Identification of loci involved in childhood visual acuity and associations with cognitive skills and educational attainment

Visual acuity significantly contributes to quality of life. Deficits in childhood are associated with reading difficulties, which can have detrimental effects on education outcomes. In adults, it has been observed that vision defects such as myopia are associated with higher educational attainment (EA). Understanding genetic factors contributing to visual acuity could help to dissect its links with cognitive skills, neurodevelopmental conditions, and education. We examined associations between distance visual acuity, cognitive measures including school grades, and neurodevelopmental conditions in a longitudinal cohort of British children (ALSPAC, n = 6807, M age = 11.8). We performed a genome-wide association study (GWAS, n = 5571) on visual acuity and tested for genetic associations with relevant phenotypes using polygenic scores (PGS) and genetic correlation analyses. Visual acuity was associated with better cognitive performance and school grades, and reduced in individuals with reading difficulties compared to controls. GWAS revealed genetic associations at the NPLOC4 locus and highlighted other genes involved in sensory function. In line with positive genetic correlations between visual acuity and cognitive measures, EA PGS were positively associated with visual acuity, while there was a less robust negative association with myopia PGS. In conclusion, increased visual acuity is associated with a range of positive outcomes, including better school grades. Our results suggest an association between a higher EA PGS and slightly increased visual acuity in childhood. This could indicate gene-environment correlation, in which environmental exposures linked to higher EA might have detrimental effects on vision offsetting the initial positive effect.


INTRODUCTION
Visual function has a significant impact on perceived quality of life, which is expressed vividly in the finding that on average, elderly subjects with reduced visual function (n = 325) would trade 20% to 50% of remaining lifetime for perfect vision 1 . Visual acuity is defined as the visual system's ability to resolve spatial detail and usually measured as distance visual acuity with the chart placed 20 feet or 6 metres away. The most common defect underlying reduced visual acuity is uncorrected refractive error. Refractive error is present when the light from an object of interest is not focussed accurately onto the retina and most commonly due to the eyeball being longer or shorter than normal 2 . In children, the risk for significant uncorrected myopia (typically defined as ≤ -8 to -5 dioptres) is inversely related to visual acuity 3 .
Variation in visual acuity has been tested for an association with neurodevelopmental conditions such as ADHD and autism spectrum disorder (ASD) with varied results [4][5][6][7] . The magnocellular theory of dyslexia suggests that a large part of the variance in reading skill is determined by visual and auditory sensitivity 8 . Several studies have focused on possible associations between visual acuity and reading skill. Among 1910 US school children, students with poor visual acuity were equally likely to be aboveaverage, average or below-average readers 9 . In contrast, in a UK sample (overall n = 9545), children with bilateral deficits in near visual acuity (but not children with, e.g., unilateral or distance visual acuity deficits) were underachieving at reading after adjustment for socioeconomic status (SES), intelligence, and sex 10 . Moreover, children with dyslexia (n = 86) have been found to perform worse on near and distance visual acuity tests than sex-, age-, and IQmatched controls 11 . Variation in visual acuity has been associated with early literacy at 4-5 years (n = 2025) 12 but has not been found to be associated with school grades after adjusting for sex, ethnicity, school, reading skill, IQ, and paternal education 13 suggesting that its proximal effects are on reading skill.
