## Main

Many previous genetic studies in autism spectrum disorder (ASD), a neurodevelopmental condition characterized by social communication difficulties and repetitive behaviors1, focused on de novo variants (DNVs) identified from parent–offspring trios2,3,4,5,6,7,8. Over 100 high-confidence ASD genes enriched with likely deleterious DNVs have been identified8, most of which are also enriched for DNVs in other neurodevelopmental disorders (NDDs)9,10,11. Statistical modeling suggests that there are ~1,000 genes with DNVs in ASD12,13. However, despite the large effect size of individual pathogenic DNVs, all DNVs combined explain only ~2% of variance in liability for ASD8,14. ASD is highly heritable14,15,16, and previous studies estimated that common variants explain up to half of the heritability14, although only five genome-wide significant loci have been identified17. Rare LoF variants in genes intolerant of variation9,18 are overtransmitted to probands compared with siblings without ASD7,8,19,20,21,22. However, identification of the individual risk genes enriched by such inherited variants has remained elusive. We have established the largest ASD cohort, Simons Foundation Powering Autism Research for Knowledge (SPARK)23, which currently includes over 100,000 people with ASD, to advance research on the genetic, behavioral and clinical features associated with ASD.

Rare LoF variants are enriched in developmental disorders including ASD22,24, but may also result from sequencing and annotation artifacts25 and present technical challenges in large sequencing studies. Methods to distinguish between high-confidence and low-confidence LoF variants18,26,27 have been used to quantify gene-level LoF intolerance18,26,28,29 and to refine the role of LoF DNVs in NDDs20.

Here, we present an integrated analysis of de novo and inherited coding variants in over 42,607 ASD cases, including cases from previously published ASD cohorts and 35,130 new cases from SPARK. In our two-stage design, we first characterized the contribution of DNVs and rare inherited LoF variants to ASD risk. Results from the first stage informed the second stage meta-analysis of 404 genes. By combining evidence from DNVs, transmission disequilibrium tests (TDTs) and case-control comparisons, we identified 60 ASD risk genes with exome-wide significance, including five new genes not previously implicated in NDDs. Finally, we estimated the effect sizes of known and newly identified genes and conducted power calculations to inform the design of future studies.

## Results

### Overview of data and workflow

We aggregated exome or whole genome sequencing (WGS) data of 35,130 new cases from SPARK and 7,665 cases from published ASD studies (ASC3,8, MSSNG6 and SSC2,30) (Supplementary Table 1) and performed a two-stage analysis (Fig. 1). In stage 1, we analyzed DNVs in 16,877 ASD trios and assessed transmission of rare LoF variants from 20,491 parents without ASD diagnoses or intellectual disability to offspring with ASD (including 9,504 trios and 2,966 single-parent-proband duos). For DNVs, we characterized the enrichment pattern in known and candidate risk genes, as well as mutation intolerance (probability of being LoF intolerant as defined by the Exome Aggregation Consortium (ExAC pLI)18, and Genome Aggregation Database (gnomAD) metrics26), and performed gene-based burden tests of LoF and missense DNVs by DeNovoWEST11. For rare inherited LoFs, we estimated the overtransmission from unaffected parents to ASD offspring in all genes and gene sets predefined by functional genomic data or results from DNV analysis. Based on DNV enrichment and overtransmission patterns in gene sets, we selected 404 genes for meta-analysis in stage 2 using 22,764 new cases with exome or WGS data. In stage 2, we applied DeNovoWEST on DNVs, conducted TDTs on inherited LoFs in trios or duos, performed burden tests on rare LoFs in unrelated cases compared with population controls (104,068 subjects from non-neuro gnomAD exomes and 132,345 TOPMed subjects) and combined the P values to estimate a final P value for each of the 404 genes. Finally, we performed a mega-analysis of rare LoFs in all cases and controls to estimate the effect sizes of known or new candidate ASD genes to inform future studies.

### Known ASD or NDD risk genes explain most de novo burden

In the first stage, we combined data from four large-scale ASD cohorts, including 16,877 unique ASD trios and 5,764 unaffected trios (Supplementary Table 1). The cohorts show similar exome-wide burden of DNVs in simplex families. The burden of LoF DNVs in cases with an ASD family history is significantly lower than those without (P = 1.1 × 10−4 by Poisson test), whereas the burden of predicted de novo damaging missense (D-mis, defined by rare exome variant ensemble learner (REVEL) score31 ≥ 0.5) and synonymous variants are similar (Extended Data Fig. 1). Compared with unaffected offspring, the excess of damaging DNVs (de novo LoF and D-mis variants) in individuals with ASD is concentrated in LoF-intolerant genes, defined as genes with an ExAC pLI ≥ 0.5 (ref. 18). Using LoF observed/expected upper-bound fraction (LOEUF), a recently developed gene constraint metric26, the burden of damaging DNVs is highest among genes ranked in the top 20% of LOEUF scores (Fig. 2a). Overall, the population attributable risk (PAR) from damaging DNVs is about 10%. We assembled 618 previously established dominant (‘known’) ASD or NDD risk genes (Supplementary Table 2). These genes explained about two-thirds of the PAR from damaging DNVs. Excluding these genes, the fold enrichment of damaging DNVs was greatly attenuated (Fig. 2a).

To assess the evidence of DNVs in individual genes, we applied DeNovoWEST11, which integrates DNV enrichment with clustering of missense variants in each gene. The initial DeNovoWEST scan of DNVs in 16,877 ASD trios identified 159 genes with P < 0.001 (Supplementary Table 3).

### Rare inherited LoFs are mostly in unknown ASD risk genes

To analyze the contribution of rare inherited LoF variants to ASD risk, we evaluated transmission disequilibrium in ultra-rare (allele frequency < 1 × 10−5) high-confidence (by the loss-of-function transcript effect estimator (LOFTEE)26 package and proportion expression across transcripts (pExt)27; see Methods and Supplementary Note) LoF variants from parents without ASD diagnoses or intellectual disability to affected offspring with ASD in 9,504 trios and 2,966 duos from the first stage (Supplementary Table 4). For a given set of genes, we quantified transmission disequilibrium using the number of overtransmitted (excess in transmission over nontransmission) LoF variants per trio; parent–offspring duos were considered half-trios. Among autosomal genes, the overall transmission disequilibrium signal of ultra-rare LoF variants is enriched in LoF-intolerant genes (ExAC pLI ≥ 0.5) and in genes within the top 20% of LOEUF scores (Fig. 2b), similar to the burden of damaging DNVs. We observed both overtransmission to affected and undertransmission to unaffected offspring, especially in genes within the top 10% of LOEUF scores. However, known ASD or NDD genes explain only ~20% of overtransmission of LoF variants to affected offspring (Fig. 2b). On the X chromosome, we only considered transmission from mothers without ASD to 9,883 affected sons and 2,571 affected daughters (Supplementary Table 4). Rare LoF variants in mothers without ASD show significant overtransmission to affected sons but not affected daughters and remain significant after removing known ASD or NDD genes (Supplementary Fig. 1). Together, these results suggest that most genes conferring inherited ASD risk are yet to be identified. Autosomal rare D-mis variants also show evidence of transmission disequilibrium to affected offspring, although the signal is much weaker (Supplementary Fig. 2).

