Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Whole-genome prediction of complex traits using kernel methods

895 views

Published on

Presented at my Ph.D. thesis defense. University of Wisconsin-Madison.

Published in: Science
  • Be the first to comment

Whole-genome prediction of complex traits using kernel methods

  1. 1. Whole-genome prediction of complex traits using kernel methods Gota Morota May 12, 2014 1 / 31
  2. 2. Outline • Part 1: Kernel-based whole-genome prediction method • Part 2: Application to dairy cattle and wheat data • Part 3: Application to dairy cow health traits • Part 4: Application to broiler chicken data using genome annotation • Part 5: Ph.D.-wide Conclusions 2 / 31
  3. 3. Quantitative genetics – related individuals 3 / 31
  4. 4. Prediction of complex traits from genotypes 1) GWAS-based prediction • select influential markers first and then predict • single marker regression (2001) • marker assisted BLUP (MABLUP, 1989) 2) Whole-genome prediction • use all available markers simultaneously • Whole-genome marker regression • Kernel-based regression 4 / 31
  5. 5. How to parameterize response variable y ? 1. prediction of additive genetic effects • y = E + a + 2. prediction of total genetic effects parametrically • y = E + a + d + a ∗ a + a ∗ d + d ∗ d g + 3. prediction of total genetic effects non-parametrically • y = E + g + 5 / 31
  6. 6. Whole-genome marker regressions 50K SNP panel (n << p) 1. additive model • 50K RV to predict 2. additive + dominance model • 50K + 50K RV to predict! 3. additive + dominance + second-order epistasis model • 50K + 50K RV + 50K(50K-1)/2 RV to predict!! ⇓ Overparameterization!!!!! 6 / 31
  7. 7. Kernel methods Regression of a phenotype on a n × n symmetric positive (semi) definite matrix K ⇓ a) Parametric • A: Pedigree kernel • G: Additive genomic kernel • D: Dominance genomic kernel b ) Non-parametric • GK: Gaussian kernel • MK: Mat´ern kernel • DK: Diffusion kernel ⇓ In non-parametric kernels, choice of the metric determines characteristics of a kernel 7 / 31
  8. 8. Example of kernel methods: Genomic BLUP y = g + (where g = Xβ) (1) BLUP(ˆg) = [I + (XXT )−1 σ2 σ2 β ]−1 y. (2) Under common marker variance assumption, σ2 β = σ2 g 2 j pj(1 − pj) (3) Then, BLUP(ˆg) = [I + G−1 σ2 σ2 g ]−1 y (4) where G = XXT 2 j pj(1−pj) → Is this the best kernel?? 8 / 31
  9. 9. Euclidean space – Gaussian Kernel Euclidean distance is a metric on a metric space called Euclidean space Figure 2 : 3-dimensional Euclidean space. −∞ ≤ (X, Y, Z) ≤ ∞ Suppose, we observed two individuals with 3 SNP genotypes. • ID1 = x1 = (0,2,2) • ID2 = x2 = (2,1,0) Euclidean distance (genetic distance) on R3 ||x1 − x2|| = (0 − 2)2 + (2 − 1)2 + (2 − 0)2 = 3 9 / 31
  10. 10. Diffusion on 3 dimensional graph (Morota et al., (2013)) 0 1 2 012 0 1 2 1st Genotype 2ndGenotype 3rdGenotype (2,1,2) (2,0,1) (0,1,2) (0,2,0) (0,1,0) (0,1,1) (1,0,0) (2,0,0) (1,1,0) (2,1,0) (1,2,0) (2,2,0) (1,0,1) (1,1,1) (2,1,1) (0,2,1) (1,2,1) (2,2,1) (0,2,2) (1,2,2) (2,2,2) (1,0,2) (1,1,2) Figure 3 : SNP codes are viewed as coordinates of genotypes in p-dimensional space. → spatial distance 10 / 31
  11. 11. Bayesian kernel ridge regression A quantitative genetics decomposition is yi = g(xi) + i (5) y − g 2 + λ g 2 H (6) • The representer theorem is used to find the optimal g. (α) = y − Kα 2 + λ Kα 2 H (7) Here, g = Kα, is the function that minimizes (7). • Kα 2 H = α Kα, so that the function to be minimized is (α) = (y − Kα) (y − Kα) + λα Kα. (8) 11 / 31
  12. 12. Kernel Averaging (Multiple Kernel Learning) • Fit three kernels simultaneously: K1, K2, and K3 K = K1 σ2 K1 ˜σ2 K + K2 σ2 K2 ˜σ2 K + K3 σ2 K3 ˜σ2 K • Example 1: Three Gaussian kernels: GK1, GK2, and GK3 K = GK1 σ2 GK1 ˜σ2 K + GK2 σ2 GK2 ˜σ2 K + GK3 σ2 GK3 ˜σ2 K • Example 2: Three parametric kernels: G, D, and G#D K = G σ2 G ˜σ2 K + D σ2 D ˜σ2 K + (G#D) σ2 GD ˜σ2 K 12 / 31
  13. 13. Part 2: Application (Morota et al., 2013) Holstein • 7,902 Holstein bulls (USDA-ARS AIPL) • 43,382 SNPs • PTA of productive life (PL) Wheat • 599 inbred lines • 1,279 binary markers • average grain yield Methods • Bayesian kernel ridge regression (RKHS method) • Cross-validation 13 / 31
  14. 14. Averages of kernel elements and their predictive correlations for the Holstein data Kernel θ k(xi, xj) Cor(ˆytest , yPTA ) DK 10 0.138 0.727 11 0.483 0.745 11.5 0.644 0.739 12 0.765 0.739 13 0.907 0.734 14 0.966 0.729 GK 5 × 10−5 0.237 0.721 2 × 10−5 0.551 0.736 1 × 10−5 0.749 0.742 5 × 10−6 0.866 0.736 3 × 10−6 0.917 0.734 1 × 10−6 0.971 0.729 G1 NA -0.000126 0.729 G2 NA -0.000113 0.730 14 / 31
  15. 15. Averages of kernel elements and their predictive correlations for the wheat data Kernel θ k(xi, xj) Cor(ˆytest , ytrain ) Diffusion 3 0.136 0.586 3.25 0.289 0.580 3.5 0.466 0.577 4 0.752 0.547 5 0.962 0.522 Gaussian 0.005 0.134 0.582 0.003 0.290 0.579 0.002 0.434 0.562 0.001 0.655 0.558 0.0005 0.809 0.556 G1 NA -0.003 0.518 G2 NA -0.003 0.521 15 / 31
  16. 16. Part 3: Application (Morota et al., 2014) Data • 4,482 dairy cows (Zoetis) • 41,266 SNPs • EBV and PCP of six health traits Two steps approach 1. variance components estimation using parametric kernels 2. predict total genetic values using parametric and non-parametric kernels Methods • Bayesian kernel ridge regression (RKHS method) • Cross-validation 16 / 31
  17. 17. Estimated ratios of variance components (weights) Traits Types Variance Components VG/VP VD/VP VGD/VP KET PCP 0.09 0.13 0.14 EBV 0.25 0.03 0.01 DA PCP 0.06 0.09 0.25 EBV 0.39 0.04 0.30 RP PCP 0.05 0.09 0.35 EBV 0.27 0.03 0.07 LAME PCP 0.06 0.07 0.39 EBV 0.39 0.03 0.27 METR PCP 0.06 0.07 0.21 EBV 0.31 0.05 0.42 CM PCP 0.06 0.07 0.26 EBV 0.36 0.02 0.16 17 / 31
  18. 18. Scatter plots of relationships among G, D, and GD q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q qqqq q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q q q q qq q qq q qq q q q q q q q q q q q q q q qq q q q q q qq q q qq q qq q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q qq qq q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq qq qqq q q q qqq q qq q qq q q q q qqq q q q q q q q q q q q q q q q q q q q q q q q q q qqqq q q q q q q qq q q q q q qq qq q qq q q q q qq q q qqq qq qq q q q q q q q q q q q qq q q q q q qq q q q qq q q q q qq q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq q qq q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq q q qq q q q q q q q q qq q q qqq q q q q q q q q q q q q q qq q q q q q qq q q q q qq qq q q q q q q qq q q q q q q q q qq qq q q q q qq q qqq q q q qq q qqq q q qq q q qqq q q q q qq q qqq q q q q q q q qq qqq q q q q q q q qq q q q q q q q qqq qq q q q q qq q q q qq q q q qqq q q q q qq q q q q q q q qq q q q qq q q qq q q q q q q q q q q q q q q q q q q q qq q q q qq q qq qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q qqq q q q q q q q q q qq q q q q q q q q q q q qq q q qqq q q q q q q q q q q q q q q q qq qq q q q q q q q q q q qq q q q q q q q q q q q q qq q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q q qq q q q qq q q q qq q q q q q q q q q q q qqqq q q q q q q q q q qqq q qq q q q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q q qqqq q q q qq q q q q q q q q q q q q qq q q q q q q qq q q q q q q q q q q qqqq q q q q q q q q q q q q q q q q q q q qq q q q q qq q q qq q q qq qq qq q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q qq qq q q qq q q qq q q q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q qq q qq q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qqq q q q q qq q qq q q q q qq q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q qq qq q q q q q q q q q q q q q q q q qqq q q q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q q qq q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q q qq q qq q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q qq q q q q q q q qq q q q q q q q q qq q q q q q q q qq q q q q q qq q q q qq q q q q q qq q q q q qq q q q qq q q qq q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q qq q qq qq q q q qq q q q qq q q qq q q q qq q q q q q q q q q q q q q qq qq q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q qqq q q q q q q q qqq q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q qq q qq q q q q q q q q q q q q q q q q qq q q q q qq q q q qq q qq q q q q q q q q q q q q q q q q q qq q qq q q q q q q qqq qq q q q qq qq q q q q q q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q qq q q q q qq q q q q qq q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q qq q q qq q q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq qq q qq q q q q q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq qq q q q q q q q q q q qq q q q qq q q q q q qqq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq qq q q qqq qq q q q q q q qqqq q q q q q qq q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q qqq q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q qq q q q q q q qq q q q q q q q qqq q q q q qq q q q q q q q qq q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q qq q q q qq q q q q q q q qq q q q q q q q q q qq q q q q qq q q q q q qq q qq q q qq qq q q q qq qq q q q qq q q q q q qq q q q qq q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q qq q q q qqq q qq q q qq q q qq q q q qq q q q q q q q q qq q q q q q qq q qq q q q q q qq q q q q q q q q q q qqq q q q q qq q q q q q q q q qq q q q q q qq q qq q q q qqq q q q q q q q q q q q q q q q q q q q q q q q q qqq q qq q qq q q q q q q q q qq q q qq q qq qq q q q q q q q q q qq qq q qq q q qqq q qq q q q qq qq q q q q q q q q q q q q q qq q q qq qq q q q q q q qq q q q q q qq qq qq q q q q q qq qq q q q qq q q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq q q qq q q q q q q q q q q q q qq q q q q q q q q qq q q qq q q q q q q q q qq q q qq q q q q q q q q q qq q q q q q q q q q q q q q qq q q q q q qq qq q q q q q q qqq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q qq q q q q q q qq q qq qq q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q q qq q q q qqqq q qq q q q q q q q qq q q q q q q qq q q q qq qq q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq qq q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q