Previous GWAS on visual function have almost exclusively been performed in older cohorts. However, the 39 lead single nucleotide polymorphisms (SNPs) associated with refractive error 28 have shown different effects on refractive error in different age groups 32,33 most likely due to gene-environment interactions 16 . For example, individuals at high genetic risk for myopia have a much more increased myopia risk if they have a University degree (OR~51 compared to the general population) than if they only have primary schooling (OR~7) 34 . Using Mendelian randomisation, it has been shown that higher educational attainment (EA) poses a causal risk factor for myopia (i.e., reduced visual function) rather than vice versa 35 . However, associations between visual acuity and cognitive measures described above suggest that visual and cognitive function are linked positively in childhood. This differing pattern in childhood vs. adulthood could be explained by gene-environment correlation. That is to say, the genetic background contributing to adult EA is associated with better childhood visual acuity (given its positive effect on cognitive skills), resulting in better school performance. This might lead to more time spent indoors, reading, and screen time and eventually increased myopia risk. If this is the case, polygenic scores (PGS) for EA should show a positive rather than negative association with childhood visual acuity ( Fig. 1, red dotted arrow). Instead, a PGS for myopia represents a biological mechanism affecting visual function unrelated to the environment and should therefore show a negative association with childhood visual acuity ( Fig. 1, black dotted arrow).
In the present study, we examined associations between visual acuity at the age of 11.8 years and cognitive measures including reading skill and school grades in the Avon Longitudinal Study of Parents and Children (ALSPAC) cohort (n = 6807). We performed a GWAS on visual acuity in children (n = 5571) and tested for associations with various cognitive measures, neurodevelopmental conditions, and visual phenotypes using PGS and genetic correlation analyses. Partial correlation analyses adjusting for sex and age revealed positive correlations between visual acuity and cognitive performance including General Certificate of Secondary Education (GCSE) scores (all p < 3.0 × 10 −7 ) (Fig. 3a, correlation plots in Supplementary Fig. 2). Partial correlation analysis between visual acuity and GCSE adjusting for sex, age, reading skill, verbal IQ, performance IQ, and SES revealed an attenuated, but significant association (r (5662) = 0.05, 95% CI = [0.02, 0.08], p = 0.001).

Visual acuity and cognitive abilities
We previously also reported associations between hearing ability and cognitive and neurodevelopmental traits 36 . To ensure that associations between visual acuity and cognitive traits are not driven by associations of visual acuity with hearing ability, we performed bivariate Pearson correlations on visual acuity and hearing threshold in the sample overlapping our previous study (n = 4929). Partial Pearson correlation analysis adjusting for sex and age did not reveal evidence for a correlation between visual acuity and hearing threshold (r (4927) = −0.02, 95% CI = [−0.05, −0.005], p = 0.104), suggesting independence of hearing and vision phenotypes. Associations between visual acuity, cognitive skills, and adult myopia. There is a negative link between visual acuity and myopia risk in childhood (not shown). Therefore, we expect that genetic factors known to increase myopia risk (myopia PGS) are negatively associated with visual acuity (black dotted arrow). However, visual acuity has been associated with increased cognitive skills, contributing to more years spent in education, which have been shown to increase myopia risk (red solid arrows). Therefore, we expect a positive association between the PGS for educational attainment (EA) and childhood visual acuity (red dotted arrow). The discrepancy of EA PGS being associated positively with childhood visual function and EA being associated negatively with adult visual function (in that it increases myopia risk) suggests geneenvironment correlation. Specifically, the same factors associated with better vision earlier (EA PGS) are also associated with environmental exposures with detrimental effects on vision. Arrows represent a positive association unless otherwise indicated with a minus symbol (-). One-way between-subjects ANOVA revealed a significant main effect of SES on visual acuity after adjusting for sex and age (F (4,6230) = 17.78, η 2 = 0.01, 95% CI = [0.01, 1.00], p = 1.6 × 10 −14 ). Post-hoc comparisons using the Tukey test indicated significant differences between most SES groups (Supplementary Tables 3  and 4), suggesting that higher SES is associated with better visual acuity (Fig. 4a). Moreover, there was a significant but small main effect of neurodevelopmental condition on visual acuity after adjusting for sex and age (F (4,2666) = 6.54, η 2 = 0.01, 95% CI = [0.00, 1.00], p = 3.1 × 10 −5 ) with post-hoc comparisons indicating reduced visual acuity in the reading difficulty group (n = 203, mean = 106.71, SD = 3.77) compared to the control group (n = 2238, mean = 107.89, SD = 3.69, adjusted p = 0.0001) (Fig. 4b).

