- •Pigmentation phenotypes and underlying genotypes are highly correlated.
- •Previous genetic prediction models did not consider phenotype correlations.
- •Testing impact of pigmentation trait correlation on genetic pigmentation prediction.
- •Observed correlated pigmentation phenotypes improve genetic pigmentation prediction.
- •DNA-predicted correlated phenotypes have no impact on genetic pigmentation prediction.
2. Materials and methods
2.1 Phenotype and genotype data
|N||Proportion of trait categories (%)||Males/Females|
|Skin colour||Very Pale||28||3.67||13/15|
|Dark to Black||28||3.67||9/19|
2.2 Statistical analyses
where and represent any two of the three correlated pigmentation phenotypes, and and represent the predicted values from respective linear models. typically ranges between 0 and 1, although values outside this interval are possible under extreme scenarios. A value of 0 indicates that the considered explanatory factors cannot explain any of the observed phenotypic correlation while 1 represents the case that the observed correlation can be perfectly explained by the considered factors. For example, with values of 0.5 for and 0.8 for the observed phenotypic correlation, 50 % of this correlation can be explained by the considered set of predictors, whereas the remaining 50 % are due to other shared genetic factors, such as other SNPs or other forms of genetic variation, and non-genetic factors, such as age, sex or environmental factors. We then applied this approach to the 41 HIrisPlex-S SNPs constituting the set of considered predictors to assess the proportion of phenotypic correlation that can be explained by these genetic markers.
where and represent explanatory factors having effects unique to and , respectively, while represents accessible genetic factors and unknown factors, whereas is used to regulate the shared component variance proportion explained by . For pigmentation traits, u1 and u2 may represent genetic and environmental factors having an effect on one pigmentation trait but not on another and vice versa, s1 may combine all 41 SNPs and s2 may represent yet to be discovered genetic factors influencing both traits. The expectation of is (see detailed derivation in Supplementary Materials). Then the estimated was investigated under a range of expectation of (). The simulation was conducted with 1000 replicates for each .
2.3 Computer simulations
where the , represents explanatory factors having effects unique for , and the and are explanatory factors unique for , while only and are accessible but and are inaccessible by investigators. Similarly, and are shared explanatory factors having effects on both and while only is accessible by investigators but is not. is used to regulate the phenotype variance proportion () explained by the inaccessible factor of . The variance explained (R [
where is the fitted using . Thus, Model I mimics a typical genotype-phenotype prediction analysis without considering phenotype and genotype correlations, analogue to strategy I in our empirical prediction analysis. Model II mimics the scenario when additional correlated phenotypes are not available, but were predicted from the same set of pre-selected SNPs and used as additional predictors, analogue to strategy II in our empirical prediction analysis. Model III mimics the scenario when truly observed correlated phenotypes are available for prediction and used as additional predictors, analogue to strategy III in our empirical prediction analysis. All simulations were conducted under . In addition, we repeated the simulation process by dichotomizing y using the mean value and estimated the AUC values using logistic models, which mimics scenarios of binary trait analysis. All simulations were conducted for 1000 replicates under each investigated model/scenario.
3.1 Data suitability check via genetic association testing
|Eye/hair/skin colour||Eye Colour||Hair Colour||Skin Colour|
3.2 Phenotype correlations and genetic contributions
|Eye colour||Hair colour||Skin colour|
|Hair Colour||0.47 (5.19 × 10E-43)||*||0.87|
|Skin Colour||0.36 (9.42E-25)||0.41 (1.64E-32)||*|
3.3 Empirical impact of phenotype correlations on genetic phenotype prediction
3.4 Simulated impact of phenotype correlations on genetic phenotype prediction
- Ralf A.
- van Oven M.
- Montiel Gonzalez D.
- de Knijff P.
- van der Beek K.
- Wootton S.
- et al.
Declaration of Competing Interest
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