qq q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q qq qq q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q q q qq q q qq qq q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q qq q qq q q q qq q q q q q qqq q q q q q q q q qq q q qq qq q q qq q q q q q q q q qq q q q qqq q q q q q q q q q q q q q q q qqqq q q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q q qq q q q qqq qq q q qq q q q q q q q q q q qq q q q q q q q qq q q q q qq q qq q q q q qq q q q q q q q q q q qq q q q q q q q q q qq q q q qq q q q q q q q q q q q q qq q q q q q q qqq q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q qqq qq q q q qq q q q q q q q q qqq q qq q q q q q q q q q q qq q q q qq q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q q q qq q q q q q q q q qqq q q q q qq q q q q q q q q q q qq q q q q q q q q q q q qq q q q q qq q qq q q qq q qq q q q q qq q q qq q q q q q q q q q q q q q qq q q q qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q qq q q q q q qq q q q qq q q qq q q qq q q qq q qq q qq q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q qq q qq q qq q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q q q q qq q q −0.05 0.05 −0.040.000.04 animal1 Additive relationship Dominancerelationship q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qqq q qq qq q qqq q q q qqq q q q q q q q q q qq q q q q qq q q q q q q q q q q q q q qq q q q qq q q q qq q q q q q q q q q q qq q q q qq qq q q q q qq q qq qq q q q q q q qqqqq q q q qq q q q q qq q q q q q q q q q q q q qq qq q q q q q q qq q qq q q q q q q q q qq q q qq q q qqqqqq q q q qqqqq q qq q qq q q q q q qq qq q q q q qq qq q q q q q qqq qq q qqqq q qq q q q q qq qq q q q q q q q qq q qq q q q q q q q q q q q q q qqq qq qq q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q qq q q qqq q q q q q q q qq qq qqqq q q qq q q q q q q q q qq q qqq q qq q q q q q qq q q qq q qq q qq q q q qq q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q qqq q q qq q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q qq q q qqqq q qq q q q qq q q qq qq q q q q q qq q q q qq q q q q q qq q q q q q q qq qq q q q q qq q q q q q q q q qq q q qq q qq q q q q q q q q q q q q q q q q qq q q qq q q qq q q q q q q q q q q q q q q q q q q q qqq qq q q q q q q q q q qq q q q q q q q qq q qqq q q qq q q q q qqqqqqq q q q q q qq q q q qq q q q q q q q q q q qq q q q q q q q qq q q qq q q q qqq q qq qqq q q qq qq q q qq q qq q q q q q q q q q q q q q q q q q qq q qq qq q q q q q q q qqqqq q q q qq q q qq q q q q q q qq q q q q qqq q q q q q q q q q q q q q q qqqq qq qqqqqq q q q q q q q q q qq q q q q q q q q q q q q q qq qq q qq qq q q q qq q q q q qq q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q qq q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q qq q q q q q q q qq q q q qq q q q q q q qq q q qq qq q q q qq q qq q qqqq q qq qqq q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q qq qq q qqq q q qq qq qq qq qq q q q q q qq qq q qq q q qqqq qq q q q qq q q q q q q q q q q q q q q q q q q q q qq q q qqqqq qq q qq q q q q q q q q qq q q q q q q q q qq q q q q q q qq q q q q qqq q q q q q qq q q q qq q q q q qq q q q qq q q qq q q q qq q q q q qq q q q q q q q qq q q q q q q q q q q qq qq q qq q q qqqq q q q qqq q q q qq q q q qq q q q q q q q q q q q q q q q q qq q q q qq q qqq q qq q qq q q q qqq qqqq qq q qq qq q q q q q q q q q q q q q q q q q q q q q q q qqq q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q qq q q q q qqqq q qq q q q qq q qq q q q q qq qq q q qq q q q q q q q q q q q q q q q qq qq q q qq q q q q qqq q q q q q q q qqq q q q q q q q q q q qq q qq qq q q q q q q qq q q q q q q qq q q qqq q q q qq q qq q qq q q qqq q q q q q qq qq qq q q q q q q q q qq q q q q q q q q qq q q q qq q qq q q q q q q qq q q q qq q q q q qq q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q qqq q q qq q q q q q q qqq q qq qq q q q q q q qqq q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q qq qqq q q q qq qq q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q qq q q q q q qq q q q qq q q q q q q q q q q q q q q q q qq q q q q qq q q q q qq q q q q q qq q q q q q q q q qq qq qqq q q q q q qq qq q q q q q q q qq q q q q q q qqq q q q q q q qq q q q q q q q q q q qq q qq q qq q q q q q q q q q q q qq q qq q q q q q qq q q q q qqq q q q q q q q q q q q q q q q q q q qqq q qq q q q q q q q q q q q q qq q q q q q q q q q q qq qq q q q q qq q q q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q qq q q q q q qq q qq q q q q qq q q q qq qqqq q qq q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q qq q q qq q q q q q qq q q qqq q q q qq q qq q qq q q q qqq q q qq q q q q q q qq q q q q q qq q qq q q q q q q q q q q q q qq q q q q q q qq q q q q q q qq q q q qq q q qq q qqq q q q q qqqqq q q qqq q q q q q q q q qq q qqq qq q q qq q q q qq q q qq q q q q q qqq q q q q q q q q qq q qqq q q q q q qqq q qq q q q q q q q qq q q q q qq q qq qq q q q q qq q q q q qq q q q q q q qq q q q q q q q qqq q q qq q q q q q q q qqq q q qqq q qq q q q q qqq q q qq qq q q q q qq q qq q q q qq q q q q q q q qq q q q q q q q q q qq qqq q qq q qq q q q q q q qq qqq q q q q qq q q q qq q q q q qq qq q q q qq qq q qqq q q q q q q q q q q q qq q q q q q qqqq q q q q q qq q q q q q q q qq qq q q q q q q q q q qq q q q q q q q q q q q q q q q qqqq q q q q q q qqq q q q q q q q qq q q qq q q q q q q q q qq q q q qq q q q q q q qqq q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q qq q q q q q q q qq q qq qq q q q q q q q q q q q qq qq q q q q q q q q qq q q q q q q qq q q qq qq q q q q qqq q q qq qqq qq q q qq q q q q q q q q q q q q q q q qq q qq q q q q q q q q q qqq q q q q qq q q q q q q q q qq q qq q q q q q q q q qq q q q q q q qq q q q q q q q q qq qq q q q q q qq q q qqq qq q qq q q q q q q q qq q q q qq q qq q q qqqq q qq q q q q q q q qq q q q q qqq qqq q q qq q qqq q q q q q q q q q q qq q q q q q q q qqq q q qq qq q q q q qq q q q q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qqq q q q qq q q q q qq qq q q qq qq qqq q q q qqq qq q q q q q q qq q q q q q q q q q q q q qqq q q q q q q q q q q q qq qq q q qq qqq q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q qq qq q q q q qqq q qq qq q q q q q q q q qq q q q q qq qq q q q qq q q q q q q q q q q qq q q qq q q q q q qqqq qq qqq q q qq q q q q qq qq q q q q q q q q q q qqq q q q q qq q q qq q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q qq q q q q q q q qq q q qqq q q q qqq q q q q q qq q q q q q q q q q q qq q q q qq q q q qq q q q q q q q q qq q qqq q q q q q q q q q q qqq q q q q q q q q q q q q q qq q q q q q qq q q q qq q q q q q q q q qqq qqqq q q q q q q q qq q q q q qqq qq q q q q q q q q q q q q qq qq q q q q q q q q qq qqq q qq q q q q q q q q q qq q qq q q qq q q q q q q qq q q q q q q q q qq qq q q q q q q qq q q qq q q q q q q q q q q q qqq q q q q q q q q qq qq q qq q q q qq q q q q qq q q q q q q q q q q qq q qq qq q qq q q q q q q q q qq q q q q qqq q q q q q q qq qq q q q q q q q q q q q q q q q q qq q q q q qq q q q qq q q q q q q q qq q q qq q qq q q qq q q q q q q q q q q q q q q qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q qqqq q q q q q q q qq q qq q q qq q q q qq q q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qqq q qq q q qq q q q q q q q q q q q q qq qqqqq qq qq qq q q q q qq qq q q q q q q q q q q qq q q q q q q q q q q qq q q qqq qqqq q q q q q qqq q q q qq q q q q q q q q qq qq qqqq q q q qq q q q qqqq q qq q q q q q q q q q q q q q q q qq q q qq q qq q q qq qq q q q qq q q q q q q q q qq q q q q q q qqq q q q q q q q q q qq q q q q q q q qq q q q qq q qq q q qq q q q qq q q q q q q q q q q q qq q q qqq q q qq q q q qq q q qq qq q q qq q q q q q qq q qq q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q qq qq q q q q q qq q q q q q q q q q q qq qqq q q qq qq q qq q q q q q qq q q q q qq q q q qq q q q q q q q q q q q q q q q q q q q q qq q qq qq q q qq qqq q q q q q q q qq q q q q q qq q qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq qqq q q q q q q q q q q qq q q qq q q q q q q q q qq q q q q q qq q q q q q q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q qq q q q q q q qqq q q qq q qqq q q q q q q q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q qqq q q q q q q qqqq q q q q q q q q q q q q qqq q q qq q q qq q q qq qq q q q q q q q q q q q qq q q q qq q qq q q qq q q q q q q q q q q q q q q q q qq q q qq q qqqq q q q q q q q q q q q q q q qq q q q q q q q q q q q q q qqq qqq q q q q q q qq qq q q q qq q q q qqq qqq q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qqq q q q q q q q q q qq qq q q q q qq q qq q q q qq q q qqq q q q qq q q q q qqq q q q q q qq qq q q qq q q q q qq qq qqq qq q q q q qq q qq q qq q q q q qq q q q q q q q q q q q q q qqq q q q q q qq q q q −0.05 0.10 0.25 −0.040.020.06 animal2 Additive relationship Dominancerelationship q q qq q qqq q q q q q qqq q qq q q q q q q qq q qq q q q q q q q qq q qq q q q qq q q q q qq q q qq q q q q q q q q q q q qq q qqq q q q qq q qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq qq q q q q qqq q qq q q q qq q q q q q qq qq q q qq qq q q q qq q q qqq q qq q q q q q qq q q q q q qq qqq q q q q qq q q q qq q q q q qq q q q q q q q q q q qq qq q q q qq q qq q q qq q qq qq q q q qqq q q q q q qq q qq q q q qq q q q q q q q q q q q q q q qqq q q q q q qq q q q qq qq q q q q q q q q q q q q q q q q q q qq q q q qqq q q q q qq q qq q q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q q q qqq q q q qq q q q q qq qq q q qq qq q qq q q q q q qq q q q q q q q q q q q q qqq q q qq q q qqqq q q q q q q q qq q q q q qqq q q q q q q q q q qq q q q q q q q qq q q qqqq q q qq q q q q q q q q qq qqq q q q q q q qq q q q q qq qq q qq q q q q q q q q q q q q q q q q qq q q q q q qq q qq qq qq qq q qq q q qqqq qq q q q q q q q q q qq q q q q qq q q q q qqq q q q q q q q qq qq q q q q q q q qq q q q q q qq qq q q q q q q qq qq q q q q q q q q q q qq q qqqq q q qq q q q qq q q q q q q q q q q qq q q q qqq q q q q qqq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q q qqq q q q q q q q q qqq qqq q qq q q q q q q q q q q q q qqqqq qq q qq q q q q q q q q qq q q qq q qq q q q qqq q q q q q q q q q q q q q q qq q qq q