GWAS
Twelve SNPs at the NPLOC4 locus on chromosome 17 reached genome-wide significance (Fig. 5a, Supplementary Table 6, QQ plot Supplementary Fig. 3). The strongest association was found for rs11656126 (p = 2.1 × 10 −8 ) with each copy of the major allele (G) (MAF = 0.35) shifting an individual 0.11 SD towards better visual acuity. The top marker on chromosome 5 (rs159195) is located in an intron of PDE4D.
In the targeted replication analysis of SNPs derived from previous literature, two genomic loci reached Bonferroni-corrected significance (Supplementary Table 7). The first locus spanned 20 SNPs in the chromosomal region 17:79526821-17:79630941, including the NPLOC4 and the PDE6G gene. Among the 20 SNPs  was rs6420484, for which each copy of the A allele has previously been associated with reduced refractive error (ß = −5.94, p = 2.8 × 10 −9 ) 17 . Likewise, in our study, each copy of the A allele shifted an individual towards reduced visual acuity (MAF = 0.35, ß = −0.11, p = 9.3 × 10 −8 ). The second locus spanned four SNPs in the chromosomal region 2:233372766-2:233385025, located in an intergenic region upstream of PRSS56 previously associated with myopia 28 and refractive error 16 .

Post GWAS analysis
In line with SNP-based analysis, NPLOC4 was the top hit in genebased analysis (Fig. 5b, QQ plot Supplementary Fig. 4, p = 1.2 × 10 −6 ). FUMA revealed that SNPs in the NPLOC4 locus have been previously linked to sensory phenotypes such as advanced age-related macular degeneration, spherical equivalent (i.e., refractive error), and refractive astigmatism (GWAS catalog, Supplementary Table 8). The significant locus spans multi-tissue eQTLS influencing the expression of genes at the NPLOC4 locus including PDE6G and TSPAN10 (Supplementary Table 9). Across samples genetic correlation SNP-h 2 for visual acuity (estimated using LDSC) was 0.18 (SE = 0.09). Visual acuity showed significant genetic correlations with cognitive performance and EA, but no genetic correlation with visual phenotypes in the UK Biobank (Table 1). Of note, smaller logMAR values correspond to better visual acuity, so negative correlation coefficients are expected. Sample sizes for visual phenotypes in UK Biobank are comparably small, explaining the large standard errors. It is of note that SNP-h 2 for logMAR values in the UK Biobank are considerably smaller (0.03 and 0.02 for the left and right eye, respectively) than for ALSPAC children (0.18), suggesting that, in spite of a much smaller sample, analysis in individuals at young age might facilitate the detection of genetic effects.

PGS
EA PGS showed a robust positive association with visual acuity (  childhood. The standardised beta coefficient indicates that an increase of 1 SD in EA PGS is associated with an increase of 0.05 SD in visual acuity. This association still holds after including myopia PGS, refractive error PGS, or intelligence PGS as additional covariates to the PGS analysis (Supplementary Table 12). In contrast, myopia PGS showed a negative association with visual acuity with 1 SD increase in myopia PGS associated with a 0.05 SD decrease in visual acuity (Table 2). There was no association with PGS for neurodevelopmental outcomes.

DISCUSSION
We report behavioural and genetic associations of visual acuity with cognitive measures including reading skill and school grades in children. We found that better visual acuity is associated with higher SES, higher IQ scores, and increased language-related cognitive skills. Increased visual acuity at 11.8 years is associated with higher GCSE scores after adjusting for sex, reading skill, IQ, and SES, suggesting long-lasting effects of visual acuity on academic achievement.
