Polygenic and developmental profiles of autism differ by age at diagnosis

3

4 Xinhe Zhang<sup>1,2</sup>, Jakob Grove<sup>3-6</sup>, Yuanjun Gu<sup>1,2</sup>, Cornelia K. Buus<sup>5</sup>, Lea K. Nielsen<sup>5</sup>

5 Sharon A.S. Neufeld<sup>1</sup>, Mahmoud Koko<sup>7</sup>, Daniel S Malawsky<sup>7</sup>, Emma M Wade<sup>7</sup>, Ellen

6 Verhoef<sup>8</sup>, Anna Gui<sup>9,10</sup>, Laura Hegemann<sup>11-12</sup>, APEX consortium, iPSYCH Autism

7 Consortium, PGC-PTSD Consortium, Daniel H. Geschwind<sup>13-16</sup>, Naomi R. Wray<sup>17,18</sup>,

8 Alexandra Havdahl<sup>11,12,19</sup>, Angelica Ronald<sup>10,20</sup>, Beate St Pourcain<sup>8,21,22</sup>, Elise B.

9 Robinson<sup>23,24</sup>, Thomas Bourgeron<sup>25</sup>, Simon Baron-Cohen<sup>1,2,26</sup>, Anders D. Børglum<sup>3-5</sup>,

10 Hilary C. Martin<sup>7</sup>, Varun Warrier<sup>1,2,26</sup>

11

12 1. Department of Psychiatry, University of Cambridge

13 2. Autism Research Centre, Department of Psychiatry, University of Cambridge, Cambridge, UK

15 3. The Lundbeck Foundation Initiative for Integrative Psychiatric Research, iPSYCH, Aarhus, Denmark

17 4. Center for Genomics and Personalized Medicine (CGPM), Aarhus University, Aarhus, Denmark

19 5. Department of Biomedicine (Human Genetics) and iSEQ Center, Aarhus University, Aarhus, Denmark

21 6. Bioinformatics Research Centre, Aarhus University, Aarhus, Denmark

22 7. Human Genetics Programme, Wellcome Sanger Institute, Wellcome Genome Campus, Hinxton, CB10 1SA, UK

24 8. Language and Genetics Department, Max Planck Institute for Psycholinguistics, Nijmegen, The Netherlands

26 9. Department of Systems Medicine, University of Rome Tor Vergata, via Montpellier 1, 00133 Rome, Italy

28 10. Centre for Brain and Cognitive Development, Department of Psychological Sciences, Birkbeck University of London, London, WC1E 7HX, United Kingdom

31 11. Research Department, Lovisenberg Diaconal Hospital, Oslo, Norway

32 12. PsychGen Centre for Genetic Epidemiology and Mental Health, Norwegian Institute of Public Health, Oslo, Norway

34 13. Program in Neurobehavioral Genetics and Center for Autism Research and Treatment, Semel Institute, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA.

37 14. Program in Neurogenetics, Department of Neurology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA.

39 15. Department of Psychiatry, Semel Institute, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA.

41 16. Department of Human Genetics, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA.

43 17. Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072, Australia

45 18. Department of Psychiatry, University of Oxford, Oxford, OX3 7JX, United Kingdom

47 19. Promenta Research Centre, Department of Psychology, University of Oslo, Oslo, Norway

49 20. School of Psychology, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom
51 21. MRC Integrative Epidemiology Unit, University of Bristol, United Kingdom.

52 22. Donders Institute for Brain, Cognition and Behaviour, Radboud University,

53 The Netherlands.

54 23. Center for Genomic Medicine, Massachusetts General Hospital, Boston, MA,

55 USA

56 24. The Broad Institute of MIT and Harvard, Cambridge, MA, USA

57 25. Human Genetics and Cognitive Functions, Institut Pasteur, UMR3571 CNRS,

58 IUF, Université Paris Cité, Paris, France

59 26. Department of Psychology, University of Cambridge, Cambridge, UK

60

61 Correspondence to Xinhe Zhang (xz452@cam.ac.uk) or Varun Warrier

62 (vw260@cam.ac.uk)

63

64
## Abstract

Although autism has been historically conceptualised as a condition that emerges in early childhood, many autistic people are diagnosed later in life. It is unknown whether earlier and later diagnosed autism have different developmental trajectories and genetic profiles. Using longitudinal data from four independent birth cohorts, we demonstrate that two different socioemotional and behavioural trajectories are associated with age at diagnosis. In independent cohorts of autistic individuals, common genetic variants account for approximately 11% of the variance in age at autism diagnosis, comparable to the contribution of individual sociodemographic and clinical factors, which typically explain less than 15% of this variance. We further demonstrate that the polygenic architecture of autism can be decomposed into two modestly genetically correlated ($r_g = 0.38, SE = 0.07$) autism polygenic factors. One of these factors is associated with earlier autism diagnosis, and lower social and communication abilities in early childhood but is only modestly genetically correlated with ADHD and mental health conditions. Conversely, the second factor is associated with later autism diagnosis, increased socioemotional and behavioural difficulties in adolescence, and has moderate to high positive genetic correlations with Attention-Deficit/Hyperactivity Disorder and mental health conditions. These findings indicate that earlier and later diagnosed autism have different developmental trajectories and genetic profiles. Our findings have important implications for how we conceptualise autism and provide one model to explain some of the diversity within autism.

## Main

Ever since its earliest descriptions in the 1940s¹,², autism has been thought of as a condition that emerges in early childhood. However, a greater proportion of autistic individuals are now receiving an autism diagnosis from mid-childhood onwards than in early childhood³⁻⁵. One factor that may explain these findings is a shift in the conceptualisation of the condition over time, including the recognition that the behavioural signs of autism may not clearly manifest in the first three years of life⁶⁻⁹. Supporting this, some studies have demonstrated that a subset of children who do not initially meet the criteria for an autism diagnosis later receive a diagnosis.⁷,¹⁰⁻¹⁴ Later autism diagnosis is associated with elevated co-occurring mental health conditions¹⁵,¹⁶, highlighting the need to understand why some autistic people are diagnosed only later in life.

Several social, demographic, and clinical factors have been linked to age at autism diagnosis¹⁷. However, past studies show that individual clinical and sociodemographic factors explain only a modest proportion (typically less than 15%) of the variance in age at autism diagnosis (Extended Data Figure 1, Supplementary Table 1). This suggests additional factors contribute to age at autism diagnosis. One of these additional factors could be genetic differences among autistic individuals. Despite the relatively high heritability of autism¹⁸, the role of genetics in age at autism diagnosis has not been studied to date.

Two theoretical models can explain how genetics impacts age at autism diagnosis. In the first model, autism has a single polygenic aetiology, with the same set of genetic variants underlying autism, regardless of age at diagnosis (Unitary Model,
112 **Extended Data Figure 2**). Under this model, later diagnosed autistic individuals may
113 have subtle clinical features that are harder to recognise early in life, suggesting that
114 they do not cross a diagnostic threshold earlier in life. This may be due to a lower
115 genetic predisposition to autism. As they get older, additional environmental factors
116 may alter their clinical features, eventually bringing individuals above the clinical
117 threshold to receive an autism diagnosis later in life.

118 An alternative model is that earlier and later diagnosed autism have different
119 underlying developmental trajectories and polygenic aetiologies (**Developmental
120 Model, Extended Data Figure 2**). This aligns with existing evidence that the genetic
121 influences on traits related to autism vary across development¹⁹⁻²¹. This model does
122 not preclude a role for environmental factors influencing when someone receives an
123 autism diagnosis, but implies that different sets of genetic variants are associated
124 with earlier and later diagnosed autism.

125 Here we examined the evidence for these two models through four linked aims
126 (**Extended Data Figure 3**). First, we investigated whether the trajectories of
127 socioemotional and behavioural development are associated with age at autism
128 diagnosis in birth cohorts. Although variable developmental trajectories have been
129 observed among autistic individuals and their younger siblings²², it is unclear whether
130 these differences in trajectories are associated with age at diagnosis. Second, we
131 estimated the proportion of variance in age at autism diagnosis explained by
132 common single nucleotide polymorphisms (“SNP-based heritability”). We then tested
133 whether this is attenuated by a range of clinical and demographic factors, as
134 predicted by the Unitary Model. Third, we investigated whether different polygenic
135 factors are associated with earlier and later autism diagnosis, as predicted by the
136 Developmental Model. Fourth, we estimated the genetic correlation between the
137 autism polygenic factors related to age at diagnosis and other mental health and
138 developmental phenotypes.

139 We provide a summary of the study and address potential questions regarding the
140 implications of the findings in the **Supplementary Summary and FAQs**.

141 **Behavioural trajectories and diagnosis age**

142 In Aim 1, we investigated whether autistic individuals have varying trajectories of
143 socioemotional and behavioural trajectories and whether these are associated with
144 age at autism diagnosis in three birth cohorts (N = 89 to 188 autistic individuals with
145 recorded age at diagnosis between 5 to 17 years). These are the Millennium Cohort
146 Study (MCS, participants born in 2000), and Longitudinal Study of Australian
147 Children: Kindergarten cohort (LSAC-K, 1999) and Birth cohort (LSAC-B, 2003)
148 **(Supplementary Table 2, Extended Data Figure 4, Supplementary Note 1)**. All
149 three cohorts collected longitudinal information on socioemotional and behavioural
150 development using the caregiver-reported Strengths and Difficulties Questionnaire
151 (SDQ)²³. The SDQ has five subscales (emotional, conduct, hyperactivity/inattention,
152 peer problems, and prosocial behaviours), and the total score of difficulties (hereafter
153 "total difficulties") is the summed score of the first four subscales. The SDQ is widely
154 used, has excellent psychometric properties²⁴⁻²⁶, and is largely invariant across age,
155 sex, and different populations²⁷⁻²⁹, suggesting that it is measuring the same latent
156 trait across these demographic variables. In addition, the SDQ is moderately
157 correlated with autism-specific measures³⁰⁻³³, although it does not capture all of the
158 core diagnostic features of autism. Because not all cohorts recorded the exact age
159 when children received their autism diagnosis, we used the child's age during the
160 study data collection when caregivers first reported the diagnosis as an
161 approximation of age at autism diagnosis.
162

163 To identify latent trajectories, we used Growth Mixture Models of the SDQ total
164 difficulties and subscale scores among autistic individuals in all three cohorts.
165 Growth Mixture Models do not require grouping based on a priori hypothesis, but can
166 identify latent subgroups based on longitudinal differences in SDQ scores.
167

168 Across all three birth cohorts, Growth Mixture Modeling identified a two-trajectory
169 model as being optimal for SDQ total difficulties and the majority of subscale scores
170 **(Supplementary Table 3, Supplementary Figures 1 - 6)**. The first latent trajectory
171 was characterised by difficulties in early childhood that remained stable or modestly
172 attenuated in adolescence (termed 'early childhood emergent latent trajectory'). The
173 second latent trajectory was characterised by fewer difficulties in early childhood that
174 increased in late childhood and adolescence (termed 'late childhood emergent latent
175 trajectory') **(Figure 1 A - C)**.
176

176 Autistic individuals in the early childhood emergent latent trajectory were more likely
177 to be diagnosed as autistic in childhood compared to autistic individuals in the late
178 childhood emergent latent trajectory in MCS ($P = 1.42 \times 10^{-4}$, $\square^2$ test) and LSAC-B ($P
179 = 2.24 \times 10^{-2}$, $\square^2$ test) **(Supplementary Table 4, Figure 1 D - F)**. This difference was
180 not significant in LSAC-K, possibly because age 11 was the earliest when an autism
181 diagnosis was recorded.
182

183 Sensitivity analyses in MCS confirmed the robustness of the two latent trajectories
184 and their association with age at diagnosis among autistic children. We identified
185 consistent results after expanding the sample to include individuals with co-occurring
186 Attention-Deficit/Hyperactivity Disorder (ADHD) (N = 238, **Supplementary Tables 3**
187 - 4), and after imputing missing data to increase statistical power and reduce bias (N
188 = 623) **(Supplementary Table 5, Supplementary Notes 2 and 3)**. We also obtained
189 consistent results when restricting the analyses to only males (N = 136,
190 **Supplementary Table 3 - 4**), suggesting that these results were not driven by sex
191 differences in age of diagnosis. We were unable to run equivalent female-only
192 analyses due to the low sample sizes.
193

194 To assess the specificity of this result to autism, we tested whether similar latent
195 trajectories were also observed in children with ADHD but not autism (N = 89;
196 imputed N = 325) in MCS using Growth Mixture Models. Two latent SDQ trajectory
197 classes emerged, but these were not significantly linked to age at ADHD diagnosis,
198 except for the SDQ hyperactivity/inattention and conduct problems subscales in the
199 imputed sample **(Supplementary Table 6, Supplementary Figures 7 and 8)**,
200 suggesting that the findings are relatively specific to autism rather than
201 neurodevelopmental conditions broadly.
202

203 Although females receive an autism diagnosis later than males on average³⁴, in all
204 three cohorts, the sex ratio was similar between the two latent trajectories
205 **(Supplementary Table 4)**, possibly due to their relatively small sample sizes.
206
207 Individuals in the late childhood emergent latent trajectories were more likely to
208 report mental health conditions (Supplementary Table 7), consistent with previous
209 epidemiological observations among later diagnosed autistic individuals¹⁵,¹⁶.

