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. 2021 Nov 11;12:6534. doi: 10.1038/s41467-021-26755-1

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — Discordant associations with educational attainment, such as observed for ASD versus ADHD risk, may arise due to different mechanisms. Scenario I: Independent markers tag independent ASD and ADHD risk alleles, either (a) at the same gene locus in regions with low linkage disequilibrium (LD) or (b) at different loci. (c) Scenario II: Ascertainment bias during the recruitment of cases may lead to an artificial association of ASD with higher socio-economic status (SES) and ADHD with lower SES (non-testable). Scenario III: Opposite alleles at the same marker may tag opposite ASD and ADHD risk alleles at (d) a single risk variant, or independent ASD and ADHD risk alleles within (e) the same gene or (f) different genes in high-LD regions. Scenario IV: Identical marker alleles tag independent ASD and ADHD risk alleles, either (g) within the same gene or (h) at different genes in high-LD regions. (i) Scenario V: Identical marker alleles tag identical ASD/ADHD risk alleles (biological pleiotropy). Within each subfigure, one or more observed marker allele is shown in linkage disequilibrium with one or more ASD and ADHD risk allele. ADHD Attention-Deficit/Hyperactivity Disorder, ASD Autism Spectrum Disorder, GWAS genome-wide association study, LD, linkage disequilibrium, SES socio-economic status.