Given the association with language-related skills, we investigated visual acuity in language-related neurodevelopmental conditions and found an association specifically with reading difficulty with behavioural data, in line with previous research 12 . According to the magnocellular theory dyslexia may result from the destabilisation of visual fixation 37 . The association between visual acuity and reading abilities was also observed in the overall sample regardless of a reading difficulty diagnosis. We did not find associations between PGS for neurodevelopmental disorders and visual acuity when controlling for SES. However, higher EA PGS were associated with better visual acuity in children before the end of compulsory education. These findings are consistent with theories that emphasise the importance of the senses in higher order cognition 38 .
Overall, 26% of the variance in visual acuity was attributed to genetic variation as captured by a genetic relationship matrix. The 12 SNPs reaching genome-wide significance in visual acuity GWAS were annotated to NPLOC4, which has been implicated in several GWAS on visual phenotypes previously. Gene-based analysis confirmed the NPLOC4 association. The top marker on chromosome 5 (rs159195) is located in an intron of PDE4D, which shows abundant expression in the rodent retina 39 and common variants in PDE4D have been reported in GWAS on sudden sensorineural hearing loss 40 . Targeted analysis for markers reported in previous GWAS for myopia and refractive error highlighted two loci in NPLOC4 and PDE6G. PDE6G is expressed in photoreceptors and encodes for key enzymes of visual phototransduction signalling in the retina 41 .
Despite the small sample size, we both identified associations with genes involved in sensory function and replicated top hits from previous vision GWAS in adults. The direction of genetic correlation coefficients between logMAR values in the UK Biobank (r g = −0.68 and −0.34 for the left and right eye, respectively) further suggests that our analysis captured similar genetics as previous relevant GWAS. The LDSC SNP-h 2 estimate in our study (SNP-h 2 = 0.18) is considerably higher than the ones in UK Biobank (0.03 and 0.02 for the same phenotype) despite a much smaller sample size. This indicates, consistent with our model, that over the course of development, environmental factors play increasingly larger effects on visual function, resulting in less phenotypic variance explained by genetic factors. Since both EA PGS 42 and access to eye examinations 43 are associated with higher SES, we ran PGS analyses while controlling for SES. EA PGS showed a positive association with visual acuity, suggesting that the behavioural associations between visual acuity and cognitive skills are either mediated by shared biological pathways or can be explained by causal relationships. By including maternal education (used as a proxy measure for SES) as a covariate, we confirm that the EA PGS is associated with visual function after accounting for differential environments relevant to education provided by the mothers. However, we cannot rule out residual confounding by unmeasured variables.
In adults, it has been shown that a higher number of years spent in education is a causal risk factor for myopia 35 . Since low visual acuity is also a risk factor for myopia 3 the positive effect of the EA PGS on childhood visual acuity is unexpected at first glance. However, as the children participating in this study have not yet reached the end of compulsory education, all have had the same number of educational years, suggesting that before environmental exposures are amplified by different educational trajectories, EA PGS are positively related to visual function. The association of higher EA with myopia in adulthood is thus likely to reflect gene-environment correlation. Specifically, genetic factors associated with higher EA might predispose to more reading and near work which increases myopia risk (Fig. 1). This is in line with a previous study confirming that EA PGS was not predictive for visual function in ALSPAC mothers (PGS R 2 = 0.14%) 44 . In contrast, we found a less robust negative association between myopia PGS and childhood visual acuity and overall confirm the model introduced in Fig. 1. That being said, while our interpretation is that the effect of visual acuity on educational outcomes is mediated by cognitive abilities, we cannot exclude a reversed effect of education on cognition 45 .
A limitation of our study is that we used a single variable, i.e., maternal education, as a proxy measure for SES, rather than capturing other dimensions such as income-based SES measures. The maternal education measure has some advantages in that it is a better control of genetic confounding, that is, it is more heritable and more likely to be predictive of offspring achievement than an income-based measure. However, we acknowledge that it also has some limitations, namely, it may be less sensitive to confounding from wealth which might increase access to a stimulating learning environment and to healthcare such as optometry services and aids. Another limitation regarding the choice of phenotype is that vision and education have only been assessed at a single time point and the corrected visual acuity prevented us distinguishing the children wearing glasses or contact lenses during assessment or determine whether uncorrected refractive error was the underlying reason for reduced visual acuity. Future work will benefit from the use of longitudinal approaches and more distinguished visual phenotypes.