210 Using multiple regression models, we then examined the extent to which these two
211 latent trajectories contributed to differences in age at autism diagnosis over and
212 above sociodemographic and cognitive characteristics (Supplementary Table 8). In
213 these models, SDQ latent trajectories explained 11.7% (LSAC-B) to 30.3% (MCS) of
214 the variance in age of autism diagnosis. In contrast, sociodemographic variables
215 explained 4.8% (LSAC-B) to 5.5% (MCS) of the total variance across cohorts,
216 consistent with previous reports (Extended Data Figure 1). In the imputed MCS
217 sample (N = 623, Supplementary Table 5, Supplementary Note 2), the SDQ latent
218 trajectories and sociodemographic variables explained 56.6% and 3.2% of the
219 variance, respectively. The effects of the sociodemographic variables were not
220 mediated by the SDQ latent trajectories (Supplementary Table 8, Supplementary
221 Note 4).

222
223
224 The associations between different SDQ trajectories and age at autism diagnosis
225 were also supported by latent growth curve models fitted on earlier- and later-
226 diagnosed autistic individuals (Supplementary Note 5, Supplementary Table 9,
227 Supplementary Figures 1 - 6, 9, and 10). These results confirm that the association
228 between SDQ trajectories and age at autism diagnosis is robust to methodological
229 choices
230

231 Age at autism diagnosis is heritable

232 The above analyses demonstrate that variation in socioemotional and behavioural
233 trajectories, measured using the SDQ, is associated with age at autism diagnosis.
234 Previous research has demonstrated that developmental variation traits related to
235 autism is partly explained by genetic factors¹⁹,²⁰,³⁵⁻³⁸. A corollary of this is that
236 genetic factors may also be associated with age at autism diagnosis.

237
238 Subsequently, in Aim 2, we tested whether age at autism diagnosis is heritable in
239 two large cohorts of autistic individuals using genetic data and information on age at
240 autism diagnosis. This includes (1) the Danish-based iPSYCH cohort (N<sub>total</sub> =
241 18,965), a population-based sample derived from the Danish national registries that
242 includes autistic individuals, and (2) the US-based cohort of autistic individuals
243 (SPARK<sup>39</sup>: N<sub>total</sub> = 28,165; Extended Data Figures 5 - 6), which recruits families with
244 at least one autistic individual through online platforms and medical centers across
245 the United States. In SPARK, we conducted initial analyses in a discovery subset of
246 18,809 autistic individuals (SPARK Discovery), and replicated key findings in an
247 additional sample of 9,356 autistic individuals that only became available after initial
248 analyses were completed (SPARK Replication). SPARK and iPSYCH differed in the
249 diagnostic classification system (iPSYCH: ICD and SPARK: DSM), and median age
250 at diagnosis (iPSYCH: median = 10, median absolute deviation = 4; SPARK: median
251 = 4, median absolute deviation = 2.7).

252
253 We conducted Genome-wide Association Study (GWAS) in iPSYCH and across both
254 the Discovery and Replication samples of SPARK, using age at autism diagnosis as
255 a quantitative trait. In all three samples, we identified significant and consistent SNP-
256 based heritability of approximately 11% for age at autism diagnosis (Figure 2A,
**Supplementary Table 10).** This is larger than, or similar to, the variance explained by several other clinical and sociodemographic factors tested in SPARK (**Extended Data Figure 1**, **Supplementary Table 1**).

In contrast to the effect of common genetic variants, in a subsample of SPARK with available data for both parents and their autistic child (N = 6,206 trios), we observed no association between age at autism diagnosis and rare *de novo* variants or inherited protein truncating or missense variants in highly constrained genes (**Supplementary Table 11**). This may possibly be due to low statistical power, or reflect later autism diagnosis in some carriers of *de novo* mutations due to diagnostic overshadowing by co-occurring intellectual disability (ID) or global developmental delay⁴⁰,⁴¹.

We next tested if this SNP-based heritability of age at autism diagnosis is consistent with either of the two theoretical models outlined earlier. The Unitary Model assumes that later diagnosis reflects subtle or less severe clinical features, and so the SNP-based heritability of age at autism diagnosis may simply reflect the severity of autism features. Alternatively, the SNP-based heritability may reflect additional genetic influences associated with co-occurring developmental delays, developmental regression, or ID, which may lead to an earlier diagnosis. It may also reflect the heritable component of parental socioeconomic status and neighbourhood deprivation - proxies for parental awareness and healthcare access that affect diagnostic timing. Controlling for any of these measures should attenuate the SNP-based heritability.

In contrast, the Developmental Model assumes that SNP-based heritability of age at autism diagnosis reflects a mixture of different polygenic factors that are correlated with age at diagnosis but independent of these covariates. Under this model, a significant SNP-based heritability should persist after controlling for clinical, developmental and sociodemographic measures.

In line with the Developmental Model, we found that the SNP-based heritability did not significantly attenuate after controlling for parental sociodemographic measures, clinical features, or co-occurring developmental delays and conditions (**Figure 2B**, **Supplementary Table 10**). This is inconsistent with the Unitary Model, although imperfect and incomplete measurement of clinical and developmental phenotypes may limit this conclusion.

A second prediction of the Unitary Model is that earlier diagnosis is associated with greater polygenic propensity for autism compared to later diagnosis (**Extended Data Figure 2**). Under this model, all autistic individuals would have higher polygenic propensity for autism compared to non-autistic controls. This would result in negative genetic correlations between GWAS of age at autism diagnosis and GWAS of autism, with the magnitude of this negative correlation decreasing as the median age at diagnosis in the autism GWAS samples increases.

We tested this prediction using 13 different but partly overlapping autism GWASs including six GWASs stratified by age at diagnosis and two GWASs stratified by sex (**Box 1**, **Figure 3**). The genetic correlation between age at autism diagnosis and different autism GWASs varied systematically, becoming increasingly positive as the
305 median age at diagnosis increased (Figure 3, Supplementary Table 12). However, 306 contrary to the expectation under the Unitary Model, we observed positive genetic 307 correlations between age at autism diagnosis and autism GWAS comprising later- 308 diagnosed autistic individuals. These findings support the existence of different 309 genetic architectures across diagnostic age groups, aligning with the Developmental 310 Model.

311 Furthermore, the male- and female-stratified autism GWAS from iPSYCH had similar 312 genetic correlation with age at autism diagnosis. This suggests that the pattern of 313 genetic correlation between age at diagnosis and the autism GWASs does not reflect 314 differences in the sex ratio of participants across the autism GWASs.

315 The genetic correlation with some of the autism GWASs differs significantly between 316 the age at diagnosis GWASs in iPSYCH versus meta-analysed SPARK (Figure 3). 317 This reflects the fact that these two age at diagnosis GWASs are only moderately 318 genetically correlated with each other (Genetic correlation ($r_g$)= 0.51, standard error 319 (SE) = 0.19, $P$ = 7.56x10⁻³), which is possibly due to the different recruitment 320 strategies and resulting differences in the median age at autism diagnosis in the two 321 cohorts (Supplementary Note 6).

322

323 Box 1: Summary of the autism GWAS used in this 324 study

325 Autism GWAS not stratified by age at diagnosis

326 • SPARK (Matoba 2020): Case-pseudocontrol design (4,535 pairs) with family- 327 based ascertainment across the United States. Median age at diagnosis = 3.5 328 (1.97) years

329 • FinnGen (Data Release r10): Population-based sample from Finland (646 330 cases vs. 301,879 controls). Median age at diagnosis = 22.66 (7.16) years.

331 • PGC-2017: Meta-analyses of several case-control and case-pseudo control 332 datasets (7,387 cases vs. 8,567 controls). The majority of the cases met the 333 diagnostic criteria for autism under DSM-IV-TR/ICD-10 or earlier (i.e., onset of 334 features before age 3) after screening using the Autism Diagnostic 335 Observation Schedule and the Autism Diagnostic Interview-Revised), making 336 this a clinically well characterised cohort. Although age at diagnosis is 337 unavailable, the majority of the participants were recruited as trios through 338 medical or research centres in the United States. Given this similarity in 339 ascertainment to SPARK, we anticipate the age at diagnosis to be similar to 340 that of SPARK trios (Matoba 2020). Approximate median age at diagnosis = 341 3.5

342 • iPSYCH (unstratified): Population-based sample derived from Danish national 343 registries, including individuals born 1980-2008 (19,870 autistic vs. 39,078 344 non-autistic individuals). Median age at diagnosis = 10.74 (5.35)

345 • iPSYCH (males): Males only subset of iPSYCH (15,025 autistic vs. 19,763 346 controls). Median age at diagnosis = 10.08 (5.07)

347 • iPSYCH (females): Females only subset of iPSYCH (4,845 autistic vs. 19,315 348 controls). Median age at diagnosis = 12.97 (4.75)
349 • Grove et al., 2019: Meta-analysis of a subset of the iPSYCH and PGC
350 samples (18,381 cases vs. 27,969 controls). As age at diagnosis for PGC is
351 unavailable, we calculated an estimated age by weighing the median age at
diagnosis of iPSYCH with the estimated median age in PGC by their
352 respective sample size. Approximate median age at diagnosis = 8.73.
353

354 Autism GWAS stratified by age at diagnosis

355 SPARK (using unaffected family members as controls), meta-analysed from the
356 Discovery and Replication subsets

357 • Diagnosed before age 11 (SPARK<sub>before11</sub>): 27,881 autistic individuals; selected
to match iPSYCH stratification; median age at diagnosis = 3.5 (1.97) years.
358
359 This cutoff period was chosen to reflect the cutoff used in the Latent Growth
Curve models, and represents a time window characterised by the onset of
360 puberty, transition from primary to secondary school, and an increase in the
361 number of autistic girls being diagnosed.
362

363 • Diagnosed after age 10 (SPARK<sub>after10</sub>): 6,243 autistic individuals; median age
364 at diagnosis = 15.83 years (7.16).

365 • Diagnosed before age 6 (SPARK<sub>before6</sub>): 21,435 autistic individuals;
categorised as "early-diagnosed" based on previous research<sup>8</sup>; median age at
diagnosis = 3 (1.23) years.
366
367

368 iPSYCH (population-based controls)

369 • Diagnosed before age 11 (iPSYCH<sub>before11</sub>): 9,500 autistic vs. 36,667 non-
370 autistic individuals; median age at diagnosis = 7.34 (2.76) years. The cutoff
371 was chosen to reflect the cutoff used in the Latent Growth Curve models and
SPARK age at diagnosis stratified GWAS.
372

373 • Diagnosed after age 10 (iPSYCH<sub>after10</sub>): 9,231 autistic vs. 36,667 non-autistic
374 individuals; median age at diagnosis = 14.55 (2.84) years.

