A Genetic Hypothesis for American Race/Ethnic Differences in Mean g: A Reply to Warne (2021) with Fifteen New Empirical Tests Using the ABCD Dataset

Abstract

Intelligence tests are excellent predictors of school and job performance and racial/ethnic differences in mean IQ are common. Based on five lines of evidence, Warne (2021) builds a case for partly genetic causes of differences in general intelligence (g) across American Self/Parental-identified race or ethnicity. Based on a careful reading of Warne (2021) and the authors he cites, we generated 15 predictions flowing from a partial genetic hypothesis. These predictions concern (1) mean differences, (2) measurement invariance, (3) high within-group heritability, (4) admixture regression for g, (5) polygenic scores, (6) brain volume, and (7) Spearman’s hypothesis. We used the Adolescent Brain Cognitive Development Study sample (N = 10,245) to test these hypotheses using classical and state-of-the-art statistical techniques. Decomposition of variance using twins showed that the heritability of intelligence and of brain/intracranial volume estimates were, respectively, moderate and high for the White and the non-White subsamples. Within all SIRE groups, both genetic ancestry and education-related polygenic scores (eduPGS) predicted both brain volume and g. Moreover, brain volume was weakly but significantly related to g (r = .14 to .25). Path and causal mediation analysis showed that total brain volume explained approximately 15% of the association between European ancestry and g and also explained approximately 8% of that between eduPGS and g. Finally, based on the Method of Correlated Vectors (MCV), a positive manifold was found for genetic, brain volume, and ancestry/SIRE-related variables. We conclude that the results support the hypotheses tested and are in line with a partial genetic hypothesis.

Full text

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A Genetic Hypothesis for American Race/Ethnic Differences in Mean g:
A Reply to Warne (2021) with Fifteen New Empirical Tests Using the ABCD Dataset
John G.R. Fuerst1,2, Jan te Nijenhuis3, Vladimir Shibaev4, & Emil Kirkegaard5
1Cleveland State University
2University of Maryland Global Campus, Bioinformatics
3Gwangju Alzheimer’s Disease and Related Dementias Cohort Research Center
4Vladivostok State University of Economics and Service, Russia
5Ulster Institute of Social Research
Abstract
Intelligence tests are excellent predictors of school and job performance and racial/ethnic
differences in mean IQ are common. Based on five lines of evidence, Warne (2021) builds a
case for partly genetic causes of differences in general intelligence (g) across American
Self/Parental-identified race or ethnicity. Based on a careful reading of Warne (2021) and the
authors he cites, we generated 15 predictions flowing from a partial genetic hypothesis. These
predictions concern (1) mean differences, (2) measurement invariance, (3) high within-group
heritability, (4) admixture regression for g, (5) polygenic scores, (6) brain volume, and (7)
Spearman’s hypothesis. We used the Adolescent Brain Cognitive Development Study sample
(N = 10,245) to test these hypotheses using classical and state-of-the-art statistical techniques.
Decomposition of variance using twins showed that the heritability of intelligence and of
brain/intracranial volume estimates were, respectively, moderate and high for the White and
the non-White subsamples. Within all SIRE groups, both genetic ancestry and education-
related polygenic scores (eduPGS) predicted both brain volume and g. Moreover, brain volume

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was weakly but significantly related to g (r = .14 to .25). Path and causal mediation analysis
showed that total brain volume explained approximately 15% of the association between
European ancestry and g and also explained approximately 8% of that between eduPGS and g.
Finally, based on the Method of Correlated Vectors (MCV), a positive manifold was found for
genetic, brain volume, and ancestry/SIRE-related variables. We conclude that the results
support the hypotheses tested and are in line with a partial genetic hypothesis.
Keywords: brain volume, g, genetic ancestry, heritability, polygenic scores, SIRE

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1. Introduction
IQ tests are statistically robust predictors of school and job performance and average
cognitive score differences between Self/Parental-Identified Race or Ethnicity (SIRE) groups
in the US such as Blacks, Whites, and Hispanics have been well documented (Murray, 2021;
Roth et al., 2017). These differences are not due to psychometric bias, as evidenced by the
finding of measurement invariance across American SIRE groups (e.g., Frisby & Beaujean,
2015; Scheiber, 2016a; b). Rather, these score differences represent real average differences in
latent intelligence. Among intelligence researchers, there is disagreement about the causes of
these differences; notably, when surveyed anonymously, an overwhelming majority of experts,
meaning people that published on this specialist topic, attributed some part of the differences to
genetics (Rindermann, Becker & Coyle, 2020). Determining the source of these differences is
important in order to better understand and address them and their social implications (Flynn,
2018; Pesta, Fuerst, & Shibaev, 2021).
1.1 Warne’s line of evidence
Recently, Warne (2021, based on Warne, 2020) outlined five lines of converging
evidence favoring a partially genetic model for the cause of SIRE group differences. In
summary, Warne’s five lines of evidence are:
1. the consistent finding of measurement invariance,
2. the finding of constraints of high within-group heritability on between-group
environmentality,
3. the findings of genetics-based studies applying the admixture regression methodology,
and
4. the findings of genetics-based studies using educational-related polygenic scores
(eduPGS)

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5. large-scale, consistent support for Spearman’s hypothesis.
The evidence and rationale for these five lines of evidence has been discussed by Warne
(2021). Our analyses in this respect constitutes an attempted replication of previous work.
1.2 Brain volume
An additional line of evidence frequently cited by proponents of a partial genetic
hypothesis is the finding of average differences in brain volume (Jensen & Rushton, 2005).
Warne (2021) did not find this sixth line convincing, and concluded:
I call upon psychologists to have an open mind and to investigate the evidence for themselves, starting
with the sources I have cited in this article. I also encourage social scientists to make research
contributions that can address this question.
Regarding brain volume, numerous meta-analyses have confirmed that brain volume/size
correlates with intelligence (Plomin & Von Stumm, 2018). In a recent meta-analysis of over
194 studies, Pietschnig, Gerdesmann, Zeiler, and Voracek (2022) found a correlation of r =.24
to .29 between brain volume and full-scale IQ. The association was found to be higher in
samples which used highly g-loaded tests, hence tests of high cognitive complexity. As for
causes, twin studies indicate that the relation between brain volume and intelligence is
predominately genetic (Betjemann et al., 2010; Van Leeuwen et al., 2009; Vuoksimaa et al.,
2015). Moreover, recent research shows that polygenic scores for education positively relate to
brain volume (Elliott et al., 2019; Judd et al., 2020), confirming that the association between
brain volume and intelligence among individuals has a genetic etiology.
A large number of studies based on autopsy, MRI, and craniometric data confirmed
differences in amount of brain volume/cranial capacity between continental ancestry groups
(Beals et al., 1984; Rushton & Rushton, 2003; Rindermann, 2018), so global craniometric
variation is well established (Relethford, 2010). Generally, groups which evolved around the

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equator have smaller brains than groups which evolved further from the equator (Beals et al.,
1984; Rindermann, 2018). In line with evolutionary interpretations of these geographic
differences, recent studies have shown that brain morphology is related to continental genetic
ancestry in admixed populations (Fan et al., 2015; Mehta, Malins, Noble, & Greun, 2017).
Since the relation between brain volume and intelligence is predominately genetic in
origin within populations, and because certain ancestry groups differ in both brain volume and
intelligence, an obvious scientific conjecture is that ancestry-related differences in intelligence
may be partially explained by ancestry-related differences in brain volume (Cochran &
Harpending, 2009; Rushton & Jensen, 2005). Thus Rushton and Rushton (2003) claim:
“[B]rain size-related variables provide the most likely biological mediators of the race
differences in intelligence” (p. 139).
1.3 Hypotheses
In this paper, we follow Warne’s call for research, and test the hypothesis that
American race/ethnic differences have a partial genetic basis. To do this, we first carefully read
through Warne’s (2021) arguments and those of the authors cited by Warne (e.g., Rushton and
Jensen, 2005; Lasker et al., 2019). From this reading, we then generated the following 7 key
hypotheses and tested them on a large database.
1.3.1 Between-group differences
Warne reviews the literature showing group differences on various measures, with
Whites generally having better scores. Our Hypothesis 1 therefore states: Between SIRE
groups, there are medium to large differences in g, educational polygenic scores (eduPGS), and
brain/intracranial volume.
1.3.2 Measurement invariance

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Several studies have shown that the differences across SIRE groups have the same
psychometric meaning as, and are caused by a subset of the same sources as, those differences
within SIRE groups and ancestry deciles (Lasker et al., 2019; Warne, 2021). This leads to our
Hypothesis 2: Intelligence differences across European genetic ancestry will exhibit strict
measurement invariance.
1.3.3 Within-group heritability and between-group environmentality
Warne (2021) argues that when heritabilities are high, differences are unlikely to be
explained by environmental-only models. Because of this, environmental differences need to
be large to account for the typically observed moderate to large phenotypic differences.
(Rushton and Jensen, 2005; Warne, 2021). This leads to our Hypothesis 3a: Within SIRE
groups, most of the variance in intelligence and in brain/intracranial volume is attributable to
genes, and our Hypothesis 3b: SIRE groups exhibit similar heritabilities.
1.3.4 Admixture regression for g
Warne (2021) describes admixture regression in some detail and we refer the interested
reader to that discussion. Admixture regression provides indirect genetic evidence for a genetic
hypothesis of differences in g (Warne, 2021; Lasker et al., 2019). The findings from admixture
regression research lead to our Hypothesis 4: The intelligence differences between SIRE
groups are explained by genetic ancestry, and as a corollary, within all SIRE groups European
genetic ancestry is positively associated with intelligence, while African and Amerindian
ancestry is negatively associated.
1.3.5 Polygenic scores and g

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Warne (2021) reviews the literature showing that polygenic scores (PGS) are
genetically related to g within SIRE groups. This leads to our Hypothesis 5: Educationally-
related polygenetic scores (eduPGS) correlate with intelligence within all SIRE groups and
among siblings within families.
1.3.6 Brain volume, g, ancestry, and eduPGS
Much has been written about the link between group differences in intelligence and
brain volume (see: Rushton & Jensen, 2005); this rich literature allowed us to test a series of
related hypotheses that could provide indirect genetic evidence for a genetic hypothesis of
differences in brain volume. Hypothesis 6a is that brain volume correlates with intelligence
within all SIRE groups and among siblings within families. Confirmation of the Hypothesis
implies that brain volume is genetically related to g within SIRE groups.
Hypothesis 6b is that brain/intracranial volume differences between SIRE groups are
also explained by genetic ancestry. Correspondingly, Hypothesis 6c is that in all SIRE groups
European genetic ancestry is positively associated with brain/intracranial volume, while
African and Amerindian ancestry is negatively associated (see: Rushton and Jensen, 2005).
Hypothesis 6d is that SES explains a portion of the relation between both ancestry and
g and between ancestry and brain volume, and that the relations are predominately genetic in
origin. Such an outcome would weaken environmentalist explanations which rely on SES to
environmentally explain differences.
In our last brain-related hypotheses, we focus on the roles that polygenic scores and
brain volume would play were a genetic hypothesis correct. Hypothesis 6e is that brain volume
differences are predicted by eduPGS in all SIRE groups. Hypothesis 6f is that the relation

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between European genetic ancestry and g is mediated both by eduPGS and brain volume;
moreover, Hypothesis 6g is that the relation between eduPGS and g is mediated by brain
volume. The last two hypotheses, which are tested at the same time, are logical extensions of
the prediction that eduPGS and brain volume account for the association between genetic
ancestry and g.
1.3.7 Spearman’s hypothesis
Warne (2021) reviews the extensive literature showing that group differences on
subtests of IQ batteries are strongly determined by the cognitive complexity of these same
subtests. Because the cognitive complexity of IQ subtests is strongly linked to their heritability,
this is indirect evidence that group differences in IQ have a genetic component. We had
various variables that are hypothesized to be genetic, so our Hypothesis 7a was that there was a
positive correlation between the effects on putative genetic variables across cognitive tests.
Rushton (1999) showed that all genetic variables in his study correlated, so that a strong
higher-order genetic factor could be computed in a factor analysis and all putative genetic
variables loaded on it. This leads to our Hypothesis 7b that there would be a higher-order
genetic factor resulting from the intercorrelating genetic variables in our study.
2. Methods
2.1. Dataset
The ABCD is a collaborative longitudinal project involving 21 sites across the US. The
ABCD is the largest longitudinal study of brain development conducted in the US to date.
Approximately 11,000 9-10-year-old children were sampled at baseline, between 2016 and
2018, using a probabilistic sampling strategy. The ABCD subjects were limited to children

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who were fluent in English and who did not have severe medical, neurological, or psychiatric
conditions. The children are broadly representative of healthy US children in this age range.
Informed consent was provided by the parents.
For all analyses, we utilized the ABCD 3.01 dataset. Since our focus was on groups
who are primarily of African, European, and Amerindian ancestry, we excluded any child who
was identified as being either Pacific Islander or Asian.
2.2. Variables for the analyses
The following variables were used for the analyses:
1. Eleven age-corrected cognitive tests
The following cognitive measures were given at baseline: the seven NIH Toolbox®
(NIHTBX) neuropsychological battery tests, NIHTBX Wechsler Intelligence Scale for
Children’s Matrix Reasoning, The Little Man Test (efficiency score), The Rey Auditory Verbal
Learning Test (RAVLT) immediate recall, and RAVLT delayed recall.
Regarding the first seven of these, the NIHTBX neuropsychological battery was
designed to measure a broad range of cognitive abilities. It consists of seven tasks which index
attention (Flanker Inhibitory Control and Attention Task), episodic memory (Picture Sequence
Memory Task), language abilities (Picture Vocabulary Task & Oral Reading Recognition
Task), executive function (Dimensional Change Card Sort Task & Flanker Inhibitory Control
and Attention Task), processing speed (Pattern Comparison Processing Speed Task), and
working memory (List Sorting Working Memory Task) (Akshoomoff et al., 2014; Weintraub
et al., 2014; Thompson et al., 2019).

