A Genome-Wide Association Study Identifies Genetic Variants Associated with Mathematics Ability.

Mathematics ability is a complex cognitive trait with polygenic heritability. Genome-wide association study (GWAS) has been an effective approach to investigate genetic components underlying mathematic ability. Although previous studies reported several candidate genetic variants, none of them exceeded genome-wide significant threshold in general populations. Herein, we performed GWAS in Chinese elementary school students to identify potential genetic variants associated with mathematics ability. The discovery stage included 494 and 504 individuals from two independent cohorts respectively. The replication stage included another cohort of 599 individuals. In total, 28 of 81 candidate SNPs that met validation criteria were further replicated. Combined meta-analysis of three cohorts identified four SNPs (rs1012694, rs11743006, rs17778739 and rs17777541) of SPOCK1 gene showing association with mathematics ability (minimum p value 5.67 × 10-10, maximum β -2.43). The SPOCK1 gene is located on chromosome 5q31.2 and encodes a highly conserved glycoprotein testican-1 which was associated with tumor progression and prognosis as well as neurogenesis. This is the first study to report genome-wide significant association of individual SNPs with mathematics ability in general populations. Our preliminary results further supported the role of SPOCK1 during neurodevelopment. The genetic complexities underlying mathematics ability might contribute to explain the basis of human cognition and intelligence at genetic level.

Mathematics serves as a fundamental instrument in modern society as it plays an important role in many fields including science, engineering, and economics. It also used as a key index of human intelligence. Exceptional mathematics ability was frequently observed among genius from many domains. Meanwhile, dyscalculia, characterized by impaired number processing skills, is a specific developmental disorder of mathematics ability that affects approximately 3 to 6% of children1. Childhood mathematics ability was associated with adult socioeconomic status and quality of life2. Understanding mathematics ability is an essential step to improve children’s numeracy skills and academic achievements and could also provide novel insights into human brain functions. Mathematics ability is a complex trait that involves neurological and cognitive development as well as postnatal education and training. In particular, it is estimated that considerable proportion of variation in mathematic ability could be explained by genetic factors.

Recent years, genome-wide association study (GWAS) has been widely applied to investigate genetic components underlying complex traits3. The first GWAS of mathematics ability was performed among children with high and low mathematics ability respectively and nominated top-performing SNPs for subsequent validation in a large sample of individuals spanning the entire distribution of mathematical ability4. The study did not observe any SNPs alone showing genome-wide significant association with mathematic ability but hypothesized that genetic contribution to mathematics ability might be explained by multiple quantitative trait locus (QTLs) of small effect4. Indeed, the top 10 candidate SNPs only accounted for 2.9% of phenotypic variance in mathematics ability4. The second GWAS of mathematics ability used children’s verbal ability as control and then divided them into groups of high and low mathematic ability5. Candidate SNPs from the discovery stage were individually genotyped for validation but none of them exceeded threshold of genome-wide significance5. In the meantime, another GWAS in monozygotic and dizygotic twin pairs also observed a number of SNPs showing signals of associations with mathematic ability, but none of them achieved genome-wide significant level6.

To date, none of studies has identified genome-wide significant association with mathematics ability in general populations due to small effects of common variants. However, research with specific populations might increase statistical power to detect significant association as it was reported that prevalence of mathematic disability was higher among children with neurodevelopmental disorders such as reading disability, attention-deficit/hyperactivity disorder (ADHD) and autism78. The GWAS performed in German dyslexic children identified rs133885 as a genome-wide significant SNP associated with mathematics ability9. This variant is a coding variant of MYO18B and is associated with intraparietal sulcus morphology9. However, a recent replication study of rs133885 failed to find its association with mathematics ability in either dyslexic or general populations10.

Previous GWAS of mathematic ability is mainly performed in Western populations of which genetic backgrounds are substantially different to Chinese populations. In the present study, we performed GWAS of mathematic ability in the Han Chinese elementary school students through QTL-based approach. In total, we identified four SNPs exceeding genome-wide significant threshold which is the first time to report genome-wide significant association of individual SNPs with mathematics ability in general populations. Our results provide novel evidence to explain genetic complexities underlying mathematic ability and the basis of human intelligence at the genetic level.