To characterize the properties of genes contributing to ASD risk through rare inherited variants, we defined 25 gene sets from five categories representing both functional and genetic evidence relevant to ASD (Supplementary Table 5 and Supplementary Fig. 3). We limited the genes to 5,754 autosomal constrained genes (ExAC pLI ≥ 0.5 or top 20% of LOEUF scores) and performed TDT (Supplementary Table 6). For each gene set, we tested if ultra-rare high-confidence rare LoF variants show a higher transmission to ASD offspring than the remaining genes in the overall constrained gene set. As a comparison with DNVs, we also tested if the same set of genes are more frequently disrupted by damaging DNVs than the rest of the genes in ASD trios using DNENRICH32.

Using functional gene sets derived from the neuronal transcriptome, proteome or regulome, we confirmed significant enrichment in damaging DNVs (P < 0.005 by simulation) in the gene sets that were previously suggested to be enriched for ASD risk genes including expression module M2/333, RBFOX1/3 targets34, FMRP targets35 and CHD8 targets36. However, this enrichment can be largely explained by known ASD or NDD genes (Extended Data Fig. 2). For ultra-rare inherited LoF variants, we found that the proportion of transmission to ASD individuals in most functional gene sets is close to all other genes; only RBFOX targets show a weak enrichment but can be largely explained by known genes (Fig. 3). We also applied two machine learning methods to prioritize ASD risk genes: forecASD37 and A-risk38. Although enrichment of DNVs in predicted genes is mainly explained by known genes, genes prioritized by A-risk are significantly enriched with inherited LoFs that are not explained by known genes. Using A-risk ≥ 0.4, 30% of constrained genes (n = 1,464) were prioritized and explain 64% of the overtransmission of LoF variants to ASD offspring (P = 2.6 × 10−5 by χ2 test). This enrichment is higher than genes prioritized by the LOEUF score; 33% of genes (n = 1,777) in the top decile of LOEUF account for 55% of the overtransmission (P = 3.5 × 10−4 by χ2 test) (Fig. 3).

We also considered gene sets that have evidence of genetic association with DNVs. Genes nominally enriched by DNVs (P < 0.01 by DeNovoWEST; n = 300) in ASD from the current study have a significantly higher overtransmission rate than other constrained genes (odds ratio = 1.39, P = 3.0 × 10−5 by χ2 test) (Fig. 3), although these genes account for only 21% of the overtransmission. Genes nominally enriched by DNVs in other NDDs11 are also significantly enriched by DNVs in ASD and weakly enriched by inherited LoFs in ASD; however, both can be largely explained by known genes (Fig. 3). This suggests that a subset of ASD genes increase risk by both DNVs and inherited variants, and new genes can be identified by integrating evidence from DNV enrichment and TDT.

### DNVs and some rare inherited LoFs are associated with intellectual disability

To evaluate the association of genotypes with phenotype in ASD, we used self-reported cognitive impairment in SPARK, a Vineland score of <70 in the SSC or the presence of intellectual disability in ASC. Damaging DNVs in genes ranked within the top 10% of LOEUF scores show a higher burden (P = 1.1 × 10−24 by χ2 test) in ASD cases with evidence of cognitive impairment than in other cases, consistent with previous results2,8 (Fig. 4a). Once known ASD or NDD genes were excluded, the residual burden of damaging DNVs in genes within the top 10% of LOEUF scores is greatly reduced and not significantly associated with cognitive phenotype in ASD (Fig. 4a). Overtransmission of rare LoFs in genes within the top 10% of LOEUF genes to ASD cases with cognitive impairment is about 2.7 times higher than to cases without cognitive impairment (P = 4.6 × 10−3 by χ2 test) and is still 2 times higher (P = 0.04 by χ2 test) once known ASD or NDD genes were excluded (Fig. 4b). However, rare LoFs in genes prioritized by A-risk are not associated with cognitive impairment (Supplementary Fig. 4). Taken together, these results suggest that rare variants in the top 10% of LOEUF genes—most of which are already known to be ASD or NDD risk genes—are associated with cognitive impairment. However, a subset of rare inherited variants, particularly those prioritized by A-risk, are not associated with cognitive impairment.

### Meta-analysis identifies five new risk genes

Based on results from the first stage, we identified 260 genes with evidence of TDT (TDT statistic39 ≥ 1) and in gene sets enriched with rare inherited LoFs (top 10% LOEUF or within top 20% LOEUF and A-risk ≥ 0.4) (Supplementary Table 6) and 159 genes with P < 0.001 from the DeNovoWEST analysis of DNVs (with 15 genes by both) (Supplementary Table 3). We performed a meta-analysis on the 367 autosomal genes with all data from stage 1 and stage 2, which includes 6,174 new ASD trios, 1,942 new duos, 15,780 unrelated cases (see Methods) and 236,000 population controls.

We used Fisher’s method40 to combine three P values that estimate independent evidence of DNVs, TDT and case-control comparison: (1) DeNovoWEST with DNVs from both stage 1 and stage 2 (n = 23,039 trios, Supplementary Tables 1 and 7) using the parameters estimated in stage 1, (2) TDT with rare LoF variants in parents without ASD diagnoses or intellectual disability with affected offspring in 15,586 trios and 4,907 duos (Supplementary Table 4) and (3) unrelated cases (Supplementary Table 8) compared with population controls using a binomial test. We used two sets of controls: gnomAD exome v2.1.1 non-neuro subset (only samples from individuals who were not ascertained for having a neurological condition in a neurological case-control study, n = 104,068) and TOPMed WGS (freeze 8, n = 132,345). We performed a case-control burden test using the two sets separately and input the larger P value for the meta-analysis. This approach avoids sample overlap and helps ensure that significant genes are not dependent on the choice of population reference. Although population reference data were processed by different pipelines, the cumulative allele frequencies (CAFs) of high-confidence LoF variants (see Methods) are similar between internal pseudocontrols (see Methods) and the two population references after applying the same LoF filters (Supplementary Fig. 5). Previous population genetic simulations predict that for genes under moderate to strong selection (selection coefficient > 0.001), deleterious variants are expected to arise within 1,000 generations and population demographic histories do not confound the CAFs of deleterious alleles in these genes41.