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For the seven NIHTBX subtests, the ABCD precomputed age-corrected scores were
used. For the remaining four tests, scores were adjusted for age by applying regression with a
cubic spline of age to the full sample. Subsequently, scores for all eleven tests were
standardized.
2. General intelligence (g) scores
Multi-group confirmatory factor analysis (MGCFA) was previously conducted based
on the 11 cognitive tests noted above (Fuerst, Hu, & Connor, 2021). We repeated the analysis
using the same model and specifications. When doing so, we first assessed if outliers and
missing data had any impact, and also if our results remained robust after imputation of
missing data, removal of outliers, and adjustments for age and sex. Next, we conducted both
exploratory factor analysis and multi-group confirmatory factor analysis. A three-broad- factor
model (memory, complex cognition, and executive function) with a general factor (g) fit the
data well. As previously found, strict measurement invariance held across the SIRE groups
(and across sex groups and age measured in months). The complete results are detailed in
Supplementary File 1.
In the best fitting and additionally most parsimonious model for SIRE group
differences, g alone explains the differences. g-factor scores from this MGCFA model were
standardized (M = 0.00; SD = 1.00) in the full sample of 10,245 children.
3. NIH Toolbox® (NIHTBX) Cognition Battery
As the g scores used for the admixture regression analyses were dependent on MGCFA
model specification, we additionally used the age-corrected NIH Toolbox® Cognition Battery
(NIHTBX) summary composite scores (“nihtbx_totalcomp_agecorrected”) precomputed by

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NIH as an alternative measure of general cognitive ability. Our choice was made for the sake
of replicability. The NIHTBX was normed for samples between ages 3 and 85; tasks correlate
highly with comparable ability assessments (Weintraub et al., 2014). The NIHTBX cognition
battery had previously been found to be measurement invariant across American Black,
Hispanic, and White SIRE groups (Lasker et al., 2019). We standardized scores, on the full
sample, prior to analysis.
4. Unadjusted and adjusted brain and intracranial volume
ABCD provides summary brain (“smri_vol_scs_wholeb”) and intracranial volume
(“smri_vol_scs_intracranialv”) variables which show volume in mm3. We standardized these
unadjusted variables.
We additionally created sex-, age-, and MRI assessment site-adjusted brain variables to
use in the path analysis models and biometric analyses. We adjust for collection site to account
for differences in MRI protocol across collection sites. Brain and intracranial volume are
adjusted for sex-, the cubic spline of age-, height- and site-related fixed effects. These adjusted
brain variables were then standardized.
5. Child US born & immigrant family
Parents were asked if the child was born in the “United States”. This variable is recoded
as “1” for “United States” and “0” for all other responses. Parents were also asked if anyone in
the child’s family, including maternal or paternal grandparents, was born outside of the United
States. This variable is also coded as “1” for “Yes” and “0” for all other responses.
6. General socioeconomic status (SES)

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A general factor of SES was computed by applying Principal Components Analysis
(PCA) to seven indicators of SES. To analyze the data, we used the PCAmixdata R package
(Chavent, Kuentz-Simonet, & Saracco, 2014) which allows handling mixed categorical and
continuous data. The first unrotated component explained 42% of the variance, indicating a
strong general factor. The loadings on the first PCA factor for the seven indicators were:
financial adversity (.31), area deprivation index (.49), neighborhood safety protocol (.31),
parental education (.54), parental income (.66), parental marital status (.43), and parental
employment status (0.23). We note that this variable was standardized in the full sample.
Details are provided in Supplementary File 1.
7. SIRE fraction & Hispanic
Based on the 18 questions inquiring about the child’s race, we created four dummy
SIRE variables: Black, White, Native American, and Not Otherwise Classified (NOC). The
latter category includes those identified as: “Other Race,” “Refused to answer,” or “Don’t
Know”. These variables were then converted into interval variables, calculated as the value
selected for each of the four groups (0 or 1) over the total number of responses (0 to 4). As a
result, individuals were assigned four SIRE fractions (frac_White SIRE, frac_Black SIRE,
frac_Native_American SIRE, & frac_NOC SIRE), each ranging from 0 to 1. For example, a
Hispanic individual who chose both White and Black SIRE receives a ½ weighting on each of
the associated group variables; an individual who chose all three of Black, Native American
and White SIRE has 1/3 weight for each. This ensures that the sum across the group variables
equals one for every individual. The White category is used as the base or benchmark group
and the associated variable is dropped from the regression. This SIRE coding is used because
interval SIRE variables had previously been found to be most predictive when included in

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models alongside genetic ancestry (Kirkegaard et al., 2019). These variables were left
unstandardized, allowing the unstandardized beta coefficients for SIRE fraction to be
interpreted as the effect of a change in 100 percent SIRE identity on one standardized unit of
the dependent variable.
We also create a dummy variable for Hispanic ethnicity, coded as “1” for “Hispanic”
and “0” for non-Hispanic.
8. Height
ABCD provided a summary variable (“anthroheightcalc”), which records the child’s
height (in inches) based on an average of up to three measures. We divide the values by 12 to
give height in feet and then standardize the results in the full sample.
9. Genetic ancestry
Subjects were genotyped using Illumina XX, with 516,598 variants directly genotyped
and surviving the quality control carried out by the data provider. We used the 3.0 release of
the genotypic dataset, which also includes an edition with imputed variants using TOPMED
and the Eagle 2.4 software. All our work was done on build 38. Files in hg17/37 were lifted to
hg38 using liftOver (https://github.com/sritchie73/liftOverPlink) and the GRC chain file at
ftp://ftp.ensembl.org/pub/assembly_mapping/homo_sapiens/ (GRCh37_to_GRCh38.chain.gz).
Before global admixture estimation, we applied quality control analyses using plink
1.9. We used only directly genotyped, bi-allelic, autosomal SNP variants (N = 494,433 and
493,196, before and after lifting, respectively). We pruned variants for linkage disequilibrium
at the 0.1 R² level using plink 1.9 (--indep-pairwise 10000 100 0.1), as recommended in the
admixture documentation

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(https://vcru.wisc.edu/simonlab/bioinformatics/programs/admixture/admixture-manual.pdf).
This variant filtering was carried out in the reference population dataset to reduce bias due to
sample representativeness. After pruning, we were left with 99,642 variants. To ensure a
reasonable balance of populations in the estimation dataset, we merged the target samples from
ABCD with reference population data for the populations of interest. We desired a k=5 solution
(European, Amerindian, African, East Asian, and South Asian), so we merged with relevant
samples from the 1000 Genomes database and from the HGDP database. The following
populations were excluded: Adygei, Balochi, Bedouin, Bougainville, Brahui, Burusho, Druze,
Hazara, Makrani, Mozabite, Palestinian, Papuan, San, Sindhi, Uygur, and Yakut. These
reference populations were excluded because they were overly admixed or because, in the case
of Melanesians and San, the individuals in the ABCD sample lacked significant portions of
these ancestries.
Because the estimation sample would still be highly skewed towards European ancestry
when using this joint sample, we used repeated subsetting to achieve balance. Specifically, we
split the ABCD target samples into 50 random subsets, each with approximately 222 persons,
and merged them one at a time with the reference data, followed by running admixture k=5 on
each merged subset. We verified that these subsets produced stable results by examining the
stability of the estimates for the reference samples. There was very little variation across runs,
e.g., for the reference sample with the most variance (European, NA12342), the mean estimate
was 98.3% with SD=0.17% across the 50 runs. Since the Admixture software does not label the
resulting clusters, we used five reference samples to index the populations so the data would be
merged correctly. In no case did this produce any inconsistencies.

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By design, the estimated ancestry proportions for an individual i, Ai1, Ai2,…,Ai5, are
non-negative and sum to one for every individual, using the following formula:
  


In order to use all ancestry variables in a regression context, one category must be
chosen as the base group and the associated variable dropped from the regression, otherwise
the unit-sum condition across the variables produces a singularity in the regression model.
When using multiple ancestries, we used the European ancestry category as the base, because it
has the largest number of nonzero observations. As an alternative approach, we used the
European ancestry variable as the single ancestry for models from which we created ancestry
by outcome predictor effect plots. This was because these effect plots use a single ancestry
predictor.
These ancestry variables were left unstandardized. This allows the unstandardized beta
coefficients for genetic ancestries to be interpreted as the effect of a change in 100 percent
ancestry on one standardized unit of the dependent variable.
10. MTAG eduPGS & poly eduPGS
We created two eduPGS. First, we used the genome-wide association study (GWAS)
results from Lee et al.’s (2018) meta-analysis, based on European-descent individuals.
Specifically, the multi-trait analysis of genome-wide association study (MTAG) eduPGS SNPs
(N = 8,898 variants in the ABCD sample). MTAG is a method for analyzing statistics from
genome-wide association studies (GWAS) on different but genetically correlated traits (e.g.,

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education and intelligence). Lee et al. (2018) applied MTAG to three traits: intelligence (n =
257,841), hardest math class taken (n = 430,445), and mathematical ability (n = 564,698).
These eduPGS, denoted MTAG eduPGS, are used because they were previously validated in
European, Hispanic, and African-American populations (Lasker et al., 2019) and also assessed
for population-structure-related confounding (Fuerst, Kirkegaard, & Piffer, 2021).
Second, we created eduPGS, denoted poly eduPGS, using the new PolyFun predictor
detailed by Weissbrod et al. (2022) (using N ~ 750,000 variants in the ABCD sample).
Weissbrod et al. (2022) trained these predictor on 334,353 unrelated individuals of British
descent from the UK Biobank. The relevant trait was having a college education or not. This
predictor uses genome-wide functionally-informed fine-mapping to precisely estimate causal
effects. In doing so, this method is known to circumvent linkage disequilibrium differences,
which can confound trans-ancestral comparisons (Weissbrod et al., 2020; Weissbrod et al.,
2022). Moreover, as the training sample only includes the UK Biobank data, it is relatively
homogenous; this characteristic should reduce population-structure-related confounding. While
this predictor does not provide an accurate estimate of the effect size, it provides a precise
estimate of causal effects. Weissbrod et al. (2022) provide the SNP set and SNP weights, based
on the UK Biobank, and the code for generating these eduPGS.
While an updated meta-analysis of educational GWAS has since been published
(Okbay et al., 2022), only about 10k variants have been made public. This is because results
based on the 23andME sample, which accounted for most of the sample size increase since Lee
et al.’s (2018) meta-analysis, were not published. Moreover, this SNP set is made available by
the Social Science Genetic Association Consortium (SSGAC) and the SSGAC currently
proscribes the use of eduPGS for making comparisons between ancestry groups. So, it is not

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possible to assess population-related confounding with these eduPGS. Given this, the eduPGS
above are the best currently available ones for the purposes of the present analyses.
11. First 20 genetic principal components
For several of the analyses involving eduPGS, we took population-structure-related
effects into account by controlling for the first twenty ancestry principal components generated
by PLINK v1.90b6.8. We used all imputed SNPs to compute these PCs.
12. Pseudo eduPGS
Using PLINK v1.90b6.8, we selected ten random sets of 8,898 variants. We randomly
assigned the MTAG eduPGS’s beta weights to these sets of SNPs. We used these individually
and we also averaged these to create averaged pseudo eduPGS weights.
2.2. Analyses
2.2.1 Analyses related to the measurement of group differences
We computed means and SDs and effect sizes for g, eduPGS, and brain/intracranial
volume. For effects sizes, we computed Cohen’s d values. This commonly used metric is
computed as the difference between the group means over the pooled standard deviation for the
two groups.
2.2.2 Analyses related to measurement invariance
We repeated the multi-group confirmatory factor analysis (MGCFA) of Fuerst et al.
(2021) as detailed in Supplementary File 1. We additionally ran Local Structural Equation
Models (LSEM) to determine if MI also held with respect to European genetic ancestry deciles
in addition to the four SIRE groups. This method was applied to the 10,245 White, Hispanic,
Black, and Other individuals with European genetic ancestry, g, and brain volume scores.