In summary, we confirm a positive association between childhood visual acuity and cognitive development. Specifically, we show that visual acuity is reduced in children with reading difficulty compared to controls. We conducted a GWAS for visual acuity and report a statistically significant association at the NPLOC4 locus, implicated in vision phenotypes in previous studies conducted in larger adult cohorts. In the ALSPAC children, the PGS for educational attainment, which is known to be associated with myopia in adults, is instead associated with a slight increase in visual acuity. This observation is in line with the assumption that the initial positive effect of EA PGS on vision is reversed by environmental exposures, e.g., more near work exposure, increasing myopia risk.

METHODS Cohort
ALSPAC is a UK population-based longitudinal cohort. Pregnant women resident in the county of Avon, UK, with expected dates of delivery from 1st April 1991 to 31st December 1992 were invited to take part in the study, resulting in 14,062 live births and 13,988 children who were alive at 1 year of age 46,47 . When the oldest children were approximately 7 years of age, eligible cases who had failed to join the study originally were contacted again, resulting in an additional 913 children being enrolled. The total sample size for data collected after the age of seven is therefore 15,454 pregnancies, resulting in 15,589 foetuses. Of these 14,901 were alive at 1 year of age.
Informed written consent was obtained from the mother for analysis of her biological samples for genetic and other purposes, and by the accompanying parent for visual and other in person tests. Informed consent for the use of data collected via questionnaires and clinics was obtained from participants following the recommendations of the ALSPAC Ethics and Law Committee at the time. Parents were informed throughout that they, or their children, could withdraw at any time 48 . At age 18, study children were sent 'fair processing' materials describing ALSPAC's intended use of their health and administrative records and were given clear means to consent or object via a written form. Data were not extracted for participants who objected, or who were not sent fair processing materials.
Ethical approval for the present study was obtained from the ALSPAC Law and Ethics Committee and the Local Research Ethics Committees. Details about the ethics committees and institutional review boards that approved aspects of the study are available on the ALSPAC study website (http://www.bristol.ac.uk/alspac/ researchers/research-ethics/).

Phenotypes
The ALSPAC study website contains details of all the data that is available through a fully searchable data dictionary (http:// www.bris.ac.uk/alspac/researchers/data-access/data-dictionary/). Assessment of visual acuity. Visual examinations were conducted in a shaded room under artificial light. Visual acuity was measured using the logarithm of the minimum angle of resolution (logMAR) visual acuity test with glasses or contact lenses if prescribed unless they had not been worn for at least six months. The order of testing was randomised between the left and right eye. The child was asked to read (or match) the first letter on each row and to go as far down the chart as possible. When they reached the point where they were unsure or made a mistake, they were taken back up two rows and asked to read across the row, letter by letter, with the examiner marking off each letter seen on the datasheet. If the child did not read the whole row correctly then the next row up was tested until there was one line fully correct. The child was then asked to continue reading down the chart. If the child read a letter incorrectly the examiner could check with a large letter whether the child knew the correct name for that letter, otherwise any errors were noted by not crossing off that letter. If one letter on a line was seen, all the rest were attempted. If a child said that they were not sure, they were encouraged to guess. Testing continued until they read a whole line wrong. The test was then repeated using the same chart but with the child holding up a pinhole. After a break used for another task, the ETDRS chart 2 was used for the second eye and the whole testing procedure repeated, including the pinhole. The number of letters in each column not seen, below the lowest fully correct line, were counted and visual acuity for each test (without and with pinhole) was calculated according to the formula: logMAR = −0.3 × (total errors × 0.02). For each eye, the best corrected visual acuity was determined as the best result from both tests (without and with pinhole). The logMAR value can adapt values from 1.00 (indicating poor vision) to −0.30 (indicating very good vision). We used the smallest value from the better eye as an indicator of visual acuity. To make the results more intuitive so that larger values refer to better visual acuity, we transformed logMAR to the Visual Acuity Rating (VAR) scale according to the formula visual acuity = 100-50(logMAR). Therefore, visual acuity = 100 refers to standard vision (logMAR = 0), while lower values indicate poorer vision and higher values indicate above-standard vision 49 . Phenotypic data were available for n = 6906 children. Children with sensory impairments (n = 26), visual acuity <85 (reduced visual acuity defined as visual impairment, n = 14 50 ) or an absolute difference in visual acuity between the left and right eye of >10 (a possible indicator for amblyopia, n = 53 50 ) were excluded from analysis, resulting in a sample of n = 6807 that was available for phenotypic analysis (3444 females, 3356 males, 7 missing values for sex, mean age = 11.81 years, SD = 0.23 years), of which~13% had corrected vision.