For 367 selected autosomal genes, the point estimates of selection coefficient under the mutation–selection balance model42 are all greater than 0.01 (Supplementary Fig. 6). Most high-confidence LoF variants in these genes are ultra-rare (Supplementary Fig. 7), and the CAFs of high-confidence LoF variants in European and non-European population samples are highly correlated (Supplementary Fig. 8). Therefore, we included population samples across all ancestries as controls. The ultra-rare synonymous variant burden is similar between cases and controls across the selected genes (Extended Data Fig. 3). To make use of all genetic data collected, we also included rare variants of unknown inheritance from ASD cases that were analyzed in the first stage. These variants come from cases that are part of unaffected parent–ASD duos; such variants were either inherited from the parent not participating in the study or DNVs. Therefore, these variants are independent of TDT, even though the same cases were included in TDT.

We identified 60 genes with exome-wide significance (P < 2.5 × 10−6), and 72 genes reached study-wide significance accounting for all 5,754 constrained genes (P < 8.7 × 10−6, Supplementary Table 9). Figure 5 summarizes the distribution of LoF variants (with different modes of inheritance) in genes that reached study-wide significance by DNV enrichment (Fig. 5a) and other significant genes by meta-analysis (Fig. 5b and Supplementary Fig. 9). Genes that are significant only in meta-analysis tend to harbor more inherited LoF variants than DNVs, consistent with their lower penetrance for ASD or NDD.

Although most significant genes were previously known, we identified five new genes that have exome-wide significance regardless of the choice of population reference: NAV3, MARK2, ITSN1, SCAF1 and HNRNPUL2 (Table 1). The combined P values based on ancestry-specific case-control analyses are similar to the overall case-control analysis for these five genes (Supplementary Table 10). As expected, most supporting variants are ultra-rare, and results are robust to the allele frequency filter. These five new genes together explain 0.27% of the PAR ratio (Supplementary Table 11). NAV3 has a similar PAR to that of CHD8 and SCN2A (~0.095%). ITSN1 is similar to PTEN (~0.065%).

The association of NAV3 with ASD risk is primarily driven by rare inherited variants (Table 1). NAV3 has a high A-risk score, suggesting that the expression pattern of NAV3 is highly similar to known ASD genes (Supplementary Data 1)7,43. NAV3 has high expression in the inner cortical plate of the developing cortex33, and in pyramidal neurons (hippocampus CA1 and somatosensory cortex) and cortical interneurons44,45 (Supplementary Fig. 10). The association of MARK2 with ASD risk is primarily driven by DNVs and is also associated with other NDDs11 (P = 2.7 × 10−5 by DeNovoWEST) including Tourette syndrome46 and epilepsy47. We find that three out of eight autistic offspring with variants in MARK2 report epilepsy, two out of eight report Tourette syndrome and seven out of eight have evidence of cognitive impairment (Supplementary Table 12).

The remaining three novel genes have support from both DNVs and rare LoFs. ITSN1 and SCAF1 show nominal significance of DNV enrichment in 31,058 NDD trios11 (P < 0.05 by DeNovoWEST). SCAF1 was among the top 50 genes from a gene-based burden test in a recent schizophrenia case-control study (P = 0.0027 by burden test)48. Both ITSN1 and NAV3 have moderate effect sizes (point estimate of relative risk 3~6; Supplementary Table 11). ITSN1 has been highlighted in our previous study with evidence of enriched inherited LoFs7. We also assessed deletions in these new genes. For both ITSN1 and NAV3, we identified four partial or whole gene deletions in 33,083 parents without ASD diagnoses or intellectual disability that also show transmission disequilibrium to affected offspring (Extended Data Fig. 4).

Although both de novo and rare inherited LoFs in the most constrained genes are strongly associated with intellectual disability in ASD (Fig. 4), the association of such variants in individual genes is heterogenous, as suggested by the lack of association of rare inherited variants in genes with high A-risk scores (Extended Data Fig. 2). We calculated the burden of cognitive impairment (see Methods) in 87 ASD individuals with high-confidence LoF variants in the four novel moderate-risk genes and compared it with that in 129 individuals with high-confidence LoF in the well-established ASD risk genes CHD8, SCN2A, SHANK3, ADNP and FOXP1, as well as 8,731 individuals with ASD (Supplementary Fig. 11). Although most individuals with variants in well-established ASD risk genes have some evidence of cognitive impairment (88%), individuals with LoF variants in the moderate-risk genes had significantly lower burden (56%, P = 4.5 × 10−7). Individuals with high-confidence LOFs in the moderate-risk genes did not have a significantly different burden of cognitive impairment than 8,731 individuals with ASD in SPARK (56% vs 50%, P = n.s.). Individuals with LoF variants in the moderate-risk genes also had a similar male:female (4:1) ratio compared with the larger cohort, whereas individuals with variants in the well-established ASD risk genes showed significantly less male bias (1.6:1, P = 0.009) (Supplementary Fig. 11), as previously reported2. We also predicted full-scale intelligence quotient (IQ) on all participants based on parent-reported data using a machine learning method49. Heterozygotes for rare LoFs in three (NAV3, SCAF1 and HNRNPUL2) of the four new genes with substantial contribution from rare inherited variants have similar IQ distribution as the overall SPARK cohort (Fig. 6a), which is substantially higher than heterozygotes with rare LoFs in well-established, highly penetrant genes that contribute to ASD primarily through DNVs (‘DN genes’) such as CHD8, SHANK3 and SCN2A. In fact, both novel and established genes with significant contribution from rare inherited LoFs are less associated with intellectual disability than NDD genes (Fig. 6b). Across these genes, there is a significant negative correlation (r = 0.78, P = 0.001) of estimated relative risk of rare LoFs with average predicted IQ of the individuals with these variants (Fig. 6c).

Most known ASD or NDD genes that are enriched by LoF DNVs harbor more de novo than LoF inherited variants in ~16,000 unrelated ASD trios (Fig. 5a and Supplementary Fig. 16), consistent with their high penetrance for ASD or NDD phenotypes and strong negative selection. Using population exome or WGS data, we calculated a point estimate of selection coefficient ($$\hat s$$)50 of LoFs in each gene (Supplementary Table 11) and found that the fraction of de novo LoFs in ASD genes is higher in genes with large $$\hat s$$, and smaller in genes with small $$\hat s$$ (Supplementary Fig. 5b), consistent with population genetic theory51. We also estimated average effect size of rare LoFs in ASD genes by comparing CAF in 31,976 unrelated cases and population exome or WGS data. As expected, known and newly significant ASD genes with higher risk for ASD are under stronger selection (larger $$\hat s$$) (Supplementary Fig. 13).