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The LSEM method has been detailed by Hildebrandt, Lüdtke, Robitzsch, Sommer, &
Wilhelm (2016) and was previously applied to genetic ancestry and intelligence by Lasker et
al. (2019) using a different sample. As with Fuerst et al. (2021), when conducting confirmatory
factor analysis we elected to use a higher-order factor (HOF) model based on theoretical
grounds (Hood, 2010; Decker, 2021) and on the absence of empirical disconfirmation of the
HOF model (Murray & Johnson, 2013).
To assess invariance across European genetic ancestry, the following model-fit indices
are used: Chi-Square, Comparative Fit Index (CFI), Root Mean Square Error of Approximation
(RMSEA), and Bayesian information criterion (BIC). CFI estimates the discrepancy between
the proposed model and the null model: larger values indicate better fit. RMSEA estimates the
discrepancy related to the approximation, or the amount of unexplained variance (residual), or
the lack of fit compared to the saturated model: smaller values indicate better fit. BIC is a
comparative measure of fit used in the comparison of two or more models; it evaluates the
difference between observed and expected covariances: smaller values indicate better fit.
We selected European ancestry as the ancestry variable since there was no sparsity of
data along this ancestral component.
2.2.3 Analyses related to within-group heritability and between-group environmentality
A same-sex monozygotic and dizygotic twin sample was nested within the ABCD
sample. Details for this twin sample are provided by Iacono et al. (2018). We used the SEM
feature from the Lavaan (Rosseel et al., 2012) and the umx (Bates, Neale, and Maes, 2019)
packages to decompose the variance using an A (additive genetic), C (shared environment),
and E (non-shared environment) model. For both NIHTBX/g and Brain/Intracranial volume,
this ACE model fits better than an alternative ADE model, which replaces the C component

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with D (dominance) or an alternative AE model, which excludes shared environment. This
assessment is based on a combination of the following fit indexes: Root Mean Square Error of
Approximation (RMSEA), Tucker–Lewis index, and χ2 /df. For the SEM, we used the
theoretical genetic correlation of 1.0 for MZ and 0.5 for DZ. The correlation for C and E, for
both kinship classes, were set to 1 and 0, respectively. In describing variance components, we
adopted Chen et al.’s (2022) guidelines, which indicates that low, moderate, and high genetic
variance components correspond to less than 30% of the variance, between 30% and 60%, and
greater than 60%, respectively.
For these analyses, twin pairs were identified and classified using the ABCD’s
precomputed family relationship and genetically-inferred zygosity variables. Variance
component estimates were computed for the eleven cognitive subtests, g scores, the NIHTBX
composite scores, unadjusted brain volume, unadjusted intracranial volume, adjusted brain
volume, and adjusted intracranial volume. For these analyses we did not use imputed data,
except in the case of the RVALT memory trials. Specifically, in this case, we imputed missing
data for, and based on only, the six RVALT trials (pea_ravlt_sd_trial_i_tc,
pea_ravlt_sd_trial_ii_tc, pea_ravlt_sd_trial_iii_tc, pea_ravlt_sd_trial_iv_tc,
pea_ravlt_sd_trial_v_tc, and pea_ravlt_ld_trial_vii_tc). This was done because the short-term
memory scores represent the average of the first five trials and so missing data need to be
handled.
To allow heritabilities for intelligence to be compared with previously-published results
(e.g., Pesta et al., 2020), for these biometric analyses, we defined “Black” as including any
non-Hispanic individual identified as being African American. Thus “Black” was defined
broadly and includes multi-racial individuals. The “Other” group, correspondingly, was

20
defined as everyone who was not White, Hispanic, or Black as just defined. Since our primary
comparison, for the biometric analyses, was between the White and the combined Hispanic,
Black, and Other subgroups, this decision did not affect the interpretation of our results. This
definition of “Black” differs from that used for the admixture regression analyses discussed
below. In those, the “Black” subgroups included only those individuals who were marked as
being Black. The latter was done for the purposes of minimizing possible sociocultural
variation which may confound admixture analyses.
2.2.4 Analyses related to admixture regression and g
The rationale for admixture regression analyses has been described in detail previously
(Kirkegaard et al., 2019; Lasker et al., 2019; Connor & Fuerst, 2022). For these analyses, we
used the pooled data with the ABCD baseline sample and the twin sample. We first subset to
cases which had admixture estimates, g scores, and brain volume, leaving 10,245 cases. We
then imputed missing data, yielding the same number of cases. We ran a series of full-sample
and also SIRE-stratified (White, Black, Hispanic, and Other) regression analyses so as to
control for potential SIRE-related environmental confounds. This was because, “stratifying on
SIRE has the potential benefits of reducing heterogeneity of these non-genetic variables and
decoupling the correlation between genetic and non-genetic factors,” since SIRE “acts as a
surrogate to an array of social, cultural, behavioral, and environmental variables” (Fang et al.,
2019, p. 764). For these analyses, the SIRE subgroups were defined using the ABCD
race_ethnicity variable. There are four mutually exclusive groups in terms of SIRE
categorization – non-Hispanic White (White) only, Hispanic of any race (Hispanic), non-
Hispanic Black (Black) only, and any other (Other).

21
These were regression analyses with g as the dependent variable and ancestries as the
main predictors. These models additionally included: Child US born, family immigrant status,
sex, age, and SES variables. For the total-sample analyses, the Hispanic and SIRE fraction
variables were also included. Likewise, the SIRE fraction variables were included for the
Hispanic subsample analyses.
As advised by Heeringa and Berglund (2021), we used a linear mixed-effects model
rather than ordinary least squares. This involved partially decomposing the residual term into
linear random effects components linked to the data collection site identifiers and same-family
identifiers within the sample. This allows for the possibility of error term correlations within
data collection sites or within families with multiple tested individuals (see: Heeringa &
Berglund, 2021). As Heeringa and Berglund (2021) note, this specification replicates that
which is used by the ABCD Data Exploration and Analysis Portal (DEAP). Thus, the use of
this multilevel model also aids in replication. For the mixed-effects regression models, we
employ the lmer command from the lme4 package (Bates, Mächler, Bolker, & Walker, 2015).
In addition to the regression results, we depicted the partial residual plots for European
ancestry with g as the dependent variable. Partial residual plots are a form of predictor effect
plot (see: Fox & Weisberg, 2018). These plots show the effect of European ancestry on g while
holding everything else in the regression model constant. These plots were created using the
effect plot command from the jtools package in R (Long, 2020). This command uses the output
from the mixed-effects regression models for genetic ancestry g.
2.2.5 Analyses related to eduPGS and g
These were regression analyses with g as the dependent variable and eduPGS as the
main predictors. These models additionally included: sex, the cubic spline of age, and the first

22
twenty genetic PCs. For these analyses we used a linear mixed-effects model as described
above. We ran the models both on the full sample and the SIRE-stratified subsamples.
Associations between intelligence and eduPGS may be confounded by demographic
factors (Zaidi & Mathieson, 2020). As such, we also run sibship analyses to assess the effects
of MTAG eduPGS and Poly eduPGS on intelligence within families. We then compare the
magnitude of these within-sibship effects to the effects found in the full sample. We use the
model detailed by Howe et al. (2021; 2022) and a modified version of the R code provided by
these authors (https://github.com/LaurenceHowe/SiblingGWAS). This model gives the effect
of the predictor on the criterion within sibships (denoted PXCi) and between sibships (denoted
PFXi) in addition to within the full sample. The sibship analyses are based on families with
multiple children, with MZ twins excluded. We use two criteria, g and NIHTBX composite
scores. Following Howe et al. (2021; 2022) all analyses include age and sex as covariates. We
also include the first 20 PCs as covariates, except when using European ancestry as the
predictor. When using European ancestry as the predictor, we instead include East and South
Asian ancestry as covariates. To maximize power for these analyses we use all available White,
Hispanic, Black, or Other individuals in a pairwise deletion fashion.
2.2.6 Analyses related to brain volume
2.2.6.1. Brain volume and g
These are regression analyses with g as the dependent variable and brain volume,
adjusted for sex, the cubic spline of age, and height. A second set of regression models added
the first twenty genetic PCs. For these analyses we used a linear mixed-effects model as
described above. We ran the models both on the full sample and the SIRE-stratified
subsamples.

23
We additionally ran the within-sibship analyses to assess the effects of brain volume on
intelligence within families.
2.2.6.2. Brain/ Intracranial volume, SIRE, and genetic ancestry
These were admixture regression analyses with unadjusted brain or intracranial volume
variables as the dependent variable and genetic ancestries as the main predictors. The baseline
model included SIRE variables but not genetic ancestries. These models, which were run on
the full sample of 10,245 children, additionally included: Child US born, family immigrant
status, sex, age, height, and SES variables.
2.2.6.3. Brain/Intracranial volume within SIRE groups
These analyses repeated the one discussed immediately above but on the SIRE
subsample. As such, SIRE fraction variables were included only for the Hispanic subsample
analysis.
2.2.6.4. SES, brain volume, & g among adopted and biological children
We investigated the relation between SES, brain volume, and g by taking advantage of
the small adoption sample in the ABCD dataset. We defined adopted children as children for
whom both parents were reported to be adoptive parents. There were 126 such children and
there were 6400 biological children. We compare the associations for adoptive children with
those for biological children. We defined biological children as children for whom both parents
were reported to be biological parents. We fit a regression model with g and, alternatively,
brain volume as the dependent variables. In these models, we included European ancestry,
SIRE, the cubic spline of age, sex, Child US born, family migrant status, and site- and family-
fixed effects. European ancestry was included in this model because, as shown in figure S14a

24
of the Supplementary Material, it was also linearly related to g in the sample of adopted
children.
2.2.6.5. Brain volume and eduPGS
These were linear mixed-effects regression analyses with unadjusted brain volume as
the dependent variable and eduPGS as the main predictors. These models additionally
included: sex, age, and the first twenty genetic PCs.
2.2.6.6. Mediation by brain volume
While path models cannot prove causal assumptions, they can provide estimates of
effects given these assumptions (Bollen & Pearl, 2013). As such, we model the relationship
between genetic ancestry, polygenic scores, adjusted brain volume, and g using the lavaanPlot
command from the lavaan package in R (Long, 2020). Since we used cross-sectional data, the
causal assumption imbedded in the brain volume → g path cannot be verified. Yet this path,
with mental ability being dependent on brain matter, is theoretically well grounded. In these
models, brain volume is adjusted for the effects of sex, the cubic spline of age, and height.
We additionally ran causal mediation analysis using the mediation R package (Tingley,
Yamamoto, Hirose, Keele, & Imai, 2013). This package estimates the proportion of the effect
that is directly causally mediated using a different set of assumptions than used with path
analysis (see: Imai, Keele, Tingley, & Yamamoto, 2014). For these models we used the poly
eduPGS, because it is supposed to estimate causal effects and be less confounded by
population structure. In these models both the outcome and mediator variables were
residualized for demographic confounds.
2.2.7 Analyses related to Spearman’s hypothesis

25
2.2.7.1 Method of correlated vectors
Finally, we applied Jensen’s method of correlated vectors (MCV) to examine the
patterns of the genetic, brain volume, and admixture variables’ effects on cognitive test scores.
To do this, we computed standardized SIRE differences for each test as described below. We
also ran the Admixture regression analyses for the genetic, brain volume, and admixture
variables with cognitive test scores as the dependent variables. The effects on the eleven
cognitive tests formed the vectors. These vectors were then correlated with and without
corrections for test reliability. A genetic hypothesis for SIRE and ancestry differences predicts
a positive manifold of genetic, brain volume, and SIRE/ancestry effects. The reason is that if
genes related to g and brain volume are largely causative of differences both within and
between groups, then these genes will cause similar patterns of effects across cognitive tests (te
Nijenhuis, Choi, van den Hoek, Valueva, & Lee, 2019). For example, if eduPGS effects are
more pronounced on Matrix Reasoning than on Card Sorting, then we would expect ancestry
effects to be likewise if these ancestry effects on intelligence are due to eduPGS differences.
For these analyses, we computed the variables in such a way that they were
conceptually and statistically independent:
1. Cognitive test g loadings were based on factor analysis using the Schmid-Leiman
Transformation. The Schmid-Leiman Transformation separates g from non-g variance.
Detailed results are provided in Supplementary File 2, tab 11.
2. The effects of MTAG eduPGS & poly eduPGS on cognitive test scores were the
betas for the eduPGS predictor from the mixed-effects models which also included the cubic
spline of age, sex, and the first twenty genetic PCs in addition to site and family fixed effects.