Results

In the initial discovery phase, we performed a GWAS scan in two cohorts of Liangshan and Dongming (Supplementary Figure S1; Table 1). Breakdown of math scores according to grades, sex and regions of all participants were presented in Table 2. After quality control, about 1.1 million autosomal SNPs were analyzed (see Methods) in 998 samples (494 from the Liangshan cohort and 504 from the Dongming cohort). We performed linear regression in each cohort with adjustment for age, sex, school and top ten significant principal components of the corresponding cohort to test the additive effect of minor alleles of each SNP. In total, 13082 and 11170 SNPs with P-value less than 0.01 were identified in Liangshan and Dongming cohort respectively (Supplementary Figure S2). Results of the two discovery cohorts were combined by meta-analysis and 81 SNPs with P-value less than 1 × 10−5 were identified (Fig. 1). Finally, 28 SNPs met the criteria selection for subsequent replication stage (see Methods; Table 3).

Table 1

Basic characteristics of three populations.

Variables	GWAS		Replication Cao (n = 599)
	Liangshan (n = 494)	Dongming (n = 504)
Grade
2	98 (19.84)	98 (19.44)	121 (20.20)
3	103 (20.85)	101 (20.04)	134 (22.37)
4	122 (24.70)	102 (20.24)	136 (22.70)
5	82 (16.60)	99 (19.64)	108 (18.03)
6	89 (18.02)	104 (20.63)	100 (16.69)
Sex
Male	213 (43.12)	202 (40.08)	283 (47.25)
Female	281 (56.88)	302 (59.92)	316 (52.75)
Age, year	9.79 ± 1.39	9.51 ± 1.44	9.40 ± 1.45
Math score*	97 (93,99)	91 (83, 95)	95 (89,98)

*Full score is 100. Data are expressed as number of participants (percentage), mean ± SD or median (Q1, Q3).

Table 2

Breakdown of math score in all participants.

	Math score*			P value
	<80	80–90	≥90
Grade
2	12 (6.22)	35 (12.15)	275 (24.64)	<0.001
3	38 (19.69)	91 (31.60)	221 (19.80)
4	44 (22.80)	47 (16.32)	261 (23.39)
5	43 (22.28)	70 (24.31)	172 (15.41)
6	56 (29.02)	45 (15.63)	187 (16.76)
Sex
Male	77 (39.90)	125 (43.40)	506 (45.34)	0.28
Female	116 (60.10)	163 (56.60)	610 (54.66)
Region
Liangshan	16 (8.29)	49 (17.01)	429 (38.44)	<0.001
Dongming	92 (47.67)	149 (51.74)	263 (23.57)
Cao	85 (44.04)	90 (31.25)	424 (37.99)
Raven score**	45.76 ± 5.63	45.13 ± 5.75	46.69 ± 5.67	<0.001

Data are expressed as number of participants (percentage) or mean ± SD.

*Full math score is 100.

**Full Raven score is 60.

Figure 1

Manhattan plot of –log10 (P values) of meta-analysis result from the additive model after adjustment for sex, age, school and nominal significant principal components in GWAS in Liangshan and Dongming population.

The genome-wide threshold for significant (P = 5 × 10−8) and suggestive (P = 1 × 10−5) association are indicated by the horizontal blue and red lines, respectively. 81 SNPs in meta-analysis had P value < 1 × 10−5, of which 28 met the criteria for further replication. The symbol for the gene where the significant SNPs are in combined meta-analysis is shown in italics.

Table 3

SNPs met the criteria in GWAS discovery phase for further replications.