### Functional similarity of new genes and known ASD genes

To better appreciate the probable functional implications of the new exome-wide-significant genes that confer inherited risk for ASD, we integrated mechanistic (STRING52) and phenotypic (Human Phenotype Ontology (HPO)53) data into a single embedding space (six dimensions, one for each archetype coefficient) using a combination of canonical correlation analysis and archetypal analysis (see Methods). This embedding space serves as an interpretive framework for putative ASD risk genes (n = 1,776). Six functional or phenotypic archetypes were identified (Fig. 7 and Supplementary Tables 1315) that represent pathways that are well understood to play a role in ASD: neurotransmission (archetype 1 or A1), chromatin modification (archetype 2 or A2), RNA processing (archetype 3 or A3), vesicle-mediated transport (archetype 4 or A4), MAPK signaling and migration (archetype 5 or A5), and cytoskeleton and mitosis (archetype 6 or A6), also enriched for intermediate filaments. These archetypes organize risk genes in a way that jointly maximizes their association with mechanisms (STRING clusters) and phenotypes (HPO terms). For instance, A1 genes (neurotransmission) are enriched for the STRING cluster CL:8435 (ion channel and neuronal system) and are also associated with seizure and epileptic phenotypes. A2 genes (chromatin modifiers) are enriched for nuclear factors and genes linked to growth and morphological phenotypes (Supplementary Table 14). We call genes that strongly map to an archetype (that is, >2× the next highest-ranking archetype) ‘archetypal’; if this criterion is not met, we call the genes ‘mixed’. Archetypal genes are generally less functionally ambiguous than mixed genes. Of the five novel inherited risk genes, two are archetypal (suggesting function within known risk mechanisms): NAV3 (A6, cytoskeleton and mitosis) and ITSN1 (A4, vesicle-mediated transport). SCAF1, MARK2 and HNRNPUL2 are mixtures of the identified archetypes, largely A4 and A5. That these new genes did not resolve clearly into archetypes (that were defined by known and suspected autism risk genes) suggests that they may operate in potentially novel mechanisms. To elucidate these possibilities, we constructed an ad hoc archetype, defined by the centroid between SCAF1, MARK2 and HNRNPUL2 (see Fig. 7c). Cell–cell junction (CL:6549) was the STRING cluster most associated with this centroid (P = 4.12 × 10−14 by the Kolmogorov–Smirnov test; Fig. 7d), which fits with its location between A4 (vesicle-mediated transport) and A5 (MAPK signaling and migration).

### Power analysis

The power of identifying risk genes with rare inherited variants or DNVs monotonically increases with increasing effect size or expected CAF under the null. New ASD genes to be discovered are likely to have smaller effect size than known ASD genes, as suggested by our results. Additionally, known ASD genes are biased toward longer genes, which have a higher background mutation rate of damaging variants (‘long genes’) (Extended Data Fig. 5). Even though longer genes are more likely to be expressed in the brain and be relevant to ASD or NDD54, among most constrained genes, long genes (LoF mutation rate55,56 above 80% quantile) and short genes (below 80%) have similar enrichment of damaging DNVs and rare inherited LoFs (Supplementary Fig. 14). Notably, for short genes, known genes have virtually no contribution to overtransmitted high-confidence LoFs to affected offspring (Supplementary Fig. 14b), suggesting that many short ASD risk genes remain to be identified.

We used a published framework41 to analyze power based on case-control association of rare variants. For rare variants in genes under strong selection, CAF is largely determined by mutation rate and selection coefficient41. We therefore modeled power of discovering risk genes as a function of relative risk and selection coefficient. With about 5,500 constrained genes, the power of the current study was calculated for 31,976 unrelated cases and an experiment-wise error rate of 9 × 10−6 (Extended Data Fig. 6).

We inversed the power calculation to determine the required sample size to achieve 90% power under the same assumptions (Extended Data Fig. 7). For genes at median LoF mutation rate across all genes, we estimated that it requires about 96,000 cases (three times the current sample size) to identify genes with similar effect size as NAV3 (relative risk = 4.5) and ITSN1 (relative risk = 5), and about 64,000 cases (twice the current sample size) to find genes with similar effect sizes as SCAF1 (relative risk = 8) and HNRNPUL2 (relative risk = 9). We note that ten and five times the current sample size, respectively, are required to detect genes similar to NAV3 or ITSN1 and genes similar to SCAF1 or HNRNPUL2 by DNVs alone.

## Discussion

In this study, we identified five new ASD risk genes by both DNVs and rare inherited coding variants. We identified rare LoF variants in new ASD risk genes with modest effect size that are not strongly associated with intellectual disability. This finding represents a difference in phenotypic association with intellectual disability compared with other highly penetrant ASD genes. To find new risk genes with relative risks of 2–5 (comparable to the low relative risk genes from this study, NAV3 and ITSN1) in the 50th percentile for gene-wide LoF mutation rate (2 × 10−6) and the 50th percentile for selection among known risk genes (0.2), our power analysis suggests that 52,000, 73,000, 116,000 or 227,000 total ASD cases are necessary, respectively (cf. equation (1) from power calculation in Supplementary material).

Our results suggest that the identification of new risk genes with rare inherited variants may substantially improve genetic diagnostic yield. We found that rare inherited LoF variants account for 6% of PAR, similar to de novo LoF variants. Over two-thirds of the PAR from coding DNVs is explained by known ASD or NDD genes. In contrast, less than 20% of PAR from rare inherited LoFs variants is explained by known genes, suggesting that most genes contributing to ASD risk through rare inherited variants are yet to be discovered. These unknown risk genes are still largely constrained to LoFs in the general population and/or have similar expression profiles in developing brains to known ASD risk genes. Combining evidence from both DNVs and rare inherited variants, we identified 60 genes associated with ASD with exome-wide significance, including five novel genes. Rare LoFs in these five new genes account for a PAR of 0.27%, about half of the PAR of the five most common highly penetrant ASD genes (KDM5B, GIGYF1, CHD8, SCN2A and SHANK3).

NAV3’s association to autism is primarily driven by rare inherited variants. Carriers of rare LoFs in NAV3 have an average predicted IQ of 81, slightly above the SPARK cohort average (IQ, 79). The prevalence of intellectual disability among NAV3 heterozygotes is similar to the SPARK cohort average. This is distinctly different from established ASD risk genes (for example, CHD8, SHANK3 and SCN2A), nearly all identified by highly penetrant DNVs, and are associated with intellectual disability in ASD cohorts2. The absence of intellectual disability is also observed in other genes (for example, SCAF1, HNRNPUL2, GIGYF1, KDM5B and KMT2C) with substantial contribution from rare inherited variants and modest effect size. Nevertheless, the data show that many individuals with variants in these new ASD genes are affected with various neuropsychiatric conditions such as epilepsy, schizophrenia, Tourette syndrome and attention deficit hyperactivity disorder (ADHD) (Supplementary Table 12). Detailed phenotyping of larger numbers of individuals carrying these rare inherited variants is needed to understand the phenotype associated with each gene. Such strategies should include a genetic and phenotypic assessment of family members who also carry the rare variant without ASD. Because all individuals consented in SPARK are recontactable, such studies will enable a more complete picture of the broad phenotypic effects of these variants without the bias of clinical ascertainment. Overall, these risk genes with modest effect size may represent a different class of ASD genes that are more directly associated with core symptoms of ASD and/or neuropsychiatric conditions rather than global brain development and intellectual disability.