26
3. The effect of European admixture on cognitive test scores were the betas for the
European ancestry predictor from the mixed-effects models which also include the cubic spline
of age, sex, US born status, immigrant family status, SIRE fraction, and Hispanic ethnicity in
addition to site and family fixed effects.
4. The effect of brain volume on cognitive test scores were the betas for the Brain
volume predictor from the mixed-effects models which also included the cubic spline of age,
sex, height, US born status, immigrant family status, SIRE fraction, Hispanic ethnicity, and the
first twenty genetic PCs in addition to site and family fixed effects.
5. Heritability estimates for the full sample were from the biometric analyses.
6. Black-White and Hispanic-White mean differences are computed as the sex- and
age- corrected mean differences divided by the standard deviations of the White group.
This procedure produced eight variables. These vectors were corrected for cognitive
test reliabilities, based on validation, standardization, and other samples. See Supplementary
File 2, Table S12a for the list of sources. Note that no reliability data were available for the
Little Man Test. For this reason, we ran the analyses for both vectors uncorrected for reliability
(N = 11) and for vectors corrected for reliability (N = 10). The uncorrected and corrected
vectors were then correlated using Pearson’s correlation (with results based on Spearman’s
correlation reported in Supplementary File 2, Table S12c).
A possible explanation for the association between the vectors of eduPGS-loadings and
both the vectors of ancestry effects and SIRE differences is that these variables are all related
to g loadings. According to this argument, these relations merely indicate that the relevant
variables are related to phenotypic g (Kan, 2012; Chapter 4). To test this conjecture, we use

27
partial correlations and control alternatively for the vector of g loadings and the vector of
eduPGS effects.
2.2.7.2 Factor analysis
As an alternative analysis, we factor analyzed the eight vectors using principal factor
analysis. This was done to determine if the SIRE/ancestry variables loaded strongly on the
same factor that genetic variables did.
2.3. Code and data
The R code used for these analyses is provided in Supplemental File 2. The complete
data set is available to qualified researchers at: https://nda.nih.gov/abcd
3. Results
3.1 Measurement of group differences
Descriptive statistics for the total sample and the four SIRE subsamples are shown in
Table 3, along with the Cohen’s d values between the White and the non-White groups. Based
on conventional standards (Cohen, 1988), there are medium to large differences between
Whites and non-White groups in g, eduPGS, and adjusted brain/intracranial volume. The
difference in g between Whites and Blacks was large and typically sized at d = 1.02. However,
the difference in g between Whites and Hispanics was only small to medium at d = 0.38. This
value is lower than that typically found (Warne, 2021). Regarding brain volume, Jensen (1998,
p. 438) notes a Black-White difference of d = .76 to .78 in brain weight based on autopsy data
of individuals without brain pathologies. Also, Rushton & Ankney (2009) note a 63 and 32
gram Black-White and Hispanic-White difference, respectively, in brain weight; however,
since standard deviations were not provided we were unable to convert these latter brain

28
weight differences into standardized units. For comparison, the Black-White adjusted brain
volume difference in this sample of healthy adolescents is approximately one standard
deviation (d = 1.12).
Table 1. Descriptive Statistics for the Total Sample and the Four SIRE Subsamples
____________________________________________________________________________
Full Sample
White
Hispanic
Black
Other
M
SD
M
SD
M
SD
M
SD
M
SD
W-H
d
W-B
d
W-O
d
Age
9.91
0.62
9.93
0.63
9.88
0.63
9.91
0.61
9.89
0.62
0.08
0.03
0.06
European ancestry
0.75
0.33
0.98
0.05
0.60
0.21
0.16
0.11
0.62
0.25
3.32
12.09
3.75
African ancestry
0.18
0.31
0.01
0.02
0.10
0.14
0.82
0.11
0.32
0.26
-1.24
-14.88
-3.48
Amerindian
ancestry
0.06
0.14
0.01
0.03
0.28
0.19
0.01
0.02
0.04
0.09
-2.72
0.00
-0.73
South Asian
ancestry
0.00
0.02
0.00
0.01
0.01
0.01
0.00
0.01
0.01
0.05
-1.00
0.00
-0.52
East Asian
ancestry
0.01
0.03
0.00
0.02
0.01
0.02
0.01
0.02
0.01
0.07
-0.50
-0.50
-0.33
Frac White SIRE
0.73
0.43
1.00
0.03
0.67
0.45
0.00
0.00
0.39
0.25
1.44
37.72
6.90
Frac Black SIRE
0.19
0.38
0.00
0.00
0.07
0.23
1.00
0.04
0.29
0.26
-0.60
-53.43
-3.33
Frac Native
American SIRE
0.02
0.11
0.00
0.00
0.03
0.13
0.00
0.00
0.18
0.28
-0.46
NA
-1.92
frac_NOC SIRE
0.06
0.23
0.00
0.03
0.23
0.42
0.00
0.04
0.13
0.34
-1.08
0.00
-1.11
Hispanic
0.20
0.40
0.00
0.00
1.00
0.00
0.00
0.00
0.00
0.00
NA
NA
NA
g
0.00
1.00
0.24
0.86
-0.10
0.99
-0.69
1.07
-0.08
1.07
0.38
1.02
0.36
SES
0.00
1.00
0.45
0.75
-0.38
0.90
-0.98
0.91
-0.39
0.99
1.05
1.82
1.08
MTAG eduPGS
0.00
1.00
0.49
0.77
-0.21
0.75
-1.34
0.57
-0.36
0.86
0.92
2.50
1.09
Poly eduPGS
0.00
1.00
0.48
0.78
-0.21
0.78
-1.30
0.60
-0.36
0.85
0.88
2.39
1.07
Brain Vol.
0.00
1.00
0.26
0.94
-0.18
0.95
-0.64
0.90
-0.13
1.00
0.47
0.97
0.41
Brain_Vol. adj.
0.00
1.00
0.29
0.92
-0.21
0.92
-0.74
0.91
-0.13
0.99
0.54
1.12
0.45
Intracranial Vol.
0.00
1.00
0.20
0.96
-0.19
1.01
-0.40
0.94
-0.21
1.01
0.40
0.63
0.42
Intracranial Vol.
adj.
0.00
1.00
0.23
0.94
-0.21
1.01
-0.47
0.95
-0.22
1.00
0.46
0.74
0.48
Height
0.00
1.00
-0.04
0.97
-0.12
0.97
0.26
1.09
0.05
0.97
0.08
-0.30
-0.09
Child US Born
0.98
0.15
0.99
0.11
0.94
0.24
0.98
0.15
0.98
0.14
0.32
0.08
0.09
Immigrant Family
0.28
0.45
0.18
0.38
0.73
0.44
0.14
0.35
0.20
0.40
-1.39
0.11
-0.05
N
10,245
5,858
2,005
1,642
740
___________________________________________________________________________________________
Notes: W-H d, W-B d, and W-B d are the Cohen’s d between, respectively, the White and Hispanic. White and
Black, and White and Other SIRE groups. A positive value indicates an advantage for the White group.

29
3.2 Measurement invariance
Using the same three broad-factor model to test for strict measurement invariance
between SIRE groups, we applied LSEM to the full sample (n = 10,245) using 11 focal points
(representing 10% ancestry increments, ranging from 0% to 100% European ancestry. Across
the full range of European ancestry, there was no deviation from strict MI. These results thus
agree with those of Lasker et al. (2019), who found that strict MI held across European genetic
ancestry in a large African and European American sample of Adolescents. This implies that
the difference in g observed cannot be attributed to other causes that differ between races, such
as test motivation differences (Lubke, Dolan, Kelderman, & Mellenbergh, 2003).
3.3. Within-group heritability and between-group environmentality
Table 2 shows the number of DZ and MZ twin pairs along with the ACE estimates for
adjusted brain and intracranial volume. ACE estimates for the unadjusted variables are
additionally provided in the supplementary material. For adjusted brain and intracranial
volume, heritability estimates were high for all groups (h2 = .75 to .95), consistent with
previously reported values for this age group (Jansen, Mous, White, Posthuma, & Polderman,
2015). With regards to brain volume, heritability estimates were somewhat higher for the non-
White sample (h2 = .94) than for the White sample (h2 = .79), however this difference was not
statistically significant. For intracranial volume, heritability was similar for the combined non-
White sample (h2 = .88) and for the White sample (h2 = .83).
Table 2. Variance Component Estimates for Brain Volume and Intracranial Volume
____________________________________________________________________________
a’
SE
c’
SE
e’
SE
a2
c2
e2
Brain Volume

30
Npairs
DZ
Npairs
MZ
All available
443
333
.87
0.04
.42
0.08
.28
0.01
.75
.17
.08
White-Hispanic-Black-Other
426
323
.87
0.04
.41
0.08
.27
0.01
.76
.16
.08
White
280
214
.89
0.05
.34
0.12
.30
0.02
.79
.11
.09
Hispanic-Black-Other
146
109
.97
0.00
.00
NA
.24
0.02
.94
.00
.06
Hispanic
43
34
.98
0.01
.00
0.00
.21
0.03
.95
.00
.04
Black
84
56
.93
0.08
.27
0.29
.24
0.03
.87
.07
.06
Other
19
19
.96
0.02
.00
0.00
.29
0.06
.91
.00
.09
Intracranial Volume
All available
443
333
.89
0.04
.39
0.08
.24
0.01
.79
.15
.06
White-Hispanic-Black-Other
426
323
.89
0.04
.39
0.08
.25
0.01
.78
.15
.06
White
280
214
.91
0.05
.32
0.13
.26
0.01
.83
.10
.07
Hispanic-Black-Other
146
109
.94
0.06
.26
0.23
.24
0.02
.88
.07
.06
Hispanic
43
34
.95
0.11
.24
0.45
.21
0.03
.90
.06
.04
Black
84
56
.90
0.08
.39
0.19
.21
0.02
.81
.15
.05
Other
19
19
.93
0.03
.00
0.00
.36
0.07
.87
.00
.13
____________________________________________________________________________
Notes: a and a2 represent, respectively, the genetic-phenotypic correlations and proportion of variance due to additive genetic effects; c and c2
represents, respectively, the shared environment-phenotypic correlations and proportion of variance due to shared environmental effects; e and
e2 represents, respectively, the shared environment-phenotypic correlations and proportion of variance due to non-shared environmental
effects; Npairs DZ is the number of dizygotic twin pairs; Npairs MZ is the number of monozygotic twin pairs. SE = standard error.
Table 3 shows the ACE estimates for the NIHTBX and g scores. More detailed results
are provided in the Supplementary File 2. Consistent with previously reported results (Pesta et
al., 2020), the heritability estimates of the NIH Toolbox scores were moderate-to-high for the
total, the White, and the combined non-White samples (h2 = .56 to .64). The heritability of the
NIHTBX battery was somewhat higher for the White sample (h2 = .64) than the non-White
sample (h2 = .56), though this difference was not statistically significant. For comparison, in
their meta-analysis, Pesta et al. (2020) found that heritabilities were approximately the same
among Hispanics, Blacks, and Whites. The heritability of our g scores was also somewhat
higher for the White sample (h2 = .67) as compared to the combined non-White sample (h2 =
.59), though, again, this difference was not statistically significant.