q q q qq qq qq q qq q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q q qq q q q q q q qq q q q q q q q qqq q q q q q qq q q qq q q q qq qqqq q q q q q q q q qq q q q q q qqq qq q q q q q q q q q qq q q q q qq q q q q q qq qq qq q q q qq q q q q q q q qq q qq q q q q q q q q q q q q q q q q qqq q q q q q q q q qq q qq q qqq q q q q q q q q qq q q q q q qq q q qq q q q q q q qq q q q q q q q q q qq qq q q q q qqq qq qq q qq q qqqq q q qq q q qq q qq q q q qq q qq qqq qq qq q q q q q q q qq q q q q q q q q q q qq q qqqq q q q q qq q q q q q q q qq q q q q q qq qq qq q qq qq q q q q q q q qq q q qqq q q q q q qq qq q qq q q qq q q q q q q q q q q q q qq q q q q q q q q qq q q q qq q q q q q q qq q q qq q qq q q q q q q q q q q q qq q qq q q q q q qqq q q q q q q q q q q q q q q qqq q q q q q q q q q q q qq q q qq q q qq q q q qqq q q q q qq q q q q q q q qqq q q q q q q q q q q qq q q q q q q q q q qqq qqq q q q q qq qq q q qq q q qq q q q qq q q qq q q q q qq q q q q q q qq q q q q q q qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qqq q q q q q q q q qq q qqq q q q q q qq q q q q qq qqqq q qq q q q q qq qq q q q qq q q q q qq q qqq q q qq q q q q q q q q qq q q q q q q q q q qqq q q q q q qq q q q q qq q q qqq q q q qq q qqq q q qq q q q q q q q q q q q qq q qq q q q q q q qq qqq q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q qq q qq q q q q q q q q q q qq q q q q q q q qqqq q q q q q q q q q q qq qq q q q q q q q q q q q q q q q q q qqqq q q qq qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q qq q qq q q q q qq q q q q q q qq q q q q q q qq q qq qq q q qq q q q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q qq q q q qq q q q q q q qq q qq q q q q q q q qq q q q q q q q q q qq q q q q q q q q qq qq q q qq q q q q q q q qq q q q q q qq q q q q q q qqq q q q q q q q q q q q q q qq q q qq q qq qq q q q q q q q q q q q q qq qqq q q qq q q q q q q q q qqqqq q q qq qq q q q q qq q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q qq q qq q q q q q q q qq qq qq q q qq q q q q q q q q qq q q q q q q q q q qq q q qq qq q q q q q q q q q qq q q qqq q q q q q q qq q q q qq qq q q qq q q q q q q q q q qqq q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q qqqqq q q q qq q q q qq q q qq q q q q q q q q qq q q qq q qqq q q q q q q q q q q qq q q q q q q q q qq q q qq q q q q q q q q q qq q q qqq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q qq q qq qq q q q q q q q q q qq q q q q q q q q q q q q q qqq q qq q qq q q qq q q q q q q q q q q qq q q q q q q q q q q q q qq qq q q q q q q q q q qq q q q q q q qq q qqq q q q q q q q q q qq q q q q q qq q qq q qq q q q q q q q q q q q qq q q q q q qq q q q qq q q q qq q q q q q q q q q q q q q q q q q q qq q qq q q q q qq q q q q q q q q q qq q q q q q q q q qq q q qq q q q q qq q q q q q q qqq q q q q q q q q q qq q q q qq q q q qq q q q qq q q q qqq q q q q q qqq q q q q q q q q q q q qq q q q qq qq qq q q q q q q qq q qqq q q q q q q q q q q q qq q q q q q qq qqq q qq q q q q qq q q q q q q q q qqq qq q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q q q qq q q q q q qq q q q qq q qq q q qqq q q q q q q q q q q q q q q qq q q q q qq q q q q q q qq q q q q q q q qq q qq qq q q q q q q q q qq q q qq q q q qq q q q q qq q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q qqq qq q qq q q q q qq q q q q qq q qqq q qq q q q qq qq q q q q q q q q q q q q qqq q q q q q q q q q q q qq q q q q q q q q q q q q q qq qq q q q q q q qq q q q q q q q q qqqqq q qqqq qq q q q q q q qq q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q qq q q q q qq q q qqq q q q q qqq q q q q q q q qqq q q q q q q q q q q q q qq q q q q q q q q q qqq q q q qq q q q q q q q q q qq q q q q q q qq q q q q q qq q q qq q q q q q q q qq q q q q qq q q qq q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q qq qqq q q q q q q qq qq qq q q q q q q qq q q q q q q q q qq q q q q qq q q q q q q q q q q q q qqq q q qq q q q q q q q q q qq qq q q q q qq q q qq qq q q q q q q q q qq q qq q q q q q q qq q q q qq q q q qq qq q q qqqqq q qq q q q q qq q q q q q q q q q qq q qqq q q q qq q qq q q q q q qq q qq qq q q qq q q q q q qq q qq q q q qq q qqq q q q q q q q q q q q q q q q q q q qq q q qq q q qq q q q qq q q q q q qq q qq q q q q q q q q qq q q qq q q q q q q q qq q q q q qq q q q q q q q q q q q q qq q q q q q q qq q q q q q q q q q qq qq q q qqqq q qq q q q q q q q q q q q qq q q q q q q qq qq qq q qqq q q q q q q q qqq qq q qq q q qq qq q q q q q q q q q q q q q q q q q q q qq q q qq qq qq q q qq q q q q q q q q q q q q q q q qq q q q q q qqq q q q qq q q q q q q qq q q q q q q qq qq q q q q q q q q q q q q q q qqqq q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q qq qq q q q qqq q q q q q qqq q qq q q q q q qqq q q q q qq q q q q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q qq qqq q q q q q q q q q q q qqq q q q qq q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q qqq q q q q q q q q q qq qq q q q q q q q q q q q qq qq q q q q q q q q q q q q q qq qqq q q q q qq q q q q q qq q q q q q q qq q q q q q q q q q q qq q qq qq q q qq q q qq q q q q q q q q q q q q q q q q qqq q q qq q qqq qq q qq qq q q q q q q q qqqq q q q q q q qq q q q q q q q q q qqqq q qq q q qq q q q q q q qq q q q q q qqq q q qq q q q q q qq q q q q q q q qq q q q q q qq q q qq q q qq q q qqqq q q q qq q q q qq q q q q qq q q q q q q q q qqq q q q q q q q q q q q qq qq q q q q q q qqq qq q q q q q q q qq qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q qq q q q q q qq qq q q q q qq q qq q qq q q q qq q q q q qq q q qq q q q qqq q q q q q q qq q qq q q q q q q qqq q qqq q q q q q q q q q q q q q q q q q qq q qq q q q qq q q q q q q q qq q q q qqq q q q q qq qq q q q qq q q q q q q q q q qqq q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q qqq q q qq q q q q q qqq q q qq q q qqqq q q qq qq q q qqq q q qq q q q q q q qq q q qq q q qq q q q q qqqq q q q q q q q q q q q q q q q q q q q q qq q q q qqq q q q q q q qq q q q q q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q qq q qq q q qqqq q q q q q q q q q q q q q q q q q q q q q q q qq q q qq q q q q q q qqq q q qq qqq qq qq qq qq q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q qq q q qq q q q q q q q q q q q q qq q q q q q q qq q q qq q qq qq q q q qqq q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q qq q q qq q q qq q q q q −0.05 0.10 −0.020.020.06 animal3 Additive relationship Dominancerelationship q q q q q q q q q q q q qq qq q q q q q q q q q q q q qq q q q qqq q q q q q qq q q q q q q q q q q q q q q q q qq q qq q q qqq q q q q q q q q q q q q q q q q q q qq q q q q qq q q q q qq qq q q qq q q qq q q q q q qq q q q q q q q q q qqq q q q q q q q qqq q q q q q q q q qqq q q q q q q q qq qqq q q q qq q q qq q q q q q q q q q qq q qq q q qq q qq q q q q q q q qqq q q q q q q q q q qq q qq q q q q qq q q q q q q qq qq q q q qq q q q q q q qqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq q q qqqq q q q q qq q q q q q q q q q q q q q q qq q q qq q q q q q qq qq q q q q q q q qq q q qqq q qq q q q q q q q q q q qqqq q q q qq q q qq q qq qqq q qq q q q qq q q q q q q q q q q qqqq q q q q qqq q qq q q q qq qq q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q qq q q qqq q qq q qq q q q qq q qq q q q q q q q q q q qq qq qq q q q q q q q q q q q q q q q qq q q q q q q q qqq q q qq q q q q q q q q q q q q q q q qq qq q q q q q qq q q q qq q q q q q q q q q q q qqq q q q qq qq q q q q q q q qqqq q q q qq q qq q q q qq q qqq q q q q q q q q q q qq q q q qq q q qq q q q q q q q q q q q q q q q q qqq qq q q q q q q q q q q qq q qq q q q q q q q q q qq q qq q q q q q qq q q qq qq q q q q q q q qqqq q q q q q q qq q q q q q q q q q q qqqq q q q qq q q q q q q q qq q qqq q q q q q q q q q q q q q q q qq q q q q q qq q q qqq q q qq q q q q q q q qq q q q q q qqq q q q q qqq q q q q qq q q q q qq q q q q q q q q q qq q qq q q q qq q q qqq qq q q q q q q q q q q q qq qq q q q q q qqq q q q q q q q q q q q q q q q q q q q qq qq q q q q qq q q q q q q q qqq qq q q qq qq q q q qq qq q q q q q q q qq q q qq q q q q q q q q qqqq q qq q q qq q q q q q q qqqq q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q qq qq q q qq q q q q q q qqq q q qq q q q q qq qq q q q q qq q q q q q q q q qq qq q q q qqqqq q q qqq q q q q qq q qqqq q q q q qq q q q q q q q q q q qq q q q q q q q q qq q q qq qq q q q q q q q qq q q qq q q qq q q q qqq qq q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q qq q q qq q q qq q q q qq qqqq q q q q q qq q qq q q q q q q q q qqq q q q q q q q q q q q q qqq q q q q q q qq q q q q q q q q q q q q qqq q q q qq q q q q q q q q q q qqq q q q q q qq q q q q q q qqq q q qq qqqq q q q q q q qq q q q q q q q qq qqqq q q q q q q q q q q q q qq q qq q q q q q q qq q q qq q q qqq q q qq q q q q q q q q qq qq q q q q q q q qqqq q qq q q qqq q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qqq q q q q q q q qqqq qqqq qq qq q q q q q q qq qqq q qq q q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q qq q qqq qq q q qq q q q q q qqq q q q q q q q q q q q qq q q q q q q qq qqqq qqq q q qq q q q q q q q q q q q q q qqq q q q q q q q qq q qq q q q q q q q q q q qq qq q q q q q q q q q q q q q q qq q q q q qqq q q q q q qq q q q q qq q qq q q qq q qqq q qq q q q q q q q q q qq q qq q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q qq q q q q q qq qq q q q q q qq q q q q q qq qq q q q q q q q q q q q qq qqq qq q q q q q qq q q q qq q q q q q q qq q q q q qqq q q q q q q q q q q q q qq q q qq q q q q q q q q q qq q q qq q qqq q q qq q q q qq q q q q qq q q q q q q q qqqq q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q qq q qq q q qq q q qq q q qq q q q q q qq q q q q q q q q q q q qqq q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q qqq qq q q q q q q q qq q q q q q qq q qq q q qq q q q q q q q q q q qqq q q q q q q q q q q qq q qqq q q qqqq q q qqq q q q q q q q q q q q q q q qq qq qqq q q q q q qq q q qq q q qq q qq q qq q q q q q q qq q q q q q q q q q q q q q qq qqq q q qq q q q q q q q q q q qqq q q q qq q q q q qq q qq qq q q q q qq q q q qq qq q q qq q q q q q q q q q q qq qq q qq q q q qq qqq q q q q q q q q q q q q q q q q q q q qq qq q q