CHR	SNP	MAF	Position	Minor allele	Major allele	Liangshan			Dongming			Meta-analysis*
						β	SE	P	β	SE	P	β	SE	P**	PQ#
1	rs10779824	0.22	230231256	T	C	−1.95	0.53	2.35E-04	−1.91	0.76	1.28E-02	−1.94	0.43	7.79E-06	0.96
1	rs12733302	0.19	230259718	A	G	−2.12	0.55	1.49E-04	−2.19	0.78	5.38E-03	−2.14	0.45	2.18E-06	0.94
3	rs13096852	0.02	99909642	G	A	−5.50	1.58	5.42E-04	−5.52	1.85	2.98E-03	−5.51	1.20	4.50E-06	0.99
4	rs10007531	0.04	31909657	C	T	−4.11	1.07	1.31E-04	−4.67	1.60	3.64E-03	−4.28	0.89	1.37E-06	0.77
4	rs10014657	0.04	31909622	T	G	−4.12	1.07	1.27E-04	−4.96	1.65	2.83E-03	−4.36	0.89	1.09E-06	0.67
5	rs1012694	0.21	136535675	T	C	−2.90	0.56	3.13E-07	−2.36	0.81	3.82E-03	−2.73	0.46	3.17E-09	0.58
5	rs11743006	0.21	136550583	A	C	−2.90	0.56	3.13E-07	−2.27	0.80	4.99E-03	−2.69	0.46	4.33E-09	0.52
5	rs11746206	0.21	136483914	A	G	−2.14	0.56	1.58E-04	−2.47	0.80	2.29E-03	−2.25	0.46	1.08E-06	0.74
5	rs17720840	0.22	136513869	C	T	−2.09	0.57	2.44E-04	−2.27	0.81	5.13E-03	−2.15	0.46	3.46E-06	0.86
5	rs17777541	0.21	136522062	C	G	−2.89	0.56	3.89E-07	−2.28	0.80	4.89E-03	−2.69	0.46	5.23E-09	0.53
5	rs17778739	0.21	136551998	G	C	−2.90	0.56	3.13E-07	−2.28	0.80	4.89E-03	−2.70	0.46	4.22E-09	0.52
5	rs6890599	0.22	136458109	A	G	−1.88	0.55	7.10E-04	−2.29	0.80	4.34E-03	−2.01	0.45	9.31E-06	0.67
6	rs117368522	0.02	109576943	A	G	−6.91	1.80	1.40E-04	−9.86	2.70	2.86E-04	−7.82	1.50	1.77E-07	0.36
6	rs140472982	0.02	65729359	A	G	−5.34	1.63	1.16E-03	−9.76	2.57	1.67E-04	−6.61	1.38	1.63E-06	0.15
6	rs6927133	0.17	49543614	G	A	−1.65	0.59	5.37E-03	−3.56	0.85	3.10E-05	−2.27	0.48	2.61E-06	0.06
7	rs61109185	0.06	149025920	G	T	−4.00	1.05	1.59E-04	−4.37	1.35	1.30E-03	−4.14	0.83	6.04E-07	0.83
9	rs10746628	0.24	82952311	C	T	−1.49	0.53	5.01E-03	−3.26	0.75	1.81E-05	−2.07	0.43	1.60E-06	0.05
11	rs117620298	0.07	17960297	C	T	−3.10	0.90	6.55E-04	−4.17	1.28	1.17E-03	−3.46	0.74	2.77E-06	0.49
13	rs17076102	0.01	52492509	C	T	−6.60	1.81	2.90E-04	−7.27	3.02	1.66E-02	−6.77	1.55	1.26E-05	0.85
15	rs3751566	0.12	22940670	T	C	−2.55	0.68	1.85E-04	−2.52	1.09	2.14E-02	−2.54	0.58	9.94E-06	0.98
15	rs956120	0.13	22937838	G	A	−2.18	0.65	9.26E-04	−3.12	0.95	1.12E-03	−2.48	0.54	4.13E-06	0.42
16	rs1345872	0.18	73500800	G	A	−1.78	0.57	1.95E-03	−2.46	0.85	3.90E-03	−2.00	0.47	2.62E-05	0.51
17	rs11657625	0.16	21381802	C	T	−1.92	0.64	2.92E-03	−3.43	0.83	4.24E-05	−2.48	0.51	9.91E-07	0.15
18	rs12968137	0.08	33796927	T	C	−2.47	0.80	2.31E-03	−4.00	1.17	7.00E-04	−2.96	0.66	8.31E-06	0.28
19	rs74260502	0.04	45101336	T	C	−6.18	1.26	1.23E-06	−4.69	1.54	2.42E-03	−5.58	0.97	9.84E-09	0.45
20	rs11698429	0.30	13009926	T	C	−1.46	0.51	4.32E-03	−2.29	0.68	7.97E-04	−1.76	0.41	1.57E-05	0.32
20	rs3761896	0.32	12989901	C	T	−1.68	0.49	6.63E-04	−2.15	0.67	1.52E-03	−1.84	0.40	3.37E-06	0.57
20	rs3859619	0.32	12993893	C	A	−1.67	0.49	6.76E-04	−2.05	0.67	2.45E-03	−1.80	0.40	5.13E-06	0.65

*Meta-analysis of discovery 1 and 2 association results.