31
Supplementary File 2, tab 21, additionally reports the heritabilities for each of the 11
subtests used to create our g scores. These subtest heritabilities were used in the MCV analysis.
Table 3. Variance Component Estimates for NIH Toolbox cognitive scores
____________________________________________________________________________
a'
SE
c'
SE
e’
SE
a2
c2
e2
Npairs
DZ
Npairs
MZ
NIHTBX
All available
443
332
0.76
0.06
0.35
0.11
0.55
0.02
0.57
0.13
0.30
White-Hispanic-Black-Other
441
330
0.76
0.06
0.35
0.11
0.55
0.02
0.57
0.12
0.30
White
291
219
0.80
0.02
0.00
0.00
0.60
0.03
0.64
0.00
0.36
Hispanic-Black-Other
150
111
0.75
0.09
0.45
0.14
0.50
0.04
0.56
0.20
0.25
Hispanic
43
34
0.82
0.14
0.40
0.28
0.41
0.06
0.67
0.16
0.17
Black
87
58
0.73
0.13
0.40
0.22
0.55
0.05
0.54
0.16
0.30
Other
20
19
0.76
0.27
0.32
0.58
0.56
0.10
0.58
0.10
0.32
G
All available
434
319
0.78
0.05
0.36
0.11
0.52
0.02
0.60
0.13
0.27
White-Hispanic-Black-Other
430
319
0.78
0.05
0.35
0.11
0.52
0.02
0.61
0.12
0.27
White
291
220
0.82
0.02
0.00
0.00
0.57
0.03
0.67
0.00
0.33
Hispanic-Black-Other
139
99
0.77
0.09
0.41
0.16
0.50
0.04
0.59
0.16
0.25
Hispanic
43
34
0.32
0.25
0.82
0.08
0.48
0.06
0.10
0.67
0.23
Black
87
56
0.80
0.12
0.30
0.29
0.52
0.05
0.64
0.09
0.27
Other
9
9
0.80
0.11
0.00
NA
0.60
0.15
0.64
0.00
0.36
____________________________________________________________________________
Notes: a and a2 represents, respectively, the genetic-phenotypic correlations and proportion of variance due to additive genetic effects; c and c2
represents, respectively, the shared environment-phenotypic correlations and proportion of variance due to shared environmental effects; e and
e2 represents, respectively, the shared environment-phenotypic correlations and proportion of variance due to non-shared environmental
effects; Npairs DZ is the number of dizygotic twin pairs; Npairs MZ is the number of monozygotic twin pairs. SE = standard error.
3.4. Admixture regression for g
The triangle admixture plot for the full sample is shown in Figure 1. Hispanics had high
variability along the Amerindian-European axis and moderate variability along the African-
European axis. The African-American group and the Other group had, respectively, moderate
and high variability along the African-European axis. White Americans exhibited little

32
variability in ancestry. This pattern of admixture is typical for the US (Bryc, Durand,
Macpherson, Reich, & Mountain, 2015).
Figure 1. Admixture Triangle Plot for SIRE Groups in the ABCD Sample
The correlation matrices for the full sample and the SIRE subsamples are provided in
the Supplemental Materials (Tables S3a-S3e). Table 4 shows the results from the admixture
regression analyses for g. In this Table, Model 1 shows the results with SIRE but not genetic
ancestry variables, while Model 2a adds the four non-European genetic ancestries. Model 2b
adds SES to Model 2a. Models 3a and 3b repeat models 2a and 2b, replacing the four non-
European ancestries with European ancestry. In these last two Models (3a & 3b), age, instead
of cubic spline of age is used. This was done so that effect plots could be reported for the
results.

33
As seen in Model 1 and 2, SIRE variables are unrelated to g, independent of genetic
ancestry. Additionally, African, Amerindian, and European ancestry had large effects on g
even when the general factors of SES was added to the model.
Table 4. Regression Results for the Effect of Genetic Ancestry on g in the Full Sample
Model 1: g ~
SIRE
Model 2a: g ~
SIRE +
ancestries
Model 2b: g ~
SIRE +
ancestries +
SES
Model 3a: g ~
SIRE +
European
ancestry
Model 4b: g ~
SIRE +
European
ancestry + SES
Predictors
B
P
B
P
b
P
b
P
b
P
(Intercept)
0.75
(0.38)
0.051
0.62
(0.38)
0.100
0.43
(0.37)
0.247
-1.12
(0.18)
<0.001
-0.76
(0.17)
<0.001
frac_Black SIRE
-0.99
(0.03)
<0.001
0.03
(0.09)
0.733
0.06
(0.08)
0.501
0.04
(0.07)
0.566
0.01
(0.06)
0.825
frac_Native_American
SIRE
-0.36
(0.09)
<0.001
-0.07
(0.09)
0.463
0.02
(0.09)
0.791
-0.06
(0.09)
0.533
0.03
(0.09)
0.717
frac_NOC SIRE
-0.42
(0.05)
<0.001
-0.09
(0.05)
0.079
-0.01
(0.05)
0.760
-0.08
(0.05)
0.102
-0.01
(0.05)
0.846
Hispanic
-0.30
(0.03)
<0.001
0.01
(0.04)
0.791
0.06
(0.04)
0.135
-0.04
(0.03)
0.223
0.03
(0.03)
0.336
Child_US_Born
0.12
(0.06)
0.049
0.14
(0.06)
0.027
0.18
(0.06)
0.002
0.12
(0.06)
0.046
0.18
(0.06)
0.003
Immigrant_Family
0.10
(0.03)
<0.001
0.15
(0.03)
<0.001
0.08
(0.03)
0.001
0.16
(0.03)
<0.001
0.09
(0.02)
<0.001
sex [M]
-0.01
(0.02)
0.483
-0.01
(0.02)
0.696
-0.01
(0.02)
0.468
-0.01
(0.02)
0.721
-0.01
(0.02)
0.491
Age
-0.06
(0.04)
0.118
-0.05
(0.04)
0.233
-0.05
(0.04)
0.234
Age’
0.08
(0.05)
0.120
0.06
(0.05)
0.222
0.06
(0.05)
0.247
African ancestry
-1.34
(0.11)
<0.001
-0.87
(0.11)
<0.00
1
Amerindian ancestry
-1.56
(0.12)
<0.001
-0.90
(0.11)
<0.00
1
East Asian ancestry
0.13
(0.33)
0.703
0.21
(0.32)
0.516
South Asian ancestry
0.42
(0.56)
0.450
0.76
(0.54)
0.161
SES
0.33
(0.01)
<0.00
1
0.33
(0.01)
<0.001
European ancestry
1.35
(0.08)
<0.001
0.81
(0.08)
<0.001

34
Age
-0.00
(0.01)
0.891
-0.00
(0.01)
0.767
Random Effects
σ2
0.41
0.41
0.41
0.41
0.41
τ00
0.46
site_id_l:rel_family_id
0.02 site_id_l
0.44
site_id_l:rel_fa
mily_id
0.03 site_id_l
0.36
site_id_l:rel_fa
mily_id
0.05 site_id_l
0.44
site_id_l:rel_fa
mily_id
0.03 site_id_l
0.37
site_id_l:rel_fa
mily_id
0.05 site_id_l
ICC
0.54
0.53
0.50
0.53
0.50
N
22 site_id_l
8600 rel_family_id
22 site_id_l
8600 rel_family_id
22 site_id_l
8600 rel_family_id
22 site_id_l
8600 rel_family_id
22 site_id_l
8600 rel_family_id
Observations
10245
10245
10245
10245
10245
Marginal R2 /
Conditional R2
0.145 / 0.606
0.178 / 0.615
0.247 / 0.625
0.175 / 0.615
0.246 / 0.625
Notes: Beta coefficients (b) and p-values (p) from the mixed-effects models, with recruitment site and family
common factors treated as random effects are shown. The values in parentheses are standard errors. The marginal
and conditional R2 of the mixed effects model are shown at the bottom. ICC = Intraclass Correlation Coefficient.
Note, only linear age was used in context to European ancestry for reasons discussed in the methods section.
The effects of European, African, and Amerindian ancestry on g, stratified by SIRE, are
summarized in Table 5. The betas are from Models 1b to 2b from Tables S4a to S4e.
Statistically significant (p < .05) values are shown in bold. The complete model results are
provided in the Supplementary File 2. The relation between European, African, and
Amerindian ancestry and g is robust to SIRE stratification.
Table 5. Validities (b) from the Mixed-Effects Regression Models for Genetic Ancestry and
Brain and Intracranial Volume in the Full Sample and in the SIRE Subsamples
___________________________________________________________________________________________
Predictor
Criterion
Controls
Full sample
White
Hispanic
Black
Other
European Ancestry
g
1.35
1.33
1.33
1.06
0.96
g
w/ SES
0.81
0.79
0.82
0.84
0.54
African Ancestry
g
-1.34
-1.72
-1.10
-1.10
-1.21
g
w/ SES
-0.87
-.81
-.065
-0.88
-0.79

35
Amerindian Ancestry
g
-1.56
-1.86
-1.40
-3.84
-1.32
g
w/ SES
-0.90
-1.11
-0.86
-3.12
-0.79
N
10245
5858
2005
1642
740
___________________________________________________________________________________________
Note: Statistically significant results (p < .05) are presented in bold.
The partial residual plots with respect to European ancestry and g is depicted in Figure
2. These plots show the effect of European ancestry on g holding everything else in the
regression models constant. Supplementary File 2, Figures S4a-S4e provide the residual plots
for each SIRE subsample. This linear relationship is evident within each SIRE group and
within the full sample.
Figure 2. Partial Residuals and Estimated Regression Fits for European Ancestry in the
Admixture Regression with g as the Dependent Variable

36
3.5 Polygenic scores
Next, we report the relation between eduPGS and g. For these analyses g is the
dependent variable and the polygenic scores are the main predictors. The regression plots for
eduPGS and g in the Black (red), Hispanic (green), Other (blue), and White (purple) samples
are shown in Figure 3.
Figure 3. Regression plot for the predictive validity of eduPGS with respect to g in the Black
(red), Hispanic (green), Other (blue), and White (purple) samples
a. MTAG eduPGS
b. Poly eduPGS

37
We report results from the regression models for eduPGS and g. Tables S5a-S5e show
the complete results. Table 6 summarizes the results from these analyses. eduPGS are
significantly related to g in all groups. The validities for Black Americans are reduced by
around one-third relative to that for Whites. This finding is consistent with previously reported
results (Lasker et al., 2019).
Table 6. Validities (b) from the Mixed-Effects Regression Models for eduPGS and g in the Full
Sample and in the SIRE Subsamples
___________________________________________________________________________________________
Predictor
Criterion
Controls
Full
sample
White
Hispanic
Black
Other
MTAG eduPGS
g
w/ 20PCs, sex, age
0.26
0.26
0.26
0.16
0.32
Poly eduPGS
g
w/ 20PCs, sex, age
0.23
0.22
0.20
0.16
0.42

38
N
10245
5858
2005
1642
740
___________________________________________________________________________________________
Notes: Statistically significant results (p < .05) are presented in bold.
Finally, Table 7 reports the beta coefficients for the sibling and the comparable full
sample analyses with either g or NIHTBX as the dependent variable. The complete model
results are provided in Supplementary File S15b. Within sibships, both EduPGS were
statistically significant predictors of intelligence. The shrinkage of the within-sibship
coefficients, relative to the full sample coefficients, ranged from 20-27%.
Table 7. Validities (b) for the Within- and Between- Sibship and Full Sample Analyses with g
or NIHTBX as the Dependent Variable and EduPGS as the Predictors
___________________________________________________________________________________________
Predictor
Criterion
Controls
Within
Sibships b
(SE; N)
Between
Sibships b
(SE; N)
Full
Sample b
(SE; N)
Shrinkage
%
MTAG
eduPGS
g
20PCs, sex, age
0.20
(0.05; 2291)
0.28
(0.03; 2291)
0.25
(0.01; 10369)
20%
MTAG
eduPGS
NIHTBX
20PCs, sex, age
0.21
(0.05; 2323)
0.30
(0.03; 2323)
0.27
(0.01; 10039)
22%
Poly eduPGS
g
20PCs, sex, age
0.17
(0.05; 2302)
0.19
(0.03; 2302)
0.22
(0.01; 10369)
23%
Poly eduPGS
NIHTBX
20PCs, sex, age
0.16
(0.05; 2323)
0.22
(0.03; 2323)
0.22
(0.01; 10039)
27%
___________________________________________________________________________________________
Notes: Statistically significant results (p < .05) are presented in bold. Shrinkage % = 1 – Within (Sibships b / Full
Sample b).
3.6 Brain volume
3.6.1 Brain volume and g

