Whole-genome prediction of complex traitsusing kernel methods

Gota Morota

May 12, 2014

1 / 31

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 genomeannotation

• Part 5: Ph.D.-wide Conclusions

2 / 31

Quantitative genetics – related individuals

Figure 1 :

3 / 31

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

How to parameterize response variable y ?

1. prediction of additive genetic effects• y = E + a + ε

2. prediction of total genetic effects parametrically• y = E + a + d + a ∗ a + a ∗ d + d ∗ d︸ ︷︷ ︸

g

+ε

3. prediction of total genetic effects non-parametrically• y = E + g + ε

5 / 31

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

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: Matern kernel

• DK: Diffusion kernel

⇓

In non-parametric kernels, choice of the metric determinescharacteristics of a kernel

7 / 31

Example of kernel methods: Genomic BLUP

y = g + ε (where g = Xβ) (1)

BLUP(g) = [I + (XXT )−1σ2ε

σ2β

]−1y. (2)

Under common marker variance assumption,

σ2β =

σ2g

2∑

j pj(1 − pj)(3)

Then, BLUP(g) = [I + G−1σ2ε

σ2g]−1y (4)

where G = XXT

2∑

j pj(1−pj)→ Is this the best kernel??

8 / 31

Euclidean space – Gaussian Kernel

Euclidean distance is a metric on a metric space called Euclideanspace

Figure 2 : 3-dimensional Euclideanspace. −∞ ≤ (X ,Y ,Z) ≤ ∞

Suppose, we observed twoindividuals with 3 SNPgenotypes.

• 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

Diffusion on 3 dimensional graph (Morota et al., (2013))

0 1 2

01

2

0

1

2

1st Genotype

2nd

Gen

otyp

e

3rd

Gen

otyp

e(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 inp-dimensional space. → spatial distance

10 / 31

Bayesian kernel ridge regression

A quantitative genetics decomposition is

yi = g(xi) + εi (5)

‖y − g‖2 + λ‖g‖2H

(6)

• The representer theorem is used to find the optimal g.

`(α) = ‖y − Kα‖2 + λ‖Kα‖2H

(7)

Here, g = Kα, is the function that minimizes (7).

• ‖Kα‖2H

= α′Kα, so that the function to be minimized is

`(α) = (y − Kα)′(y − Kα) + λα′Kα. (8)

11 / 31

Kernel Averaging (Multiple Kernel Learning)

• Fit three kernels simultaneously: K1, K2, and K3

K = K1σ2

K1

σ2K

+ K2σ2

K2

σ2K

+ K3

σ2K3

σ2K

• Example 1: Three Gaussian kernels: GK1, GK2, and GK3

K = GK1

σ2GK1

σ2K

+ GK2

σ2GK2

σ2K

+ GK3

σ2GK3

σ2K

• Example 2: Three parametric kernels: G, D, and G#D

K = Gσ2

G

σ2K

+ Dσ2

D

σ2K

+ (G#D)σ2

GD

σ2K

12 / 31

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

Averages of kernel elements and their predictivecorrelations for the Holstein data

Kernel θ k(xi , xj) Cor(ytest , yPTA )DK 10 0.138 0.727

11 0.483 0.74511.5 0.644 0.73912 0.765 0.73913 0.907 0.73414 0.966 0.729

GK 5 × 10−5 0.237 0.7212 × 10−5 0.551 0.7361 × 10−5 0.749 0.7425 × 10−6 0.866 0.7363 × 10−6 0.917 0.7341 × 10−6 0.971 0.729

G1 NA -0.000126 0.729G2 NA -0.000113 0.730

14 / 31

Averages of kernel elements and their predictivecorrelations for the wheat data

Kernel θ k(xi , xj) Cor(ytest , ytrain)Diffusion 3 0.136 0.586

3.25 0.289 0.5803.5 0.466 0.5774 0.752 0.5475 0.962 0.522

Gaussian 0.005 0.134 0.5820.003 0.290 0.5790.002 0.434 0.5620.001 0.655 0.5580.0005 0.809 0.556

G1 NA -0.003 0.518G2 NA -0.003 0.521

15 / 31

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 andnon-parametric kernels

Methods

• Bayesian kernel ridge regression (RKHS method)

• Cross-validation

16 / 31

Estimated ratios of variance components (weights)