375 • Diagnosed before age 9 (iPSYCH<sub>before9</sub>): 5,451 autistic vs. 36,667 non-autistic
376 individuals; created to provide additional age resolution; median age at
diagnosis = 5.74 (1.69) years
377

378 Two autism polygenic factors

379 These findings suggest that the age at autism diagnosis reflects a mixture of different
380 age-dependent polygenic traits (Developmental Model) rather than a single
381 polygenic trait (Unitary Model). Under the Developmental Model, one would expect
382 that the genetic correlations between different autism GWAS will differ according to
383 the difference in the median age of diagnosis between the GWAS.
384

385 In Aim 3, we tested this by estimating genetic correlations among the 13 autism
386 GWASs (Box 1). We observed genetic correlations ranging from 0.02 (SE = 0.13) to
387 1 (SE = 0.01) (Figure 4A, Supplementary Table 13). We observed a gradient in the
388 genetic correlations related to the similarity in median age at diagnosis between
389 cohorts. Cohorts with the most similar median ages at diagnosis (differing by ≤2
390 years) showed the highest genetic correlations (r<sub>g</sub> = 0.88-1), while correlations
391 progressively decreased as age differences increased. The lowest genetic 392 correlation of ($r_g$ = 0.02, SE = 0.13) was observed between SPARK$_{before6}$ (median 393 age ~ 3) and SPARK$_{after10}$ (median age ~ 16).

394 Hierarchical clustering of the genetic correlations identified two broad, overlapping 395 clusters that differed by age at autism diagnosis. One cluster comprised GWAS of 396 autism in cohorts with predominantly childhood diagnosed individuals, and the other 397 comprised GWAS of autism in cohorts with a large fraction of individuals diagnosed 398 in adolescence or later, consistent with predictions from the Developmental Model. 399

400 We formally tested this by modelling the genetic covariance using structural equation 401 models in GenomicSEM⁴², testing six theoretical models (**Supplementary Table 14**). 402 Using six minimally overlapping GWAS for autism with wide variation in age at 403 autism diagnosis among those listed in Box 1. We found that a correlated two-factor 404 model was the most parsimonious and fit the data best (Akaike information criterion: 405 38.64, confirmatory fit index : 0.99, standardised root mean residual: 0.08, **Figure 4B**). 406 Factor 1 (Earlier diagnosed autism factor) was defined by the GWAS with 407 predominantly early childhood diagnosed individuals (PGC-2017, SPARK$_{before6}$, with 408 a median age at diagnosis of 3). Factor 2 (Later diagnosed autism factor) was 409 defined primarily by GWAS with adolescent or adult diagnosed individuals 410 (iPSYCH$_{after10}$, FinnGen, and SPARK$_{after10}$). The cross loading of iPSYCH$_{before9}$ 411 (median age at diagnosis ~5.7) suggests that Factor 2 may impact behaviours in 412 mid/late childhood as well. The two factors had a modest genetic correlation ($r_g$ = 413 0.38, SE = 0.06). Sensitivity analyses confirmed the robustness of the above results 414 using partly different GWAS, where we identified a two-correlated-factor model as 415 the best fitting model, with similar moderate genetic correlations between the two 416 factors ($r_g$ = 0.37, SE = 0.06 - 0.52, SE = 0.10, **Supplementary Table 14**). 417

418 The earlier diagnosed autism factor was negatively genetically correlated with age at 419 autism diagnosis (**Figure 5**). The later diagnosed autism factor was positively 420 genetically correlated only with age at autism diagnosis from SPARK. Genetic 421 correlation with the autism GWAS stratified by sex showed that both autism factors 422 had stronger genetic correlations with autism in males than females, with a larger 423 difference for the earlier diagnosed autism factor (**Figure 5**), consistent with 424 established sex differences in age at autism diagnosis.

425 Additional analyses using polygenic scores confirmed that the association between 426 the two polygenic autism factors and age at autism diagnosis is not due to several 427 confounding factors using within-family approaches, nor due to differences in clinical 428 and demographic factors, and co-occurring developmental conditions 429 (Supplementary Note 7, Supplementary Table 15 - 17). Taken together, the above 430 findings demonstrate that earlier and later diagnosed autism have different polygenic 431 aetiologies, supporting the Developmental Model.

432
433
434
435
Genetic correlations with autism factors

436 The above analyses indicate that there are at least two polygenic factors associated 437 with age at autism diagnosis. Since later-diagnosed autistic individuals have higher 438 rates of mental health conditions¹⁵,¹⁶, we hypothesised this might partly be because 439 earlier and later diagnosed autism factors have differing genetic correlations with
440 mental health and cognitive phenotypes. In Aim 4, we investigated this hypothesis
441 using genetic correlation analyses.

442
443 The earlier diagnosed autism factor (Factor 1) had modest (r<sub>g</sub> ~ 0.1-0.2) but
444 significant genetic correlation with educational attainment, cognitive aptitude, ADHD,
445 various mental health and related conditions (**Supplementary Table 18, Figure 5**).
446 The later diagnosed autism factor (Factor 2) showed a statistically similar genetic
447 correlation with educational attainment but significantly higher genetic correlations (r<sub>g</sub>
448 ~ 0.5-0.7) with ADHD and a range of other mental health and related conditions,
449 including Depression, PTSD, childhood maltreatment, and self-harm. After
450 accounting for genetic effects on ADHD, we saw an attenuated but significant
451 moderate genetic correlation between later diagnosed autism (Factor 2) and mental
452 health conditions, suggesting shared genetics with ADHD do not fully explain the
453 elevated correlation between later diagnosed autism and mental health phenotypes
454 (**Supplementary Table 18, Supplementary Figure 11**). Sensitivity analyses using
455 age at diagnosis stratified GWAS from iPSYCH and SPARK yielded largely
456 consistent genetic correlation results, suggesting that these results are not due to
457 cohort differences (**Supplementary Table 19, Extended Data Figure 7**).

458
459 The higher genetic correlation between later diagnosed autism and other mental
460 health conditions may indicate diagnostic misclassification (where individuals with
461 other conditions incorrectly receive an autism diagnosis) or diagnostic
462 overshadowing (where the presence of co-occurring mental health conditions can
463 delay an autism diagnosis). Under the Unitary Model, the genetics of later diagnosed
464 autism would reflect the additive genetic effects of earlier diagnosed autism and of
465 other mental health conditions. However, decomposition of the autism genetic signal
466 using genomicSEM indicated that later diagnosed autism cannot be entirely
467 attributed to the polygenic effects of earlier diagnosed autism and six other mental
468 health conditions tested: schizophrenia, ADHD, anorexia nervosa, depression,
469 bipolar disorder, and PTSD (Supplementary Note 8). Thus, the later diagnosed
470 autism genetic factor does not represent the additive genetic effects of earlier
471 diagnosed autism and mental health conditions.

472
473 Finally, we investigated whether the two autism polygenic factors related to age at
diagnosis differ in their associations with developmental traits. Cross-sectionally,
474 these genetic factors showed few significant differences in genetic correlation or
475 polygenic score association with developmental phenotypes measured at age three
476 or earlier. The exceptions were age at onset of walking<sup>43</sup> and expressive vocabulary
477 at 2 - 3 years<sup>44</sup>, with which the earlier diagnosed autism factor was positively
478 genetically correlated, but the later diagnosed was not (Supplementary Note 9,
479 Supplementary Table 20 - 22). However, longitudinal polygenic score analyses
480 across two birth cohorts revealed differential genetic effects of earlier versus later
481 diagnosed autism factors on SDQ total difficulties scores over time (Supplementary
482 Note 9, Supplementary Table 23).
483

Discussion
---

These results indicate that earlier and later diagnosed autism are associated with
485 different developmental trajectories, and are only modestly genetically correlated
486 with each other. This possible framework provides one axis of heterogeneity to
487
488 describe the widely acknowledged clinical and genetic heterogeneity within autism,
489 that thus far has been challenging to identify. This finding of two or more
490 developmentally variable polygenic latent traits for autism is robust to various
491 observed clinical and demographic factors (Supplementary Note 10), including sex
492 and ID.
493

494 Consistent with the larger literature on developmental variation in autism²², our
495 analyses of socioemotional and behavioural trajectories across multiple birth cohorts
496 converge with the genetic findings - polygenic scores for earlier and later diagnosed
497 autism have different associations with developmental changes in SDQ total
498 difficulties scores (Supplementary Note 9). These results suggest that the timing of
499 autism diagnosis may partly reflect etiologically different developmental pathways,
500 rather than purely environmental or diagnostic factors. Our findings are consistent
501 with the wider literature that demonstrates that genetic influences on traits related to
502 autism vary across development in the general population¹⁹,²⁰.
503

504 This two-polygenic trait genetic model provides one framework to understand genetic
505 heterogeneity in autism, and the varying patterns of genetic correlations between
506 different GWAS of autism and other phenotypes. For example, previous GWAS of
507 autism (including PGC-2017) found limited genetic correlation with ADHD, contrary
508 to findings from more recent autism GWAS (e.g., Grove et al., 2019). We show that
509 this is explained by the different average age at diagnosis across these GWAS (Box
510 1, Figure 4), as the genetic correlation between autism and ADHD increases with
511 later age at autism diagnosis (Figure 6). These findings were confirmed using within-
512 family analyses that demonstrated over-transmission of ADHD polygenic scores
513 primarily to individuals with a later autism diagnosis (Supplementary Table 24).

514
515 Both the later diagnosed genetic autism factor (Figure 5) and the late childhood
516 emergent latent trajectory of SDQ total difficulties scores (Figure 2) are associated
517 with greater mental health problems (Figure 6 and Supplementary Table 7). This
518 suggests that epidemiological findings of greater mental health difficulties among
519 later diagnosed autistic individuals¹⁵,¹⁶ may be partly explained by the
520 Developmental Model of autism. Given that autistic females are, on average,
521 diagnosed later in life, research that investigates sex and gender differences in both
522 autism and co-occurring conditions¹⁶,⁴⁶ needs to account for genetic confounding
523 associated with age at autism diagnosis. Findings that may appear to reflect sex
524 differences may additionally reflect differences associated with age at diagnosis. For
525 example, the higher prevalence of mental health problems in autistic females¹⁶,⁴⁶
526 compared to males attenuates when restricting to autistic individuals diagnosed
527 before age five¹⁶.
528

529 These findings must be interpreted considering several limitations. First, the SNP-
530 based heritability for age at autism diagnosis is only about 11% (Figure 3), and other
531 observed developmental and demographic factors typically explain less than 15% of
532 the variance (Extended Data Figure 2). This suggests that there are several other
533 factors that contribute to age at autism diagnosis. We find that the genetic effects on
534 age at autism diagnosis are not mediated by several of these measured
535 developmental and demographic factors, but we acknowledge that there may be
536 several unmeasured factors that may mediate the genetic effects. Furthermore, the
537 substantial variation across the datasets explored highlights that age at autism
538 diagnosis is immensely complex, and varies across geography and time. Local 539 cultural factors, access to healthcare, gender bias, stigma, ethnicity, and 540 camouflaging likely have an impact on who receives a diagnosis and when. Second, 541 our trajectory models (Figure 2) were built using only the SDQ, which measures a 542 wide range of parent-reported neurodevelopmental and mental health traits. 543 Although the SDQ is correlated with an autism diagnosis, it does not fully capture 544 core autistic traits, and other measures of autistic traits were not available in the birth 545 cohorts. Third, it is likely that other dimensions contribute to genetic heterogeneity in 546 autism. For example, a significant proportion of the variation in the FinnGen autism 547 GWAS was not explained by either of the two factors (Figure 5). Fourth, we use 548 'earlier' and 'later' diagnosed autism as relative terms, reflecting that developmental 549 and polygenic differences represent a gradient (Figure 5, Supplementary Figure 550 551 thresholds for early versus late diagnosis⁴⁷). Fifth, autism diagnoses in the birth 552 cohorts used in the current study rely on community-based caregiver or self- 553 reporting rather than standardised clinical assessments. As such, there may be 554 varying delays between the emergence of autistic features and a formal autism 555 diagnosis. However, our findings can guide future research using longitudinal 556 cohorts, and particularly sibling studies, that systematically track the emergence of 557 autism features over time. Finally, our genetic analyses focused on common genetic 558 variants in genetically inferred European ancestries due to limited GWAS data from 559 other populations, highlighting the need for future research to examine the 560 transferability of these findings across diverse genetic ancestries. 561

561 In conclusion, we find that the developmental trajectories and polygenic architecture 562 of autism varies with age at diagnosis. These findings partly explain the varying 563 genetic correlations among the different GWAS of autism and between autism and 564 various mental health conditions. These findings provide further support for the 565 hypothesis that the umbrella term “autism” describes multiple phenomena with 566 differing aetiologies, developmental trajectories, and correlations with mental health 567 conditions. These findings have implications for how we conceptualise 568 neurodevelopment more broadly, and for understanding diagnosis, sex and gender 569 differences, and co-occurring health profiles in autism. 570
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687

688

689
690 **Methods**

691 **A note on terminology**

692 We use the term autistic and non-autistic to refer to people with and without an
693 autism diagnosis⁴⁸. Sex, males, and females refer to sex assigned at birth.

