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Relatedness disequilibrium regression estimates heritability without environmental bias


Heritability measures the proportion of trait variation that is due to genetic inheritance. Measurement of heritability is important in the nature-versus-nurture debate. However, existing estimates of heritability may be biased by environmental effects. Here, we introduce relatedness disequilibrium regression (RDR), a novel method for estimating heritability. RDR avoids most sources of environmental bias by exploiting variation in relatedness due to random Mendelian segregation. We used a sample of 54,888 Icelanders who had both parents genotyped to estimate the heritability of 14 traits, including height (55.4%, s.e. 4.4%) and educational attainment (17.0%, s.e. 9.4%). Our results suggest that some other estimates of heritability may be inflated by environmental effects.

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Fig. 1: Relatedness disequilibrium.
Fig. 2: Comparison of heritability estimates from different methods.


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A.I.Y. was supported by a Wellcome Trust Doctoral Studentship (099670/Z/12/Z) for part of this project. A.I.Y. and A.K. were supported by the Li Ka Shing Foundation for part of this project.

Author information




A.I.Y. conceived and designed the study, performed statistical analyses, contributed analysis tools, developed theoretical results, and wrote the paper. M.L.F. performed statistical analyses and contributed analysis tools. D.F.G. contributed analysis tools, processed raw genotype/sequencing data, and collected and processed phenotype data. G.T. contributed analysis tools, and collected and processed phenotype data. G.B. collected and processed phenotype data. P.S. collected and processed phenotype data. G.M. processed raw genotype/sequence data. U.T. supervised generation of genotype/sequence data and phenotype data. K.S. jointly supervised research and wrote the paper. A.K. conceived and designed the study, jointly supervised research, and wrote the paper.

Corresponding authors

Correspondence to Alexander I. Young or Augustine Kong.

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Competing interests

The following authors affiliated with deCODE Genetics are or were employed by the company, which is owned by Amgen, Inc.: A.I.Y., M.L.F., D.F.G., G.T., G.B., P.S., U.T., K.S., and A.K.

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Supplementary Figure 1 Determination of offspring relatedness.

The diagram shows how the identity-by-descent sharing states of two individuals i and j are determined by the identity-by-descent sharing states of their parents and the segregation events in the parents during meiosis. The identity-by-descent sharing states of i and j are represented by the four chromosomes in the centre, with black bands indicating regions shared identical-by-descent. The four chromosomes represent the four possible pairs of homologous chromosomes (maternal-maternal, paternal-maternal, maternal-paternal, and paternal-paternal): the identity-by-descent sharing between the chromosome inherited from i’s father, Pi, and j ’s mother, Mj, etc. The identity-by-descent sharing states of the four possible pairs of parents, one from each individual, are shown in the corners (Pi and Pj, Pj and Mi, Pj and Mi, and Mj and Mi). The segregation event in i’s father is represented by I(Pi), the segregation event in j ’s mother represented by I(Mj), etc. Note that for simplicity we ignore recombination in this diagram. See the Relatedness Disequilibrium Lemma in the Supplementary Note for a mathematical description of this process and its consequences.

Figure Supplementary 2 RDR variance component estimates.

Estimated variance components of the RDR covariance model for 14 quantitative traits in Iceland (Supplementary Table 4), expressed as a % of phenotypic variance, shown with intervals +/- 1.96 standard errors around the estimate. Trait abbreviations: BMI, body mass index; AFCW, age at first child in women; AFCM, age at first child in men; education (years), educational attainment (years); HDL, high density lipoprotein; MCH, mean cell haemoglobin; MCHC, mean cell heamoglobin concentration; MCV, mean cell volume.

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Supplementary Figures 1 and 2, Supplementary Tables 1–9 and Supplementary Note

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Young, A.I., Frigge, M.L., Gudbjartsson, D.F. et al. Relatedness disequilibrium regression estimates heritability without environmental bias. Nat Genet 50, 1304–1310 (2018).

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