Traits Types Variance ComponentsVG/VP VD/VP VGD/VP

KETPCP 0.09 0.13 0.14EBV 0.25 0.03 0.01

DAPCP 0.06 0.09 0.25EBV 0.39 0.04 0.30

RPPCP 0.05 0.09 0.35EBV 0.27 0.03 0.07

LAMEPCP 0.06 0.07 0.39EBV 0.39 0.03 0.27

METRPCP 0.06 0.07 0.21EBV 0.31 0.05 0.42

CMPCP 0.06 0.07 0.26EBV 0.36 0.02 0.16

17 / 31

Scatter plots of relationships among G, D, and GD

●●

●

●

●

●●

●

●

●

●●

●

● ●●

●

●●

●

●

●

●

●

●

●

● ●

●

●● ●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●●●●

●

●

●●●

●

●

●

●

●

●

●●

● ●

●

●●

●

●●

●● ●

●

●

●● ●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

● ●

●

●

●

●●

●

●●

●

●

●

●

●●

●●

●

●●

●

●●●

●●

●●●

●

●●

●

●

●●

●●

●

●

●

● ●●●

●

●

● ●●

●●●

●●●

●●●

●●

●

●

●●

●

●

● ●

●

●

● ●

●

●●●

●●

●

●

●

●

●

●●

● ●●●

●

●

●

●

●●●

●● ●● ●●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

● ●

●

●

●

●

●

●●

●

●

●

●

●

● ●●

●

●●

●●

● ●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●● ●●

●●

●

●

● ●

●

●

● ●●

●●

●

●

●●●

●

●●

●

● ●

●● ●● ●●

●●●

●

●

●

●●●●

●●

●

● ●

●

●

●●

●●● ● ●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●●●●●

●●

●

●●

●●

●

●●

●●

●●

●●●

●●●

●

●

●

●●

●●

●●●●●

●●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●●

●●

●

●●

●●

●

●

●●

●

●

●

●

●

●

● ●●

●●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●

● ●●

●

●●

●

●

●●

●

●●

●●

●

●

●

●

●

●●

●

●

● ●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●●

●

●●●

●●

●●

●

●●

●

●

●●

●

●●

●●

●

●●

●

●●● ●

●

●

●

●●

●●

●

●

●

● ● ●●

●

●

●

●

●●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●●

●

●●●

●

●●

●●● ●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●●

●

●

●

●●●● ●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●●

●●

● ●

● ●

●

●●

●●

●

●●●

●

●

●●

●

●

●

●

●

●

●● ●

●

● ●●

● ●

●

●

●●

●

●●

●

●

●

●

●●●

●●

●●

●●

●●

●

●

●

●●

●

●●●

●●●● ●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●●

●

●●

●

●●●●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●●●●

● ●●

●

●●

●

●●●

●

●●

●●

●

●●●

●

●

●● ●

●

●●●

●

●

●

●

●●

●

●●●

●●

●

●

●

●●

●●

●●●●

● ●

●

● ●

●

●●

●

●

●●

●

●●

●●●

●●● ●

●

●

●●

●● ●

●●●

●

●

●●●

●

●

●●

●●●

●● ●

●

●

●

●●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●

●

●

●●●

●

●●

●●●

●●

●

●

●

●●

●

●●

● ●

●

●

●

●●

●

●

●

●

●

●● ●

●

●

●

●

●

●

●

●

●

●●

●●● ●

●●●

●●

●●

●

●

●●

●●●

●●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

● ●●

●

● ●●●

●

●

●●

●

●

●

●

●

●

●●

●

●

● ●●●●

●

●

●●

●

●

●

●●

●●●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●●

●

●●●●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●●

●

●

●

●●

●● ●●

●

●●

●

●●●

●

●

●●●

●

●●●●

●

●

●

●

●

●●

●

●

●

●

●●●●● ●

●●

●

●●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●● ●

●●

●●●

●

●

●

●

●●

●

●●

●

●

●●

●●●

● ●●●● ●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●●

●

●

●●

●

●

●●

●

●

●●

● ●●●●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●●

●

●

●●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●● ●

● ●●

●

●

●●●

●

●●●

●

●

●

●●●

●

●●

●●

●

●

●

●

●

●● ●

●●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●●

●

●●●

●●

●

●

●

●

●●● ●●●

●

●

●

●

●●

●●

●

● ●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●●

●●●●

●●

●

●

●●

●

●●●

●

●

●

●●

●

●●

●

●

●●

●

●

●● ●

●●●

●

●

●

● ●

● ●●

●

●

●

● ●

●

●

●●

●

●

●

●

●●

●●

●●

●●

●●

●

● ●●

●

●

●

●●

●

●

●

●

●●●●

● ●●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●●

●

● ●●

●

●●

●

●

● ●●●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●● ●