qqq qq qq qq q q q q q qq q q q q q q qq qqq q qq q q q qq q q q q q q q q q q q qq qqq q qq q q q q q qq q q q q q qq qq qq qqq q q qq qq q q q q q q q q q q q q q q q q q qqq qq qqq q q q q q q q q q q q q q qq q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q qq q qq q q q q qq q q q q q q q q q q q q q q q q q qq q qqq q q q qqq qq q q q q q q q qqq q q q q q q q q qq q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q qqq q qq q q q q q q q qq q q q q qq qqq qq q q q q q q qqq q q qq qq q q q q q q q q q q qq q q q q q qq q q q qqq q q q q q q q q qq q q q q q q qq q q qq q qq q q q q q q q q qq q q q q q q q qq q q q q q qq q q q q q q q q q q qq q q q q q q q q q qq q q qq q q q q q q qq q q q q q q q q q qq qq q q q q q q q q q q q qqqq q q q qq qq q q qq q q q q q q q q qq q q q qq q q q qq q q q qq q q q q q q q q q qq q q q q q q q q q q q q qq qqq q q qqq q qq qq q qq q q q q q q q qq q q q q q q q q q q qq qq q qq q q q q q q q q qq q q q q q q q q q q q qq qqq q q qq qqq qq q q q q q qq q q q qq q qq q q q q q q q q q q q q q q q qq q q q q q q qq qq qq q q q q q qq q q q q q q q q q q qq qq q q qq q q qq q q q q q qqqqq qq q q q q q q qq q q q q q q q qq q q qq q q qqq qq q qq q q q q q q q q qq qq q q q q q q q qq q qq q q qq q q q q q q q q q q q q q q q q q q q qq qq q q q q q qq q q q q q q q qqq q q q q q q q qq qq q q q q q qq q q q q q q q q qq q q q qq q q q q q q q qq q q q qq qq q q q q q qq q q q q q q q q q q qq q q q q qqq q q qq q q q q q q q q q qq qq qqqq qq q qq q qq q q q q q qq q q q q q q q q q q q q q q q q q q qqqqq q qq q q q qqq q q q q q q q q qq q q qq qq q qqq q q q q q q q q q qqq q q qq qqq qq q q q q q q q q q q q q q q qq q qq q q q q qq q qq q q q qqq q q q q q q q q q q q qqq qq q q qqqq qq q qq qq q q q q q q q q q q q q q q qqq q q q q q qq q q q q q q q q q q q q q qq q qqqq qqq q q q q qqq q q q q qq qq q q q q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q q qq q q q qqq q q qq q q q q q q qq q q qq q q qq q q q q q q q q q q qq q q q q qq q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q qq q q q q q q qq q q q qq q q q q qqq q q qqq q q q q q q q q qq q qq qq q q q qq q q q q q qq q q q q q q q q q qq q q q qq q q q q q q qq q q q q q q qq q q q q q qq q q q q q q q q q q q q q qq q q q qq q q qq qq q q q q q q qq q q q q q q qq q q qq q q qq q q q q q qq q qqq q qqq q q q q qqqqq q q q q q q qqqqqq qq q q q qq q qq q q qq q qq q q q q q qqq qq q qq q q q q q q q qqq q qq q qqq q q q q q q q q q q q q q q qqq q q q q q q qq qq q qq q q q q q q q q q q q qq qq q q q q q qq q q qqq q q q q q qq q q q q q q q q q q q qqqq q q q q q q qq q q q qq q qq qq qq qq q q q q q qq qq qqq q q qq q q q qqq q qqq q q q qq q q q q q q q q q qq q qq q q q q qq q q q qq q q q q q q q q qq q q q q q qqqqq q q q q q q q q q q q q q qq q q q qq q q q q q qqqq q q q q q q q q qq q q q q qq qq q q qqq q qq q q q q q qq q q q q q q q q q q q q qq q q q q q q q q q q qq q qqq q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q qq q q qqq q q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q qq q qq qq q q q q q q q q q q qq q qq q q q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q qqq q q q qqq q q q q q q q q q q q q q q q qq qq q q q q q q q qq qq q q q q q q q q q q qq q q qq q q q q qq q qq q q q qqq q q q q q q qqq q q q q qq q q q q q q q q q q qq qqq q q q q qq qq q q qq qqqq qq q qq qq q q q q q q q q q qqq q q q q qq q q qq q q q q q qq q q q q q qq q q q q q q q q q q qq qq qq q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q q qqq q q q q q q q q q q q q q qq q q q q q q q qq q q q q q qq q q q q qqq q q q qq q q qq qq q q qq q q q q q q q q q qq q q q q qq q q q q q q q q q q q q q q qq q q q q q qq q qq q qq q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q qq q qq q q q q q q q q qq q qqqq q qq q q q q qq q qq q qq q qq q q q q q q q q q q q q 0.0 0.2 −0.040.020.06 animal4 Additive relationship Dominancerelationship qq q q q qq q qq q q q q qq q qq q qq qq qq q q q qq q qqqq q q q q q q q qq q q q qq q q q q q q qq q q q qq qq qq qq qqq qqq q q q q q q q q qq q qq q qqq q qqq q q qq qq q qqqqq qq q q q qq q q q q q q q q qq q qq q qq q qq qqq q q q qqqq q q qq q q q qqq q q qqqq q qqq qqq q q q qqq qq q qq q q q q qqq qq qqq q q q qq qqq q qq q qqqqq qq q q qq q q q qqqqq q q q q qq qq q q q qqq q qqq q qq q qq qq q q qqq q qq q q qq q qqqqq qqqq q qq qq q qqqq q q qqqq qq qqq qq q q q q qq q q q qqqq q qqqq q q q qq qqqqq qq q qqq qqq q qqqq qq qqq q q qq q qqq q qq q qq q qqq qqq q q qqqqqq q qq qqq qq qq qq q qq qqq qqq q q q qq qq qqq qq qq q qq q qq q qq qqq q qq qqq q qqq q qq q qq q qqq q qq q q q qqqqq qq q qq qq qqq q qqqq q q qqqqqqq qq q qq q qqqq qq qq q q q q qq q q qq q qqq q q q q qq q qqq q qqq q q qqqqq q qqq q qq q q qq qqqqq qq q q q qqq q q qq q qq q q q q q q q q q qq qqqqq q qqqqqq qq qqqqqq q q q qqqq qqq q qqq q qq q qq q qqq qq qq qqqq q qqqqqqqqqqq qq qq q qq q q q qqq q q qq q q q qq q q q qqq q q q qqq qqq q qq qq qqq q q q q qqq qqqqq q qq q q qq qq q qqq qq q qq q qq qq q qqqq qq q q qq qq q q qqq q qq qqqqq q q q q qq qqqqqqqqqq qq q q qqq q q q qq qq q q q qq q qqq q qq q qq q qqqq q qq qqq q qqqq q qqq q qq q qq qq qqqqq q qqq qqqqq q q qqq q q qqqqqq q q q qq qqqqq q qq qqqqqq qq q q q q qq q q q qqq q qqqq qqqqqq qqq q q q q q q q qqqq q q qq q q q q qqq qq q q q q q qq q q q qq qqq qq q qq qqq q q qqq q q qqqq q q qq qq q q qqq qq q q qqqq q q q q q q qq q qqqq qq qqq q q q qqqqq qq q q qq qqq qqq qqq q q qq q qq q q qqq q qqq q q qq qq qqq q q qqqq q q qqq q q qq qq q q q qq qqqq q qq qqqqqqqqqqq q q q q q q q q q q qqq q q q qq q q q q q qq qq qq qqqq qqqq q qqq q q qqqq q q qqqqq q q q qqqqq q qq q qqq q qqqq qq q q qq qqq qq qqq q q qq q qqqq q q qqqq qqq q qqqqqq qqqq q q q q q qq q q qq q qqqqqqqqqqq q q q q q qq q q q qqq qqqqq qq qqq q q q qq q q q qqqq q q qqq q q q q qq q qqq qqq qq qqqq q q qq q q q q q q q q qq q qqqqq q q qq q q q q qqqq qq q q q q q qqq q q qq q q q q q q q q q qq q q q q q q qqq q q qqq q q qq q qqq q q qq qqq q q qq q q q q q qqq q q qq q qq qq q qqqqq qq q qq q q q qq qq q qqq qq q q qqq q qq qqq qq q qqqq qqqq qq q qqq qqq q q q q q qqq q q q qq qq qqq q qq qqq q q q q qqqq q q qq q q qq qq q qqqq q q q q qq q qq qq q q qq q q qq q q q qqq q qq qq qq q qqq qq qq qq q q q qq qq q q qqqq q qq qq qqqqq q q q q q qq q q q qq q q q q qqqqq q qq qqq q qq q qqqqq qq qqqqqqq q q qq q q q q qq q q qq q qq qq q qqqq qq q q q q q q q qq q q qqq q qq q q q qqqqqq qqq q q qq q qq q q q qqq q q q qqqq qqq q q qq qq q q qq q qq q qq q qq q q q q qq qqqq q q q q qq q qq q q q q q qq qq qq qqq qq q qq qqq q q q q qqq qqq q qqq q q q q q qqqq q qq q q q q q q qqq qq qq qqq q q qqq qq qq qq q q qq qq q qq q qq qqq q q q qq q q q qq q q qq q qqq qqqq q qq qqq q q q q q q q q qq q qqqq qqqq q q q q q q qq q q q q qq qq qqq q qqq qq q q qq q qq q qqqq q qq qqqq qqq q qqqq qq qq q qqqq q qqqq q q q qq q q q q qq q q qqq q q qqqqq qq q q qq q q q qq q q q q qq q qqq q qq q q q q q q q qq qqqqq q q qqq qq qqqq qqqqq qq qq qqqqqqq q q q qq qqqqq q q q q qqq q q qqq qq qqqqq qqqq q q qq q q q q q qq qq q qqqqqqqq qq qqqq q qq q q q q q q q q q q qq q q q q qqqqq qq q qq qq qq q q q q qq q q q q qq q q q qqq qqqq q qqq qqq qq qq qqqq qq q q q qqqq q qqq q q q q q q qq qqq qqqq q q qq q qq qq q q q qq q q q q q q q q qq q q qq qq qqqq q q q q q qqq q q q q q q qq qq q qq q q qq qqqq q q q q q qq q q qqqqqq qqq q q q q q q qqq qqq q q q q q q q qq qq q q q q qqq qq q q qq q q q q qq q qqqq q q q q q q q q q qq qqq q q qq q q qqq qq qq q q q q qqq qqqqqq q q q qqq qq q q q q qq qqq q qqq q qq qqq q q qq qq q qqqq q qqqq q qqqqq qqqqq qq qqq q q q q q qq q q qqq q q q qq q q q q qqq qqqqq q q q q qqqqqq q q q q q q q q q qq q qq q qq qqq qqqq qqq qqqq q q qq qq qq qq qqq q qqqqq qq q q q qq qqqqqq qqq qqqq qqqq qqqq qqq q q q qq q qqq qqqq q q qq qqq q q q qq qq qq qqqqq q qq qq q q q q q q q qq q qq q qqq q q q q q q q q qq q q qqq q qqqq q q q q q qq q qq qqqqqq qqq q q q qq q qqq q qqq qq q q q q qq q q q q qq qqq q q qq q q q qq q q q q qqq q qq q q q q qqq q qqq qqq qqq qqq qqqqqq q qqq q q q q qq q q q qq q qq q qq q q q qqq q q qq q q qqqqq q q qq q qq q q q q qq q q q qqq q q q q q q qq q qqqq qq q q q q q q q q q q q q qqqq qq q q q q qq qq q q qq q qqq q q q q q q qq qqqqqqqq q qq qq qq qqqq q qq qq q q q qq qqqq q qq q qq qq qq qq q qq q q qq q qqq q q q qq qqq q q qqq q q qq qq q qq q qq qqqqqqqqq q q qq q qqq qq qqq q qq qq qq q qq q q q qq qqq q q q qqq qqq qq q q qq qq q q qqq qq q qqq qqq qq q qqqq qq q qqqq q q q qq q qqq q q qq qqq q qqq qqq q q q q q q qq q q q qqqqq q qq qqq q q q q qqq qq q q q qq qq qqqq q q qq qqq qq qqqq qqqq qqqqq qqqqq q qq q q q qq q q qqqqqq qqqqq q qq q qqqqqq q q q qqqqqq q qqqqqqq q qq q qqqq qq q q qq qq q q q qqq qq qqqqqq q q q qq q q q q qqqq qqq qq qqq q q qqq qq q q q q q q q qqqq qq qq q q q q qqq q q q q qqqq q q qqq q qq q q qq qq qq qq q q qq qqqq q q q qqqq q q qqq q q qqqq q qqq q q qq qqqqq qq q qq q qqq q qq q qq qq q qq qqq q q q q q qq qq q qqq qq qq q q qq q q qq q qqq qq q qq q q q q qq qq q q qq q qq qqq q q q qqqq q q q q q qq qqq q q qq qqqqqq qqq q qq q q q q q q q q qq qqqq q q qq q q q qqqqq q qq q q q qq q q qqqq q q qqq q qq q qq q q qqqq q qq qq q qqq qq q q qq qq q qq q qq qqqqq qq q q qq q q qq q q qqqq qq q qq qqq qqq q q qqqq q q q q q q q q q qq q q qqqq qq q q q q q q qq q qq q q qqq q q q qqqq q q q qqq q qqqq q q q q qqq qq q qqqqq q q q q qq qq q q qq q q q qqqqq q q q q q q qq q q q q q q q q q qq q q q q qqqq qq q qq q q qq qq qqq q qq q q q q q qqqq qqqq q q qq q q qq q qq q q q qq qq q q q q qq q qq q q q q q qqqqqq q q q q q q qqqq qq qq q qqq q q q qq q q q q qqq q q q q q qqq qq q qq q qq q q q qq q q qq qqq qq q q q q q q q qq q q q qqq q qqqq q q q q q q q q qqq q q q q qq q q q q q qqq q q qq qqqq q qq q qqq q q q q q q q q q qqqq qq q q qqqq q qqqqqq q q q q q q q qqq q q qqq q q q qqq qqq q qq q q qq qq qqqq qq qq qqqqq q q q q q qq qqqqq qq q q qq q q q q q q q q qqq qq q q q q qqq qq q qq qq q q q q qqqq qq qqq q qq qq qqq qqq qq qqq qqq qqq qq qqqqq q qqq q q q qqqq qq qqqqq qq q