**P value from fixed model.

#PQ is the p value for Cochran’s Q statistic.

The 28 SNPs met the replication criteria were evaluated in an independent cohort (Cao, Table 4). After meta-analysis of all data from discovery and replication stages, four SNPs (rs1012694, rs11743006, rs17778739 and rs17777541) mapping to SPOCK1 gene exhibited association on genome-wide significant level for multiple testing (P < 5 × 10−8; Fig. 2; Table 4). However, rs17777541 did not show significant association with mathematics ability in the replication population. Results of these four significant SNPs were summarized in Table 5.

Table 4

Results of association of 28 SNPs with mathematics ability in replication and combined meta-analysis.

CHR	SNP	Position	Minor allele	Major allele	Cao			Combined Meta*
					β	SE	P	β	SE	P**	PQ#
1	rs10779824	230231256	T	C	0.64	0.79	4.16E-01	−1.34	0.38	4.26E-04	0.02
1	rs12733302	230259718	A	G	0.21	0.85	8.02E-01	−1.62	0.40	4.99E-05	0.05
3	rs13096852	99909642	G	A	0.73	1.80	6.87E-01	−3.59	1.00	3.27E-04	0.02
4	rs10007531	31909657	C	T	0.31	1.48	8.33E-01	−3.06	0.76	5.59E-05	0.03
4	rs10014657	31909622	T	G	−0.55	1.55	7.22E-01	−3.41	0.78	1.10E-05	0.09
5	rs1012694	136535675	T	C	−1.61	0.75	3.35E-02	−2.42	0.39	6.84E-10	0.39
5	rs11743006	136550583	A	C	−1.71	0.75	2.33E-02	−2.43	0.39	5.67E-10	0.44
5	rs11746206	136483914	A	G	−1.14	0.77	1.40E-01	−1.95	0.39	7.64E-07	0.44
5	rs17720840	136513869	C	T	−1.13	0.76	1.35E-01	−1.87	0.39	2.12E-06	0.51
5	rs17777541	136522062	C	G	−1.35	0.76	7.39E-02	−2.33	0.39	3.13E-09	0.27
5	rs17778739	136551998	G	C	−1.63	0.76	3.24E-02	−2.41	0.39	8.18E-10	0.40
5	rs6890599	136458109	A	G	−0.92	0.75	2.21E-01	−1.72	0.39	9.60E-06	0.42
6	rs117368522	109576943	A	G	−2.58	2.05	2.09E-01	−6.00	1.21	6.97E-07	0.08
6	rs140472982	65729359	A	G	4.12	2.58	1.10E-01	−4.23	1.21	5.07E-04	0.00
6	rs6927133	49543614	G	A	0.93	0.89	2.96E-01	−1.54	0.42	2.85E-04	0.00
7	rs61109185	149025920	G	T	−0.59	1.35	6.63E-01	−3.17	0.71	7.51E-06	0.08
9	rs10746628	82952311	C	T	−0.23	0.75	7.61E-01	−1.61	0.37	1.63E-05	0.02
11	rs117620298	17960297	C	T	0.48	1.53	7.53E-01	−2.72	0.66	4.39E-05	0.05
13	rs17076102	52492509	C	T	2.32	2.09	2.69E-01	−3.57	1.25	4.17E-03	0.00
15	rs3751566	22940670	T	C	−0.22	0.89	8.05E-01	−1.85	0.48	1.26E-04	0.09
15	rs956120	22937838	G	A	−0.17	0.88	8.42E-01	−1.85	0.46	5.84E-05	0.06
16	rs1345872	73500800	G	A	−0.31	0.79	6.94E-01	−1.55	0.41	1.40E-04	0.15
17	rs11657625	21381802	C	T	1.05	0.91	2.53E-01	−1.65	0.44	2.01E-04	0.00
18	rs12968137	33796927	T	C	2.85	1.09	9.14E-03	−1.39	0.57	1.45E-02	0.00
19	rs74260502	45101336	T	C	0.93	2.03	6.49E-01	−4.37	0.88	6.46E-07	0.01
20	rs11698429	13009926	T	C	0.87	0.68	1.99E-01	−1.06	0.35	2.30E-03	0.00
20	rs3761896	12989901	C	T	0.75	0.67	2.60E-01	−1.17	0.34	6.12E-04	0.00
20	rs3859619	12993893	C	A	0.79	0.67	2.40E-01	−1.14	0.34	8.23E-04	0.00

*Meta-analysis of all three populations.