●

●●

●

●●

●

●

● ●

●●●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●●●

●●

●●

●●

●

● ●

●

●●

●

●

● ●

●

●

●●●

●●

●

● ●●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●●● ●

●

●

●

●

●●

●

●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●●●

●

●

● ●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●●

● ●●

●●●

●●●

●●

●

●

●

●●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●●●

●●●

●

●●●

●●

●●

●

●●

●

● ●

●●●

●

●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

● ●

● ●●●

●●

●

●●●●

●

●

●

●●

●● ●

●●

●

●

●●

●

●●

●●

●

●●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●●

●●

●

●

● ●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

● ●

●

●

●

●

●

●●

●

●

●●

●●

●

●●●

●

●

●

●●

●

●

●●●

●

●

● ●●

●

●

●●

●●

●

●

●

●

●● ●●

●●

●

●

●

●

●

●●

●

●

●

●●●●

● ●

●●

●● ●●●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

● ●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●●●

● ●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●

●●

●●

●

●●

●●●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●●●● ●●

●●

●

●● ●●

●

●

●●

●

●

●

●

●●

●

●

●●

●●●●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●●

●●

●●●

●

●●

●●●●

●

●

●●

●●

●

●

● ●

●●

●

●

●●●●

●

●

●

●

●

● ●

●

●

●●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●

●●

●●

●●●●

●

●

●

●

●

●

●

●

●● ●

●

●

●

●

●●

●

●

●●

●

●

●

●● ●

●

●

●

●

●●

●●

●

●●

● ●

● ●

●●

●●●

●●

●

●

●● ●●

●

● ●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●● ●

●●

●

●

●●

●

●●

●

●

●

●●

●●

●

●●

● ●● ●●

●●

●●

●

●

●

●●

●

●

● ●●

●●

●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●

● ●

●● ●

●●

●

●

●●

●● ●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

● ●

● ●● ●●

●● ●

●

●●●

●●

●

●

●

●●

●●●

●●●

●

●

●

●

●●

● ●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

● ●

●●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

● ●●

●●

●

●

●

●

●●

●

●

●●●

●

●●●

●

●●

●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●

●

●

●●

●●

●

●●●

●●

●

●

●●

●

●●

●

●●

●

●

●●●●

●

●

●

●●

●

●

●

●

●●

● ●

●●●

●

●

●

●

●

●●

●

●●

●

●●

●●

●

●● ●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●● ●

●●

●●

●

●●

●

●●

●

●●

●

●

● ●●●

●

●

●

●

●

●●●●

●●

●

●

●●

●

●

●

● ●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●●

●

● ●

●●

●●

●

●

●

●

●

● ●

●●

●●●

●●

●

●

●

●●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

● ●

●

●●

●● ●

●●

●

●

●●

●● ●

●

● ●● ●●

●

●●

●●●

●

●

●

●

●●

●

●

● ●●

●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●●

● ●●

●●

●●

●●●

●●●

●

●●

●

●●●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●●

●

●●

●

●

●●

●

●●●●

●

●

●

●●

●

●

●●●●

●●

●

●●●

●

●

●

●●

●

●●

●●●●

●

●●

●●

●

●●

●●

●

●●●

●

●

●

● ●●

●

●

●

●● ●

●●

●

●

●

●

●

●

●●

●

●

●●●

●●●

●

●●

●

●●

●

●●

●

●●●

●●

●●

●

●●

●● ●●

●

●

●

●

●

●

●

●●

●●●●●

●

●●●●

●●●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●●●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●●●

●●

●

●●●

●●●

●●

●

● ●●●

●●

●●

●●

●●

●

● ●●

●

●

●

●

●

● ●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●●

●●

●

●●

●●

●

●

●

●●●

●

●

●●

● ●

●

●

●

●

●

●

●

●●

●

●●

●

● ●

●

●●

●

● ●●●

●

●●●

●●

●

●●

●

●

●●●

●

●●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●●

●

●●●

●●

●●

●

●●●●

●

●

●

●

●

●●●●

●

●

●

●●

●

●

●

●

●● ●

●

●●

●

●

●●

●●●

●

●

●

●

●

●●

●

●

●

● ●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●● ●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●●●