694

695 **Variance explained in age at autism diagnosis: literature review and analyses**
696 **of the SPARK cohort**

697 To contextualise the SNP-based heritability and the variance explained by SDQ total
698 difficulties and subscale scores, we conducted a review of the variance in the age at
699 autism diagnosis explained by various sociodemographic and clinical factors,
700 including sex and autism severity. Using Google Scholar and PubMed, we searched
701 for studies published between 1998 and December 10, 2024 using combinations of
702 the following terms in the title or abstract: "age at diagnosis" AND "autism", "autism"
703 AND "age," and "diagnosis age" AND "autism". We also used these search terms
704 with alternative terminology for autism, including "autism spectrum condition,"
705 "autism spectrum disorder," and "ASD". This search resulted in over 1,700 studies.
706 Manual review identified 184 studies that investigated factors associated with age at
707 autism diagnosis. Of these 13 quantified the variance explained using measures
708 such as R² or η², and were included in our final analyses (Supplementary Table 1).
709

710

711 In addition, we also calculated the variance explained in the US-based cohort of
712 autistic individuals and their families, SPARK³⁹, where we used the v9 release of the
713 phenotypic data. We focussed on the variance explained by sociodemographic
714 factors (sex, reported race, household income, mother's education, and father's
715 education), cognitive and developmental factors (reported IQ score, reported
716 intellectual disability, age at walking independently, age at first words, language
717 regression, other regression), and autism severity (scores on the Social
718 Communication Questionnaire and Repetitive Behaviour Scale-Revised). After
719 excluding individuals with missing data, we quantified the variance explained by
720 these factors using relative importance analysis (Lindemann, Merenda and Gold -
721 1980 method) in 5,773 autistic individuals diagnosed before age 22. Thereafter,
722 analyses were conducted using the relaimpo (v2.2-7) package in R, which allowed
723 us to examine all variables' contributions simultaneously ⁴⁹.

724

725 **Trajectory analyses of birth cohorts**

Cohorts

726 We used four population-based birth cohorts that vary both in the ages at which data
727 was collected from participants and the calendar years of data collection (Extended
728 Data Figure 3). Briefly, the four cohorts included are the UK-based Millennium
729 Cohort Study (MCS)⁵⁰, the Australia-based Longitudinal Study of Australian Children
730 - Birth (LSAC-B) and Kindergarten (LSAC-K) cohorts⁵¹⁵², and the Ireland-based
731 Growing Up in Ireland (GUI) Child cohort (aka Cohort 98')⁵²⁵¹. All children included in
732 the cohorts were born in the 21st century. Further details about the cohorts are
733 provided in the Supplementary Note 1. We used data from MCS, LSAC-B, and
734 LSAC-K for the Growth Mixture Models. We did not use data from GUI for Growth
735 Mixture Models as there were only three time points, which is not sufficiently
736 powered to identify two or more trajectories. All four cohorts were used for Latent
737 Growth Curve Models.

738
739 As indicated in **Supplementary Table 2**, these cohorts were selected because they 740 were (1) longitudinal in nature, (2) nationally representative, and (3) included key 741 data on behavioural profiles and neurodevelopmental diagnosis. These overlapping 742 features across datasets allowed for cross-country comparisons and 743 generalisation⁵³.

744

745 Measures

746 *Autism and ADHD diagnosis and age at diagnosis*

747 In all cohorts, across multiple sweeps, the main caregiver was asked if the 748 participant had a diagnosis of autism (**Extended Data Figure 3**). For age at 749 diagnosis, we used the age at the sweep when caregivers first reported their child's 750 autism diagnosis in every cohort, to maximise sample sizes and ensure consistency 751 across cohorts for effective comparisons. For instance, if an autism diagnosis was 752 reported for the participant for the first time at the age 11 sweep, we considered age 753 at diagnosis to be 11 years. Although the specific age at diagnosis was provided for 754 LSAC-B and LSAC-K, we opted not to use this, as we identified errors in some 755 reports where months and years of diagnosis were swapped or not reported.

756 In MCS, we used reports of both autism and ADHD diagnoses to conduct additional 757 sensitivity analyses. For our primary analyses, we included a narrowly defined 758 sample of children with consistently reported autism diagnoses by primary and proxy 759 caregivers (when both were available) and no other reported neurodevelopmental 760 diagnosis (particularly ADHD). To assess the generalisability of our results and 761 increase the sample size, we then expanded the sample to include all children with 762 any reported diagnosis of autism (results reported in **Supplementary Note 3**). This 763 expanded sample included cases regardless of whether the diagnoses were 764 consistent across sweeps or caregivers, and included those with co-occurring 765 ADHD. Additionally, we imputed the independent variables and covariates for autistic 766 individuals with missing information, as detailed below (more details in 767 **Supplementary Note 2** and **Supplementary Note 3**). Finally, to assess the 768 specificity of the trajectories for autism, we conducted analyses among children who 769 had a consistent ADHD diagnosis but no diagnosis of autism. Imputation was also 770 performed within this ADHD-only sample, to increase the sample size.

771 *Strengths and Difficulties Questionnaire (SDQ)*

772 We used the SDQ to capture social, emotional, and behavioural profiles of 773 participants, with repeated measures from 3 to 18 years across cohorts (**Extended 774 Data Figure 3**). SDQ comprises 25 statements that caregivers are asked to rate on 775 a 3-point Likert scale (“not true”, “somewhat true”, and “certainly true”) based on the 776 child’s symptoms or behaviours over the past six months. There are five subscales, 777 each containing five items, which assess emotional symptoms, conduct problems, 778 hyperactivity-inattention, peer relationship problems, and prosocial behaviours 779 respectively²³. The first four subscales assess difficulties, and their combined total 780 score ranges from 0 to 40, with higher scores indicating greater difficulties. The fifth 781 subscale (prosocial behaviours) represents strengths and ranges from 0 to 10, with 782 higher scores indicating more prosocial behaviours. We analysed the total score and 783 each subscale separately. The SDQ demonstrates good test-retest reliability and 784 criterion validity across countries²⁴⁻²⁶. Its five-factor structure (each subscale as a 785 factor) has shown consistency and invariance across age, sex, and ethnic 786 background²⁴,²⁸. The SDQ captures several core features of mental health and
787 neurodevelopmental conditions, including autism and ADHD⁵⁴. Only children with
788 complete data of SDQ across all sweeps were included in the analyses, except for
789 imputation analyses.

790

791 *Sociodemographic measures*

792 Sociodemographic measures were included as covariates to account for their impact
793 on age at diagnosis in each cohort (Supplementary Table 25). Specific measures
794 and available information vary across cohorts, but we generally included sex, ethnic
795 background, maternal age at delivery, child's cognitive aptitude, household socio-
796 economic status (SES), and deprivation level of the living area, to account for factors
797 that may impact the age when someone receives an autism diagnosis⁵⁵,⁵⁶. Only
798 subsets of children in the complete-SDQ samples, with complete data for these
799 sociodemographic factors, were included in the respective analyses.

800

801 In MCS, although various census classifications for ethnic groups were available, we
802 opted to use a binary indicator to identify non-white ethnic minorities. Ethnicity data
803 were not collected in either LSAC cohort. Instead, visible ethnic minority status was
804 determined primarily by parental country of birth and the language(s) spoken at
805 home.⁵⁷ Maternal age at delivery was collected only in MCS. In other cohorts, we
806 used maternal age (in years) at first sweep of data collection to reflect the variation in
807 maternal age at delivery.

808

809 In MCS, we identified multiple variables linked to cognitive ability, SES, and area
810 deprivation. Similarly, in LSAC-B, we identified multiple measures linked to SES,
811 although there were no measures with sufficient sample size linked to cognitive
812 ability or area deprivation. Subsequently, we conducted principal component
813 analysis (PCA) for cognitive abilities, SES, and area deprivation in MCS, and for
814 SES in LSAC-B. PCA was performed using a wide range of measures collected
815 across sweeps (Supplementary Table 25), with one variable excluded from any pair
816 with a correlation coefficient greater than 0.70 to address multicollinearity. The first
817 principal component (PC1) explained more than 40% of the variance for each
818 corresponding factor. In contrast, subsequent components contributed substantially
819 less, supporting the use of the respective PC1 as the summary measure for
820 cognitive ability, SES, and area deprivation (Supplementary Table 25).

821 Intellectual disability (ID) was defined as scoring two standard deviations below the
822 mean on the PC1 of the cognitive aptitude factor, consistent with prior studies. No
823 autistic children in the MCS or LSAC cohorts who had measures of cognitive
824 aptitude met the criteria for ID, likely due to participation bias. All PCA analyses were
825 conducted in R using the *prcomp()* function⁵⁸.

826

827 **Statistical analyses**

828 *Growth Mixture Models and Latent Growth Curve Models*

829 We used two methods to model the longitudinal trajectories of SDQ total and
830 subscale scores. First, we conducted Growth Mixture Models to identify whether
831 there were latent groups of autistic individuals based on their trajectories of SDQ
total and subscale scores. Growth Mixture Models assume that the sample consists
832 of multiple mixed effects models, each capturing a subgroup trajectory with shared
833 intercept and slope⁵⁹. We fitted models with one to four groups for each subscale
834
and SDQ total scores in each cohort, using the *lcmm* (v2.1.0) package in R<sup>60</sup>. The optimal number of latent trajectories were then determined by comparing fit indices, including Bayesian Information Criterion (BIC) values, classification quality measure (entropy), and substantive interpretation. Models with lower BIC values and higher entropy were favoured<sup>61</sup>. Models identifying subgroups with less than 5% of the sample size were not considered due to poor statistical reliability and limited practical significance<sup>62</sup>. We compared the distribution of group memberships across diagnostic ages and across sexes using ☐<sup>2</sup> tests.

Second, we used linear Latent Growth Curve Models to identify the latent trajectories of SDQ total and subscale scores in the three groups (childhood diagnosed, adolescent diagnosed, and the general population) for all cohorts. Each linear model included a latent intercept to represent the initial level of the outcome variable, and a linear latent slope to represent the mean rate of change over time. Childhood diagnosed (diagnosed before ages 9 - 11, depending on the cohort), and adolescent diagnosed (diagnosed after the ages of 9 - 11, depending on the cohort) were a priori defined (see Extended Data Figure 3). We chose this 9 - 11 age window as our cutoff since it aligns with the onset of puberty, the transition from primary to secondary school, and aligns with epidemiological evidence showing increased autism incidence among females during this window<sup>34</sup>. An earlier cutoff was not feasible as only MCS (ages 5, 7) and GUI (age 7) recorded autism diagnoses before this window. A later cutoff was not possible due to no autism diagnoses in MCS after age 14. To further examine the relationship between age at diagnosis and socioemotional and behavioural outcomes, we conducted additional Latent Growth Curve Models for autistic children using stepwise groupings by age at diagnosis in MCS and LSAC-B (see Supplementary Note 5 and Supplementary Figure 10). All individuals who lacked an autism diagnosis (and additionally, an ADHD diagnosis in MCS) were included in the general population group.

Given the well-known sex differences in age at autism diagnosis<sup>34</sup>, we also applied the same models stratified by sex, i.e., estimating latent intercept and slope for each sex, within the autistic samples. All Latent Growth Curve Models were fitted under the structural equation modelling framework using the *lavaan* (v 0.6-19) package in R<sup>63</sup>.