The approaches used in this study made full use of rare variation, and this analytical method is generalizable to many conditions. In particular, the multiple methods used to reduce noise in LoF alleles present in control samples were particularly effective in assessing the signal within the novel genes of moderate effect. We also leveraged gene expression profiles informed by machine learning methods to help prioritize genes for the meta-analysis stage of our analysis38. Future studies that leverage additional multiomic data such as the Genotype–Tissue Expression (GTEx) project may further improve the signal-to-noise ratio.

Our archetypal analysis (Supplementary Tables 1315) provides some clues to the potential mechanisms of the five newly identified risk genes. ITSN1 was unambiguously mapped to A4 (vesicle-mediated transport) and has a role in coordinating endocytic membrane traffic with the actin cytoskeleton57,58. NAV3 (A6, cytoskeleton and mitosis) is associated with both axon guidance59 and malignant growth and invasion60 and is thought to regulate cytoskeletal dynamics. Indeed, A6 is enriched for processes related to intermediate filaments (Supplementary Table 14), a known determinant of cell motility and polarity61. Although MARK2, SCAF1 and HNRNPUL2 were not identified as archetypal (potentially suggesting divergence from well-known autism risk mechanisms), a search for functional enrichment of this interstitial region between A4 and A5 found that their roles in developmental risk may be most relevant at the cell–cell junction, particularly as it relates to migration (see Fig. 7d).

Taken together, our results suggest that a continued focus on DNVs for ASD gene discovery may yield diminishing returns. By contrast, studies designed to identify genomic risk from rare and common inherited variants will not only yield new mechanistic insight, but also help explain the high heritability of ASD. SPARK is designed to recruit individuals across the autism spectrum, without relying on ascertainment at medical centers. As a result, SPARK may be better suited to identify genes with transmitted variants that have lower penetrance and to identify the genetic contributions to the full spectrum of autism. The strategy used by SPARK—to recruit and assess large numbers of individuals with autism across the spectrum and their available family members without costly, in-depth clinical phenotyping—is necessary to achieve the required sample size to fully elucidate genetic contributions to ASD. The ability to recontact and follow all SPARK participants will also be critical to deeply assess the phenotypes associated with the newly discovered genes and to develop and test novel treatments.

## Methods

We established the SPARK cohort to facilitate genotype-driven research of ASD at scale23. All participants were recruited to SPARK under a centralized institutional review board (IRB) protocol (Western IRB Protocol no. 20151664). All participants provided written informed consent to take part in the study. Written informed consent was obtained from all legal guardians or parents for all participants aged 18 and younger and for all participants aged 18 and older who have a legal guardian. Assent was also obtained from dependent participants aged 10 and older. Participants with autism were compensated US\$25–50 depending on other registered family members. The mean age of the SPARK cohort in this analysis was 16.5 years (s.d., 19.2 years). Cases made up 46% of the SPARK cohort (the remaining 54% were controls). The sex breakdown of the full SPARK cohort was 57% male and 43% female. The sex breakdown of the SPARK case cohort was 77% male and 23% female.

The first stage of analysis included 28,649 SPARK participants, including 10,242 ASD cases from over 9,000 families with exome sequencing data that passed quality control (Supplementary Data 1). A subset of 1,379 individuals was part of the published pilot study7. To replicate prioritized genes from the discovery stage, we performed a second-stage analysis that included an additional 39,926 individuals with 16,970 ASD cases from over 20,000 families with exome or WGS data available after the analysis in the discovery cohort was completed. New exome sequencing samples in this study were captured using an IDT xGen research panel and sequenced on Illumina NovaSeq. DNA samples were also genotyped for over 600,000 single nucleotide polymorphisms (SNPs) using Infinium Global Screening Array. Supplementary Table 16 outlines the software version and parameter settings for each analysis below. Details on data preprocessing, variant-level quality control procedures, variant annotation, high-confidence LoF variant filtering, and copy number variants, as well as descriptions of other publicly available ASD cohorts (SSC, MSSNG and ASC), are in the Supplementary Note.

### DNVs

We identified candidate de novo single nucleotide variants (SNVs) or insertion–deletion mutations (indels) from SPARK and SSC cohorts from per-family variant call formats files (VCFs) generated by GATK64 (v.4.1.2.0) and freebayes65 (v.1.1.0) and a cohort-wide population VCF generated by weCall66 (v.2.0.0) using a set of heuristic filters that aim to maximize the sensitivity while minimizing false negatives in parents7 (Supplementary Table 16). Candidates were retained if they were called by DeepVariant67 (v.0.8.0) in offspring and had no support in parents, identified in multiple offspring that passed the DeepVariant filter in all trios, or were shared by siblings in the same family and the de novo quality estimated by triodenovo was higher than 8 (or 7 for SNVs in CpG context). Before creating the final call set, we selected subsets of variants (see Supplementary Table 16) for manual evaluation by Integrative Genomics Viewer (IGV) to filter out candidates with failed review. Finally, we merged nearby clustered de novo coding variants (within 2 bp for SNVs or 50 bp for indels) on the same haplotype to form multinucleotide variants (MNVs) or complex indels. We removed variants located in regions known to be difficult for variant calling (HLA, mucin, and olfactory receptors). DNVs in the final call set follow a Poisson distribution with an average of 1.4 coding DNVs per affected offspring and 1.3 per unaffected offspring (Supplementary Fig. 15). The proportion of different types of DNVs, the mutation spectrum of SNVs, and indel length distributions were similar between SPARK and SSC (Supplementary Fig. 15). A small fraction of variants in the final call set are likely postzygotic mosaic mutations (Supplementary Fig. 16).

### Rare variants

Rare variant genotypes were filtered from cohort-wide population VCFs with quality-control metrics collected from individual and family VCFs (Supplementary Fig. 17a). In brief, we initially extracted high-quality genotypes for each individual for variants that appear in less than 1% of families in the cohort. Evidence for the variant genotypes was re-evaluated by DeepVariant from aligned reads and collapsed over individuals to create site-level summary statistics including the fraction of individual genotypes that passed DeepVariant filter and mean genotype quality over all individuals. For variant genotypes extracted from GLnexus68 (v1.1.3) VCFs, we re-examined variant genotype from per-family VCFs by GATK to collect GATK site-level metrics (including QD, MQ and SOR), then took the read-depth weighted average over families to create cohort-wide site metrics. For variant genotypes extracted from GATK joint genotyping VCFs, these site metrics were directly available from INFO fields.