Cognitive measures. In line with our previous study 36 cognitive skills were assessed in terms of reading skill, communication skills, listening comprehension, short-term memory, total IQ, verbal IQ and performance (nonverbal) IQ, and EA measured as General Certificate of Secondary Education (GCSE) scores.
Reading skill. Reading skill was measured using the basic reading subtest of the Wechsler Objective Reading Dimensions (WORD) 51 at target age 7. Seven pictures were used for decoding and 48 words were used for word reading. The task was ended after six consecutive errors. The final reading skill score was derived by the number of correctly read words and corrected for age in weeks.
Short term memory. Short term memory was measured using an adaptation of the Nonword Repetition Test 52 at target age 8. The child was asked to listen to and repeat nonsense words presented via an audio cassette recorder. Twelve nonsense words (consisting of either 3, 4 or 5 syllables) conforming to English rules for sound combinations were used. Items were scored as correct if there was no phonological deviation from the presented word. The number of correctly repeated items was scored and corrected for age in weeks.
Listening comprehension. The Wechsler Objective Language Dimensions (WOLD) 53 was used to measure listening comprehension at target age 8. The tester reads aloud a paragraph about a picture that is shown to the child. Afterwards, the child verbally answers questions about that paragraph that require making inferences about what they heard. The task was ended after three consecutive errors. A sum score was calculated from the number of correct items (ranging from 2-15) and corrected for age in weeks.
WISC performance IQ. The Wechsler Intelligence Scale for Children (WISC-III UK) 54 was administered at target age 8. The WISC comprises five performance subtests (picture completion, coding, picture arrangement, block design, object assembly). Using the WISC manual, age-scaled scores were obtained from the raw scores and a total score was calculated for the WISC performance IQ.
WISC verbal IQ. The WISC includes five verbal subtests (information/knowledge, similarities, mental arithmetics, vocabulary, comprehension). Age-scaled scores were obtained as described above and a total score was calculated for the WISC verbal IQ.
WISC total IQ. The total WISC IQ score was calculated as the sum of all 10 age-scaled WISC subtests (picture completion, coding, picture arrangement, block design, object assembly, information/ knowledge, similarities, mental arithmetics, vocabulary, comprehension).
Communication skills. Communication skills were measured using the children's communication checklist (CCC) 55 at target age 9. The CCC consists of 70 items grouped into 9 subscales (intelligibility and fluency, syntax, appropriate initiation, coherence, stereotyped conversation, use of conversational context, conversational rapport). Higher scores indicate higher communication skills. Sum scores were corrected for age in weeks.
GCSE scores. Educational attainment (EA) was measured as capped General Certificate of Secondary Education (GCSE) scores. GCSEs are the main qualification taken at the end of compulsory education in the UK. Capped GCSE scores represent the best eight grades at GCSE. GCSE scores were available for 6773 children.