Association with sex and mental health phenotypes

To examine the association between GMM-derived SDQ latent trajectories and mental health phenotypes in MCS, LSAC-B, and LSAC-K, adjusting for sex), we applied multiple regression in autistic individuals.

Variance explained in age at autism diagnosis and mediation analysis in birth cohorts

Multiple regression analyses were conducted in MCS, LSAC-B and LSAC-K to investigate the association between an age at autism diagnosis (the outcome variable), SDQ total difficulties and subscale latent trajectories memberships identified in optimal Growth Mixture Models, while also accounting for other sociodemographic covariates. We did not detect any multicollinearity among the variables using variance inflation factors.
884 The relative importance of each predictor was assessed using dominance analysis⁶⁴.
885 We employed the *misty*⁶⁵ (v 0.6.8) package in R for this analysis, using a correlation
886 matrix extracted from the fitted model via the *lavInspect* function from the *lavaan* (v
887 0.6-19) package⁶³. This approach leverages the correlation matrix to consider not
888 only individual predictors but also the correlations among them, providing a more
889 comprehensive assessment of their relative importance⁶⁶.

890
891 To examine potential causal pathways, mediation analyses were conducted, allowing
892 sociodemographic factors to indirectly influence the age at diagnosis through their
893 effects on SDQ latent trajectory memberships identified in the optimal Growth
894 Mixture Model. Using structural equation modelling in the *lavaan* (v 0.6-19) package
895 ⁶³, both direct and indirect effects were assessed, with their significance calculated
896 using bootstrapping analysis. Further details are provided in **Supplementary Note 4**.
897

897
898 To investigate the specificity of our findings to autism, we conducted Growth Mixture
899 Models, Latent Growth Curve Models, regression, and mediation analyses in
900 individuals with ADHD but without a co-occurring autism diagnosis in the MCS cohort
901 (N = 89, **Supplementary Table 6**, results presented in **Supplementary Note 5**).
902 ADHD diagnoses were available in the same sweeps as autism diagnoses, reported
903 at ages 5, 7, 11, and 14. Carers were asked the following question: 'Has a doctor or
904 other health professional ever told you that <child's name> had Attention Deficit
905 Hyperactivity Disorder (ADHD)?'.
906

906
907 Imputation

908 To assess the impact of missingness, we applied *softImpute* (v.1.4-1), to impute
909 missing data for all children with an autism or ADHD diagnosis reported by any carer
910 in any sweep in the MCS cohort (Autism: N = 623, **Supplementary Table 5**; ADHD:
911 N = 325, **Supplementary Table 6**). *SoftImpute* was chosen for its computational
912 efficiency in handling large-scale matrices through low-rank approximation,
913 effectively preserving underlying structure of input data. Further information is
914 provided in **Supplementary Note 2**.
915

915
916 SPARK cohort: Genotyping, quality control and imputation

917 We used data from the SPARK cohort³⁹ iWES2 v1 dataset (released in Feb 2022)
918 which included data from 70,487 autistic individuals and their families as the SPARK
919 Discovery cohort. Data from SPARK iWES v3 (released August 2024) which
920 included an additional 71,267 autistic individuals and their families was included in
921 the SPARK Replication cohort. All participants in the Discovery cohort were
922 genotyped using the Illumina Global Screening Array (GSA_24v2-0_A2) and in the
923 Replication cohort using the Twist Bioscience genome-wide SNP capture panel for
924 genotyping-by-sequencing. To avoid false positives due to fine-scale population
925 stratification, we restricted the analyses to individuals of genetically-inferred
926 European ancestries (Discovery: N = 51,869 and Replication: N= 50,211, autistic
927 and non-autistic participants), which was provided by the SPARK consortium. From
928 this, we excluded individuals with genotyping rate < 98%, individuals with sex
929 mismatches, and those with excess heterozygosity (3 standard deviations from the
930 mean heterozygosity). Where trio data was available, trios with greater than 5%
931 Mendelian errors were excluded, resulting in 47,170 (Discovery) and 48,750
932 (Replication) autistic and non-autistic individuals. We included genetic variants with
933 minor allele frequency [MAF] > 1%, genotyping rate > 95%, and that were in Hardy
934 Weinberg Equilibrium (HWE P > 1x10⁻⁶), resulting in 518,189 (Discovery) and
935 1,225,308 (Replication) SNPs.

936
937 We used this quality controlled genotype data for imputation, calculating genetic
938 principal components, and inferring relatedness among individuals. We inferred
939 genetic relatedness using KING⁶⁷ (v.2.3.2). For genetic principal component
940 analysis, we pruned SNPs for linkage disequilibrium (LD) (maximum r² = 0.1) and
941 removed the human leukocyte antigen (HLA) region. Using PC-AiR⁶⁸ in GENESIS
942 (v2.22.2), we first calculated principal components (PCs) in genetically unrelated
943 individuals and then projected the PCs onto related individuals. We imputed
944 genotypes using the TOPMED imputation panel⁶⁹ on the Michigan imputation server
945 (v1.7.3)⁷⁰ using Minimac4⁷⁰ and after phasing using Eagle v2.5⁷¹. Post imputation,
946 variants were converted from GRCh38/hg38 to GRCh37/hg19 using liftOver. We
947 restricted downstream analyses only to variants with MAF > 0.1% and with an
948 imputation R² > 0.6.

949

950

951 SPARK cohort: Association analyses

952 *PGS association analyses*

953 Polygenic scores (PGS) were calculated using PRScs⁷² (v. 1.1.0) which uses a
954 Bayesian shrinkage prior. PGS were calculated for autism diagnosed before age 11
955 (iPSYCHbefore11), and autism diagnosed after age 10 (iPSYCHafter10), generated using
956 the iPSYCH2015⁷³ cohort, details of which are provided below. For simplicity we
957 refer to this cohort as iPSYCH throughout. PGS were calculated and analysed
958 separately for the Discovery and Replication cohorts and meta-analysed using
959 inverse-variance weighted meta-analysis⁷⁴.

960

961 We ran separate linear regression analyses between each of the two PGS and age
962 at autism diagnosis (converted to years in all analyses) in the quality controlled
963 dataset. We excluded individuals older than 22 to focus on those who had an autism
964 diagnosis using either the DSM-IV⁷⁵ or DSM-5, retaining a maximum of 18,809
965 (Discovery cohort) and 9,383 (Replication cohort) autistic individuals for PGS
966 analyses. This criteria also allowed us to focus on individuals who received their
967 diagnosis in childhood or adolescence, as older adults may have missed an earlier
968 diagnosis of autism due to secular changes in societal attitudes towards autism. The
969 baseline model included ID (16.34% had caregiver reported ID), sex, and the first 10
970 genetic principal components as covariates. We ran eight different sensitivity
971 analyses by including various covariates in addition to the covariates included in the
972 baseline model. First we ran three models to account for developmental and clinical
973 covariates: age at walking and age at first words (Model 2), age at walking and first
974 words, autism severity (SCQ and RBS-R total scores), caregiver reported IQ scores,
975 and language or other regression (Model 3), stratified analyses restricted to
976 individuals without ID who can speak in longer sentences (Model 4). Next we ran two
977 models accounting for sociodemographic factors: parental SES (Model 5) and,
978 additionally, area deprivation (Model 6). We controlled for any attentional and
979 behavioural diagnosis (Model 7), for DSM edition (DSM 4 vs DSM 5, Model 8), and
980 trio status (Model 9). Finally, we also ran sensitivity analyses after stratifying by sex.
981

982

982 In the SPARK cohort, we obtained data for age at achieving nine developmental
983 milestones (in months) for autistic individuals. For all milestones, we excluded
984 individuals who were greater than five median absolute deviations from the median.
985 We ran multiple linear regression with PGS for iPSYCH<sub>before11</sub> and iPSYCH<sub>after10</sub>
986 GWASs with sex and the first 10 genetic principal components as covariates. Yet
987 again, we ran the analyses for both the Discovery and Replication cohorts and meta-
988 analysed it using inverse-variance weighted meta-analysis.
989

990 *Rare high-impact de novo variants and inherited variants*

991 We identified rare (MAF < 0.1%) *de novo* and inherited variants in complete trios
992 from SPARK as previously described⁴⁰. We identified high impact protein truncating
993 variants by restricting to variants in loss-of-function observed/expected upper bound
994 fraction (LOEUF)⁷⁶ highly constrained decile (LOEUF < 0.37) that were annotated as
995 either frameshift, stop gained, or start lost; and had a loss-of-function transcript effect
996 estimator (LOFTEE) "high confidence annotation". To identify high-impact *de novo*
997 missense variants, we restricted to variants in LOEUF highly constrained genes
998 (LOEUF < 0.37), and had an MPC (missense badness, PolyPhen-2, and constraint)
999 score⁷⁷ > 2.
1000

1001

1002 We ran regression analyses for (1) high-impact de novo and inherited protein
1003 truncating variants, (2) missense variants, and (3) by combining both protein
1004 truncating and missense variants. We included sex and the first 10 genetic principal
1005 components as covariates.
1006

1007

1008

## Genome-wide association studies

1009 *GWAS of age at autism diagnosis*

1010 We generated a GWAS of age at autism diagnosis (in years) in the quality controlled
1011 dataset from SPARK, restricting it to autistic individuals who were under 22 years of
1012 age (Discovery: N = 18,809 and Replication: N = 9,356), and SNPs with a MAF >
1013 1%. GWAS was generated using FastGWA⁷⁸ with sex, ID, and the first 10 genetic
1014 principal components as covariates. We meta-analysed the GWAS from the SPARK
1015 Discovery and Replication cohorts using inverse-variance weighted meta-analysis in
1016 Plink⁷⁹,⁸⁰ (2.0). In iPSYCH, we generated an additional GWAS of age at autism
1017 diagnosis (in years) in a quality controlled dataset of unrelated individuals with sex
1018 and ID included as covariates using FastGWA⁷⁸, restricting to SNPs with an MAF >
1019 1%. To keep it consistent with SPARK, we excluded individuals who were diagnosed
1020 after age 22, leaving a total sample of 18,965 individuals. Briefly, pre-imputation
1021 quality control of the iPSYCH data was performed using the Ricopili pipeline⁸¹,
1022 prephased using Eagle v.2.3.5, and imputed using Minimac3⁸², using the
1023 downloadable version of the Haplotype Reference Consortium (HRC)⁸³ (accession
1024 no. EGAD00001002729). Further details of quality control and imputation are
1025 provided in Als et al., 2023⁸⁴.

1026

1027 *GWAS of autism stratified by age at diagnosis*

1028 We generated three age at autism diagnosis stratified GWAS in SPARK using
1029 (unscreened) non-autistic parents and siblings as controls (Discovery: N<sub>control</sub> =
1030 24,965 and Replication: N<sub>control</sub> = 33,302). The three GWAS were: (1) SPARK,
1031 diagnosed before age 6 (SPARK<sub>before6</sub>; Discovery: N<sub>autistic</sub> = 14,578 and Replication:
1032 N<sub>autistic</sub> = 6,857); (2) SPARK, diagnosed before age 11 (SPARK<sub>before11</sub>, N<sub>autistic</sub> =
1033 18,719 and Replication: N<sub>autistic</sub> = 9,162); and (3) SPARK, diagnosed after age 10
1034 (SPARK<sub>after10</sub>, N<sub>autistic</sub> = 3,358 and Replication: N<sub>autistic</sub> = 2,885). For these analyses,
we did not restrict it to individuals under 22 to increase sample size. Of note, SPARK<sub>before11</sub> overlaps with the SPARK<sub>before6</sub> cohort. GWAS were generated using quality controlled SNPs with a MAF > 1% using FastGWA-GLMM<sup>85</sup>. We included age at recruitment into the study (to account for the use of parents as controls, who potentially lack an autism diagnosis due to secular changes in attitudes and diagnosis), sex and the first 10 genetic principal components as covariates. Fast-GWA GLMM can account for relatedness and fine-scale population stratification even in family-based samples like SPARK. Given the relatively low sample size of the Replication cohort we meta-analysis the Replication and Discovery cohort GWAS using inverse-variance weighted meta-analyses in Plink<sup>79,80</sup> (v2.0).