q qqq q q q q q q qqq qq qqq qqqqqqq qq q qq qq q qqq q q qq q q q q q q qq qqq qqq q q q q qq qqq qqq q q q qqqqq q q qq qqqqq qq qqq qq q qq q qq qq qqqq q q q q q q qqq qq q q q q qq q qq q qqqqq q qqq qq q qq q qqqqqq q qqq qqqq q q qq q qqqqq q qq qq q q q q q q qq qq q qq qq qq q q qq q qq q q qq qq qq q q q q q q q q q qq q q q qq q qqq qqqq qqqqq qqqq q q q q qqq q q qq qq qqqq q q qqq q qq qq q qqq q q q qqq q qq q qqq q q q qq q qqqq qqqqqq qq q qqqqq q qqq qqqqq qq qq qqqqq qq qq q qq qq q q qq q q qq q q qqq qqqqqqq qq q q qq qq qq q q qqq qqq q qq q q qqqqqqq q q qqq q q q q q q q q q qq qqq q qq q q qq qq q qq q qqqqq qqqqq qqqq q qqqq qq qqqqqq qq qq q qqq qqq q q qq q q q qqqq qq q qq q q q q qq q q qq q qq q q qqq q q qqq q q q q qqq q qqqqq q q q qqq q q q qq q q q q q q q q q qq q q qqq q qqqq qq q qqqq q q q q qq −0.05 0.05 0.0000.0040.008 animal1 Additive relationship Additivebydominancerelationship qq qqq qq qq qqqqq q q qqqqq qqqqqqq q q q q qqqq qq qqqqqqqqqqqqq qqqqqqqqqq qq qqqqq qqqqqqqqq qqq q qq qq qqqqqqqq qqqqq qqqqqq q qqqqqqqqq qqqqq qq qqqq qq q qqqq qqqqqq qqqqqqqqqq q qqqqqqqqqqqqqqq qqqqqqq qq qq q qqqqqqqq qq q q qqqqqqq qq qqqqqq q q qqqqqqq qqqqqqqq qqqq qq q qqqqq qqqq qqqqqq qq q qqqqqqqq qqq qqqqqqqqqq qqqqqqqq q q q qqqq q qqq qqq qqqq qq q qqqqqqq q qqq qqq q q q q qqq qqqqq q qqq q qqqqqqqqq qqqqqq qqqq q qqqqqq qqq q q qq qqqq q q qqq q q q qq qqqqq qqqqqq qq qqqqq qqq qq q qqq qqqqqqqqqq qqqq qq qqqqq q qqqq q qqqqqqq q qqqqqqqqqqqqqqqqqqq qqqqqqq qqqqqqqqqq qqqqqqqqqqq q qqqqq qqqqq qqqq qqqqqqq qqqqq qqq qqqqqqqq qqqqq qqqqq qqqq qqq q q qqq qqq qq qqq qqqqqq qqqq q q qqq q qqq qqq qq q q qqqq qqqqq qqqqq q qq qq qqq q q qq qqqqqqqq qqqqqqqqqqqqqqq qqqqqqqq qqqq q q qq q q qq qq q qq q q qq qqqqqq qqqqqqq qqqqqqq q qqqqq qqqq qqq qqqq qq qqqqq q qqq qqqqqq qq qqqqqqqqqq qqqq qqqqqqqqqq qqq qqqqqqqqqqqqq qqq q q qq qqqqqqqqqqqqqq qqqqq qqqqqqqqqqqq qqqqqqqqqq qqqqqqqqqq q qqqq qqqqqq q qqqqq qqq qqqq qqqqq qqq q qqq q qq q q qqqq qqq qq q qqqqq qqqqqq qqqqqqqq q qqq qqqq qq q qqq qqqqqq qqqq qqq qq qqqqq qqqqqq q q qq qq q qqq qq qq qq qq qq qqqqqqqqqqq qqqqqqq qq qqq qq qqq qqqq q qqqqqqqq qq q q qqqqqqqqqqqqq qqqq qqq q q qq qqqqq qqq qqqqqqqqqqqq qq q qq qqq qqqqq qqq qq q q qqqqqqqqqqqqqq q q qq q q q qqqqq qqqq q q qqqq q q q qqqqq qqqqqqq q qq qqqq q qqqqq qqqqqqqqqq qqq qq qqq qqqqqq qqqq qq qqq q qqqq q q q qqq qqqqqq qqqqq qq qqqqqqq qqq q qqqqq qq q qqqq qq qqqqqqqq qq qq qqqq qqq qqqqqqqqqqqqqqqq qqqq q qqqq q qq q q q q qq q qqq qqqqqqqq qqqqq qqq qq qqqqqqq q qqq qqqq qqqqqqq qqqqqqq qq q qqqq q qqqqq qq q qqqqqqqqqqqqqqq qqq qq qqqq qqq qqqqqqqqqqqqqqqqqq qqq q qqqqq qqq q q qqqq q qq qqqqqqqqq q qqqq qqq qqqqq q qqqqq q qq q qq qqqqqqqq qqqq qqqqq qqqqq qqq qqqqqqq qqqq qqq qqqqq qqqqq qqqqqqqq qq q q qq qqq qqqqqqqqqqq qq qq q qqqq qqqqqqqq qq qqq qqqqqq qqqq qqqqqqqq qqqqqqqq qqq qqqq qqqqq qqqq qq qqq qq q qqqqq qqqq qqqq qqqq qqqqqq q qqq qqqqqq qqq qqqqqqqq qq qqqqqq qq qqqqq q qqqqqq q q q qqqqqq qq qqqq qqqq q q qqqqqq q qq q qqqq qq qq qqqqq q qqq qqq qq qq qq qqqqq qqqqqq qqqqqqqqq q qqqq qqqqq q qqqq qqqqqq qq qqqqqqqqqqqqqqqq qqqq qqqq qqqqqqq qqqqqqqqqqqq qqqq q q qq qqq qqq qqqqqq qqqqqqqqqqqqqqqqq qqqqqqqqqqqq qq qqqqq qqqqqqqqq qq qqq qqqq qqqqqqqq qqq qqqqq qqq qqqqq qqqqqqq q qqqqqqq q qqq qqqqq q qqqqqqqqq qqqq qqqq qqqqqqq qqqqqq qq qqq qq q qqqqqq q qqqq qqq q q qqq qq qqq q qqq qqqq qq qqqqq qqqqqq qqqqqqq qqqqqqqqqqqqqq qqq qq qq q qqq qqqq qqqqq qqq qqqqqqqqq q q q qqqq qqqqqqqqqq qqqqq qqqqqqq qqqqqqqqqq qqqq qqqq qq qqq q qqqqqq qqq qqqqq q qqq qqqq qqqq qqq q q q qq qq q qqqq q qq qqqqqqq qq q qqqqqq qq q qqqq qq qqq qq qqqqqqq qqq qq qq qqqqq qqqqq qqqq qqqqqqqqqqqqq qq qqq qqqqqqqqqqqq qqqqq qqqqq qqqqq qqqqq qqq q q qq q qqq qqq q q qqqqq qqq qqqq qq qqq qqqqqqq qqqqq qq qqqq qqqqqqqq qqqqqq qqqq qqq qq qq q qqqqqqq qqqqqqqq qqq qq q q qqqqqqqqq q qq qqq qqqqqqqqqq qqq qqqqqqqqqqqq qq qqq qqq qq qq qqqqqqq qqq qqqqq qq qq qqq qq q qqq qqqqqq qqqqqq q qq q qqqqqqq qqq qqq qqq qqqqq q qq q qq q q qqqqqqqqq qqq qq qqq qq qq qqqqqq qqqq qqqqqq qq qqq qq qq qqqqqqq qqqq q qqqq qqqqqqqqqqqqq qq qq qq q q qqqqq q qqq qqqqq q q qq qq q qqqqqqqqqqq q qqq qqqqq qq qqqq q qq qqqqq qqqqqq q qqqq qq qqq qqqqqq q qqq q qqq qqqqqqq qqqqq qq qqqqqqqqq qqqqqq qqq qqq qqqqq qqq qqqqqqqqqqq qqqqq qqqqqqq qqqq q qq qqqq qqq qq qqqq qqqqqqq qqqqqqq q qq qqq q qqq qqqq qqq qqqqqqqq qq qqqq qq qqqqq qqq qq qq qqqq qqqqq qqqqqqqq qqqqqq qqqqq qqqqqq qq qqqq qq qq q q qqqqq qq qqqq qqq qq q qqqq qqq qqqqqq qqqq qq q qq qq q qq qqqqqq qq q q qq qq q q qqq q qqqq q qq qqqqqqqqq q q qq qq qqqq qqqq qqqqqqqqq qqqqq qqqq qqq q qqqqqqq qqqqqqqqqq qq qqqqqq qqqqq q q qq qqqq q qqqq q qqqq qqqqq qq q qqqqq qqq q q q qqq q qqqq q q qq qqqqqqqqqqqqqqq qqqqqqqqqqq q qq qqq qqqq qqqqqqqqq qqqqqq qqq q qq q qqq qqqqqqqqqqqqqq qqq qqq qqqqq qqq qqqq q qqqqqq qqqq q qqqqq qq qqq qqqqqqqq qqqq qqqqqq qqqqqqqqqq qq qqqq qqq qqqqqqq qqqq qqqqqqqqqqq q qqqqqqqqqq qq q q qq qqqqqq qq q qq qqq qqqqqq qqq qq qqq qqqqqq qqqqqq qqqqqqqq q q q qqq qqqqqqqq qqqqqqqqqq qqq qqqqqqqqqqqqqq qqqqq qqq q q q qqq q qqqqq q qqq q qqqqq qqqqq qqq qqq qqq q qqq qqqq qqqqqqqqqq qq qq q q qq qqqqq qqqqqqqq qqq q q qq qqq qqq q q q qq q qqq qq qq qqq qqq qqq qq qqqq qq q q q qqqqq qq q qqq qqqq q qqq q q qqqqqqq qqqqq q qqqqqq qq qqqqq q q q qqqqq qq qqqqqqq qqqq qqq qqqqqq q qqqq qqq q qqqq qq qqq qqqqq qq qqqqqqqqqqq q qqq qq qq q q qqq q qq q q qqqq q qqqqqqqqq qqqqqqqqqqq qqq qqq q qq qqq qqq qqq q qq qqqqqqqq q qq q q q qqqqqqqqq q qqq q q qq qqq qq qqqqqq q qq qq qqqqqq qqqq qqq qqqq qqqqq q qq qqqqqqq qqqqq qqqqqq qq q qqqq q qqqqqq q qq qq qqqqqqqqq qqq q q qqq qqqqq qqq q qq qqqqqqqq qqqqqq q qqqqqqqq q q qq q q qqq qqq q qqq qq q q q qq qq qq q q q qqqq qqqqqqqqq qqqqqqq qqq qq qq q q qqqq qqq qqqqqq qqqqqqqqqqqqq qq qq q qq qqq q qqqqqq q q qq qqqqqqqqq qqq qqqqq qqqqqqqqq q q qqqqqqq qqqqqqq qqqqqqqq q qqq q qqq q q q q q qq qq qq q qqqqq qqqqq qqqq qqqqq q q qqqqqqqq qq qqq qqqqq qqq q qqqqqqqqq qqqqqqqqqqq qq qqqqqqqqqqq q q q qq qqqqqqqqqqqqqqqqqq qqqqqqqq qqq qqqqqqq qqqqqq qqqq qq qqqq qqqq qqqqqqq qq q qqqq qqq qqqqq qqqqq qqq qqqqqqqqqqqqqqqq q q qqqqq qqqqqqq q qq qq q qq qqqqqqq qq qq q qqqqqqqqqq qq q q qqqqqqqqqqqqq q qq qqqqq q q q qqqq q q q qqqq qqqqqq qqq qqqqqqq q q q qqqq qq q qqq qqq q qq q qqqq qq q q qqq q q qqqq qqqq q qqq qqqqqq q q q qq q q q q qqqqqqqqq q qqq qq qqqqqqqqqqqqqqqqqqqqqq qqqqqq qqqqqqqqq q qqq qq qqqq qqqqq q qq qqqqq qqq qqq qqq q qqqqq qqq q qqq q qqq qqq qqqqqqqq qqqqqqq qqqqq q qq q q qq qqq q qq q qqq qqq qqqqqqqqqqqqqqqqq qqqqq qqq qqqqqq q qqq q qq qqqq qq qq q qqqq q qqq qq q qq −0.05 0.10 0.25 0.0000.0100.020 animal2 Additive relationship Additivebydominancerelationship q qqq q qqq qq qqq qqqq q qq qq q qqqq qqq qq qq q q qqqq qqqqq q qq qqq qq qqqqqqq qq qqq qqqqqqqqq qqqqqqqqqqqqq qqqqqqqqqq qqqq q qqq qq qqqqqqq qqqqqqqqqqq qqq q qqq qq qq qq qqqqqqqq qqq qqqqqqq qqqqqqqq qqqq q q qqqqqqqqqqq q q qq qqqq q q qqqq qqqq q q q qqq q qqq qq qqqqqqqq q qqqqqqqqq q q qqq qqqq qqq qqqqqqqq qqqqqqq qqqq qq qqqqqq qqqqq qqqqq qqqqqq qq qq qqqq qqqqqqq q qqqqq qqqqqqq qq qqqqq q q qqq qqq q qq qqq q q qqqqqqqqqqqqqqqqqq qqq qqq qqq q q q q qqq q qq qq q qq q qqqqqqqqqqqqqqq qqqqqq qqq qq q qqq q q qqq q qqq q q qqqqqq q q qqqqq qqqq qq q qqqqq q q qqqqqqq qq qq qqqq qqqqq qqqqq qqqq q q qqqqqq qqqqq qq qqqqqqqqqqq qqqqq qqqq qq qqq qq qq qqq q qqq qqqqqqq qqqqqqqqqqqqqq qq qqq qq qqqq qqqqqqq qqqqqqqqq qqq qqqq q q qqqq qqqqqq qqqqqqq qq qqq qqqq qqqqqqqq qqqqqqqqq qqqqq qqqqqqq qqqqq q q q qqq qqqq qqqq qqq qqq qqqqqqq qqqqqqq q qqq qqq qqqqqq qqq qqqqqqqqq q qq qq qqqqqqqq qqqqqqqqqq q qq qq qqqqqqqqqq qqqqq q qq qqq qqqqqqq qqqqqq qq qqq qqqqqqq q qqqqqqq q q qqqqqq q qq qqqqqqqqq qqqqqqqqqqq qqq qq qqqq qq qqqqq qq q qqq q q qqqq qqqqqqqqq qqqq qqq qqq qq qqq qqqqqqqqq qqqqqqqqq qqqqqq qqqq qq qqqqqqq qq qqq qqqqqqqq qq qqqqqq q q q qq qqqqqq q q qqqqqq qq qqqqq qqqq q qqqqqqqq q q qqqqqq qq qqqq q qqqqq q qqqqqq qqqqqqq qqqqqqqqqq qqqqqqqqq qqqqqqqqq qq qqqqqqqqqq qqqq qqq qq qqqqqqqqqqqqqqqqqqq qqqq q qqqq qqq qqq qqqq q qqqqqq q qqqq qqqqqqq qqq qq qqqqqqq qq qq qq qqq qqqqq qq qq qqqqqq qqqqqqq qqqq qqqq qqqqq q qqqq qqqqqqqqqqq q qqqq qqq q qq qqqq q q qq qq qq qqqq qqqq q qqqqqq qqq q qqqqq qqqqqqqq q q qqq q qq qq qqq qqqqqqqqq qq qqqqqqqqqqq qq qqqqqqq qq q qq qqq qqqq qqq q qqq q qqq qqqq qqq qqqqq qqq q qqqqqqqqq qqqqq qqqqqqqqqqqqq qqqqqqqq qqqq qq qqq q qqqqq qq qqqq q qqq q qqqq qqqq qqqq q q qqqq qqqqqqqq qqqqqqq qq qqqqq qqq qqqqqqqqqq qqqqqqqq qqqqq qqqqqqqqqqq qqq qqqqqqqqqqq q qqq qqqqqq qqq qqqqqq q qqqq qqqqqqqqqq qqqqqq q qqqqqqqqqq qqqq qqqq qqqq qqq q q qqq q qq qqqqq qqqqqq q q qqqqqq q qq qqqqq qqqq q q qqqq qqqqq qq qqqq qq q q q qqqqqqq qqqq qqq qq qqq q qqqqqqqqqqq qqqqqqq qq qq q q qq q qqqq qqqq qqqq qqqqqqq qqqq qqqqq q qqq qqqqqqqqqq qqqqqqqqqq qqqqqq qq qq qqqqq q qqqq qq q q qq qqqqqqq q q qq qqqq qq qq qqqqq qqqqq q qq q qqqqqqq qqqq qqqq q qqq q q qq qqqq qqqqq qqqqq qqqqq qqqq qq qq qqqqqqqqqqqqqqqq qqqq qqq q q qqqq qq qq qqq qqqqq qqqqqqqqqq q qqqqqq qqq q qq qq q q qqqqqqqqqqqqqq qqqq qqqq q qq qqqqqqqqq qqq qqqqqqq qqq qq qqqq qqq qqqq qqq qqqq q qqqqqq qqqq q q qqqqqq qqqqqqqqq q q qq q qq qqqqqqqqqqqqqqqqqqqq qq qq qq q qqqqq qqq q q q qq qq qqq qqqq qqqq qqq qq qqqq qq qqq qqqqq qqq qqq qqqqq qqqqqq q q qq q qqqqqq qq qqq qq q qq q qq qq qq qqq q qqq qq q q q qqqqq qqqqq qq qqq qqqqqqqqq qqq qqq qqqq qqqq qqqqq qq q qqqq q q qqqqqqqqqq qqqqqq q qq qqqqqqqq q q qqq qqqqqqq q qqqqq qq q q qq q qqq qqq qqq q q qqq qqq q qqqq qqq qq qqqq qqqqqqq q qq q qqq qq qq q q q q qq qqq qqqqqqqq qqq qqqqqq qqqqqq q q qq qq q qq qqqq qqq qqqq qqq qqq qq qqq qqqqqqqqqqqqqqqqqqq qqqq qqqqqqqqq qqqqqq qq q q q qq qq qqqqqqqqqqqqqqqqqqqqq qqq q q qq qqq qqqq qqqq qqqqq q q q q qqqqqq qq q qqqqqq qq qq qq qqqqqq q q qqqqqqqqqqqqqq q qq qqqq qqqqqqqq qq q qqqqqqq qqqqqq qqqqqqqqqqqqqqq qqqqqqq qqqqqqqqqqqq qq qqqqqqqqq qqq q q qq qqqqq qqqqq qqq qqqqqqqqqq q qqqqq qqqqqqq q qqqqqqqq qqqqqqqqq qqqq qqq q qq qqq q qqqqq q q qqqqqq qqqqqqqqqqqqq qqqqq qq qqq q qq q q q qqqqqqqqq qqq qqq qq qqq q qq qq qq