SES. SES was assessed using maternal highest educational qualification during pregnancy (at 32 gestational weeks) 56 . SES was grouped into 'CSE and no education', 'Vocational', 'O level', 'A level' and 'University Degree'.
Hearing. We previously reported associations between hearing ability and cognitive and neurodevelopmental traits 36 . The overlap between the sample used for the current study and the sample used for the previous study was n = 4929 (2490 females, 2439 males). Detailed descriptions of the hearing phenotypes have been reported previously 36 . Briefly, air conduction thresholds were assessed using an audiometer at different frequencies and averaged for each ear. Hearing threshold was defined as the average air conduction threshold in decibel (dB) on the better ear (note that lower values correspond to better hearing). We tested for correlations between visual acuity and hearing threshold using Pearson correlation.

Subsample assignment
Group assignment followed the strategy described previously 57 . Briefly, from the overall ALSPAC sample (n = 15,443) we excluded individuals with incomplete data on measures used for sample assignment and individuals not reporting white European ethnicity. Next, individuals with a WISC performance IQ below 85 were excluded. The remaining individuals were assigned to the groups of reading difficulty (n = 173), language impairment (n = 184), ADHD (n = 26), comorbid combinations of these disorders (language impairment + reading difficulty, n = 47; language impairment+ADHD, n = 7, reading difficulty+ADHD, n = 5; reading difficulty+language impairment+ADHD, n = 3) or unaffected (n = 3305) according to the following criteria.
Reading difficulty. Children scoring < −1 SD on tests of ageadjusted single-word reading at 7 and 9 years were assigned to the reading difficulty group.
Language impairment. An assignment of language impairment was given if an individual scored positive for at least two of the following four criteria, which target different aspects of language problems: 1. CCC score < −1 SD 2. Nonword Repetition < −1 SD 3. WOLD score < −1 SD 4. positive response on speech/language therapy questionnaire ASD. An assignment to ASD was based on maternal report (Have you ever been told that your child has autism, Asperger's syndrome or autistic spectrum disorder?) at the age of 9 years.
ADHD. An assignment of ADHD was based on a DAWBA DSM-IV clinical diagnosis.
Numbers of participants were slightly different from previous publications given updates in the most recent release of the ALSPAC data.
The control group was sex-matched to maintain the same M/F ration of 1.57 observed in the cases, resulting in a control sample matched for sex of n = 2238 (Table 3).

Genomic analyses
Genome-wide genotype data were available for n = 5571 children with phenotypes (2749 males, 2822 females). Visual acuity was inverse rank-transformed for genomic analyses.
Genotype quality control and imputation. Genotypes were generated on the Illumina HumanHap550-quad array at the Wellcome Trust Sanger Institute, Cambridge, UK and the Laboratory Corporation of America, Burlington, NC, US. Standard quality control was performed as described elsewhere 58 . Population stratification was assessed by multidimensional scaling analysis and compared with Hapmap II (release 22) European descent, Han Chinese, Japanese and Yoruba reference populations. All individuals with non-European ancestry were removed. In total, 9115 subjects and 500,527 SNPs passed quality control filtering. Haplotypes were estimated using ShapeIT (v2.r644) which utilises relatedness during phasing. Quality control-filtered autosomal SNPs were imputed using Impute v3 using the HRC 1.1 reference data panel. Poorly imputed SNPs (Info score < 0.8) and SNPs with low minor allele frequency (MAF < 0.05) were excluded from further analysis. Overall, 5,305,352 SNPs with MAF > 0.05 that were either directly genotyped or imputed and passed quality control were tested for association with visual acuity.