Although inclusion of unscreened related individuals as controls can decrease heritability and statistical power to identify loci<sup>86</sup>, we used the GWAS to primarily conduct genetic correlation and related analyses. To ensure the robustness of these models we: (1) confirmed that the attenuation ratio for all GWAS was not significantly greater than 1; (2) generated an additional GWAS of SPARK without stratifying by age at autism diagnosis using the same methods and confirmed a high genetic correlation (r<sub>g</sub> = 0.92, SE = 0.17) with a previous SPARK GWAS<sup>87</sup> which used a case-pseudocontrol approach; and (3) in the genomicSEM analyses, ran sensitivity analyses using a trio-based SPARK GWAS<sup>87</sup> in lieu of the age at diagnosis stratified GWAS from SPARK and confirmed our findings.

We generated three GWAS of autism stratified by age at autism diagnosis in the iPSYCH cohort<sup>73</sup>. The primary GWAS used in the analyses were GWAS of autism diagnosed before age 11 (iPSYCH<sub>before11</sub>: 9,500 autistic and 36,667 non-autistic individuals) and autism diagnosed after age 10 (iPSYCH<sub>after10</sub>: 9,231 autistic and 36,667 non-autistic individuals). We chose to subdivide the iPSYCH cohort at age 10 because we observed an increase in SDQ scores in birth cohorts at this age, and because age 10 is associated with an increase in diagnosis of females in epidemiological samples<sup>34</sup>. Additionally, we conducted a GWAS of autism diagnosed before age nine (iPSYCH<sub>before9</sub>: 5,451 autistic and 36,667 non-autistic individuals).

All individuals included in these GWAS from iPSYCH were born between May 1980 and December 2008 to mothers who were living in Denmark. GWAS was conducted on unrelated individuals of European ancestry, with the first 10 genetic principal components included as covariates using logistic regression as provided in PLINK.

## Heritability, genetic correlation, and genomicSEM

Heritability analyses for age at autism diagnosis were conducted using a single-component genome-wide complex trait analysis with genomic-relatedness-based restricted maximum likelihood approach (GCTA-GREML v1.94.1)<sup>88,89</sup> in unrelated autistic individuals using the quality controlled genetic data in SPARK. We estimated SNP-based heritability first after including sex and the first ten genetic principal components as covariates, and then additionally with ID as a covariate (baseline model). We ran several sensitivity analyses after including additional covariates: (1) developmental milestones (age at first words and age at walking); (2) developmental milestones and developmental regression (language regression and other regression); (3) developmental milestones, developmental regression, and IQ scores; (4) SCQ and RBS-R scores; (5) SCQ and RBS-R scores, developmental
1083 milestones, and developmental regression; (6) developmental milestones and SES;
1084 and (7) developmental milestones, SES, and deprivation.

1085 We conducted genetic correlation analyses using LDSC, using linkage disequilibrium
1086 scores from the north-west European populations.

1088 We conducted genetic correlation analyses among different autism GWAS using
1089 LDSC (v.1.0.1). This included a European-only case-pseudocontrol GWAS in
1090 SPARK⁸⁷ (4,535 case-pseudocontrol pairs); GWAS from FinnGen (Data Release -
1091 r10)⁹⁰ (646 cases and 301,879 controls), the PGC-2017 autism GWAS⁹¹ (7,387
1092 cases and 8,567 controls), GWAS from iPSYCH, and age at diagnosis stratified
1093 GWAS from SPARK. The iPSYCH GWAS included an unstratified (19,870 autistic
1094 individuals [15,025 males and 4,845 females] and 39,078 controls) and sex-stratified
1095 GWAS⁹², and three age at diagnosis stratified GWAS as mentioned earlier.

1097 For genomicSEM⁴² (v.0.0.5) analyses, we restricted to six GWAS with minimal
1098 sample overlap, without high genetic correlation (r<sub>g</sub> > 0.95), and with wide variation in
1099 age at diagnosis to conduct genomicSEM analyses using autosomes. Using the
1100 patterns of genetic correlations observed we tested an age at diagnosis related
1101 correlated two-factor model. We additionally tested: (1) a single-factor model; (2) a
1102 correlated two-factor "geography" model where three US-based autism GWAS
1103 loaded onto one factor, and three Europe-based autism GWAS loaded onto a
1104 second factor; (3) a bifactor model based on age at diagnosis; (4) a bifactor model
1105 based on the geography of the cohorts; and (5) a hierarchical factor model based on
1106 age at diagnosis. The two-factor model was chosen as it had lower RMSEA and
1107 higher CFI and was more parsimonious than the bifactor model. We ran sensitivity
1108 analyses using different GWAS of autism as input and confirmed that the two-
1109 correlated-factor model was the best fitting model of the models tested.
1110

1111

1112

1113 Analyses in ALSPAC and MCS

1114 Genetic quality control for ALSPAC

1115 We obtained quality controlled and imputed genotype data from ALSPAC⁹³⁻⁹⁵.
1116 Further details about the cohort are provided in the **Supplementary Note 1**. Briefly,
1117 ALSPAC children were genotyped using the Illumina HumanHap550 quad chip
1118 genotyping platforms by 23andme. Individuals were excluded due to sex
1119 mismatches, excess heterozygosity, missingness > 3%, and insufficient sample
1120 replication (Identical-By-Descent [IBD] < 0.8). After multidimensional scaling, and
1121 comparison with Hapmap II (release 22), only individuals of genetically inferred
1122 European ancestries were retained. SNPs with low frequency (MAF < 1%), poor
1123 genotyping (call rate < 95%) and deviations from Hardy-Weinberg equilibrium (P <
1124 5x10⁻⁷) were removed. 9,115 subjects and 500,527 SNPs passed quality control.
1125 Genotypes were phased using ShapelT, and imputation was done using the
1126 Haplotype Reference Consortium panel using the Michigan imputation server. After
1127 imputation, we further removed low frequency SNPs (MAF < 1%). Further details of
1128 the quality control and imputation of ALSPAC are provided here:
1129 https://proposals.epi.bristol.ac.uk/alspac_omics_data_catalogue.html#org89bb79b.

1130 Genome-wide genotype data was generated by Sample Logistics and Genotyping
1131 Facilities at Wellcome Sanger Institute and LabCorp (Laboratory Corporation of
1132 America) using support from 23andMe.
1133

1134 Genetic quality control for MCS

1135 We also obtained quality controlled and imputed data from MCS. Briefly, MCS
1136 samples were genotyped using the Illumina Global Screening Array⁹⁶. Individuals
1137 were excluded due to sex mismatches, excess heterozygosity, and missingness >
1138 2%. We identified European samples using the GenoPred pipeline⁹⁷
1139 (https://github.com/opain/GenoPred). SNPs with low frequency (MAF < 1%), poor
genotyping (call rate < 97%) and deviations from Hardy-Weinberg equilibrium (P <
1140 1x10⁻⁶) were removed. Imputation was conducted using Minimac4⁷⁰ using the
1141 TOPMED reference panel⁶⁹ in the Michigan imputation server⁷⁰. Post imputation,
1142 SNPs with an imputation R² INFO score < 0.8, with > 3% missing, and with a MAF <
1143 1% were excluded. Further details are available here: https://cls-
genetics.github.io/docs/MCS.html

1146

1147 PGS association with SDQ

1148 PGS for both ALSPAC and MCS were calculated in individuals of genetically inferred
1149 European ancestries. Genetic principal components were calculated for both cohorts
1150 using PC-AiR as described earlier. We calculated PGS for iPSYCH<sub>before11</sub> and
1151 iPSYCH<sub>after10</sub> and used these in all analyses in the MCS to keep it consistent with
1152 analyses in SPARK.

1153

1154 We obtained scores on the SDQ total and subscales for six ages in the MCS and five
1155 ages in ALSPAC. We ran cross-sectional analysis at each age using multiple linear
1156 regression with PGS for iPSYCH<sub>before11</sub> and iPSYCH<sub>after10</sub>, with sex, age, and the first
1157 10 genetic principal components as covariates. Additionally, we ran multiple linear
1158 mixed effects regression using *lme4* (v.1.1.27.1) package in R<sup>98</sup>, fitting a PGS by age
1159 interaction term to investigate if the effects of PGS on SDQ change over time.

1160

1161 To investigate if the differences in association between MCS and ALSPAC were due
1162 to differences in ascertainment between the two cohorts, we matched ALSPAC to
1163 MCS using entropy balancing⁹⁹ and re-ran the PGS association analyses. Entropy
1164 balancing is a reweighting technique that ensures the covariate distributions are
1165 identical between groups. This method uses optimisation algorithms to assign
1166 weights to individuals such that the weighted average of the covariates in ALSPAC
1167 (the larger genotyped cohort) matches that of MCS (the smaller genotyped cohort),
1168 minimising confounding biases and increasing comparability. We used the child's
1169 biological sex, maternal age at delivery, and maternal highest educational
1170 qualification at first data collection in each cohort as matching factors. Entropy
1171 balancing was conducted using the *ebal* (v 0.1-8) package in R¹⁰⁰.

1172

1173 PGS association with social communication skills and autism diagnosis

1174 In ALSPAC, we obtained understanding of simple phrases (e.g., "do you want that",
1175 or "come here") and gesture scores from the Macarthur-Bates Communicative
1176 Development Inventories¹⁰¹ at 15 months of age (Supplementary Note 9). We
1177 conducted multiple linear regression using PGS for iPSYCH<sub>before11</sub> and iPSYCH<sub>after10</sub>,
1178 with sex, age, and the first 10 genetic principal components as covariates.

1179

1180 Autism diagnosis in the MCS was obtained using parent/caregiver reports of
1181 autism/asperger syndrome diagnosis by a doctor at ages 5, 7, 11, and 14. We
1182 identified individuals with an autism diagnosis at age 7 or earlier, age 11 or earlier, or
1183 between ages 11 and 14. We conducted Firth's bias-reduced multiple logistic
1184 regression (logistf (v 1.26.0) package in R) using PGS for iPSYCH<sub>before11</sub> and
1185 iPSYCH<sub>after10</sub>, with sex, age and the first 10 genetic principal components covariates.
1186

1187 Ethics

1188 Ethical approval for individual cohorts were obtained independent of the current
1189 study. Ethical approval for ALSPAC was obtained from the ALSPAC Ethics and Law
1190 Committee and the Local Research Ethics Committees. Ethical approval for each
1191 sweep of MCS was obtained from NHS Research Ethics Committees (MREC).
1192 Ethical approval for LSAC was obtained from the Australian Institute of Family
1193 Studies Human Research Ethics Committee. Ethical approval for GUI was obtained
1194 from a dedicated Research Ethics Committee set up by the Department of Children,
1195 Equality, Disability, Integration and Youth. Ethical approval for SPARK was obtained
1196 from the Western Institutional Review Board- Copernicus Group IRB Protocol
1197 #20151664). The Danish Scientific Ethics Committee, the Danish Health Data
1198 Authority, the Danish data protection agency and the Danish Neonatal Screening
1199 Biobank Steering Committee approved the iPSYCH study. Ethical approval for the
1200 analyses of de-identified data used in this study was obtained from the Cambridge
1201 Human Biology Research Ethics Committee (HBREC.2020.07).