**P value from fixed model.

#PQ is the p value for Cochran’s Q statistic.

Figure 2

Signal plot of the discovery-stage GWAS meta-analysis for new math score associated locus.

Signal plot of GWAS meta-analysis results and recombination rates in the GWAS discovery stage. The results (−log10P) are shown for SNPs around the region of SPOCK1 on chromosome 5. The genes within the region of interest are annotated, and the direction of the transcripts is shown by arrows. The key SNP (rs11743006) are shown in purple and the linkage disequilibrium values (r2) for the other SNPs are indicated by the heat scale.

Table 5

Summary of GWA scan and replication studies for the significant SNPs.

SNP	Stage	β	SE	P	PQ#
rs1012694 T/C* chr5:136535675**	Discovery 1	−2.90	0.56	3.13E-07
	Discovery 2	−2.36	0.81	3.82E-03
	Discovery combine	−2.66	0.49	8.41E-08
	Discovery meta	−2.73	0.46	3.17E-09	0.58
	Replication	−1.61	0.75	3.35E-02
	Combined meta	−2.42	0.39	6.84E-10	0.39
rs11743006 A/C* chr5:136550583**	Discovery 1	−2.90	0.56	3.13E-07
	Discovery 2	−2.27	0.80	4.99E-03
	Discovery combine	−2.61	0.49	1.28E-07
	Discovery meta	−2.69	0.46	4.33E-09	0.52
	Replication	−1.71	0.75	2.33E-02
	Combined meta	−2.43	0.39	5.67E-10	0.44
rs17778739 G/C* chr5:136551998**	Discovery 1	−2.90	0.56	3.13E-07
	Discovery 2	−2.28	0.80	4.89E-03
	Discovery combine	−2.62	0.49	1.18E-07
	Discovery meta	−2.70	0.46	4.22E-09	0.52
	Replication	−1.63	0.76	3.24E-02
	Combined meta	−2.41	0.39	8.18E-10	0.40
rs17777541 C/G* chr5:136522062**	Discovery 1	−2.89	0.56	3.89E-07
	Discovery 2	−2.28	0.80	4.89E-03
	Discovery combine	−2.61	0.49	1.25E-07
	Discovery meta	−2.69	0.46	5.23E-09	0.53
	Replication	−1.35	0.76	7.39E-02
	Combined meta	−2.33	0.39	3.13E-09	0.27

Discovery 1: Liangshan population.

Discovery 2: Dongming population.

Discovery combine: Liangshan and Dongming populations combined directly.

Discovery meta: meta-analysis of discovery 1 and 2 association results.

Replication: Cao population.

Combined meta: meta-analysis of association results in three populations.

*Minor allele/Major allele.

**Chromosomalposition (Build 37).

#P value for Cochran’s Qstatistic.

Discussion

Despite substantial heritability underlying mathematics ability, contribution of SNPs to this complex cognitive trait remained inconclusive. Previous GWAS of mathematics ability in general populations proposed candidate SNPs spanning chromosome 2, 3, 4, 5, 6, 7, 11, 12, 13, 20 and 21456. However, none of them showed consistent association during subsequent replication and therefore failed to exceed genome-wide significant level. Meanwhile, some studies reported sporadic association of copy number variations with mathematics ability but few of them been validated independently111213. In the present study, we performed GWAS of mathematics ability in the Han Chinese general populations. Our genome-wide scan during discovery stage covered all previous nominated regions that might associate with mathematics ability. Although some SNPs located near previous reported region showed significant signal, only four SNPs (rs1012694, rs11743006, rs17778739 and rs17777541) were successfully replicated and achieved genome-wide significant level (minimum P value 5.67 × 10−10). Each minor allele of these four SNPs was associated with decrease of math score ranges from 2.33 to 2.43 points approximately. To our knowledge, it is the first time to report association of a single SNP with mathematic ability at genome-wide significant level in general populations.