SNP-h 2 and genetic correlations. A genetic-relationship matrix was created for unrelated individuals (n = 5153; identity by descent (IBD) < 0.05) based on directly genotyped SNPs. SNP-h 2 was estimated using sex, age in weeks, and the first two principal components (PCs) as covariates using GREML analysis in GCTA 1.94.0 59 . PCs were calculated using genotyped (MAF > 0.05) and LD pruned (r 2 < 0.01 within a 50 kb window) SNPs (excluding high LD regions) using Plink v2 60 . We used bivariate GREML to estimate genetic correlations (r g ) between visual acuity and cognitive skills.
We also tested for genetic correlation between visual acuity and hearing threshold in n = 3833 unrelated children with genotypes and phenotypic data for both visual acuity and hearing threshold.
GWAS. Association testing for visual acuity was performed using a linear mixed model (LMM) in BOLT-LMM v2.3.4 61 . GWAS was run on the whole available sample with phenotypes and genotypes using sex, age, and the first two PCs (see above) as covariates (n = 5571).
LD score regression. We applied LD score regression (LDSC) 62 implemented in the Complex Traits Genetics Virtual Lab (CTG-VL 0.4-beta) 63 to the GWAS summary statistics for visual acuity. Mean χ 2 was 1.03 and the small LDSC intercept (1.01, SE = 0.007) indicates negligible bias contributing to the signal. The genomic inflation factor revealed no evidence of population structure (λ = 1.05). Genetic correlation analyses 64 were performed with traits of interest from publicly available GWAS summary statistics (Supplementary Table 1).
Post GWAS analysis. We applied FUMA v1.3.7 65 and FINDOR 66 on the GWAS summary statistics for visual acuity. FUMA implements MAGMA v1.08 67 to perform gene-based analysis and gene set analysis. Functional consequences of SNPs were obtained by performing ANNOVAR 68 using Ensembl genes (build 92). Functionally annotated SNPs were mapped to genes based on positional mapping. Intergenic SNPs were annotated to the closest genes upstream and downstream. Input SNPs were mapped to 18,360 protein-coding genes. Genome-wide significance for gene-based GWAS was defined as p = 0.05/ 18,360 = 2.7 × 10 −6 . Gene set p values were computed for 7343 gene ontology (GO) terms for biological processes obtained from MsigDB v5.2. The Bonferroni-corrected significance level was set to 0.05/7343 = 6.8 × 10 −6 . FUMA was also used to link independent significant SNPs to results from previous GWAS via the GWAS catalog. The visual acuity summary statistics were reweighted for functional annotations using FINDOR.
PGS. PGS analyses were carried out using PRSice 2.3.3 69 . We tested for associations of PGS for neurodevelopmental disorders (ASD, bipolar disorder, ADHD, schizophrenia, dyslexia), education (intelligence, EA), and visual function (refractive error, myopia) on visual acuity (Supplementary Table 2). After LD-clumping (r 2 < 0.1 within a 250 kb window), PGS were derived as the weighted sum of risk alleles according to test statistics from the base GWAS summary statistics. We performed linear regression analyses with visual acuity as the outcome and the respective PGS as predictor. Based on an effect of SES on visual acuity on the behavioural level, SES, sex, age, and two PCs were included as covariates, resulting in a sample size of n = 5160 for PGS analyses. The Bonferronicorrected significance threshold for nine base GWAS and nine p value thresholds (the threshold explaining maximal phenotypic variance as well as 0.001, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, and 1) was set to 0.05/81 = 0.00062.
Data preparation and visualization was performed using R v.4.1.2. All analysis scripts are available through Github (https:// github.com/Judith-Schmitz/vision_gwas). Reporting summary Further information on research design is available in the Nature Research Reporting Summary linked to this article.

DATA AVAILABILITY
Data used for this submission will be made available on request to the ALSPAC Executive (alspac-exec@bristol.ac.uk). The ALSPAC data management plan (http:// www.bristol.ac.uk/alspac/researchers/data-access/documents/alspac-datamanagement-plan.pdf) describes the data sharing policy, which is through a system of managed open access.