1202
1203
1204 Code availability

1205 • Lavaan (LGCM) (v.0.6-19) : https://lavaan.ugent.be/tutorial/growth.html

1206 • lcmm(GMM), v 2.2.1: https://github.com/CecileProust-Lima/lcmm

1207 • Softimpute (v.1.4-1): https://cran.r-project.org/web/packages/softImpute/softImpute.pdf

1209 • Misty (v 0.6.8) : https://cran.r-project.org/web/packages/misty/index.html

1210 • PRScs (v.1.1.0): https://github.com/getian107/PRScs

1211 • fastGWA and GCTA (v.1.94.1):
1212 https://yanglab.westlake.edu.cn/software/gcta/#Overview

1213 • GenomicSEM (v.0.0.5): https://github.com/GenomicSEM/GenomicSEM

1214 • LDSC (v1.0.1): https://github.com/bulik/ldsc

1215 • KING (v.2.3.2): https://www.kingrelatedness.com/manual.shtml

1216 • Plink 2.0: https://www.cog-genomics.org/plink/2.0/

1217 • GENESIS (v2.22.2): https://github.com/UW-GAC/GENESIS

1218 • Lme4 (v.1.1.27.1): https://github.com/lme4/lme4/

1219 • Logistf (v.1.24): https://cran.r-project.org/web/packages/logistf/index.html

1220 • Ebal (v 0.1-8): https://cran.r-project.org/web/packages/ebal/ebal.pdf

1221 • Relaimpo (v2.2-7): https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf

1223

1224 • SPARK quality control, imputation and GWAS:
1225 https://github.com/vwarrier/SPARK_iWES2_imputation/

1226 • Bespoke genetic analyses code:
1227 https://github.com/vwarrier/autism_agediagnosis/

1228

1229
1230

1231 **Data availability:**

1232

* SPARK autism GWAS:

1233

https://bitbucket.org/steinlabunc/spark_asd_sumstats/src

1234

* Finngen autism GWAS: https://www.finngen.fi/en/access_results

1235

* iPSYCH autism GWAS (unstratified, sex-stratified and age at diagnosis stratified, age at diagnosis) can be obtained from Anders Borglum and Jakob Grove.

1236

1237

1238

* Psychiatric GWAS summary stats: https://pgc.unc.edu/for-

1239

researchers/download-results/

1240

* GWAS educational attainment: https://thessgac.com/papers/

1241

* GWAS cognitive aptitude: https://cncr.nl/research/summary_statistics/

1242

* For ALSPAC, the study website contains details of all the data that is

1243

available through a fully searchable data dictionary and variable search tool":

1244

http://www.bristol.ac.uk/alspac/researchers/our-data/

1245

* For MCS, data can be obtain after application through the UK Data Service:

1246

https://beta.ukdataservice.ac.uk/datacatalogue/series/series?id=2000031

1247

* Summary statistics for the SPARK-based age at diagnosis GWAS, and the

1248

age at diagnosis stratified GWAS generated from the genomicSEM models

1249

will be made available upon publication.

1250

1251 **Acknowledgements**

1252

This research was supported by funding from the Simons Foundation for Autism

1253

Research Initiative, the Wellcome Trust (214322\Z\18\Z and 226392/Z/22/Z),

1254

Horizon-Europe R2D2-MH (grant agreement number 101057385), and UKRI

1255

(10063472). For the purpose of open access, we have applied a CC BY public

1256

copyright licence to any author-accepted manuscript version arising from this

1257

submission. S.B.-C. also received funding from the Autism Centre of Excellence at

1258

Cambridge, the Templeton World Charitable Fund, the MRC and the National

1259

Institute for Health Research Cambridge Biomedical Research Centre. The research

1260

was supported by the National Institute for Health Research Applied Research

1261

Collaboration East of England. Any views expressed are those of the author(s) and

1262

not necessarily those of the funder. Some of the results leading to this publication

1263

have received funding from the Innovative Medicines Initiative 2 Joint Undertaking

1264

under grant agreement no. 777394 for the project AIMS-2-TRIALS. This joint

1265

undertaking receives support from the European Union's Horizon 2020 research and

1266

innovation program and the EFPIA and Autism Speaks, Autistica and the SFARI.

1267

The iPSYCH team was supported by grants from the Lundbeck Foundation (R102-

1268

A9118, R155-2014-1724 and R248-2017-2003), the NIMH (1R01MH124851-01 to

1269

A.D.B.), and EU's Horizon Europe program (R2D2-MH; grant agreement no.

1270

101057385 to A.D.B.). The Danish National Biobank resource was supported by the

1271

Novo Nordisk Foundation. High-performance computer capacity for handling and

1272

statistical analysis of iPSYCH data on the GenomeDK HPC facility was provided by

1273

the Center for Genomics and Personalized Medicine and the Centre for Integrative

1274

Sequencing, iSEQ, Aarhus University, Denmark (grant to A.D.B.). The UK Medical

1275

Research Council and Wellcome (Grant ref: 217065/Z/19/Z) and the University of

1276

Bristol provide core support for ALSPAC. This publication is the work of the authors

1277

and the authors will serve as guarantors for the contents of this paper. A

1278

comprehensive list of grants funding is available on the ALSPAC website
1279 (http://www.bristol.ac.uk/alspac/external/documents/grant-acknowledgements.pdf).

1280 R2D2-MH has been funded by Horizon Europe [grant agreement no. 101057385], by
1281 UK Research and Innovation (UKRI) under the UK government's Horizon Europe
1282 funding guarantee [grant no.10039383] and by the Swiss State Secretariat for
1283 Education, Research and Innovation (SERI) under contract number 22.00277. A.H.
1284 and L.E.H. were supported by the Norwegian Research Council (#336085) and the
1285 Norwegian Health Authority (#2020022; #2022029; #2022083). EV and BSTP are
1286 funded by the Max Planck Society.

1287

1288 We are grateful to the Centre for Longitudinal Studies (CLS), UCL Social Research
1289 Institute, for the use of these data and to the UK Data Service for making them
1290 available. However, neither CLS nor the UK Data Service bear any responsibility for
1291 the analysis or interpretation of these data. This paper uses unit record data from
1292 Growing Up in Australia, the Longitudinal Study of Australian Children. The study is
1293 conducted in partnership between the Department of Social Services (DSS), the
1294 Australian Institute of Family Studies (AIFS) and the Australian Bureau of Statistics
1295 (ABS). The findings and views reported in this paper are those of the author and
1296 should not be attributed to DSS, AIFS or the ABS. Growing Up in Ireland (GUI) has
1297 been funded by the Government of Ireland through the Department of Children,
1298 Equality, Disability, Integration and Youth (DCEDIY) and the Central Statistics Office
1299 (CSO). Results in this report are based on analysis of data from Research Microdata
1300 Files provided by the Central Statistics Office (CSO). Neither the CSO nor the
1301 DCEDIY take any responsibility for the views expressed or the outputs generated
1302 from these analyses. We are extremely grateful to all the families who took part in
1303 this study, the midwives for their help in recruiting them, and the whole ALSPAC
team, which includes interviewers, computer and laboratory technicians, clerical
1304 workers, research scientists, volunteers, managers, receptionists and nurses. This
1305 study includes data from the Norwegian Mother, Father and Child Cohort Study
1306 (MoBa), conducted by the Norwegian Institute of Public Health. We are grateful to all
1307 the participating families.
1308

1309 We thank Alex Kwong, Tamsin Ford, Will Mandy, and Andrew Grotzinger for helpful
discussions.

1311 **Ethics declarations**

1312 ADB received speakers' fee from Lundbeck. The authors declare no competing
interests.

1314 **Author contributions**

1315 XZ and VW conducted most of the analyses, with the remainder being conducted by JG, YG,
1316 CKB, and LKN. MK, EV, AG, LH, AH, AR, BSt.P, and ADB provided summary statistics for
1317 various analyses. SASN, DSM, and EMW carried out data preparation and quality control,
1318 with assistance from KES, VKC, PD, SL, TM, MK, SA and DB. VW supervised the analyses
1319 and directed the study with inputs from HCM and JG. VW and XZ wrote the initial draft with
1320 input from HCM. AG, SASN, AH, BSt.B, AR, DSM, EW, DHG, NRW, EBR, TB, and SBC
1321 provided intellectual input. All authors read and commented on the final manuscript.

1322
1323 APEX Consortium

1324 Deep Adhya, Carrie Allison, Bonnie Ayeung, Rosie Bamford, Simon Baron-Cohen,

1325 Richard Bethlehem, Tal Biron-Shental, Graham Burton, Wendy Cowell, Jonathan

1326 Davies, Joanna Davis, Dori Floris, Alice Franklin, Lidia Gabis, Daniel Geschwind,

1327 Ramin Ali Marandi Ghoddousi, David M. Greenberg, Yuanjun Gu, Alexandra

1328 Havdahl, Alexander Heazell, Rosemary Holt, Matthew Hurles, Yumnah Khan, Meng-

1329 Chuan Lai, Madeline Lancaster, Michael Lombardo, Hilary Martin, Jose Gonzalez

1330 Martinez, Jonathan Mill, Mahmoud Koko Musa, Kathy Niakan, Adam Pavlinek, Lucia

1331 Dutan Polit, Marcin Radecki, David Rowitch, Jenifer Sakai, Laura Sichlinger, Deepak

1332 Srivastava, Alexandros Tsompanidis, Florina Uzefovsky, Varun Warrier, Elizabeth

1333 Weir, Xinhe Zhang.

1334

1335 iPSYCH Autism working group

1336 Anders Borglum, Jonas Bybjerg-Grauholm, Jakob Grove, David M. Hougaard, Ole

1337 Mors, Preben Bo Mortensen, Merete Nordentoft and Thomas Werge.

1338

1339 PGC-PTSD consortium

1340 Caroline M. Nievergelt, Adam X. Maihofer, Elizabeth G. Atkinson, Chia-Yen Chen, Karmel

1341 W. Choi, Jonathan R. I. Coleman, Nikolaos P. Daskalakis, Laramie E. Duncan, Renato

1342 Polimanti, Cindy Aaronson, Ananda B. Amstadter, Soren B. Andersen, Ole A. Andreassen,

1343 Paul A. Arbisi, Allison E. Ashley-Koch, S. Bryn Austin, Esmina Avdibegović, Dragan Babić,

1344 Silviu-Alin Bacanu, Dewleen G. Baker, Anthony Batzler, Jean C. Beckham, Sintia Belangero,

1345 Corina Benjet, Carisa Bergner, Linda M. Bierer, Joanna M. Biernacka, Laura J. Bierut,

1346 Jonathan I. Bisson, Marco P. Boks, Elizabeth A. Bolger, Amber Brandolino, Gerome Breen,

1347 Rodrigo Affonseca Bressan, Richard A. Bryant, Angela C. Bustamante, Jonas Bybjerg-

1348 Grauholm, Marie Bækvad-Hansen, Anders D. Børglum, Sigrid Børte, Leah Cahn, Joseph R.

1349 Calabrese, Jose Miguel Caldas-de-Almeida, Chris Chatzinakos, Sheraz Cheema, Sean A. P.

1350 Clouston, Lucía Colodro-Conde, Brandon J. Coombes, Carlos S. Cruz-Fuentes, Anders M.

1351 Dale, Shareefa Dalvie, Lea K. Davis, Jürgen Deckert, Douglas L. Delahanty, Michelle F.

1352 Dennis, Frank Desarnaud, Christopher P. DiPietro, Seth G. Disner, Anna R. Docherty,

1353 Katharina Domschke, Grete Dyb, Alma Džubur Kulenović, Howard J. Edenberg, Alexandra

1354 Evans, Chiara Fabbri, Negar Fani, Lindsay A. Farrer, Adriana Feder, Norah C. Feeny,

1355 Janine D. Flory, David Forbes, Carol E. Franz, Sandro Galea, Melanie E. Garrett, Bizu

1356 Gelaye, Joel Gelernter, Elbert Geuze, Charles F. Gillespie, Slavina B. Goleva, Scott D.

1357 Gordon, Aferdita Goçi, Lana Ruvolo Grasser, Camila Guindalini, Magali Haas, Saskia

1358 Hagenaars, Michael A. Hauser, Andrew C. Heath, Sian M. J. Hemmings, Victor Hesselbrock,

1359 Ian B. Hickie, Kelleigh Hogan, David Michael Hougaard, Hailiang Huang, Laura M. Huckins,

1360 Kristian Hveem, Miro Jakovljević, Arash Javanbakht, Gregory D. Jenkins, Jessica Johnson,

1361 Ian Jones, Tanja Jovanovic, Karen-Inge Karstoft, Milissa L. Kaufman, James L. Kennedy,

1362 Ronald C. Kessler, Alaptagin Khan, Nathan A. Kimbrel, Anthony P. King, Nastassja Koen,

1363 Roman Kotov, Henry R. Kranzler, Kristi Krebs, William S. Kremen, Pei-Fen Kuan, Bruce R.

1364 Lawford, Lauren A. M. Lebois, Kelli Lehto, Daniel F. Levey, Catrin Lewis, Israel Liberzon,

1365 Sarah D. Linnstaedt, Mark W. Logue, Adriana Lori, Yi Lu, Benjamin J. Luft, Michelle K.

1366 Lupton, Jurjen J. Luykx, Iouri Makotkine, Jessica L. Maples-Keller, Shelby Marchese,
1367 Charles Marmar, Nicholas G. Martin, Gabriela A. Martínez-Levy, Kerrie McAloney,

