grow up, they increasingly select, modify and even create their own experiences in part on the basis of their genetic propensities. (The heritability of general cognitive ability increases linearly from childhood to young adulthood)”

      Why don’t we start here. Why do you think “The high heritability estimate in adulthood is very likely DUE to those correlations”?

      We’ll go from there.

    • Chuck says:

      I’m not sure what you’re saying here:

      “Furthermore, you appear to interpret CE correlations as if they say something on the level of the individual (‘imagine someone…’). That would be incorrect. The G-E correlations say something about the population.”

      If you mean to say that heritability estimates — and their derivatives — say nothing on the individual level, you are incorrect. You can make probablistic claims about individuals based on population estimates. See, for example: Tal’s “From heritability to probability” and “The Impact of Gene–Environment Interaction and Correlation on the Interpretation of Heritability.”

      If you want me to translate my statement into a probabilistic one I can.

      • Kees-Jan Kan says:

        No, I meant that the GE correlation is a population statistic, not a correlation between G and E within a person. Within a person G does not vary but a constant. Thus there is no covariation between G and E..

  13. Kees-Jan Kan says:

    + in old age cognition declines + even the rank order among same aged people is then not that stable anymore

  14. Kees-Jan Kan says:

    Whereas we know that genetic influences on IQ and environmental factors (education) are indeed correlated, so h2_estimated also indeed contain cor(E, G).

    What we don’t know is how the pathways are. As I explain in my thesis these need to be modeled better n order to investigate these pathways: 1. cov G and E should be taken into account, hence modeled, 2. use longitudinal designs, because crossectional modeling won’t discriminate among the different hypothesized mechanisms.

  15. Kees-Jan Kan says:

    Sorry I messed up the layout!

  16. Kees-Jan Kan says:

    Hi Chuck,

    No, I don’t have such access. Pity..

    KJ

  17. 猛虎 says:

    This was a stimulating conversation overall. But speaking of GxE interaction, what do you make of this ? It’s a passage of Jensen’s Educability and Group Differences :

    One of the conceptually neatest methods for detecting one kind of G x E interaction, first proposed by Jinks and Fulker (1970, pp. 314-15), is applicable to our data on MZ twins reared apart. We can ask: Are different genotypes for intelligence equally affected by environmental advantages (or disadvantages)? In the case of genetically identical twins, any phenotypic difference between them reflects some environmental difference. One twin can be said to be environmentally advantaged and the other disadvantaged, relative to one another. While the phenotypic difference between the twins, |t1 – t2|, reflects only environmental effects, the average of their phenotypes, (t1 + t2)/2, reflects their genotypic value (plus the average of their environmental deviations). If this correlation is significantly greater than zero, we can claim a G x E interaction. A positive correlation would mean that genotypes for high intelligence are more susceptible to the influence of good or poor environments; a negative correlation would mean that genotypes for lower intelligence are more sensitive to the effects of environment. The correlation of IQ differences with IQ averages of the 122 MZ pairs is -0.15, which is not significantly different from zero. When measurement error is removed by using regressed true scores instead of the obtained IQs, the correlation falls to -0.04. Thus the twin data reveal no G x E interaction. This finding is consistent with Jinks and Fulker’s (1970) failure to find any evidence for a G x E interaction in their analysis of a number of studies of the heritability of intelligence.

    Curiously, to my knowledge, Jensen is the only one who has made this argument against the GxE hypothesis. I would like to see more studies like this.
    Besides, when looking for studies of g, h2, c2, e2, I found this (and think it is really worth reading) :
    Common DNA Markers Can Account for More Than Half of the Genetic Influence on Cognitive Abilities

  18. Pingback: A Meta-Analysis of Jensen Effect on Heritability and Environmentality of Cognitive Tests Using the Method of Correlated Vectors | Human Varieties

  19. KJK says:

    Dude, that’s (statistical) GxE interaction, not GE covariance

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