39
Table 8 summarizes the effects (b) for brain volume on g for the full sample and the
SIRE subsamples. For these analyses, the adjusted brain volume variable is used. This adjusted
variable was then included in the mixed-effects model along with the first twenty genetic PCs.
The complete results are provided in Supplementary Tables S8a-S8e. As can be seen, brain
volume has a weak relation to g in the full sample and in all SIRE subsamples (bs = .12 to .25).
Adjusting for genetic PCs attenuates the effect somewhat in the full sample and also in the
three non-White samples, however the effects remain significant in all cases.
Table 8. Validities (b) from Mixed-Effects Regression Model for Brain Volume and g in the
Full Sample and in the SIRE subsamples
____________________________________________________________________________
Predictor
Criterion
Controls
Full sample
White
Hispanic
Black
Other
Brain Volume Adj
g
0.22
0.13
0.18
0.15
0.25
Brain Volume Adj
g
First 20
genetic PCs
0.14
0.13
0.12
0.13
0.20
N
10245
5858
2005
1642
740
__________________________________________________________________________________________
Note: Statistically significant results (p < .05) are presented in bold.
Finally, Table 9 reports the beta coefficients for the sibling and the comparable full
sample analyses with either g or NIHTBX as the dependent variable. The complete model
results are provided in Supplementary File S15a. Within sibships, brain volume was a
statistically significant predictor of intelligence. The shrinkage of the within-sibship
coefficients, relative to the full sample coefficients, ranged from 0-6%.
Table 9. Validities (b) for the Within- and Between- Sibship and Full Sample Analyses with g
or NIHTBX as the Dependent Variable and Brain Volume as the Predictor

40
___________________________________________________________________________________________
Predictor
Criterion
Controls
Within
Sibships B
(SE; N)
Between
Sibships B
(SE; N)
Full
Sample B
(SE; N)
Shrinkage
%
Brain volume
g
20PCs, sex, age
0.15
(0.04; 2258)
0.16
(0.03; 2258)
0.15
(0.01; 10247)
0%
Brain volume
NIHTBX
20PCs, sex, age
0.15
(0.04; 2189)
0.15
(0.03; 2189)
0.16
(0.01; 9920)
6%
___________________________________________________________________________________________
Notes: Statistically significant results (p < .05) are presented in bold. Shrinkage % = 1 – Within (Sibships b / Full
Sample b).
3.6.2 Brain volume, SIRE, and genetic ancestry
Table 10 shows the results from the admixture regression analysis for both brain
volume and intracranial volume. In this Table, Model 1a and 1b show the results for brain
volume as the dependent variable, while model 2a and 2b show those when intracranial volume
is the dependent variable. In both model 1b and 2b, European ancestry is used as the only
ancestry predictor.
As seen in all models, there was no association between SIRE and brain volume
independent of genetic ancestry. Moreover, the effect of African (b = -.89) and Amerindian (b
= -.96) ancestry, or conversely European (b = .91), on brain volume was large independent of
sex, age, height, migrant status, SIRE, the general factor of SES, and both site- and family-
related fixed effects. For intracranial volume the ancestry effects were moderate: European (b
= .68), African (b = -.68) and Amerindian (b = -.71).
The associations with European, African, and Amerindian genetic ancestry were
stronger for brain volume than for intracranial volume. It is not clear why this is the case as
these two variables correlate at r = .86 in the full sample. Both height and SES are significantly

41
related to brain and intracranial volume. These associations could be a result of genetic and
environmental factors.
Table 10. Regression Results for the Effect of Genetic Ancestry on Brain and Intracranial
Volume in the Full Sample
Model 1a:
Brain volume ~
non-European
ancestries
Model 1b:
Brain volume ~
European
ancestry
Model 2a:
Intracranial volume
~ non-European
ancestries
Model 2b:
Intracranial volume ~
European ancestry
Predictors
B
P
B
p
b
P
b
p
(Intercept)
0.54
(0.33)
0.098
-0.26
(0.16)
0.095
0.25
(0.32)
0.437
-0.41
(0.17)
0.016
African ancestry
-0.89
(0.09)
<0.001
-0.68
(0.09)
<0.001
Amerindian
ancestry
-0.96
(0.10)
<0.001
-0.71
(0.09)
<0.001
East Asian
ancestry
-0.39
(0.29)
0.175
-0.22
(0.27)
0.419
South Asian
ancestry
-1.73
(0.48)
<0.001
-1.68
(0.45)
<0.001
frac_Black SIRE
-0.00
(0.08)
0.969
0.01
(0.06)
0.820
-0.00
(0.07)
0.998
0.01
(0.05)
0.913
frac_Native
American SIRE
0.05
(0.08)
0.551
0.04
(0.08)
0.598
0.00
(0.08)
0.999
-0.01
(0.07)
0.924
frac_NOC SIRE
0.03
(0.04)
0.464
0.03
(0.04)
0.456
0.01
(0.04)
0.799
0.01
(0.04)
0.792
Hispanic
-0.00
(0.03)
0.894
-0.01
(0.03)
0.627
0.01
(0.03)
0.692
0.01
(0.03)
0.761
Child US Born
-0.02
(0.05)
0.720
-0.02
(0.05)
0.679
-0.06
(0.05)
0.209
-0.06
(0.05)
0.192
Immigrant Family
0.03
(0.02)
0.161
0.03
(0.02)
0.184
0.02
(0.02)
0.329
0.02
(0.02)
0.372
Sex [M]
0.94
(0.02)
<0.001
0.94
(0.02)
<0.001
0.86
(0.01)
<0.001
0.86
(0.01)
<0.001
Age’
-0.08
(0.03)
0.020
-0.05
(0.03)
0.114
Age”
-0.01
(0.05)
0.736
-0.00
(0.04)
0.950
Height
0.16
(0.01)
<0.001
0.16
(0.01)
<0.001
0.19
(0.01)
<0.001
0.19
(0.01)
<0.001
SES
0.10
(0.01)
<0.001
0.11
(0.01)
<0.001
0.10
(0.01)
<0.001
0.10
(0.01)
<0.001
European ancestry
0.91
(0.07)
<0.001
0.68
(0.07)
<0.001
age
-0.09
(0.01)
<0.001
-0.05
(0.01)
<0.001
Random effects
σ2
0.27
0.27
0.24
0.24

42
τ00
0.36site_1_id^rel_family
_id
0.01site_id_1
0.36
site_1_id^rel_family_id
0.01 site_id_1
0.30 site_1_id^rel_family_id
0.17 site_id_1
0.30 site_1_id^rel_family_id
0.17 site_id_1
ICC
0.58
0.58
0.66
0.66
N
22site_id_1
8600rel_family_id
22site_id_1
8600rel_family_id
22site_id_1
8600rel_family_id
22site_id_1
8600rel_family_id
Observations
10245
10245
10245
10245
Marginal R2/
Conditional R2
0.368/0.732
0.367/0.731
0.289/0.761
0.289/0.761
Notes: Beta coefficients (b) and p-values (p) from the mixed-effects models, with recruitment site and family
common factors treated as random effects are shown. The values in parentheses are standard errors. The marginal
and conditional R2 of the mixed effects model are shown at the bottom. ICC = Intraclass Correlation Coefficient.
Note, only linear age was used in context to European ancestry for reasons discussed in the methods section.
3.6.3 Brain/intracranial volume within SIRE groups
The effects of European, African, and Amerindian ancestry on brain and intracranial
volume, stratified by SIRE, are summarized in Table 11. The betas are from Models 1a to 2b
from Tables S6a to S6e, which report the equivalent model results from Table 8, above, for
each SIRE group. Statistically significant (p < .05) values are shown in bold. The complete
model results are provided in the Supplementary File 2. Generally, the finding of a positive
effect of European ancestry and a negative effect of both African and Amerindian ancestry is
robust to SIRE stratification.
Table 11. Validities (b) from the Mixed-Effects Regression Models for Genetic Ancestry and
Brain and Intracranial Volume in the Full Sample and in the SIRE Subsamples
___________________________________________________________________________________________
Predictor
Criterion
Full sample
White
Hispanic
Black
Other
European Ancestry
Brain Volume
0.91
0.85
0.91
0.96
0.80
African Ancestry
Brain Volume
-0.89
-0.74
-0.73
-1.02
-0.84
Amerindian Ancestry
Brain Volume
-0.96
-1.02
-0.92
-2.80
-0.91
European Ancestry
Intracranial
Volume
0.68
0.65
0.61
0.79
0.50

43
African Ancestry
Intracranial
Volume
-0.68
-0.40
-0.54
-0.84
-0.52
Amerindian Ancestry
Intracranial
Volume
-0.71
-0.93
-0.59
-2.45
-0.42
N
10245
5858
2005
1642
740
___________________________________________________________________________________________
Note: Statistically significant results (p < .05) are presented in bold.
Finally, Figure 4 depicts the partial residual plots with respect to European ancestry and
both brain and intracranial volume. As can be seen, there is a clear linear relationship between
European ancestry and both brain and intracranial volume. Supplementary File 2, Figures
S5a1-S53e2 provide the residual plots for each SIRE subsample. This linear relationship is
evident within each SIRE group.
Figure 4. Partial Residuals and Estimated Regression Fits for European Ancestry in the
Admixture Regression with Brain and Intracranial Volume as the Dependent Variables
a. Brain Volume

44
b. Intracranial Volume

45
3.6.4 SES, brain volume, and g among adopted and biological children
The full results for the adopted and biological child analyses are provided in
Supplementary File 2, Tab 14. In the model for g, the betas for SES were b = -.05 (S.E.: 0.12)
and .36 (S.E.: 0.02) for the adoptive and biological sample, respectively. In the model for brain
volume, the betas for SES were b= .01 (S.E.: 0.10) and .11 (S.E.: 0.02) in the adoptive and
biological sample, respectively. We reran the adoptive analyses, this time including an
interaction term for adoptive status and SES. Adoption status was statistically significant in
context to g (t-value = -3.405), but not brain volume. Overall, these adoptive results suggest
that the association between SES and g, in this ABCD cohort, may not be mediated by parental
environment. This may also be the case for brain volume, however the power is too limited to
draw conclusions.
3.6.5 Brain volume and eduPGS
For subsequent analyses, we restricted focus to brain volume, because it is more
plausibly a causal mediator of the relation between genetic ancestry and intelligence than is
intracranial volume. In these analyses, we first examine if brain volume is predicted by our two
eduPGS. We would expect this if variability in brain volume is related, genetically, to
variability in g (within and between SIRE groups). Table 12 shows the results from the
regression analysis for eduPGS and brain volume. Model 1a and 2a include sex, the cubic
spline of age, and height, along with site- and family-fixed effects. We do not include SES,
which includes parental education, since this is a criterion of eduPGS. Model 1b and 2b added
the first twenty genetic PCs to control for population structure. As seen, both eduPGS metrics
are significantly related to brain volume, in the full sample, with and without controls for
population structure.

46
Table 12. Regression Results for the Effects of Polygenic Scores on Brain Volume in the Full
Sample
Model 1a:
Brain Vol. ~
MTAG eduPGS
Model 1b:
Brain Vol. ~
MTAG eduPGS +
PCs
Model 2a:
Brain Vol. ~
Poly eduPGS
Model 2b:
Brain Vol. ~ Poly
eduPGS + PCs
Predictors
b
P
b
P
b
p
b
p
(Intercept)
0.26
(0.33)
0.436
0.33
(0.32)
0.302
0.18
(0.33)
0.588
0.31
(0.32)
0.344
MTAG eduPGS
0.27
(0.01)
<0.001
0.09
(0.01)
<0.001
Sex [M]
0.94
(0.02)
<0.001
0.94
(0.02)
<0.001
0.94
(0.02)
<0.001
0.94
(0.02)
<0.001
Age’
-0.08
(0.04)
0.029
-0.08
(0.03)
0.015
-0.07
(0.05)
0.051
-0.08
(0.03)
0.019
Age’’
0.00
(0.05)
0.960
-0.01
(0.05)
0.839
0.00
(0.05)
0.974
-0.01
(0.05)
0.814
Height
0.15
(0.01)
<0.001
0.16
(0.01)
<0.001
0.15
(0.01)
<0.001
0.16
(0.01)
<0.001
Poly eduPGS
0.26
(0.01)
<0.001
0.09
(0.01)
<0.001
Random effects
σ2
0.28
0.27
0.28
0.27
τ00
0.39site_id_1:rel_family_
id
0.01site_id_1
0.36
site_id_1:rel_family_id
0.01 site_id_1
0.39
site_id_1:rel_family_id
0.01 site_id_1
0.36 site_id_1:rel_family_id
0.01 site_id_1
ICC
0.59
0.57
0.60
0.58
N
22site_id_1
8600rel_family_id
22 site_id_1
8599 rel_family_id
22 site_id_1
8600 rel_family_id
22 site_id_1
8599 rel_family_id
Observations
10245
10244
10245
10244
Marginal R2/
Conditional R2
0.308/0.716
0.364/0.716
0.305/0.719
0.364/0.730
Notes: Beta coefficients (b) and p-values (p) from the mixed-effects models, with recruitment site and family
common factors treated as random effects are shown. The values in parentheses are standard errors. The marginal
and conditional R2 of the mixed effects model are shown at the bottom. Model 1b and 2b additionally control for
the first twenty genetic PCs. ICC = Intraclass Correlation Coefficient. Note, only linear age was used in context to
European ancestry for reasons discussed in the methods section.
Table 13 summarizes the effects (betas) for the eduPGS on brain volume for the full
sample and SIRE subsamples. The complete results are shown in Tables S7a to S7e of
Supplementary File 2. For Hispanics, Blacks, and the Other group, controlling for genetic
ancestry components attenuates the associations somewhat. However, except in the case of