1368 Alexander McFarlane, Katie A. McLaughlin, Samuel A. McLean, Sarah E. Medland, Divya

1369 Mehta, Jacquelyn Meyers, Vasiliki Michopoulos, Elizabeth A. Mikita, Lili Milani, William

1370 Milberg, Mark W. Miller, Rajendra A. Morey, Charles Phillip Morris, Ole Mors, Preben Bo

1371 Mortensen, Mary S. Mufford, Elliot C. Nelson, Merete Nordentoft, Sonya B. Norman, Nicole

1372 R. Nugent, Meaghan O'Donnell, Holly K. Orcutt, Pedro M. Pan, Matthew S. Panizzon, Gita

1373 A. Pathak, Edward S. Peters, Alan L. Peterson, Matthew Peverill, Robert H. Pietrzak,

1374 Melissa A. Polusny, Bernice Porjesz, Abigail Powers, Xue-Jun Qin, Andrew

1375 Ratanatharathorn, Victoria B. Risbrough, Andrea L. Roberts, Alex O. Rothbaum, Barbara O.

1376 Rothbaum, Peter Roy-Byrne, Kenneth J. Ruggiero, Ariane Rung, Heiko Runz, Bart P. F.

1377 Rutten, Stacey Saenz de Viteri, Giovanni Abrahão Salum, Laura Sampson, Sixto E.

1378 Sanchez, Marcos Santoro, Carina Seah, Soraya Seedat, Julia S. Seng, Andrey Shabalin,

1379 Christina M. Sheerin, Derrick Silove, Alicia K. Smith, Jordan W. Smoller, Scott R. Sponheim,

1380 Dan J. Stein, Synne Stensland, Jennifer S. Stevens, Jennifer A. Sumner, Martin H. Teicher,

1381 Wesley K. Thompson, Arun K. Tiwari, Edward Trapido, Monica Uddin, Robert J. Ursano,

1382 Unnur Valdimarsdóttir, Miranda Van Hooff, Eric Vermetten, Christiaan H. Vinkers, Joanne

1383 Voisey, Yunpeng Wang, Zhewu Wang, Monika Waszczuk, Heike Weber, Frank R. Wendt,

1384 Thomas Werge, Michelle A. Williams, Douglas E. Williamson, Bendik S. Winsvold, Sherry

1385 Winternitz, Christiane Wolf, Erika J. Wolf, Yan Xia, Ying Xiong, Rachel Yehuda, Keith A.

1386 Young, Ross McD Young, Clement C. Zai, Gwyneth C. Zai, Mark Zervas, Hongyu Zhao, Lori

1387 A. Zoellner, John-Anker Zwart, Terri deRoon-Cassini, Sanne J. H. van Rooij, Leigh L. van

1388 den Heuvel, AURORA Study, Estonian Biobank Research Team, FinnGen Investigators,

1389 HUNT All-In Psychiatry, Murray B. Stein, Kerry J. Ressler and Karestan C. Koenen

1390

1391

1392
1393 **Figure Legends**

1394 **Figure 1: Trajectory analyses in three of the four birth cohorts.**

<figure><img src="image_1.png" /></figure>

1395

1396

1397

1398

1399

1400

1401

1402

1403

A - C: Longitudinal growth mixture models of SDQ total scores among autistic individuals, demonstrating the presence of two groups in the MCS (A), LSAC-B (B) and LSAC-K (C) cohorts. Shaded areas indicate 95% confidence intervals of the line of best fit in D - F: Stacked bar charts providing the proportion of individuals who had been diagnosed as autistic at specific ages, categorised by membership in the latent trajectories identified from the growth mixture models in MCS (D), LSAC-B (E), and LSAC-K (F) cohorts. Darker colours indicate males and lighter colours indicate females. P-values (P, inset in panels D-F) are from $\chi^2$ tests (two-sided) comparing the distribution of age at autism diagnosis between the two latent trajectories (pooling the two sexes).
<figure><img src="image_2.png" /><figcaption>1404 Figure 2: Heritability of age at autism diagnosis</figcaption></figure>
1406 A. SNP-based heritability for age at autism diagnosis in the SPARK (calculated using single-component genome-wide complex trait analysis with genomic-relatedness-based restricted maximum likelihood approach [GCTA-GREML] for the SPARK Discovery cohort (orange dashed line, N = 16,786), SPARK Replication cohort (lilac dashed line, N = 8,558) and a meta-analysis of the two (light blue solid line, N = 25,344)) and iPSYCH (calculated using LDSC, green, N = 18,965). B. SNP-based heritability (GCTA-GREML) in the SPARK cohorts after accounting for various clinical and sociodemographic factors. '+' indicates the baseline model in addition to the specified covariates. The x-axis has been truncated at 0 and 0.25. For A and B, central points represent SNP-based heritability estimates and error bars indicate 95% confidence intervals. Sample sizes for 3B are provided in Supplementary Table 10.

1416

1417 **Figure 3: Median age at autism diagnosis and genetic correlations with age at autism diagnosis across different GWAS cohorts.**
1418

<figure><img src="image_3.png" /></figure>
1420 Left panel: Median age at diagnosis (years) with error bars representing median absolute deviation.
1421 Circle size indicates the number of autistic individuals (cases) in the GWAS, and exact sample sizes
1422 are provided in Box1. Beige circles represent GWAS unstratified by age at diagnosis. Red circles
1423 represent GWAS stratified by age at diagnosis. Lighter, more transparent circles indicate studies with
1424 no information about age at autism diagnosis, and the median ages have been inferred based on
1425 other available information (i.e., PGC and Grove). Right panel: Genetic correlations with age at autism
1426 diagnosis for both SPARK (blue, meta-analysis, N = 28,165) and iPSYCH (green, N = 18,965)
1427 datasets, with error bars representing 95% confidence intervals.

1428 **Figure 4: Two genetic latent factors in autism.**
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

1429

1430 A. Genetic correlation heatmaps of all GWAS of autism (left). Asterisk indicates significant genetic

1431 correlations after Benjamini-Yekutieli adjustment. The right panel provides median age at autism

1432 diagnosis for the same GWAS (indicated by the number on top of the circle). Error bars indicate

1433 median absolute deviation. Size of the circles indicate sample size of cases. For both panels, GWAS

1434 have been ordered based on hierarchical clustering of the genetic correlations. B. Structural Equation
1435 Model illustrating the two-correlated-genetic-factor models for autism, using six minimally overlapping autism GWAS datasets. F1 = Factor 1, F2 = Factor 2. One-headed arrows depict the regression relationship pointing from the independent variables to the dependent variables; the numbers on the arrows represent the regression coefficients of the factor loadings, with the standard errors provided in parentheses. Covariance between variables are represented as two-headed arrows linking the variables. The numbers on the two-headed arrows can be interpreted as genetic correlation estimates with the standard errors provided in parentheses. Residual variances for each GWAS dataset are represented using a two-headed arrow connecting the residual variable (u) to itself. Standard errors are provided in parentheses.

1444

1445 Figure 5: Genetic correlation between the two autism polygenic factors and a range of mental health, neurodevelopmental, and cognitive traits.

1446

<figure><img src="image_6.png" /></figure>

1447

1448 Central points indicate the estimate (genetic correlation), error bars indicate 95% confidence intervals,

1449 and points with an asterisk (*) indicate significant p-values (two-sided) with Benjamini-Yekutieli

1450 adjustment. Sample sizes are provided in Supplementary Table 18.
1451

1452 Extended Data Figures

1453 Extended Data Figure 1: Variance in age at diagnosis explained by various

1454 clinical and sociodemographic factors

<figure><img src="image_7.png" /></figure>

1455

1456 Variance explained (R² or η²) in age at autism diagnosis by clinical and sociodemographic factors,
1457 identified from the review of literature (1998-2023). Variables are grouped into sociodemographic
1458 (MAD, SES), socioemotional-behavioural (SDQ scores), sex, clinical (e.g., IQ, regression, language
1459 ability), and autism severity (e.g, SCQ, ADOS, ADI-R, RBS-R) categories. Circle size represents
1460 sample size, with larger circles indicating larger cohorts. Colored points denote variables analysed in
1461 the current study. Inset shows factors that explain greater than 10% of the variance in age at autism
diagnosis. Note: None of these studies account for additional family, service access, and contextual
1462 factors known to influence diagnostic timing. Abbreviations: MAD, Maternal Age at Delivery; IQ,
1463 Intelligence Quotient; SES, Socio-economic Status; ADOS, Autism Diagnostic Observation Schedule;
1464 ADI-R, Autism Diagnostic Interview-Revised; RBS-R, Repetitive Behavior Scale-Revised; SCQ, Social
1465 Communication Questionnaire; SDQ, Strengths and Difficulties Questionnaire; SDQ Total, SDQ Total
1466 Difficulties.
1467
<figure><img src="image_8.png" /><figcaption>1468 **Extended Data Figure 2: Two aetiological polygenic models of autism**</figcaption></figure>

1469

1470 In Model 1 (Unitary Model), we assume a single liability threshold polygenic model. In this model, autism emerges from a unitary polygenic aetiology. Autistic individuals diagnosed later have lower polygenic predisposition than individuals diagnosed earlier. In Model 2 (Developmental Model), we model two correlated age-dependent polygenic liabilities.

<figure><img src="image_9.png" /><figcaption>1474 **Extended Data Figure 3: Schematic of the study aims.**</figcaption></figure>

1475

1476 The study consists of four linked aims to understand whether the developmental trajectories and polygenic etiology of autism differs by age at diagnosis. In Aim 1, we modelled socioemotional and behavioural trajectories among autistic individuals in birth cohorts and investigated their association with age at autism diagnosis. In Aim 2, estimated the SNP-based heritability of age at autism diagnosis and whether it attenuates when accounting for various clinical and demographic factors. In Aim 3, we investigated whether the varying patterns of genetic correlations observed among different GWAS of autism can be explained by different polygenic factors associated with age at diagnosis. In Aim 4, we investigated the genetic relationship between the two autism polygenic factors and mental health and developmental phenotypes.
<figure><img src="image_10.png" /><figcaption>1485 Extended Data Figure 4: Schematic diagram of the birth cohorts included in the study</figcaption></figure>
1497 Extended Data Figure 5: Schematic diagram of age at autism diagnosis GWAS
1498 and age stratified autism GWAS

<figure><img src="image_11.png" /></figure>

1499 Schematic diagram illustrating the main GWAS conducted in the study using the SPARK and iPSYCH
1500 cohorts. We conducted two age at autism diagnosis GWAS. In addition, we conducted six case-
1501 control GWAS, where autistic individuals were stratified based on their age at autism diagnosis.
1502

1503 Extended Data Figure 6: Distribution of age at autism diagnosis in iPSYCH and SPARK
1504
1505

<figure><img src="image_12.png" /></figure>

1506 Frequency histograms of age at autism diagnosis in iPSYCH and SPARK. Median and median
1507 absolute deviation (MAD) for age at diagnosis, and sample sizes (N) have been provided.
1508
<figure><img src="image_13.png" /><figcaption>1509 Extended Data Figure 7: Within-cohort genetic correlation between age at diagnosis stratified autism GWAS and mental health and cognition related phenotypes</figcaption></figure>

1512 Genetic correlation between age at autism stratified GWAS in SPARK (meta-analysed from Discovery and Replication cohorts) and iPSYCH and other mental health and cognition related phenotypes.
1513 Points represent genetic correlation estimates and whiskers indicate 95% confidence intervals. Green represents the earlier diagnosed autism GWAS (iPSYCH before 9 and SPARK before 6), and purple represents later diagnosed autism GWAS (iPSYCH and SPARK after 10). Asterisk (*) indicates significantly different genetic correlation between the earlier and later diagnosed GWAS (P < 0.05, two-tailed Z test).
1514
1515
1516
1517
1518
1519
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