### De novo analysis

In the discovery-stage analysis, the DNV call sets of SPARK and SSC were merged with published DNVs from ASC3,8 and MSSNG6. To infer likely sample overlaps with published trios for which we do not have individual-level data, we tallied the proportion of shared DNVs between all pairs of trios. For a pair of trios, let N1 and N2 be the number of coding DNVs, and let O be the number of shared DNVs between the pair. To account for mutation hot spots, if a DNV is an SNV within CpG context or a known recurrent DNV identified in SPARK and SSC, it contributes 0.5 to the count. Likely overlapping samples were identified if (O/N1) ≥ 0.5 or (O/N2) ≥ 0.5 and they have identical sex.

To determine the expected number of DNVs in the cohort, we used a 7-mer mutation rate model55 in which the expected haploid mutation rate of each base pair depends on the 3-bp sequence context on both sides. The per-base mutation rates were adjusted by the fraction of callable trios at each base pair, which was the fraction of trios with ≥10× coverage in parents and ≥15× coverage in offspring. For published trios, we used an in-house WGS dataset of 300 trios (average, 36× coverage) to approximate the callable regions. Gene-level haploid mutation rates for different classes of DNVs were calculated by summing up the depth-adjusted per-base mutation rate of all possible SNVs of the same class. The rate for frameshift variants was presumed to be 1.3× the rate of stop-gained SNVs56. Mutation rates in haploid X chromosome regions were adjusted for the observed male:female ratio (4.2), assuming that mutation rates in spermatogenesis are 3.4 times higher than in oogenesis9. The exome-wide rate of synonymous DNVs closely matches the observed number of DNVs (Extended Data Fig. 1). We also observed similar fold enrichment of damaging DNVs (vs expected rate) in ASD cases across four cohorts after accounting for samples with family history (Extended Data Fig. 1).

To identify risk genes through DNVs, we applied DeNovoWEST11. We used the empirical burden of DNVs to derive weights for different variant classes in constrained genes (ExAC pLI ≥ 0.5) and nonconstrained genes separately based on positive predictive values (PPVs) (Supplementary Table 18). For ASD, we defined de novo D-mis variants by REVEL score ≥ 0.5. For other NDDs, we defined two classes of de novo D-mis variants by MPC score ≥ 2 or MPC ≤ 2 and CADD score ≥ 25. We first ran DeNovoWEST to test the enrichment of all nonsynonymous DNVs (pEnrichAll). To account for risk genes that harbor only missense variants, we ran DenovoWEST to test the enrichment of de novo missense variants only and applied a second test for spatial clustering of missense variants using denovonear9, then combined evidence of missense enrichment and clustering (pCombMis). The minimal of pEnrichAll and pCombMis was used as the final P value for DeNovoWEST. The exome-wide significance threshold was set to 1.3 × 10−6 (=0.05/(18,000 genes × 2)). The analysis on the replication cohort used the same weights as derived from the discovery cohort. Compared with the original publication11, our implementation of DeNovoWEST used different ways to stratify genes, determine variant weights and calculate per-base mutation rates. We applied our DeNovoWEST implementation on 31,058 NDD trios. The results are highly concordant with published results on the same data (Supplementary Fig. 18). We used P values from our reanalysis on other NDD trios in comparative analysis with ASD.

Gene set enrichment analysis of DNVs was performed using the DNENRICH framework32. We included all de novo LoF and D-mis variants in 5,754 constrained genes from 16,877 ASD and 5,764 control trios. For each gene set, we calculated the fraction of weighted sums of damaging DNVs using PPV weights of constrained genes (Supplementary Table 18) for cases and controls respectively. The test statistic for each gene set is the ratio of such fractions in cases over controls. To determine the distribution of the test statistic under the null hypothesis, we randomly placed mutations onto the exome of all constrained genes, while holding the number of mutations, their trinucleotide context and functional impact to be the same as observed in cases and controls separately. Note that by conditioning on the observed number of damaging DNVs in cases and controls, we tested enriched gene sets in cases that are not due to an increased overall burden. At each round of simulation, the permuted test statistic in each gene set was calculated. Finally, the P value was calculated as the number of times that the permuted statistic was no less than the observed statistic. Fold enrichment was calculated as the ratio between observed and average test statistics over all permutations. We also approximated the 95% confidence interval for fold enrichment by assuming that log[fold enrichment] follows normal distribution with mean 0 and s.d. determined by the P value.

In all DNV analyses above, DNVs shared by full or twin siblings represent single mutational events and were counted only once. When an individual carries multiple DNVs within 100 bp in the same gene, only one variant with the most severe effects was included in the analysis.

### Transmission disequilibrium analysis

The effect of inherited LoF variants was analyzed using TDT in each individual gene or in gene sets. Rare LoF variants were first identified in parents without ASD diagnoses or intellectual disability, then for each parent–offspring pair, the number of times the LoF variant was transmitted from parents to offspring was tallied. For variants in the (non-PAR part of the) X chromosome, we only used rare LoF variants carried by mothers without ASD diagnoses or intellectual disability and analyzed transmission in different types of mother–offspring pairs. For TDT analysis of rare inherited missense variants, different D-mis definitions and allele frequency cutoffs were used (Supplementary Fig. 2).

The overtransmission of LoFs to affected offspring was evaluated using a binomial test assuming that under the null hypothesis the chance of transmission is 0.5. In the discovery stage, ultra-rare LoFs with pExt ≥ 0.1 were used in exome-wide transmission disequilibrium and gene set enrichment analysis. For the per-gene test, all rare LoFs with pExt ≥ 0.1 were also used, and the TDT statistic39 for each gene was calculated by $$z = \frac{{T - NT}}{{\sqrt {T + NT} }}$$, where T(NT) is the number of times LoF variants were transmitted (not transmitted) to affected offspring. When offspring included monozygotic twin pairs, only one was kept in the transmission analysis. We prioritized 244 autosomal genes with z > 1 in the top 10% of LOEUF or in the top 20% of LOEUF and A-risk ≥ 0.4. In the second stage gene-based test, if a gene-specific pExt threshold was available, we used high-confidence LoF variants that passed the gene-specific pExt filter (see Supplementary Note).

In the gene set enrichment analysis of inherited LoFs, the rate of transmission to affected offspring in each gene set was compared with the transmission rate in the rest of the genes in the background using the χ2 test.