47
MTAG eduPGS in relation to Blacks, the effects remain statistically significant when
controlling for genetic principal components, as would be expected were eduPGS causally
related to brain volume.
Table 13. Validities (b) from the Mixed-Effects Regression Models for eduPGS and Brain
Volume in the Full Sample and in the SIRE Subsamples
___________________________________________________________________________________________
Predictor
Criterion
Controls
Full sample
White
Hispanic
Black
Other
MTAG eduPGS
Brain Volume
0.27
0.10
0.19
0.08
0.21
MTAG eduPGS
Brain Volume
w/ 20PCs
0.09
0.10
0.11
0.01
0.09
Poly eduPGS
Brain Volume
0.26
0.09
0.17
0.12
0.23
Poly eduPGS
Brain Volume
w/ 20PCs
0.09
0.09
0.11
0.08
0.14
N
10245
5858
2005
1642
740
___________________________________________________________________________________________
Note: Statistically significant results (p < .05) are presented in bold.
3.6.6 Mediation by brain volume
We next report the path model results. In the following analysis, brain volume is
adjusted for the effects of sex, the cubic spline of age, height, and site- and family-related fixed
effects. As seen in Figure 5a/b both eduPGS and brain volume partially explain the association
between European ancestry and g. Moreover, the path between eduPGS and g is partially
mediated by brain volume. Note that in these models the effects are calculated by multiplying
the coefficients for each path and summing the products. For example, the effects of European
ancestry on g by way of brain volume is calculated as 1.004*0.119 (for European Ancestry →
Brain volume → g) + 2.14*0.111*0.119 (for European Ancestry → MTAG eduPGS → Brain
volume → g) = 0.15. The full model fit results along with the results for each SIRE subsample
are provided in Tables S9a-S9j of the Supplemental Material.

48
Figure 5. Path diagram for the relation between European ancestry, MTAG eduPGS, adjusted
brain volume and g in the Full sample
a. Path model using MTAG eduPGS
b. Path model using poly eduPGS

49
Note: N = 10,245. Full model results are provided in the Supplementary File.
It is possible that our eduPGS are simply capturing non-causal genetic European
ancestry effects. To test this conjecture, we ran a robustness analysis using pseudo eduPGS,
created by weighing random SNPS with the eduPGS beta weights. If eduPGS are simply acting
as proxies for global genetic ancestry, these pseudo eduPGS should do the same and produce
similar results. The results of this analysis are shown in Supplementary File 2, Tab 17. For the
ten individual pseudo-PGSs, path associations between European ancestry and pseudoPGSs
varied around zero (ranging from b = -1.13 to 1.05. The average of the ten showed no ancestry-
related association. Neither the average nor the individual pseudoPGSs predicted g or brain
volume. So, our eduPGS do not seem to be simply capturing non-causal genetic ancestry
effects.
A number of researchers (e.g., Warne, 2021; Nisbett et al., 2012) have objected to the
ancestry-brain volume argument using an analogy with sex differences. According to this

50
argument, there are large sex differences in brain volume favoring males, yet little to no
general intelligence ones. It is reasoned that, therefore, ancestry-associated differences in brain
volume do not need to be related to cognitive differences. Since in the ABCD sample there are
trivial sex differences in general intelligence, we could directly evaluate this hypothesis by
repeating the path model (b) above, but with two alternations. We changed European ancestry
to dummy-coded sex (Female = 1, Male = 0). Moreover, we replaced g scores, which were
adjusted for sex in the MGCFA model, with age-corrected NIHTBX composite scores (N =
9,904 in this subsample), which were unadjusted for sex.
Girls had trivially higher (d = .02) NIHTBX scores, overall. Figure 6 shows the path
model, with the full results provided in the Supplementary File. The path model for sex
differences shows that brain volume has a suppression effect on the female cognitive
advantage. Conditioned on brain volume girls, score higher than boys, but they have smaller
brains and so score about the same overall. Thus, brain volume is indeed related to sex
differences in general intelligence. Whereas brain volume has a suppression effect in context to
sex differences, it is a mediator of the European ancestry cognitive advantage. This is because
non-European ancestry is associated with lower, not higher, intelligence independent of brain
volume. Full model results are provided in the Supplementary File, tab 16.
Figure 6. Path Diagram for the Relation between Sex, Poly eduPGS, Adjusted Brain Volume
and g in the Full Sample

51
Note: N = 9,904.
The results for the causal mediation analyses are summarized in Table 14. The full
results are provided in Tables S10a-S10t of Supplementary File 2. All proportions were
statistically significant for all samples. Notably, brain volume mediated 11-23% of the
European ancestry and g association and 6-13% of the association between poly eduPGS and g.
Poly eduPGS, in turn, explained 14-25% of the relation between European ancestry and brain
volume.
Jensen (1998, p. 442) argued that brain size could explain 40% of the Black-White
SIRE differences based on an assumed within-population correlation, between brain volume
and g, of r = .40. In contrast, we find that brain volume can explain only approximately 15% of
the association between European genetic ancestry and g. This is because the beta for brain
volume with respect to g is relatively low within our sample of 10-year-old children. It is

52
notable, though, that the portion of ancestry difference explained corresponds approximately to
the within-SIRE effect of brain volume on g. This suggests that if the brain-volume-by-g
correlation increases with age, then a proportionately larger amount of the ancestry-by-g
relationship could be explained by brain volume. Since the ABCD follows the children for ten
years it will be possible to test this conjecture in the future.
Table 14. Summary of the Causal Mediation Results for the Full Sample and SIRE Subsamples
___________________________________________________________________________________________
Proportion of association mediated
Predictor
Mediator/
Component
Criterion
Full sample
White
Hispanic
Black
Other
European Ancestry
Brain Volume
g
15.50
18.62
11.36
17.49
23.20
European Ancestry
Poly eduPGS
Brain Volume
17.10
15.76
14.18
14.18
25.01
European Ancestry
Poly eduPGS
g
37.40
48.64
22.80
25.10
88.60
Poly eduPGS
Brain Volume
g
8.23
5.68
9.38
12.50
8.52
N
10245
5858
2005
1642
740
___________________________________________________________________________________________
Notes: Statistically significant results (p < .05) are presented in bold.
3.7 Spearman’s hypothesis
Table 15 reports the vectors of g loadings, eduPGS effects, European ancestry effects,
brain volume effects, heritabilities, and standardized Black-White (B-W) and Hispanic-White
(H-W) group differences for each of the cognitive tests.
Table 15. Vectors for MCV Analysis
___________________________________________________________________________________________
Subtests
Subtest
Reliability
g-
loading
Poly
eduPGS
MTAG
eduPGS
European
ancestry
Brain
Volume
h2
B-W
gap
H-W
gap
Picture vocabulary
0.80
0.612
0.206
0.228
1.351
0.121
0.338
1.09
0.70
Flanker
0.83
0.386
0.045
0.070
0.534
0.053
0.238
0.42
0.14
List sorting
0.77
0.559
0.162
0.169
0.858
0.092
0.384
0.85
0.44

53
Card sorting
0.81
0.433
0.075
0.098
0.601
0.046
0.335
0.59
0.27
Pattern comparison
0.73
0.338
0.045
0.058
0.308
0.015
0.205
0.43
0.12
Picture sequence memory
0.84
0.267
0.086
0.126
0.458
0.024
0.434
0.69
0.21
Oral reading recognition
0.90
0.600
0.189
0.223
0.957
0.145
0.497
0.67
0.31
Matrix
0.85
0.510
0.164
0.188
0.828
0.099
0.175
0.82
0.44
Little man test
0.228
0.063
0.088
0.194
0.070
0.345
0.64
0.23
RVLT immediate
0.76
0.530
0.120
0.151
0.634
0.023
0.461
0.79
0.38
RVLT delay
0.66
0.540
0.121
0.137
0.588
0.018
0.259
0.64
0.21
___________________________________________________________________________________________
Notes: h2 = cognitive test heritability estimates; B-W gap = standardized Black-White differences; H-W gap =
standardized Hispanic-White differences.
Table 16 shows the Pearson correlations between the vectors. (Table S12c in the
Supplementary material, additionally shows the Spearman correlations, but these were more or
less the same.) The results uncorrected for cognitive test reliabilities appear above the
diagonal; those corrected for test reliabilities appear below. Note the latter are based on one
less test, owing to missing data. As can be seen, all correlations are moderately to strongly
positive, with the exception of the correlation between g loadings and heritability (r = .17 to
.21) and heritability and brain volume (r = .08 to .21). For comparison, the literature reports a
bare-bones meta-analytic correlation of r = .31 (SDr = .43) (k = 12) between g loadings and
heritability (te Nijenhuis et al. 2019). A possible explanation for these low correlations with
heritabilities is that this sample consists of 10-year-old children and at young ages the specific
heritability estimates of cognitive tests is relatively high compared to the heritability
conditioned on g (Procopio et al., 2022). Alternatively, it is likely that the statistical
imprecision in estimation of ACE biases the correlations towards zero. Supplementary File 2,
Table S18 reports published vector correlations; the correlations in Table 14 generally agree
with those. Moreover, the results are in line with previous findings that both European genetic
ancestry and eduPGS are highly correlated with g loading.

54
The factor analysis of the eight vectors produced a single factor, which explained no
less than 71 percent of the variance. The factor loadings are provided in the final column of
Table 16. EduPGS, genetic ancestry, and the SIRE group differences had the highest loadings
on this common factor.
Table 16. Matrices of Correlations Between Vector Correlations, Uncorrected and Corrected
for Test Reliability along with Loadings on the Common Factor for the Vectors
___________________________________________________________________________________________
Vectors
Vector correlations (rs)
Factor loadings
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[1] g loading
1.00
0.84
0.79
0.86
0.45
0.17
0.58
0.67
.80
[2] Poly eduPGS
0.82
1.00
0.99
0.90
0.65
0.32
0.84
0.84
.99
[3] MTAG eduPGS
0.77
0.99
1.00
0.88
0.88
0.40
0.83
0.81
.97
[4] European Ancestry
0.76
0.90
0.88
1.00
0.64
0.20
0.77
0.87
.95
[5] Brain Volume
0.42
0.63
0.59
0.68
1.00
0.08
0.40
0.54
.60
[6] Heritability
0.21
0.32
0.39
0.21
0.21
1.00
0.30
0.19
.28
[7] B-W gap
0.66
0.85
0.84
0.83
0.33
0.30
1.00
0.96
.85
[8] H-W gap
0.68
0.84
0.82
0.91
0.52
0.20
0.95
1.00
.90
___________________________________________________________________________________________
Note: Correlations of cognitive test scores with g loadings, the effects of poly eduPGS, MTAG eduPGS, %
European ancestry, and adjusted brain volume on subtest scores, and the Black-White (B-W) and Hispanic-White
gaps. N = 11 subtests above the diagonal (with corrections for subtest reliability), and N = 10 below diagonal
(with no corrections for subtest reliability).
Finally, Table 17 shows the results, controlling alternatively for the vector of g loadings
and the vector of eduPGS effects using partial correlations. As seen, when g loadings are
controlled for, the positive manifold persists. This implies that the positive manifold is not
solely due to a common association with g loadings. In contrast, when eduPGS effects are
controlled for, the vector correlations often turn null or negative.