These SNPs are intron variants of SPOCK1 and in highly linkage disequilibrium. The most significant SNP rs1012694 is located between exon 3 and 4 of SPOCK1. This gene is located on chromosome 5q31.2 and encodes sparc/osteonectin, cwcv and kazal-like domains proteoglycan (testican) 1. Testican-1 is a highly conserved glycoprotein that involved in regulating proliferation, cell-cycle progression, apoptosis, adhesion, and cell-matrix interaction14. SPOCK1 and its gene product testican-1 have been associated with tumor progression and prognosis of different cancer types. Expression of SPOCK1 at mRNA and protein level was upregulated by the transcription factor CHD1L which could directly bound to promoter region of SPOCK115. In hepatocellular carcinoma and gallbladder cancer, elevated expression of SPOCK1 resulted in activation ofPI3K/AKT signaling which could block apoptosis and promote proliferation, invasiveness and metastasis of cancer cells1617. In addition, increased expression of SPOCK1 was implicated in epithelial-to-mesenchymal transition (EMT) which promoted migration and invasion in lung cancer and esophageal squamous cell carcinoma and conferred acquired drug resistance in gastric cancer181920. Therefore, SPOCK1 has been considered as a novel prognostic and therapeutic target for various cancer types.

Although the role of SPOCK1 in cancers has been relatively well understood, its contribution to neurological and cognitive development remains elusive. Recently, novel de-novo SPOCK1 mutation was reported in a female proband with developmental delay, microcephaly and agenesis of corpus callosum21. Her features were similar to previously reported microdeletions of 5q31 for intellectual disability21. As there were no mutations or variants of other genes identified in the proband showed potential relevance, SPOCK1 located within 5q31 was suggested to be a candidate gene of observed developmental abnormalities. The identified de-novo mutation of SPOCK1 might be protein-damaging which could potentially lead to developmental delay and microcephaly. Therefore, SPOCK1 might play a critical role during neurogenesis. Indeed, testican-1, encoded by SPOCK1, was shown to inhibit attachment of Neuro-2a cells and their ability to form neurite extensions22. In addition, it also served as a strong competitive inhibitor of the lysosomal cysteine protease cathepsin L23. During early development of mice embryos, testican-1 was strongly expressed in developing brain and modulates neurogenesis and axonal growth24. At later developmental stage, testican-1 was particularly prevalent within developing synaptic fields25. Altered expression pattern of testican-1 mRNA was observed in reactive astrocytes after brain injury therefore suggested a role of testican-1 in regenerating axons26.

Some potential limitations of the present study should be noted. The effect sizes might have been slightly overestimated due to lack of the adjustment for risk factors such as family socioeconomic status. Using nonverbal intelligence as an exclusion criteria might result in biased distribution of children’s math scores as it was assumed that children with lower nonverbal intelligence seems more likely to have lower math scores as well. In addition, sample size of our study were relatively small compared with genome-wide studies of chronic diseases such cancer or diabetes. However, the strengths of our study include its stringent quality control procedures and all participants genotyped by using the Affymetrix Axiom Genome-Wide CHB1 and CHB2 arrays which contain over one million SNPs specifically designed for Chinese population.

In conclusion, we reported four genetic variants of SPOCK1 that showed genome-wide significant association with mathematic ability in Chinese children. Mathematic ability is a complex trait that involved polygenic and environmental factors. SPOCK1 and its gene product tesican-1 showed potential functional relevance to neurodevelopment. Our study has identified a susceptibility gene, SPOCK1, which provides novel genetic insights into development of mathematics ability and the basis of human intelligence.