qq qqqqqqqq qqq qqqqqqq qqqqqqqqqq q q q qq qqqq qq qqqqqqq qqqqqqqq qq qqq q q q qqq q qq q qqqqqqqqq qqqqq qq q q qqq qqq qq qq qqqq qq qqqqqqqqqq qq qqqq qqqqqq q qqqq qqqqqqqqqq qq q qqqqqqqqqqqqqqq qqq qq q qq q qq q q qqqqq q qqqqqqq q q qq qqqq qqqq qqqq q q qq qqqqqqqqqq qqqqq q qq qqqqqqqqq qqqq qqqqqqqqq qq qqqqq qqqq qq qqqq qqqqq qq qqqq q qq qqq qqqqqqq qqqq qqqqqqqqqqq qq qq q q qq qqq qqqqq q q qqq qqqq qqqqqq qqqqqq q qqqqqqqqqq qq q qqqqqqq qqqqqq qq qqqqq qqqqqqqqq qqqqqq q q qqqqqq q qqqqqqqq qq q q q qqq q qqqqq qqq q qqqqqqqqq qqqqqq qqqqqqqq qq q qqqq qqq qqqqq qqq qqqqqqqqqqq qq qq qq qq q qq qqqq q qqq qq q qqqqq qqqq q qqqqqqq qq qqqqqq qqq q qqqqq qq qqqq qqq q q qqqq qqqqqq qq qqqq qqq qqqqqq qqqqqq qqqqq qqqqq qqq qq qqqq qqq q q qq qqqq q q qqqqqq q q q q qq qqq q qqqq q q qqqq qqq qq qqqq qqqqqqqqqqq qqq qqqq qq qqq qqq qqqq qqqq qq qqq qqq qqqqqqqqqqqqq qqq qqqqq qqqq q qqqq qqqq qqq qqq qqqqqq qqqqq qqq qq qq qqqq qqqqqqqqqqqqqq qqqq q q qqqqqqqqqqq q qqqqqq qqqq q qq qqqq qqqq qqqqq qqqqq qq qq qq qqq qqqq qqqq qq qqqqqqq qqqqqqq qqqqq qqqqqqqqq qq qqq q qqqqqqqq qqq qq qq qqqq q qq qqqqq q q qqq qqqq qqqqq qq qqqqqqqqqqqq q q qqq qqqq q q qqqqqq qq qqqqqqqq qqqq qqqqqq qqq q qqqq q q q qqqqq qqqqq qqqqqqqqqqqqqq qqqqqqqqqqqqq qqqqq qqq qq q q qqqqq qqq qqqqqqq q q qqq qqq qqqq qqqq qqqqqqq qq q q q q q qq qqqqq qq qq qqq qqqq qqqq qqqq qqqq qq qqqq qq qqq qqqqqq qqqqq qqqqq qqqqqq q qqq qqq qqqq qqq qqqqqqq qqq qqq qqq qq qqqq q q q qqqq q q qqqqqq qqq qq q qqq q qqqqqq qqqq qqq qqqqqqqqqqqqq q qq qqqq q qqqqqqq qqqqq qqqq qq qq q q qqqqqqqqqq q q q qqqqq qq qq q q qqqqqqq q qqq q q q qqq q qqqqq q qq q q qqqqq q q q q qq qq qqqq qqqq q qqqqq qq q q q qqqqqq qqqqqqqqqqqq q q qqqq q q qqq qqqq q qqqqq qq qqq q qq qqqqqqqqq qqqqqq qq qqq q q qqqqqqqqqqqqqqqqqqqqqqqqq qqq qqqqqqqq qqqqqqqqqq q qq qqqq q q qqqqqqqqq q qqqqq qqqqqqq qqqqqqq qqqqqqq q qqqq qqqqqq qq q qq qqqqqqqqqqqqqqqqqqqqq qq q q qqqqqqq qqq qqq q qqq qq qqqqq qq qqqqqqqqqqq qq qq qq qqqq q q qq qqq qqqqq qq q q q qqq qq q q qqqqq qqqqq qqqqqqqq qqqq q qqqqqqq qqqqqqq qqq q qqq q q qq qq qqqqqqq qqqqqqq qq qq qq qq q q qq qqqq q qq qqqqq q qqq qqqq qq q q qq q qqqq qq q q q q qq qqqqq q q qqq qqq q qqq q qq qq q qqq qqqq q qqqqq qq q qqqqqqqqq q q qqqq qqqqq qq qq q q q q q q q qqqqq q qq q q qqqq qqq qqqq qqqq qq qq −0.05 0.10 0.0000.010 animal3 Additive relationship Additivebydominancerelationship qq q qqqqqqq q q qq qq qqqqqq qqq qqq qqqqqqqq q qqqqqq qqqq qqqqqqqqqqqqqq qqqqqqqqq q qq qqqqq q q qqq qqqqqqqqqq qqqqqq qqqqqq qqqqqqqqq qq qqqqqqqqqq q qqq qqq q q q q qqqqq q qqqq qqqqqqq qqqqqqqqqqq q qqqqqqqqqq q q qqqqqqqqq qqqqqq qqq qqqq qqqqqq q qqq qqqqqqq q q qqqqq qq q q qqqqqq qqqqqq qqqqqqq q q q qqq q q qqq qqq qq q qqqqqqqq q qqqq q qq q q qqqq qqqqqq q qqqqqq qq q q qq qqqqq q qqqq qqqqq qqqqqqqq qqqq qqqq qq qqqq qqqqq qqqqqq qqqqqqqqqq q qqqqqqqqq q qqqqq qq q qq qqqqqqqqqqqq qq q qqqqqq qqqqq qqqqq qqq qqqqqqq q q qqqq qqqq qq qqqqqqqqq q qq qq q qqqqq q qq qqq q qq q qqq qqqqqqqqqqqqqqq qqq qq qqqqq q qqqqqqqq qqqqqqqq qqq qq qqqqqqq qqqqqqq q q q q q qqqqqqqqqqq qqqqqq qq qq q qq qqqq qq qqq qqq q qqq qqq qqq qq q q q qqqq qqqq qqq qqqq qq qqqqqqqqq q qqqqqqq qqqqqq q q qq qq qqqqq q q qq qq qq qqqqqq qq qqqqqqqqqqqqqqqqqqqqqqqqq qqq qq qqqqqqq qqqqqqq qqqqqq q qqqqqqq q qqqqqqq qqqq q q qq qqqqq qqq q qqqqqqqq qqq qq q qqqqqqqqqqqq qqqqq q qq q q qq qq qq qqqqqqqqqq qq qqqq qqq qqqqqqq qqqqq qqqqqqqqqqq qqqqq q qq qqq qq qq q q qqq qqqq q qq qqqqq qqqqq q q qq qq qqqqqq qq qqqqqqqq qqqq q qq qqq q qq qq q q qqqq qq qqqqqqqqq q qqqqqqq qqq qqqqq qqqq qqq q q qq qq q q qq qq q q qqq q qqqqqqqqq qq q q qq q q qqqq qqqqqqqqqqqqq qq qqqq qq qqqqq qqq qqqqqqqqq qqqq qqqqqq q qqqqqqqqqqqqqqqq q qqq qq qq qq qqqqqqqqqqqqqqqq qqq qqqqqqqqq qq qq qqq qqq q q q qqqq qqqq qq qqq qq qqqqqqqqq qqqqqqqq qq qq qqqqqq qqqqqqqqq q qqqqqq qqqqq qq qqqqq qqqqq qqqq qqqqqqqqqqqqqq qqq qqqqq qqqq q qqqqqqqq qqqqq qqq qqq qqq qq qqqqqqqq q qq qqqq q qq qqq qq q qqqqq q q q qqqqqqqqqq qqqqqq qq qqqqq q qqq qq qqqqqqqq qqqqqqq qqqqqqqq q qq qqqqq q qqqqq qqqqqqqqqq qq qqqqqq qqq qqqqqq q q qqq qqqqqqqqqqqqq qq q qqq q qqqq qqqq qqqqqqqq qqqq qqqqq q q q q qq q qqqqqq qqqqq q qq qqqqq qqqq qqq q q qq q qq qqq q qqq qq q q qq qq qqqqqqqqq qqq qq qqqqqqqqqqqqqqqqqqq qqqqqqqqq q q qq q qqqq qq qqq qqq q q q q q q q qqqqqq q q q qq qqq q q qq qqqqq q qqqqqqq qqq q qqq q qqq qqq q q q q qq q qqq qqq qqqqq q qq qqqq qqqqq qq q qq q q q qqq qq q q qqq qqq q q qq qqq qqqq q qq qqq q qqqqqqq qq qq q qqq qqqq qqqqqq qqqq q qqqqq qqq qqqq qq q qqqqqqqq qqq qq q q q q qqqq qqqqqqqqqqqqq q q q qqq qqq q q qqqq qq q qqqqqq qqqqqqqqq q q qq qqqqq qqqqqqq q q q qqq qq qq q qqqq q q qqqqqqq qqq q q q qqq qq qqqqqqq qqqqq qqqqqqqqq q qqq qqqqqqqq qqq qq qqq qqqq qqqq qqqqqq qqqq qqqqqqqqq qqqq qq qqq qqqqq q q qqqqq qqq q qqq q qqq qqqqq q qqqqqqqqqqqqq qqq qq qqq qqqqqqqqq qqqqqqqq qqqqq qqqq qqqqq qqqqqq qqqqqq qqq qqqqq qqqq qq qqq qqqqq qqqqqqq q q qqqq qqqqqqqq qqqqqq qqqq qqqqqqqqqqqqqq q qqqq qq q qq qq qq qqqqq q qqqqqq q qq qqqqqqqqqq q q qqq q q qqq qqqqqq qq qqq qqqqqqqqqqqq qq qqqqqqq qqq qqqqqqqqqqq q q q qq qqq q qq qqqqqq q q qq qq qqq qqqqqqqq qqqqq qqqq qqqqqqqq qqq qq qqqqq qq q q qq qq qqqq qq qq qqqqqqq qqqqqqqq qqqq qqqqqqqqqq qqqqqqqqq qq qqqqqqq qqqqqq qqqqqqqqqqq qqqqqqq qq qqqq qqq qqq qqqqqqqqq qqqq qqq qq qqqq qqq qqqqqqq qqqqqqq qq qqq qqq q qq qqq q qqqqqq qqq qqqq qq qqqq qqq qq q q q qq qqqqq q q qq qqqqqqqqqqqq qqqqq q qqqqqqqqqq q qqqqqq qq qqqqq qqqq qqqq q qqq qqqqqq qqq q qq q q qq qq qqqq qq qqqq q qqq q q qqq q qq q qqq q q q q q qq qqqqqqqqq q qqqq q q qq q q q qq q qq qqqqqqqq qq q qq q q qqqqq q qqqqqqqqqqqqqqqqq qqq qq qqq qq q qq qqqqqq q q q qqqq qqqqq q qq q qq q q q qqqqqqqq qqqqqqqqqqq q qq qqqqqqqqq qqqqqq qqqqqqqqq qqqqqqqqqqqqqqqq qqqq qqqqqqqqqqqqq q qqqqq qqqq q q q q q q q q q q qqqqqq qqqqqqqqqqqqqqq qqq qqqqqqqq q qqq qq qqqqqqqqqqqqqq qq qqq q qqqq qqqqqqqq qqqqqqqqqq qqqq q q q qqqq q qqqq qqqq qqq qqqqq qq qqqqqqqqqqqq q q qq qq qqqqqq qqqq qqqqqqqqqqqqqqqqqqqqq qqq qqqqqqq qqqqqqqq qqqqqq qqqq qqqqq qqqq qqqqqqqqqq qqqqqqq qqq qqq qq qqqqq qqqqq qqqqq qq qqqqqqqqqqqq qqqq qq qqqqq qqqqqqqqqqqqqqq q q qqqqqqqqqqqq q qqq qqqqqqqqqqq qqqqqqq qqq qqqqqq qqqqqqqqqq qqq qq qqqq q q q qqqqqqq qq q qqq qqqq qqqqqqq qq q q q qqqqqq qq qqqq qqqqqqqqqqq q qq q qqq qqqq qqqqqq qq qqqqqqqqqqq qqqqqq q q qqq qq qqq q q q qqq qq q qqqqqq qqqqq qqqq qqqqqqqqqqqq qqqqq qqqqq qqqqqq qqq qqqqqq qq qqqqqqqqqqqq qqqqqq qqqqqq qqqqqqqqq qqq qq qqqqq qqqq qqq qqqqq qqqq qqqqqqqqq qqq q q qqqq q q qqqqqqqqqq qqq qq qqqqq qqq qqqqqqqqqqqq qqq qqq qqqqqqqq qq qqq qqq q q q qq qqqqqqq qqqq q qqqqq q qqqq q qqqqqq qqqqqqqqqq qqqq q q qq qq qqqqqqq qq q qq q qqq qqq qqqqqqqqq qqqqqq qq qqqqq q qqq qqqq q qqq qqq q qqqqqqqqqqqq qqqqqqq qqqq q qqq qq qqqq qqqq q qqqqqqqqqq qq qq qqqqq q q q qqqqqq qqqq qqqqqqqqqqqqq qqq qqq qqqqqq qq qq q qqq qq qqq q q qqqqqqq qqqq qq qq qq qqqq qqqqq q qq qqqqqq qqq qqqqqqqqqqqqqqqqqqq qqqqqqqqqqqqqqq qq qqq qq q qqqqqqqq qqqqqqqqqqq qqqqqqq qqq qqq qqqqqq q qqqq qq qqq qqqqqq q q qq qqqqq qqqqqqqqqqqqqq qq qqqqqqqqqq qqqqqqqqqqqq q qq qqq q qqqqqqq qqqqqqqqqqqqqqqqqqqqqqq qq qqqq qq qqqqqqqqqq qqqqqqq qq qqq qq q q q q qq q qqqqq qq qqqqqq q qq qqqqqqqqqqqqqqq qqqqqqqqqq qq qqqq qq qq qqqqqq q qqqqqqq q q q q qqq qqqq q q q qqqq qqqqq q qqqq qq q qqqqqqqqqqqqqqqqq qqqq qqqqqqqqqqq q q q qqqqqqqqq q qqqqq qqqqq qq q qqq q qqqqqqqqqq qqq qqqqq qqqq qqqqqqqqq q qqqqq qqqqqq qqqqqqqq q qqqq qqqqqqq q qq q q qqq qq qq qq qqq qqqq qqqq qqqqqqqqqq q qq qqqqqqqqqq qq qqqq qqqqqqqq qqqqqqqq q qqqqqqq qq q qqqqqqq qq q qq qqqqq qqqqqqq qqqqqqq qqqq qqqqq qqqqqqqqqqq qq qqqqq qqqqqq qqqq qqqqqqqqqqqq qqqqqq qq qqqqqqqqqqq qqqq qqqqqqq qqqqqqqqqqqqqq qq qq qq qqqqq qq qq qqqq qqqqqqqqqq qqqq qqqqq qqqqqqqqqqqqqqqqqqqqqqq qq qqqqq qqqq qq q q qq qq qq q qqq q qqqqq qqqq qq qqq qqqq q q qqq qqqqqqqq qqqqqq qq q qqqqqq q qqq q q q q q q q q q qqqqqqq qq q q qqq qqqqqqq q q q q qq q q qq q qqqq q q qqqqq q qqq q qq qqq qq q qqqqq q qqqqq qqqq q qqqqqqqqqqq qqq qq qqqqqq qq q q qqq qq qqq 0.0 0.2 0.0000.0100.020 animal4 Additive relationship Additivebydominancerelationship qqq q q qq q qq qq q qqqq qq q q q qq qq qq q qq q q qq q q qq q qq q qq q q q qq qq q q q q qq q q qqq qq qq qq qqqq q q q q q q q q q q qqqqq q qq q q qq qq q q q qq q qqq qqq q q q qqq q q qq q q q q qq q qq q qqq qq qqq q q qq q qq q q q q q q q qqq q qqq qq q qqqqqq q q q qqq qq q qq q q q q qqq qq q qq q q q qqqqq q qq q qqqqqqqqq qq q q q qqqqq q q q q qq qq q q q qqqqq qq q qq qqq qq q q qqq q q q q q qq q qqqqqq qqq q qqq q q qqq q q q q qqqqq qqq q q q q q qqq qq q q qqq q qq q q q q qqqqqqqq qq qqqq qqq q qqq q qq qqq q q qq q qqq q qq q q q q qqq qqqq q qq qqqqqqqqqq qq qqqqq qq qqq qqq q q q qq qq qqqqq qq q qq q qq q q q qqq q q q q qq q qqq q qq q qq q qqq q qq q q qqqqqq qq q qq qq qqq q qq qq q qqq qqq qq qq q qq q qq qq qq qqq q qq qq q q q q q qq q q q q qqq q q qq q qqq q qqq qqq q q qq q qq q q q q qqqqqq q q q q qqq q q qqqqq q q q q qqq q q qq q qq qq q q qq qqqq qqqq qqqqqqqqqq qq q q qq q q qq q qqq qq q qq qqq qqq qq qqqqq q qqqq qq q q q qq q q q q q q q q qq q q qqq q q q qqq q q q qqq qqqq qqq qq qqq q q q qqqq qqqq q qq q q qqqq q qqqq qq qqq qq qq q q qqq qq q q qq qq q q qqq q qqqqqqqqq q q qq qq qqqq q qqq qq q q qq q q q q qqqq q q q q q q qqq q qq q q q q qqqq q qq qqqq qqq q q qqq q qq q q q qqqq qqqq q qqqq qqq q qq q q q qq qqqqqq q q qqq qqq q q qq qqq qqq qq q q q q qq q q q qqqq qqqqq q qqqqqqqq q q q q q q qqqq q q qq q q q q qq q qq qq q q q qq q q qqq qq q qq q qq qqq q qq qq q q q qqqq q qq qq q q q qq qq q q qq qq q q qq q q qqqqq qqqq qqq q q q qqqqq qq q q qq qqq qq q qq qq q qq qqq q qqqq q qqqq q qq qq qqq q qqqqq q q qq q q q qq qq q q q qq qqqq q qq qqqq qq qqqqq q q q q q q qq q q qq q q q q qq q q q q q qq qqqq qqqq qqqq q qqq q q qqqq q q qq qqq q qq qqqqqq qq q qqq q qqqqqq q q qq q qq qq q qq q qqq q qqqq q q qqq q qqq q qq qqqqqqqqq q q q q qq q q qq q q qq qqqqqq qq q q q q q qqq q q qqqqqqqq qq qq q q q q q q q qq qqqq q q qq q q q q q qq q qqq qqq qq qqq q q