### Case-control analysis

Pseudocontrols are constructed from parents without ASD diagnoses or intellectual disability in simplex families, using alleles that were not transmitted to affected offspring. Each parent without ASD diagnoses or intellectual disability contributes a sample size of 0.5 to pseudocontrols. Rare LoFs in ASD cases whose parent data are not available and from other cases that were not used in DNV enrichment or TDT analysis were analyzed in this stage. Specifically, for each ASD case, we found out all of their most recent unaffected ancestors without ASD diagnoses or intellectual disability in the pedigree and calculated the contributing sample size as 1 minus the summation of kinship coefficients with these ancestors. If the contributing sample size was greater than 0, then the sample was included in pseudocases after removing alleles that were observed in any unaffected ancestors without ASD diagnoses or intellectual disability used in TDT and alleles included in DNV analysis if any. Examples of such rare LoFs in cases and their contributing sample sizes are given in Supplementary Fig. 19.

Rare LoFs in cases and controls for the X chromosome were categorized separately for males and females. Male controls include all fathers. In contrast, male cases include only those whose mothers do not have ASD diagnoses or intellectual disability (thus not included in TDT analysis). For females, because we include only mothers without ASD diagnoses or intellectual disability and affected sons in TDT, female pseudocases include all affected females. Female pseudocontrols were established from unaffected mothers in simplex families using alleles that do not transmit to affected sons. Each unaffected mother contributes a sample size of 0.5 to pseudocontrols. In both sexes, DNVs were removed from pseudocases.

For gene-based case-control association in stage 2, we used population data as controls, including gnomAD exomes26 (v2.1.1 non-neuro subset) and TOPMed genomes69 (freeze 8). Variants in the population controls were filtered to keep those that passed the default quality-control filter in released data. For variants in gnomAD data, we further removed variants located in low-complexity regions70 using the same procedure that was already applied to cases and TOPMed data. In gene-level case-control comparison of LoF burden, we used a baseline pExt ≥ 0.1 filter or gene-specific pExt threshold if available to define high-confidence LoF variants (see Supplementary Note). For LoF variants in selected genes, we also extracted curation results by gnomAD to remove curated non-LoF variants, and manually reviewed IGV snapshots from the gnomAD browser if available to remove likely variant calling artifacts (Supplementary Data 1). The number of high-confidence LoF variants was obtained from the allele counts in site-level VCF files. The gene-level burden of high-confidence LoF variants between cases and population controls is tested by comparing the high-confidence LoF variant rates between cases and controls using the Poisson test. The gene-level burden of ultra-rare synonymous variants (allele frequency < 1 × 10−5) between cases and population controls is assessed by a quantile–quantile (Q–Q) plot among all ancestry and European ancestry (Extended Data Fig. 3). To account for difference in depth of coverage, sample sizes are multiplied by the fraction of callable coding regions of each gene (≥15× for autosomes or female X chromosome, ≥10× for male X chromosome) in ASD cases and in population controls respectively.

To account for sample relatedness in case-control analysis, we created a relationship graph in which each node represents an individual and each edge represents a known first-degree or second-degree relationship between two individuals. We also added edges to pairs of individuals without known familial relationship but have an estimated kinship coefficient ≥ 0.1. From the graph, we select one individual from each connected component to create unrelated case-control samples. For the X chromosome, father and sons were treated as unrelated. For population controls, only gnomAD data included sex-specific allele counts and were used in the sex-specific analysis.

Meta-analysis was performed for prioritized autosomal genes that are constrained (defined as ExAC pLI ≥ 0.5 or ranked in the top 20% of the LOEUF scores; Supplementary Data 2). We integrated evidence from the enrichment of all DNVs, transmission disequilibrium and increased burden in cases compared with population controls by combining P values using Fisher’s method40. Study-wide significance was set at 9 × 10−6 (Bonferroni correction with 5,754 constrained genes). In mega-analysis, we combined all unrelated ASD cases together and compared CAFs of high-confidence LoF variants with two population control sets.

### Power calculation

To calculate statistical power of the current study and to estimate sample size for future studies, we adopted the statistical framework from ref. 41, comparing CAF of LoF variants in N unrelated cases fcase with CAF f in the general population. The effects of LoFs in the same gene are assumed to be the same (relative risk = γ). We focus only on constrained genes. We assume f to be at mutation–selection equilibrium f = μLoF/s, where μLoF is the LoF mutation rate and s is the selection coefficient. The test statistic asymptotically follows a noncentral χ2 distribution with 1 d.f. and noncentrality parameter (NCP):

$$\lambda = 4N\left[ {\gamma f\ln \gamma + (1 - \gamma ){{{\mathrm{ln}}}}\frac{{1 - \gamma f}}{{1 - f}}} \right]$$

Given the significance threshold α, power can be calculated analytically by

$$1 - \beta = 1 - F\left[ {F^{ - 1}\left( {1 - \alpha ,0} \right),\lambda } \right]$$

where F(x, λ) is the cumulative distribution of $$\chi _1^2$$ with NCP λ.

To calculate the sample size to achieve desired power 1 − β at significance level α, we first solve NCP λα,β from the above equation, then estimate sample size by

$$n_{\alpha ,\beta } \approx \frac{{\lambda _{\alpha ,\beta }}}{{4f\left[ {\gamma \ln \gamma - \left( {\gamma - 1} \right)} \right]}}$$

The current study has a sample size of n = 31,976 and the type I error rate is α = 9 × 10−6 (experimental wide significant). Given continuing expansion of biobank-scale sequencing, treating f as known without error is a reasonable assumption for future studies. To calculate power for the new genes identified in this study, we used point estimates of γ and f from mega-analysis using gnomAD exomes as population controls, and used μLoF computed from the 7-mer context-dependent mutation rate model55 to convert f to s = μLoF/f. The required sample sizes were calculated to achieve 90% power.

Power and sample size are both calculated as a function of relative risk for ASD (γ) and selection coefficient (s) across different haploid LoF mutation rates (μLoF). We only considered s between 0.01 and 0.5, because most prioritized genes have point estimates of s > 0.01 (Supplementary Fig. 5) and genes with s > 0.5 are expected to harbor more de novo than inherited LoF variants and can be identified from the enrichment of DNVs. We limited relative risk (γ) between 1 and 20 to focus on risk genes with moderate to small effects. The reduction in fitness s is correlated with the increases in ASD risk γ by s = γπ under the assumption of no pleiotropic effect, where π is ASD prevalence and sD is decreased reproductive fitness of ASD cases. Based on epidemiological studies, the current estimated prevalence of ASD is $$\hat \pi = 1/54$$71, and the estimated sD is for 0.75 male and for 0.52 female72, so sex-averaged $$\hat s_D = 0.71$$ (assuming male:female ratio of 4.2). In reality, most known ASD genes also show pleiotropic effects with other NDDs or are associated with prenatal death; therefore, $$s \ge \gamma \pi s_D \approx \gamma \hat \pi \hat s_D = 0.013\gamma$$. So, we considered only combinations of (s, γ) that satisfy the condition s ≥ 0.013γ.