55
Table 17. Results from Method of Correlated Vectors Analysis Controlling for Poly eduPGS
(Above the Diagonal) and Controlling for g loadings (Below the Diagonal)
___________________________________________________________________________________________
[2]
[3]
[4]
[5]
[6]
[7]
[1] g loadings
0.42
-0.22
-0.18
-0.39
-0.11
-0.40
[2] European ancestry
1.00
0.16
-0.21
0.09
0.47
-0.09
[3] Brain Volume adj.
0.54
1.00
-0.17
-0.28
-0.02
-0.12
[4] Subtest Heritability
0.11
0.01
1.00
0.07
-0.15
0.55
[5] B-W difference
0.66
0.18
0.25
1.00
0.85
0.01
[6] H-W difference
0.76
0.35
0.10
0.94
1.00
-0.16
[7] MTAG eduPGS
0.65
0.49
0.44
0.73
0.63
1.00
[8] Poly eduPGS
0.65
0.56
0.32
0.78
0.68
0.97
___________________________________________________________________________________________
4. Discussion
4.1. General discussion
In the US, there are medium-to-large general mental ability differences between
Whites, Hispanics, and Blacks. Warne (2021) recently argued for a model of partial genetic
differences. We closely read Warne’s (2021) argument and the papers he cited. Based on this
careful reading, we identified 15 hypotheses.
4.1.1 Measurement of group differences
The first research question was if there were medium to large mean differences between
American SIRE groups in g, eduPGS and brain/intracranial volume. The data showed that this
was mostly the case. The exception was that Hispanics in our sample showed only a small to
medium sized difference in g (d = .38) which is smaller than typically reported. Overall, the
group differences in the ABCD sample were generally comparable to what was found in
previous studies.

56
4.1.2 Measurement invariance
The second research question was whether strict measurement invariance held across
the full range of European genetic ancestry. This was found to be the case. This is not entirely
surprising since strict measurement invariance held across the four SIRE groups, which differ
markedly in European genetic ancestry.
4.1.3. Within-group heritability and between-group environmentality
The third research question was if both general intelligence and brain/intracranial
volume are heritable in the full sample and within SIRE groups. In this national sample of ten-
year-old children, the heritability estimates of general intelligence were moderate to high in
both the White and the combined non-Whites sample. This is in line with the findings from
Pesta et al. (2020), who report similar heritabilities across White and non-White groups.
Moreover, both brain and intracranial volume were highly heritable in the full sample, the
White sample, and the non-White sample. The only other comparable SIRE-specific
volumetric estimates we are aware of are those reported by Rushton and Osborne (1995) for
cranial capacity. Those authors found White and Black heritabilities of h2 = .56 (111 pairs) and
h2 = .31 (125 pairs), respectively, for their age, height and sex adjusted cranial capacities. The
heritabilities in the present sample are higher.
The fourth research question was whether the heritability estimates for the White and
combined non-White groups were similar in magnitude. We found this to be the case. For NIH
Toolbox and g, the heritability estimates were somewhat higher for the White group (∆h2 =
.08), but nonetheless fairly similar. For brain and intracranial volume, the heritability estimates
were somewhat higher for the non-White group (∆h2 = .15 and ∆h2 = .05, respectively).

57
However, none of these differences were statistically significant. Generally, these results
suggest that adverse environments are not substantially depressing the heritabilities in the non-
White sample as predicted by some (e.g., Scarr-Salapatek, 1971; Van den Oord & Rowe,
1997).
4.1.4 Admixture regression for g
The fifth research question was if genetic ancestry explained SIRE differences in g.
This was found to be the case, in line with recent research results (e.g., Fuerst, 2021;
Kirkegaard et al., 2019; Lasker et al., 2019). In the full sample, SIRE variables had no validity
independent of genetic ancestry. Moreover, within all SIRE groups, European genetic ancestry
was positively related to g, while Amerindian and African ancestry were negatively so.
4.1.5 Polygenic scores
The sixth research question was whether eduPGS predicted intelligence within all SIRE
groups and within sibships. This was found to be the case. Consistent with previous results
(Howe et al., 2022), we found a within-sibship shrinkage, relative to the association within the
full sample, of between 20-27%. Generally, this finding supports the conclusion that eduPGS is
causally related to g within SIRE groups.
4.1.6 Brain volume
The seventh research question was if brain volume differences are related to g and to
eduPGS within all SIRE groups. Within all SIRE groups and within sibships brain volume was
related to g.
The eighth research question was whether brain/intracranial volume differences
between SIRE groups are explained by ancestry-associated genetic variation. We found that

58
SIRE differences were completely accounted for by genetic ancestry. African and Amerindian
ancestry both had a large negative effect on brain volume, while European ancestry had a
positive effect. For intracranial volume, the effects were moderate, but the same patterns were
found.
The ninth research question was if brain/intracranial volume correlated with genetic
ancestry within all SIRE groups. This was found to be the case. Generally, the results agree
with those from older studies, which report that either brain size/volume or cranial capacity is
related to ancestry among admixed American populations (e.g., Bean, 1906; Herskovits, 1969;
Pearl, 1934;).
The tenth research question was whether SES would be related to g and brain volume
among biological children but not adoptive children subsamples. It was found that SES was
uncorrelated with both g and brain volume among adopted children, while it was positively
correlated with both variables among biological children. These results are consistent with
previously reported ones which show that parental SES is unrelated to adoptive child IQ (e.g.,
McGue et al., 2007). The current findings suggest that the relation between parental SES and g,
in this sample, is primarily genetic in origin. Owing to low power, and thus relatively high
standard errors, a clear conclusion was not possible for parental SES and the brain volume of
adopted children.
The eleventh research question was if brain volume differences were predicted by
eduPGS in all SIRE groups. It was found that eduPGS predicted brain volume in 19/20 of the
models, and this included 9/10 of the models with controls for the first 20 principal
components. The sole exception involved MTAG eduPGS, but not the more causally-relevant
poly eduPGS, in relation to African Americans when controls for the first PCs were also

59
included. The interpretation in this one case is uncertain, since controlling for genetic PCs may
correct for causal genetic effects (Lawson et al., 2020). Considering the overall consistency of
the results, this one non-significant finding could be a fluke due to insufficient power.
Generally, these results confirm that eduPGS are related to brain volume and also that brain
volume is related to g in all SIRE groups.
The twelfth and thirteenth research questions concerned whether the relation between
European genetic ancestry and g was mediated both by eduPGS and brain volume and if the
pathway running from European ancestry through eduPGS to g was also mediated by brain
volume. The association between European genetic ancestry and g was partially statistically
accounted for by brain volume. Moreover, the pathways between European ancestry, polygenic
scores and g were also mediated by brain volume. This later finding supports the interpretation
that ancestry-related eduPGS differences are causally related to ancestry-associated differences
in g.
Various authors argue that there is a lack of relationship between brain size differences
and sex differences in intelligence and that ancestry differences in brain size might likewise be
unrelated to intelligence differences (Nisbett et al., 2012; Warne, 2021). However, we find that,
between sexes, brain size is indeed related to intelligence; specifically, the smaller brain
volume of girls moderates the female cognitive advantage. As there is no corresponding
African or Amerindian ancestry advantage, brain volume acts, instead, as a mediator with
respect to ancestry.
4.1.7 Spearman’s hypothesis
The fourteenth research question was if a positive manifold of effects across tests
would be found for SIRE/genetic ancestry, eduPGS, and brain volume. MCV provided

60
corroborating support for a model according to which ancestry and SIRE group differences are
partially genetic. The vectors of cognitive test effects associated with genetic, brain, and
ancestral/SIRE variables, exhibited a positive manifold as would be predicted if the variables
captured common g-related genetic effects. Moreover, the eduPGS correlated with ancestry
and SIRE group differences independent of g loadings.
To see if latter this finding replicated, we re-analyze data from Fuerst et al. (2021;
Table S5). Again, we find that eduPGS-loadings correlate with both the vectors of ancestry
effects and SIRE differences independent of g loadings (rs = .77 to .87). Results are reported in
Supplementary File 2, tab 19. This is a phenomenon in need of an explanation by a non-genetic
hypothesis. This pattern of effects on subtests is as would be predicted by a hypothesis of
partially genetic causation and is not readily predicted by non-genetic explanations. That said,
MCV is a crude method. This issue could be investigated further using biometric
decomposition of phenotypic mean differences (Jensen, 1998, pp. 464-467) or variants of this
method. Another solution is to carry out several replications, and to carry out a series of meta-
analyses and correct for well-known measurement errors (Jensen, 1998).
Finally, the fifteenth research question was whether there would be a higher-order
putative genetic factor resulting from the intercorrelating genetic variables and SIRE/genetic
ancestry in our study. This was found to be the case, though our heritability estimates loaded
weakly on this factor. This was perhaps due to the unreliability inherent in these estimates,
which had wide confidence intervals.
4.2. Limitations of the study
A number of researchers have called into question the trans-ancestral-group portability
of eduPGS (e.g., Harden, 2021). While there is continuing uncertainty in this regard, in these

61
analyses we used polygenic scores which either have previously been investigated for obvious
forms of confounding (in the case of European and African ancestries), or which have been
claimed to be precise indicators of causal effects. Thus, the forms of bias are limited.
Researchers who believe that these eduPGS differences do not correspond with genetic
differences which are causally related to intelligence should formulate specific, testable
hypotheses for the origin of these observed differences.
That said, the eduPGS scores of SIRE groups vary somewhat across different eduPGS.
This could be a result of bias in the eduPGS, or, alternatively, to differences in the underlying
trait indexed by the specific eduPGS (e.g., general intelligence, mathematical ability, or
educational attainment). In future research, it would be worthwhile to examine to what extent
group differences are consistent across an array of cognitively- and educationally-related
eduPGS.
It should be noted that for the admixture regression, path, and causal mediation
analyses we used g scores from a confirmatory factor model for which strict factorial
invariance (SFI) held across our four SIRE groups and the full range of European genetic
ancestry. SFI implies that the etiologies of between-group differences are a subset of the causes
of within-group ones (Lubke et al., 2003). Thus, the set of possible environmental explanations
of SIRE and ancestry differences in g is constrained (Warne, 2021).
This study builds upon previous admixture regression results by incorporating
neurological data. We use whole-brain volume as the neurological predictor due to its
evolutionary significance and also because of the large amount of research relating this
variable to both intelligence and evolutionary history. However, whole-brain volume is a crude
index of intelligence-related neurological features (Warne, 2021). This line of research could

62
be extended by developing a better neurological predictor of intelligence, using machine
learning, from the rich set of structural and functional MRI variables in the ABCD dataset.
There is a substantial body of research to work from in this regard (e.g., Pohl, Thompson,
Adeli, & Linguraru, 2019).
4.3. Conclusion
Taken together these results provide convergent genetically- and neurologically-
informed evidence for a partial genetic hypothesis with regards to differences in intelligence
between American self/parental identified race or ethnic groups. To paraphrase Sandra Scar
(1981, p. 528), holes can be poked in each line of evidence, but when the evidentiary lines are
laid on top of one another, like sheets of paper, the holes do not go all the way through.
However, although all this evidence points in the same direction, further replications and
extensions of the current results are clearly needed before drawing conclusions.
Author Contributions: JGRF conceptualized the project with EOWK’s input. All analyses
were conducted by JGRF. JtN, EOWK, & VS helped write and edit the manuscript.
Acknowledgments: Data used in the preparation of this article were obtained from the
Adolescent Brain Cognitive Development SM (ABCD) Study (https://abcdstudy.org), held in
the NIMH Data Archive (NDA). This is a multisite, longitudinal study designed to recruit more
than 10,000 children age 9-10 and follow them over 10 years into early adulthood. The ABCD
Study® is supported by the National Institutes of Health and additional federal partners under
award numbers U01DA041048, U01DA050989, U01DA051016, U01DA041022,
U01DA051018, U01DA051037, U01DA050987, U01DA041174, U01DA041106,
U01DA041117, U01DA041028, U01DA041134, U01DA050988, U01DA051039,

63
U01DA041156, U01DA041025, U01DA041120, U01DA051038, U01DA041148,
U01DA041093, U01DA041089, U24DA041123, U24DA041147. A full list of supporters is
available at https://abcdstudy.org/federal-partners.html. A listing of participating sites and a
complete listing of the study investigators can be found at
https://abcdstudy.org/consortium_members/. ABCD consortium investigators designed and
implemented the study and/or provided data but did not necessarily participate in the analysis
or writing of this report. This manuscript reflects the research results and interpretations of the
authors alone and may not reflect the opinions or views of the NIH or ABCD consortium
investigators. The ABCD data repository grows and changes over time. The ABCD data used
in this report came from Version 3.01. The raw data are available at
https://nda.nih.gov/edit_collection.html?id=2573. Instructions on how to create an NDA study
are available at https://nda.nih.gov/training/modules/study.html). Additional support for this
work was made possible from supplements to U24DA041123 and U24DA041147, the National
Science Foundation (NSF 2028680), and Children and Screens: Institute of Digital Media and
Child Development Inc.
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