q qq q q q q q q q qqq q qq qqq qq qq q q q q q qqq qq q q q q q qqq q q qq q q q q q q qq q qq q q q q q q q qq q q q qq q q qq q qqqq q qqqq q q qqq q qqq q qqq q q qqq qq qq q q qqq q qq qqq q q q qq qq q qqq qq q qq qqq qq qqqq q q qqqqqqq q qq q qqqq qq q q q q qqqq q q q q qq q qq qq q q qqq q q q q qqq q qq q q q q qq qq q q qqq q q q q qqq qq q q q q qq q q q q q q q qqq q q qqq qq q q qq qq qq qq q q q qq qq qq qqqq qqq qq qqqqqq q q q q qq q q qqq qq q q qq qq qqqqqqq q qq q q qqqqq qq q qq qq q q q qq q qq q qqq q qq q qq qq q qqqqqqq q q q q q q q qq q qqq q q q q q q qqqq qq qqq q q qq q qq qq q qq q q qq qq qqq qq q qqq qqq q qq q q q q qq q qq qq q q qq q qqq q q q q qq q qq q q q q q qq qq qq qqqq q q qqqqq q q q q qqq q qq q q qq q q q q q qq qq qqq q qq q q q qqq qqqqq qq q q qqq q q qq qq q q q qq q q qq qq q q qq q q q qq q q q qq q q qq q qqq qqqq q qqqq q qq q q q q q qqq q q q qq qqqq q q qq q q q qq q q q qq qq qqq q q qq q q q qqqq qq qqqqq q qq qqq q q qq q qqq qqq qq q qq q qqq qqq q q q qq q q q q q q q qqqq q q q qqqq qq q q qq q q q qq q q q q q q q q qq q qq q q q q q qq q q q qqqqq q qqq qq q qqq q qqqqq qqqq qq q qqq q q q qqqqqqq q q q q qqq q q qqqqqq qqqqqqqq q qqqq q q q q qq qq q qqq qq qq q q q q qqq q qq q q q q q qq q q q q q q q q q q qqqq qq q qq qq qqq q q q qq q q q q qq q q q qq q qq q q q qqq q qq qq qq qqq q qq q q q q qqq q qq q q q q qq q qq qqq q qq q q q qq q qq qqq q q qq q q q q q q q q qq q q qqqqqqqq q q q q q qqq q q q q q qqqq q q qq q q qq qqqq q q q q q qq q qqqq qq qqqq q q q q q qq q qqq q q q qq q q q qq qq q q q q qq q qq q q qq q q q q qqqqqqq q q q q q qq q q qqqqqq q qq q q qqq qq qqq q q q qqq qqq qqqq q q qqq qq q q q q qqqqq q q qq q q q qqq q q qqqq q qqq q q qq qq q qq qq qqq q qq qq qqqq q q q qq q q qqqqq q q q q q q q qqq qqq qqq q q q qqqqqqq q q q q q q q qq qq q qqq qqqqq q qq q qqq q qq q q qqq qqq qqqqq q q q qqqq qq q q q qqqqqqqqq qq q qqqq qqq qq qq qqq q q q qq q q qq qqq qq q qq qqq q q q qq q qq qq qq qq q qqq q q q q q q q qq q q q q q qqqqq q q q q q q qq q q qqq q qqqq qq q q q qq qqq qqqqq q qqq q q q qq qqq q q qqqq q q q q qqq q q q q qqqq q q q qq q q q qq q qq q qqq q qq q q q q qqq q qqq qqqqqq qqq qqqqqq q q qq q q qqqq q q q qq q qq q qq q q qqqq q q qq q q qqqqqq q qq q qq q q qq qq qq q q qq q q q q q qqq q q qqqq q q q q q q q q q q q q q qq qqqq q q q q qq qqq q q q q qqqq q q q q q q q qq qq qqqq q qq qq qq q qqq q qq qqq q qqqqq qq q qqq q qq q qq qq qqq q q qq q qqq q q q qq qqq q q qq q q qqq qq q qq q qq qq qqqqqqqq q qq q qqq qq qqqq qq qqq q q qq q q q qqqq qq q q q qq q qqqq q q qqqq q qqqq qq q qqqqq q qq q qqqqqq q qq q q q q q qq q qqq q q q qqqq q q qqqqq q q q q q qqq q q q qqq qq q qq qqqq q q q qqq qq q q q qq qqqqqq q q qq qqq qqqqqq qqqq qqqqq qqq qq q q q q q q qq q qq qq qqq qqqqq q q q q q qqqq q q q q qqqqqq q qqqq qqq q q q q qqqq qqq q qq qqq q qq qq qqq qqq q q q q qqq q q q qqqqq qqq qq qqq q q qqq qqq q q q q q q q qqqqq qq q q q q qq qq q q q q qqq q qqqq q qq q q qq qq qq qqq q qq qqqq q q qqqqq q q qqq q qqq qq q qqq q q qqq qqqq qq q qq q qqq q q q q q q q q q qqqq q q q q qq qqqq q q qq qqqq q qq q q q q q q qqq q q q qq q q q q qqqq q q q q q qq q qq q q q qqqq qq q q qq q qqq q q q q qqqqqqqqq q q q q q q qq q q q qqq qqq q q qq q q qq qq qq q qq q q q qq q q qqqq q q qqqq qq q qq q q qqqq q qq qq q qq qqq q qqqqq q q q q qqq qqqq qq q qq q qq qq q q qqqq qq q q qqqq qqq q q q qqq q q q q q q q q q qq q q q qq q qq q q q q q qq q q qq q q qq q q q q qqqq q q q qqq q qqqq q qq q q qq qq q qqqqq q q q q qqq q q qqq q qqqqqqq q q q q q qqq q q q q q qq q q q q q q q q qq qq qq q qq q q qq qq qqqq qq q q q q q qq qqq q qq q q qq q q qq q qq q q q qq qq q q q q qq q qq q q q q q qqq qqq q q q q q q qq q q q qqq qq qq q q qqq q q q qq qq q q q q q q qq qq q qq q qq q q q qq q q q q qqq qq q q q q q q q qq qq q qqq q qqq q q q q q q q q q qqq q q q q qq q q q q q q qq q q q q qqqq q q q q qq q q q q q q q q q q qqqq qq q q qqqq q qqqq q qq q q q q qq q qq q q q qq q q q qqq qqq q q q q q qq qqqqqqqq qq qqqq q q q q q q qq qq qqq qq q q qqq q q q q q q q qqqq q q q q q qqq qq q qqq q q q q q qqqqq q qqq q qqqq qqqq qq qq qqqq qq qq q qqqq q qq q qqq q q q qqqq qq qqq qq qq q q qqq q q qq q q qqq qqqqqqqqq qqqqqqqq qq q qqq q qqq q q q q q q qqqqq qqq q q qqqqqqqq qq qq q qqq qqq q qqqqqqq qq qqq qq q qqq qq qq qqqq q q qq q qqqqqq q q q qqq q qq qqqq qq qqqqqq q qq q qqq qqq q qqqqqqq q q q qq qqqqq q qqq q q q q q q qqq qq q qqqqqq q q qq q qq q q qq qqqqqq q qq qq q q qqq q q qqq qqqq qqqqq qqq qqqq qq q q q qq q q qq qqqq qqq q q qqq qq qq q qqqq q q qqq q q q q qqq qq q qq q qq qq qqqq qq qq q qqqqq q qqq qqqqqq q q qq qq qq qq qq qqq qq q q qq q q q q q q qqq qqqqqqq qq q q qq qqqqq q q qqqq q q qq q q qqqqq qq qq qqq q q q q q q q q q q q qqq q qq q q qq qqq qq q qqqqq qqqqqqqqq qq qqq qqqqqqqq qq qqq qqq qqq q qq q q q q qqqq qq q qq q q q q qq q q qq q q qqq qqq q q qqq q q q q qqq q qqqq qq q q qq q q q qq q q q q q q q q q q qq q q qqq q qq qqqq q qq qqq q q q q q −0.04 0.02 0.06 0.0000.0040.008 animal1 Dominance relationship Additivebydominancerelationship qq qq q qqqq qqqq q q q qqqqq qq qqq qq q q q q qqqqq qqq qqqqqq qqqqq qqqq qqqqqq qq q qqqq qqq qq qq qq qqq q qqq qqqq qq qqq qq qqqq qqqqq qqqqq qqqqq qq qqqqq qqq qqq q qqqqqq qqqq qqqqqqqq qq q qq qqqqqq qq qq qqqq qqqqqq qqqq q qq qqq q qqq q q q q qqqq qq qq qqqqqq q qqqqqqqq qqq qqqq qqq qq qq q q qq qqqqqq q qq qqqqq q qqqqq qqqqqqqq qqq qq qqqq qq qqq q q q q q qq qq q q qq qqq qqqqq qq qq qq q qq q qqq qq qq q q q qqq qq qq q q q qq q qqqqq qqqq q qqqqqqqqq q qqqqqq qqq q q qq qqqq q q qqq q q qqq qqqqqqqqqqq qqqq qqq qqqqq q qqq qq qqqqqqqq qqqqqq qq qqq q q qqq q qq qq qq q q qqq qqqqq qqq qqq q qqqq qqqq qqq qqqqqqqq qq qqqq qqq qqqq q qqqqq q qqqq qqq qqq qqqq qqqq qqqq qqqqqqqqqqq qqqqq qqq qqqqq qqq q q qq qqq qq qqq qqqqqq qqqqq q q qq qq qq qqq qq q qqqqq qqq qqq qqqq q qqqq qqq q qqqqqqqqq qqq qq qqqqqqqqqq qq qqqqqqqq qqqqq q qq q q qq qq q qq q qqqq qqqqqq qqqqqqqqqq qqq q qq qqq qqqq qq qqq qq qq qqqq q q qqq qqqqqqqq qq qqqqqqq qqqqq q qqq qq qq qqqqqqq qqqqqq qq qq q qqq q qqq qqqqqqqqqqqqqq qqq qqq qqqq qqq qqqq qq qqqqqqqqqq qqq qqqqq qqqqq qqqqqq q qqq qq qq qqqqq qqq qqq qq q qqq q qq qq qq qq qqqqq q qqqqq qqq qqq qqq qqq qq q qqq qq qqqq q qqq qqqqq qq qqqq qq qq qqqqq qqqqqq q q q q qq q qqq qq q q qq qq qqqqqqqq qqqqqqqqq qq qqq qqqqqq qq q qqq q qqq q qqqq qq qq qqq qqqq q qqqqqqqqq qqq q q qqqqqqqqqq qqqqqqqqq qqqqq q qq qqq qqqq q qqq qq q q qqq qqqqqq qqqqqq q qq q qq qqqqq qq qq q qqqq q q q q qqq qq qqqqq qq q qqqqqqq qqqqq qqq qqqqqqq qqqqq qq qqq qqqqq qqq qq qqq q q qqq q q q qqq qqqqqq qqqqq qqqqqqqqqqqq q qqqq qqq qqq qqqq qqqqqqqq qqqq qqqqqqq qqqqqq qqqqqqqqqq qqqq q qqqq q qq q q q qqq q qqq qqqqqqqq qqq qqqqqq qqq qqqq q q qqq qqqq qqqq qqq qqq qqq qqq q qqqq q qqqqq qq q qqqq qqqq qqqqqq q qq q qqqq qq q qq qqqqqq qqqq qqq qqqqq qqq q q qqqq qqq q q qqqq q qq qqqqqqqqq q q qqq qqq qq qqqq qqqqq q qq q qq qqqq qqqqqqq qqqq qq qqqqq qqq qqqq qq q qqq qqqq qqqqqqqqqq qq qqqqq q qq qq q q q qq qq qqq qqq qqq qqqq qqqqq qqqq qq qqqqqqq qqqqqqqqqqqq qqqqqq qqqqqq qq qqq qqq q qqqqq qqq qq qqqq qq qqq qqq qqq q qqqq qqq qqqqqqq q qqq qqqqqq q qq qqq q qqqq qq qqqqqq q q qqqqq q qq q qqq q q q qq qqq qqqq qqq qqqq q q qqq qq q q qq q qqqq qq qq qqqqqq qqq qq qqq qq qq qqqq qqqqq qq qq qqqqq qqqq qqqqqqqq q qqqqqqqqqq qq qqq qq qqq qqq qqq qq qq qq qqq qqqq qqqq qqqq qqqqq qqqqqqqq q qq qqqqq q qqqqqqqqq qqqqq qqqq qq qqq q qqqqqq qqqqqqq qqq qq qq qq q qqqq qq q qqqq qqqqq qqqqq qqq qqqqqqqq qq qq q q qqq qqq q qqqqq qq q qq qqqq qq q qq qqqq qqqqqqqqq qq qqq qqqqqqqqqq qq q qq qq q qq qqq qq qqqq qqq q q q qqqq qq q q q qq qqqq qqqq qqq qq qqqq q qqqqqq qqq qqqqqq qqqqq qqq qqqqqqqq qqqq qqq qq qq qqqq qqqqqq q q qqq qqq q qqqq qqqqqqqqq qqq qqqq qq qqqqqqqqqqqq qq qq qq qqq q qqqqqq qqq qqq qq q qqqq qqq qqqqqqq q q q qq qq q qqqq q qqqqqq qqq qq q qq qqqqq q q q qqq qq qqq qq q qqqqqq qqq qq qqqqqqq qqqq qqqqqqqqq qq qqqqqqqqq qqq qqq qqqq qqqqqqqqqq qq qqqqqqqqqqq qqqqq q q qq q qq qqqq q q qqqqq qqq qqqq qq qqqqqqqqqq qq qq q qqqqq qq qqqqqqqqqqqqq qqqq qqq qq qq q q qqq qqqqqqqqq qq qqqqq q q qqq qqqqqq qqq qq qqq qqqqq qq qqqq qq qq qqq qqqqq qqqqq qqq qq qq qqq qqqq qqq qqqqq qq qq q qqqq q qqq qqqqqq qqq qqq q qq q q qqq qq qqqq qqq qqq qqqqq q qq q qq qq qqqqq qq qqqq qqqqqq qqqq qqqqqqqqqq qqqq qq qqqqq qq qq qqq qqqqqq qq q qqqqqq qqqqqqq qqqq qqqq q q q qq qqq qq qqq qqqqqq q qq qq q qqqq qqqqq qq qqq q qqqqq qqq qqq q qqqqq qq qqq qqq q qq qq qqqqqqqqqqq qqqq q qqq qq qqq qq qq qqqqq qqq qqqqq qqqqqq qqqq qq qqqqqqqqq qqqq qqq qqqqqqqq qqq qqq qq qqqq qq q qq qq qqqqqqqqqqq qqqqq qqqq qq q q qqq qq q qqqqqq q qqq qq qqqqqq qqqqqqq q qqq qqqqq qq qq qqqqqqq qqq qqqqqqq q qqqqqqqqqq qqqq qq qqq qqqqq qq q qqq qqq qqqqqq qq q qq q qqqq qqqqqq qqqqqqq qq q qq qq q qq q qqqq qqq q qqqqq q q qqq q qqqq qq qqqqqqqqqq q qqq qqqqqq qqqqqqqqqqq qqqqqqq q q qqq qq q qqq qqqq qqqqqqqqqq qq qq qq qqqq qqq q qqq qqqq q qqqq q q qqqqqqqqqq q qqqqq qq q q q q qqq qq qqq q qqq qqqqqqqqqqqqqqq qqqqqq qqqqq qqq qqqqqqq qq qq qqqqq qqqq qq qqq q qq q qqq qqqqqqqq q qqqqq qqq qqqqq qqq qqqq qqq q qqq q qqqqqq q q qqqq qq qqqq qqqqqqq qq qq qqqqqqqq qqqqqq qqq q qqqq qq qqqqqq qq qq qq q qqq qqqqqqq q qq qqq qq qqqqqq q qq qqq qq q qq q qq qqq qq qqqq qqqqq qqqqqqqq qqqqqq qqqq qqq qq q q qqqqqqqq qqqqqqqq qqqq qqqqq qqqq qq qqqqqqqqqqqqq qqq q q q qq qq qqqqqqq qq q qqqqq qqq qq qqq qq q qq q qqqq qqqq qqqqqqq qqqq qqq q qqq qqqqqq qqqq qqq qqq q q qq qqq qqqq q q qq q qqq qq qq qqq q qq qq q qq qqqq qqq q q qqq qq qq q qqqqqqq q qq qq q qqqq qqq qqqq q q qqq qqqqq qq qqq q q q q qq qq qqqq qqqq qqqq q qqq qqqqq qq qqqq qqq q qqqq qq qqq qqqq qqqqqqqq qqqqqq q qq qqq qq q qq qq q qq q q qqq qqqqqqqqqqq qqqqqqqqqqqqq qqqq q qq qqq qq q qqq q qq qqqqqqqq q qqq q q qqqqq qq qq q qq qq q qq qqqqq qqq qqq q qq qq qqqqq qqqqq qqq qqqq qqq qq q qqqqqq qq q qqqq q qqqqqqqq q qq qq q qqqqqq q qqqq qqqq qqq qq qqq q qqqq qqqqq qqqqqqqqq qqq qqqqqqqq q qqqqq qq q q q qq q q qqq qqq q qq qqqq q q q q