### Gene sets

To evaluate the contribution of known ASD risk genes to the burdens of DNVs and inherited LoF variants identified in this study, we collected 618 known dominant ASD or NDD genes from the following sources: (1) Known NDD genes from DDG2P73 (2020-02) that are dominant or X-linked and have an organ specificity list that includes the brain or cause multisystem syndrome; (2) high-confidence ASD genes collected by the Simons Foundation Autism Research Initiative (SFARI)74 (2019-08) with score of 1 or 2, excluding known recessive genes; and (3) dominant ASD genes reported in recent literature and included in the SPARK genes list75 (2020-07).

To evaluate the gene sets enriched by damaging DNVs or inherited high-confidence LoFs, we used all constrained genes by ExAC pLI ≥ 0.5 or in the top 20% of the LOEUF as the background. Gene sets of the following five categories were collected for gene set enrichment analysis.

#### Transcriptome and proteome

(1) Genes with brain-specific expression, defined as the genes with average reads per kilobase of transcript per million mapped reads (RPKM) > 1 in the brain and over four times the median RPKM of 27 tissues in processed RNA sequencing (RNA-seq) data from ref. 76. (2) Genes in coexpression modules M2 and M3 derived from weighted gene correlation network analysis (WGCNA) of BrainSpan developmental RNA-seq data, previously reported to be enriched for known ASD genes33. (3) Genes expressed in excitatory or inhibitory neurons. We selected genes from ref. 77 that have average transcripts per million (TPM) > 100 in excitatory neurons and in inhibitory neurons. (4) Synaptic genes collected from SynaptomeDB78.

#### Neuronal regulome

(1) Putative CELF4 target genes, defined as genes with an iCLIP occupancy > 0.2 in ref. 79. (2) CHD8 target genes, defined as genes with promoter or enhancer regions that overlap with CHD8 binding peaks in human neural stem cells or midfetal brain in ref. 36. (3) FMRP target genes35 with a false discovery rate (FDR) < 0.1 that mapped them to orthologous human genes (Mouse Genome Informatics80, 2018-07). (4) RBFOX2 target genes34 that have Rbfox2 tag counts ≥ 8. Due to high correlations between RBFOX1 and RBFOX3, targeted genes by the two RNA binding proteins were merged in one gene set and selected to have total Rbfox1 and Rbfox3 tag counts > 24.

#### Autism gene predictions

(1) ForecASD is an ensemble classifier that integrates brain gene expression, heterogeneous network data and previous gene-level predictors of autism association to yield a single prediction score37. We created two sets of genes with forecASD prediction score greater than 0.4 or 0.5. (2) A-risk is a classifier that uses a gradient boosting tree to predict autism candidate genes using cell-type specific expression signatures in the fetal brain38. We created three sets of genes with prediction score greater than 0.4, 0.5 or 0.6.

#### Genetic evidence

(1) Genes enriched with DNVs in ASD, with nominal statistical evidence (P < 0.01 or P < 0.05 by DeNovoWEST) in the SPARK discovery cohort of 16,877 trios. (2) Genes enriched with DNVs in other NDDs (Supplementary Data 3), with nominal statistical evidence in 31,058 NDDs11. (3) Genes implicated in schizophrenia, with nominal statistical evidence (P < 0.05)48.

#### Genetic constraint

Four constraint gene sets are defined by genes in top 10% of the gnomAD LOEUF, 10–20% the gnomAD LOEUF and genes with selection coefficient for heterozygous protein-truncating variants estimated from ExAC data (sHet) ≥ 0.25 and ≥ 0.2.

### Archetypal analysis

Archetypal analysis81 is an unsupervised learning approach that has similarities to other dimensionality reduction and clustering approaches. An important distinction of archetypal analysis from comparable approaches is that it seeks a set of k archetypes, which are points along the convex hull of the data, from which all data points may be expressed as a mixture. The output of archetypal analysis is an N by k matrix, α, of [0,1] coefficients that represent the contribution of each archetype to each data point. Whereas cluster centroids are embedded within the interior of a cluster, archetypes are, by design, at the extremes of the data (that is, along the convex hull). In practice, this ensures that the archetypes are appreciably distinct from one another, which is often not the case for cluster centroids. Here, we use archetypal analysis as a means to organize putative ASD risk genes in a space that has meaning from a mechanistic (STRING) and phenotypic (HPO) standpoint. Genes of particular interest to this study can then be considered and interpreted in the context of the archetypes that define this space. STRING (v11)52 clusters and HPO53 terms were formatted as gene-by-term binary matrices. The working gene list was taken as the union of forecASD top decile genes and the 62 autism-associated genes from this study (total of 1,776 genes). A total of 583 genes from this set had annotations in both STRING and HPO, and using these genes, a canonical correlation analysis (CCA) was carried out using the RGCCA package for R (https://cran.r-project.org/web/packages/RGCCA/index.html) using five components and sparsity parameter c1 set to 0.8 for both the HPO and STRING matrices. Component scores for all 1,776 genes were calculated using the STRING cluster annotations and the corresponding coefficients from the CCA and was used as input for archetypal analysis81, with the optimal k (number of archetypes) selected using the elbow plot heuristic82 and the residual sums of squares (RSS) plotted as a function of k. We displayed the archetypal embedding using the simplexplot() function of the archetypes R package. Genes were identified as ‘archetypal’ if their top archetype coefficient was >2× the next highest archetypal coefficient. Those genes that did not fulfill this criterion were classified as ‘mixed’, whereas those that did were assigned to their maximally scoring archetype. We applied the following heuristic to guide the naming of each archetype: each MSigDB83 gene set (v7.4) that has two or more autism genes (n = 62 as described above) annotated is tested for association with the archetypal coefficients (A1–A6, simultaneously) in a quasibinomial generalized linear model (GLM) (Supplementary Table 15). The one-sided association P value (that is, positive association) for each archetype is reported in Supplementary Table 12 (top 20 for each archetype). To name each archetype, the top 20 gene sets with the strongest associations with that archetype were considered; this leads to the following naming conventions: A1, neurotransmission; A2, chromatin modification; A3, RNA processing; A4, vesicle-mediated transport; A5, MAPK signaling and migration; and A6, cytoskeleton and mitosis (see Supplementary Table 15 and Fig. 7). Representative genes for each archetype were chosen from among the list of 62 risk genes identified in this study, using the top six genes for each archetype (note that these genes do not necessarily fulfill the ‘archetypal’ criterion described above, but are simply the top six of the 62 for each archetype).

### Statistics and reproducibility

No statistical method was used to predetermine sample size, and no data were excluded from the analyses.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.