Methods and Materials

Participants

We recruited 2,425 grade two to grade six primary students aged 7 to 13 from three counties, Liangshan, Dongming and Cao, in Shandong Province in China. In the first step, Raven’s Progressive Matrices test for nonverbal intelligence was administered to these eligible children individually, whose nonverbal intelligence scores lower than the 25th percentile were excluded from this study. In total, 1622 participants (Liangshan: 501, Dongming: 522, Cao: 599) were eligible for subsequent genotyping and association analysis. Mathematic ability was measured by children’s academic performances of mathematics according to their mid-term and final exam of each semester. The examination papers were designed by education authorities of Shandong Province for each grade respectively according to the curriculum. Therefore, different tests will be applied to children in different grades but children in same grade will take exactly the same test. The tests aimed to evaluate children’s academic performances of mathematics from three perspectives including “understanding numbers”, “computing and knowledge” and “non-numerical processes”. The teacher’s rating process was double-blinded as student’s answer sheet will be randomly and anonymously distributed to different teachers. Answers of all questions are clear and definite. There was no arbitrariness in scoring as teachers from different schools received unified training to ensure that their rating criteria for each student are standardized and objective. The mean score of mid-term and final exam within in same semester that were usually conducted within a 3-month interval was calculated for the analysis. This study was approved by the ethical committee of Tsinghua University School of Medicine. The methods were carried out in accordance with the relevant guidelines. Informed consent was obtained from all subjects.

Genotyping and quality control in the GWAS

DNA was extracted from blood samples and SNP genotyping was performed with the Affymetrix Axiom Genome-Wide CHB1 and CHB2 arrays (1,284,609 SNPs) by CapitalBio Technology (Beijing, China). Quality control was performed followed by standard quality control metrics27. Six samples in Dongming were excluded as they had sex discrepancies between the records and the genetically inferred data, three and four samples in Liangshan and Dongming respectively were excluded as they had overall successful genotyping call rates <95% orhad outlying autosomal heterozygosity rates (out of range of mean ± 3 SD). Next, we removed four and eight individuals in Liangshan and Dongming respectively who had unexpected duplicates or probable relatives (all PI_HAT > 0.20). Finally, we detected population outliers using a method based on the principal component analysis. Common autosomal SNPs in each cohort were employed to identify population outliers in the samples that had passed the quality control, with four original HapMap populations (CEU, CHB, JPT and YRI). In the next step, we performed basic quality control on genotyping data. In total, 40428 and 117542 SNPs in Liangshan and Doming respectively were excluded with call rate of <95%, 57985 and 56307 SNPs in Liangshan and Doming respectively were excluded with minor allele frequency (MAF) of <0.01, 3679 and 2323 SNPs in Liangshan and Doming respectively were excluded with genotype distribution that deviated from the Hardy–Weinberg equilibrium (P < 1.0 × 10−5). After quality control procedures had been performed, 494 children with 1182517 SNPs from Liangshan and 504 children with 1108437 SNPSs from Dongming were included in the final analysis.

Cao sample genotyping

Replication samples were typed at CapitalBio Technology (Beijing, China) with Sequenom MassARRAY platform (San Diego, U.S) according to the manufacturer’s protocol. Briefly, genomic DNA was extracted from saliva of each individual through OrageneTM DNA self-collection kit according to the manufacturer’s instructions (Ottawa, Canada). DNA concentration was determined by Nano Drop 1000 (Waltham, U.S). Specific assays were designed using the MassARRAY Assay Design software package (v3.1). Mass determination was carried out with the MALDI-TOF mass spectrometer and Mass ARRAY Type 4.0 software was used for data acquisition.

Genome-wide association analysis

After quality control, association analyses and meta analyses were performed using PLINK1.928, fitting an additive model to the data by linear regression model with adjustment for sex, age and principle components in GWAS Liangshan and Dongming samples respectively. SNPs with a P-value < 0.01 were further analyzed by the meta-analysis based method to combine the results from Liangshan and Dongming samples as the discovery phase. SNPs with a P-value < 1.0 × 10−5 were selected for replication in Cao population. Finally, a meta-analysis was conducted to combine results from the three populations. A fixed-effect model with inverse variance weighting was used when there was no indication of heterogeneity (P for Cochran’s Q statistic >0.05); otherwise, a random-effect model for the corresponding SNPs was adopted. A Manhattan plot of −log10P was generated using the ggplot2 package29 in R 2.15.1.

Power

Power calculations were performed using Quanto version 1.2.4 (http://biostats.usc.edu/Quanto.html). Under the additive model, it had 80% power at the p < 0.05 level to detect association with an allelic variant of 20% frequency accounting for 1.58% and 1.55% of the variance in math score in Liangshan and Dongming populations respectively.

Additional Information

How to cite this article: Chen, H. et al. A Genome-Wide Association Study Identifies Genetic Variants Associated with Mathematics Ability. Sci. Rep. 7, 40365; doi: 10.1038/srep40365 (2017).

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