qq qq q q qqq qq qqq qq qqqqqqq qqqq qqq qq qq q q qq qqq qq qq qqqq qqq qqqqqqq qq qqq qqq q q qqq qqq qqqq q q qq qqqqqq qqq qqq qqq qqqq q qqqqqqq q qqqqqqq qqq qq qqqq qqqq qq q qqq q q qq q q q q q q q qqqq q qq qqq qqqqq qqqqqqqqqq q q qqqqqqq qqqqqqqqq qqqq q qq qqqq qqqqq qqqq qq q qq qq qqqqqqqq qqq q q q qqqqqq qqq qqqqqq qqqqq qqqq qqqq qqqq qq qq qqqqqq qq qq qq qq qq qq qq qq qq qqqqq qqq qqqq qqq qqqqqqqqqq qqqqqqqq qq q qqqq qqqq q qqqq qq qq qqqqq q qq q q q q q qqqqq qq q q qq q qqqqqq qqq qqq q q qqq qq qqqqqqq q q qq qqqqq q q qqqq q q q q qqqqqq qq qq qqq qqqqq q q q q q qq qq q q q qqq q qqq qq q q qqq qq qqqq qq qqqqqqq qqqqqq qqqqqq q q q q q q q q q qq q qqqqq q q q qq qq qq qqqqq qqq qqqq qqqqqq qq qqqqqqqqqqqqq qq q q qq qq qq qq qqqqq q qq qq qqqqqqq qqqq q q qq qqq qq q qqqq q qqqqqqqq qqqqqqq qqqq qq qqqq q q qq q qqqqqq q qq q qqq qqq qqqq qqq qq qqqqqqqqqq qqq qqqqqq qqq q qq q q qq qqqqqq qq q qqqq q qqq qq qqq −0.04 0.02 0.08 0.0000.0100.020 animal2 Dominance relationship Additivebydominancerelationship q qqq q qqq qqq qq qqqq q qqqq q qqqq qqq qqq qq qq qqqqqqqqq qq qq q qqqqqqqqqq q q qq qqq qq qqqq qqq qq qqqqq qqq qqq q qq qq qq qqq q q qqq qq qqqqqqqqq qq qq qqqq qq q q q qqq qq qq qqqq qqqqqq qqq qqqqq qq q qqqqqqqqqqq q q qqqqq qqqq qqqq qqq qqq q qqq qq qqqqqq q qqq q qqqqqqq qq qqq q q q qqqq qqqq q q qqqqqqq qqq qqqqqqqqqqq qqqqqqq q qqq q qqqqq qq qqqqqq qqqqqqqqq qqqqqq q qqqqqq q qqqqq qq qqq qqqq qqqqqq qqqqqqq q qqqqq q qqqq qqqqqqq qq qqqqq q qqqqqqqqq q q q q qqq qqq qq q qq q qqqq q qqqqqqqq qq qqq qqqq qqqqqqq q q q qqq q qqqq q qqqqqq q qqq qqq qq qq qq q qqqq q q q qqqq qq qqq qqqqq qqqqqq qqqqq qq qqq q qqqqqq qqq qqqqqqq qqqqq qqqqq qqq qqqq qqqqq qq qqqqqq qqq qqqqqqqqqqqqqq qqqqqqqqq qqq qqq qqqqq qqqqqq qqqqqq qq qq q qqqq q q qq qq qqq qq qqqqq qqq qqqqqqqqqqqqqqqqqqqqq qqqqq qqqqqqq qq qqq qqqq q q q q qqq qqqq qq qq qqqqqq qqq qqq qqqq qqqqq qqq qq q qqqqqqqq qqqqqqqqqq q qq qqqq qqqqqq qqqqqqqqqq q qq qqqqqqqqq qqqqqqqqq qqqqq qqq qqqq qq qqqq qq qq q qqq qq qq q qqq qqqq qq qqqqqq q qq qqq q qq qqq qqqq qq qqq qq qqq qq qqqq qqqqqqq qq q qqq q qqqqq qqq qq qqq qqqqq qqq qqq qq qqqqqqq qqqq qq qqqq qqqqqqqqqqqqqqq q qq qqq qq qqqqq qqqq qqqqqq qq qqqq q q q qq qqqq qq q q qq qqqqqq qq qqqqqqq q q qqqq qqq qqqqqqqq qq qq qq q qqq qq q qqqqqq qqqq q qqq qqqqqqq qq qqqqqq qq qqqqqqqqq q qq q qqqqq q qqq qqqqqqqqqqq qqqqqq qqqq qqq qq qq qqq qqqqqq qqqqqq qqqq q qq qqqq q qqqq qqqqq qq qqqqqqq qqq qqqq qq qq qqq qqqqqqq qq qqqqq q qqq qqqq qq qqq qq qqq qqqqqqqqq qq qqq qq qqq q qq qqqq qq qqqqqq q qqq qqqq qq qqqqq q q qqqqqq qq q q qqq qq qq qqqqqq q qq q q q qq qqqqq qqqq q qqq qqqqqqqqq qqq qqqqq qqqqqq qq q qq q qqqqq q q q q qqqq q qqqqqqqqqqqqqq qqqqqqqqq qqqqqqqq qq qqqqqqqq qq qqq qq qqq qqqq qqqqq qqq q qqqq q qq qqqq q qq q q qqqqq qqqq qqqq q q qqqq qqqqq qqq qqq qqq qqqqqqq qqq qq qqq qqqqq qqqq qqqqqqqqqqqqq qq qqqq qqqq qqqqqqqqqqq q qqq qqqqqq qqqqqqqqqq qqqq qqq qq qqqq qqqq qqq q qqqqqqqq qq qqqq qqq qqqqqq qq q q qqq q qqqqqqqqqqq qq q q q qqq qq q qq qqqqqq qqq q q qqqqqqqqq qqqqqq qq qq qqqq qq qqqqqq q qqqq qq qq q qqqqq qqqq q qqqqqqq qq qq q q qq qqqqq qq qq qqq q qqqq qqq q qqq qqqqq q qqq qqq qqqqqqqqq qq qqq qqqqq qqqq qqqqq qqqq q qqqq qq q q qq qqqq q qq q qqq qq qq qq qqqqq qq qqqqq q qq q qqqqqqq q qqq qqqq q qqq q q qqqqq q qq q qq qqqqqqq qqq qqqq qq qqq qqqqqqq q qq qqqqq q qq qqq q q q qqqq qqqqqqq qqqqq qqqq qqqq qq q qqqqqqqqq q qqqq q q qqqqqqq qqqqqqqqqqqqqq qq qqqqq qqqq qqqqq qqqqqq q qqq qq qqqq qqq q qq qq qqq qqq q qqq qq qqq qq q q qqqqqqq qqq qq qqq q qqqqqq qq qqqqqqqq qqqq qqqq qq qqqq qqq qqq qqqq qq q q qq qq qqq qq qq qqqqqqqqq qqqq qq qqqqq qqq qqq qq qqqqqq qqq qqqq q qq q qqqqqq qqqq q qq q qq q qq qq qqqq q q qqq qq qq q qq qqqqqqqq qq qqq qq qqq q qqqqq q qq q qqqq qqqqqqqqq qq q qq qq q qqqq qqq qqqq qqqq qq qqqqqqq qq qq q qqqqqqqqqqq qqqqqq q q q q qq qqqqqq q qqq q q q qqqqq q qqq qqq q q qqq qqqqqqq qq q qq q q qqqqqq q q q q qq qq qqq qqqqqq qqq qqq qqqqqq qq qq q qq qq q q qq qqq qq qq qqqqqq q qq qqq qq qq qq qq qq qq qqqqqqqqqq qq qqqq qqqq qq qqqqqq qq q q q qqqqq qqq qq qqq qqq qq qqq qqqqq qqq q qq qq qqq qq qq qqqqq qq q q q q qq qqq qqq q qq qqqq q qqq q q qqq qqqq q qqqq qqq qqq qqqq q qq qq qqq qqqq qqq qq q qqqqq qqqq qqqq qq qq q qqq qqqqq qqq qqqqqq qqqq qqqqq qqq q qqqqqqq qqq qqqq q qqq qqq q q qq qqqqq qqqqqq q qq q qq qq q q qqqqqqq q qq qqq qqq qq q qq qq qqqq qq q qq q q qqq q q qqqqq q q qqqq qqqqq qqqq qqqqqq qq qq q qqqqqq qq q q q qqq qq qqqq qqq qqq qqq qq q qqqq qq qq qqqq qq qqqqqqqqqqqq qqq qqq qq qq q q qqqqqqqqq qqqqqqq qqq qqqqq qqqqqq q q qqq q qq q qqqqqqq qqqq qqqqq q qq qqq q q qq qqqqqqqqq qqq qqqqqqqqq qqq qq qqqq q qqqqqq qq qqqqqq qq q q qqqqqqqq qqqqqq qq qqq q qq q qq q qqqqqq q qqq qq qq q q q q q qqq qqq q qqqqq q qq qqqqqqq qq q qqqqq q qq qqqqqqqq q qqqq q qq qqqqq qqq qq qqqqqqqqqqq q qqq qq qqq qq qq q q qqqqqqqq qqq qq qq qqqqqq qqq qq qq qqq q qq qqq qqqq q q q qq qqqqqqqqqq qqqq qqqq qq qqqqqqqq qq q qqq qqqqqqq qqqqq qqqqq qqqqqqq qqq qqqq q q q qq qq qq q q qqqq qqq qq q q q q q q q qqqqq q qq q qqq qqqqqqqqq qqq qqqqq qqq qq q qqqq qqq qq qqqqqq qqqqqqqqqqqqqqq qq q qqqq qqqq q qqqq q q qq qqqq qqq q qqq qqqqqqqqq qqqqqq qqq qq qqq qqqqq qqq q qqqq qqqqq qqqqqqq qqqq qqqqq qqq qqq qqqqqqq qqq qqq qqqq qq qqq q qq qqqqq q q qq qqqqq q q q qqqqq q qqq q q q qqqq q q qqq qqqqqq qqq qqqqqqqqq qq qq qqqq qqqqqqqqqqqqqqqqq qqqq qq qqq qqqq qqqqqqq qqqqq qqq q qqq q qq qq qq qqq qqqq qqqqq qqq qqq qq qq qq qqqqq qqqqqqqqqqqqqqq q q qqq qqqq qqqq q q qq qqqqqqq qqq q qq qqq qq qqqqq qqq qqqqqq qq qqq qqqq qq qq qq qqqqqqq qqqqqqqqqqqq qqqqq qqqq qq q qq q qqqq qqqq qqq qqqq qqqq q qqqqq qq q qqqqq qqq qq qq qqq q qqq qq qqq qqq q q qqq qqqq qq q qqq qqq qqqqq qq qqq qq qqqqqqq qqq q qq qq q q q qq qqqq qq qq qqqq qqqqq qqqqqq qqqqqqqqqqq qqq qqq qqqqq q qqqqq qqq qqqqqq qq qq qqq qq qqq qq qqqq qq qq qqq qq q qq q qqq qq qqqqqqq qqqq qqqq qqq qq q qq qqq q qqqqq qq qqq qqqqqq qqqqq qqqqq qqqqqq qqqqqqqq qq qq qqqqqqqqq qqq qqq q qq qq q qqq qq q qqqqq q qq q qqq qqq qq q q qq q qqqq qqqqqq qqqqqqqq qqqqqqq q q qqq qqq q q qq qq q q qqq qq qqqqq qqq q q qqqq qqq qqq q q q q qqqqqq qq q qq qq qqqq q qqq q q q qqq q qqqqq q qq q qqq qqq q q q qq q q q qqqq qq qq q qqqq qqq q q q qqqq qqq qqq qq qqq qqq q q qqqqq q q qq qqqq q qqqqqqqqqq q qq qqqqqq qqq qqqqqq qqqq q q q qqqqqq qqqq qqqqqqqqqqqqqqq qq qqqq qqqqq qqq qqqqqq q q qqq qqq q q qqq qqqq q q q qqqq q qqqq qq q qq qqqqq qqqq q qqq qq q q qqq qqqqqq qqq qq qqqqqq qqq qqqqqqqqqqq q q qqqqqqqq qqq qq q qq q qq qq qqq q q qqqqq qq qqqq qq qq qq qq qq q q qq qqq qq qqqqq q q q q qqqq q q qq qqq q qq qq qqqqqqqq qq qq q q qqq q qq qqqqqqq qqq q qqq q q qqqqq qqq qqq qq qqqqqqqq q qq qq q q qq qqqqqqqqqqqq q qqqqqqq qq q q qq q qqqq qqq q q q qq qqqq q q q m m 18 31
  19. 19. Predictive correlations for six health traits Traits Types Kernels G GKA GKD GKALL ALL KET PCP 0.16 0.18 0.16 0.19 0.18 EBV 0.85 0.86 0.84 0.87 0.86 DA PCP 0.07 0.08 0.07 0.08 0.07 EBV 0.59 0.61 0.53 0.59 0.60 RP PCP 0.03 0.05 0.05 0.06 0.05 EBV 0.65 0.67 0.60 0.66 0.65 LAME PCP 0.07 0.08 0.04 0.07 0.05 EBV 0.64 0.66 0.58 0.65 0.64 METR PCP 0.05 0.07 0.04 0.05 0.05 EBV 0.48 0.52 0.43 0.50 0.49 CM PCP 0.07 0.08 0.05 0.07 0.07 EBV 0.72 0.74 0.68 0.73 0.73 19 / 31
  20. 20. Part 4: High-density genotyping chips • Cattle Figure 5 : 50K SNP array (2007) Figure 6 : 778K SNP array (2010) • Chicken Figure 7 : 60K SNP array (2011) Figure 8 : 600K SNP array (2013) 20 / 31
  21. 21. International Sequencing Consortiums Figure 9 : Human (2001) Figure 10 : Chicken (2004) Figure 11 : Bovine (2009) Figure 12 : Swine (2012) Coding DNA sequences cover only tiny fraction of the entire genomes. The role of non-coding sequences? 21 / 31
  22. 22. Functional? Figure 13 : FANTOM (2000∼) Figure 14 : ENCODE (2003∼) Figure 15 : Evolutionary genetics Figure 16 : Quantitative genetics?? Which genomic regions are influential in the context of quantitative genetics? 22 / 31
  23. 23. Methods • Data • 1,351 chickens (Aviagen Ltd. ) • body weight at 35 days (BW), ultrasound area of breast meat (BM) and hen house production (HHP) • Affymetrix 600K chips (580,954 SNPs) • Kernel-based Bayesian ridge regression • (α|λ) = ||y − Kα||2 + λ||α||2 • 600K → n • 10 fold CV Purpose of this study Which genomic regions play an important role in prediction of complex traits? 23 / 31
  24. 24. Genomic regions Physical positions of SNP were mapped to Gallus gallus 4.0 assembly • genic vs. intergenic regions (IGR) Figure 17 : Illustration of intergenic DNA (Wikipedia) • 5’ and 3’ UTR, exon, intron Figure 18 : Gene structure (Wikipedia) 24 / 31
  25. 25. Annotation Table 1 : Numbers of SNPs assigned to each genomic region. Annotation # of SNPs annotated after filtering IGR 299,498 193,970 Genes ± 1kb 281,455 184,047 Genes 266,947 183,768 Exons 29,764 19,511 CDS 21,975 14,416 Genomic region specific kernels • All → K0 • IGR → K1 • Genes±1kb → K2 • Genes → K3 • Exons → K4 • CDS → K5 25 / 31
  26. 26. Body Weight (BW) All CDS Exons Genes Genes1kb q q q 0.16 0.18 0.20 All CDS CDS−IGR Exons Exons−IGR Genes Genes−IGR Genes1kb Genes1kb−IGR Genomic regions Predictivecorrelation 26 / 31
  27. 27. Breast Meat (BM) All CDS Exons Genes Genes1kb q q 0.25 0.26 0.27 0.28 0.29 All CDS CDS−IGR Exons Exons−IGR Genes Genes−IGR Genes1kb Genes1kb−IGR Genomic regions Predictivecorrelation 27 / 31
  28. 28. Hen House Production (HHP) All CDS Exons Genes Genes1kb q q q 0.19 0.20 0.21 0.22 0.23 0.24 All CDS CDS−IGR Exons Exons−IGR Genes Genes−IGR Genes1kb Genes1kb−IGR Genomic regions Predictivecorrelation 28 / 31
  29. 29. 3D Chromosome Structure Figure 19 : Lieberman-Aiden et al. (2009) Science. 29 / 31
  30. 30. Ph.D.-wide Conclusions No single approach stands out (traits dependent) Figure 20 : Methods Figure 21 : Kernels ⇓ Functional genomics + quantitative genetics 30 / 31
  31. 31. Acknowledgements Advisor • Daniel Gianola Committee • Corinne Engelman • Guilherme Rosa • Grace Wahba • Kent Weigel Data • USDA-AIPL • CIMMYT • Aviagen • Zoetis Animal Genetics group • 4th floor • 6th floor 31 / 31

×