● ●

●

●

●●

●●●

●

●●

●

●

●●●●

●●●●

●

●

●

●

●

●

●●

●

●

●

●

●● ●

●

●●

●

●●● ●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●●● ●

●●

●

●

●

●

●

●●

●●

●●

●

●●

●

●●

●

●

●

●●

●● ●●

●

●

● ●

●●

●

●

●●●

●

●

●

● ●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●●

●●

●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

● ●

●●

●●

●

●

●●

●●

●●

●●●

●

●●

●●

●●

●

●●●

●

●

● ●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

● ●

●

●

●●

●

●

●●

●●●●●

●

●

●●

●

●

●●

●

●

●●

●

●●

●

● ●

●

●

●

●

●●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●● ●

●●

●

●

●●

●

●●

●

●●

●

●

●

●

● ●

●

●

●

●●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●●

●

●

●●

●● ●

●

●

●

●

●

●

●●

●●

●● ●

●●●

●

● ●●

● ●

●● ●●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●●

●●

●

●

●

●

●

●●

●

●●

● ●●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●

●●●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●●

●

● ●●●●

●●

●

●

●●●●

●

●

●

●

●

●

●●●

●

●

●●

●●

●

●

●● ●

●

●

●●

●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●●

●

● ●

●●

●

●●

●

●

●●● ●

●

●

●

●

●●

● ●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●●●

●

● ●●●●●

●●

●●

●●

● ●

●●

●

●

●

●

●●

●

● ●●

●●

●

●●●

●

●●●●

●

●●

●

●

●●

●● ●●● ●

●

●

●●

●

●

●●

●

● ●●

●

●●

●●

●●

●

●

●

●●

●

●

●

●● ●

●●

●

●

●●

●●

●

●

●●

●

● ●●●●

●

●

●

●

● ●●

●

●●

● ●●

●

●

●

● ●

●●●●

●

●●

●

●●

●

●●●●●

●● ●

●●●

●

●

●

● ●

●●

●●●

●

●●●

●●

●

●

●

●

● ●

●

● ●

●

●●

●● ●●

●

●

●

●

●●

●

●

● ●

●

●

●●

●●

●●

● ●

● ●●

●●●

●

●

●

●

●

●

●

●

● ●

●●

● ●●

●

●●

●●

●●

● ●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●●

●●

●

●

●

●●

● ●

●

●

●●●

●●

●●

●●

●

●●

●

●●

●

●●

●

●

●●●●

●

●

●

●

●

●

●●●●

●●

●●

●●●

●●

●

●

●

●●

●

●

●●

●

●

●●

●

●●

●●

●●

●●

● ●

●

●●● ●

●●

●

●●●

●

●●

●●

●

●

●●

●

●●●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

● ●●●

●●

●●

●●

●

●

●●

●

●

●●

●●

●●

●●●

●

●

●

●●

●

●●●

●●

●●

●

●

●● ●

●●●

●●●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●● ●

●

●●

●

●

●

●●●

●●

●

●●

●●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●●

● ●

●●●

●

●

●

●●●●

●

●●

●●

●

●

●● ●

●

−0.05 0.05

−0.

040.

000.

04

animal1

Additive relationship

Dom

inan

ce r

elat

ions

hip

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●●

●●

●

●

●●●●●

●●

●●●

●●●●

●

●

●●●●

●

●

●●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●●

●●

●

●

●●●

●

●

●●

●●

●●●●

●

●●

●●

●

●

●

●●●

●

●

●

●●●●

●●

●

● ●●

●

●●●●

●●

●

●●

●

●●●●●●

●●

●●

●

●

●●●●

●●●

●

●

●●

●

●

●●

●●●

●●

●

●● ●

●

●

●●

●

●●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●●●●●●

●

● ●●●●●●

●

●●

●

●●●

●

●●

●

●●

●●

●

●

●

●●● ●●

●●

●

●

●

●●● ●● ●●●●●

●

●●●

●●

●●●

●●

●

●

●

●

●● ●

●●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●●●●

●●●

● ●

●●●

●

●

●●

●

●●●

●

●

●●

●● ●

●●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●●

●

●

●

●

●●

●● ●●●●

●

●●●

●●

●

●

●●

●●

●●

●●●

●

●●●

●

●

●

●

●●●

●

●●●

● ●●

●●●●

●

●●●

●

●

●

●●

● ●

●

●

●●

●

●●

●

●●●●●●

●

●

●●

● ●●

●

●

●●●

●

●

●●● ●

●

●

●

●

●

●

●

●●

●●

●●●●

●

●

●●

●

●●

●

●

●●●

●

●●

●

●●

●

●●●●●●

●●

●

●

●

●●

●

●

●●

●●

●●

●

●●●●

●

●

●●●

●

●

●●

●●●

●

●●

●

●●

●●

●●●

●

●

●●●

●●

●●

●●●

●

●● ●●

●●●

●●●● ●

●

● ●

●

●

●

●

●

●●

●

●●

●●

●

●●●

●●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

● ●●●●

●●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●●

●●

●●●●

●

●●●

●

●●

●●●●●●●●●

●

●

●●●

●●

●●●

●

●●

● ●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●●●●

●●

●●●●●● ●●●

●

●

●●

●●

●

●

●●

●●●

●

●

●● ●●

●●

●●

●

●

●●

●

●

●●●

●●●

●●●

●

●

●

●

●

●

●●●●●

●●

●●●

●

●

●●

●●

●

●

●

●●●

●●

●

●

●●●●●

●

●●

●

●

●●

●

●

● ●●

●●●●●●

●●●

●●●

●●

●

●

●

●

● ●

●

●●●

●●

●

●●●

●

●

●

●

●●

●●●●

●●●

●●

●

●

●●●

●

●●

●●●

●●●

●

●●

●

●●

●

●●

●

●

●●●

●●

●●

●

●● ●

●

●

●

●●

●

●

●

●

● ●●

●

●

●

●●

● ●●

●

●●

●●●

●●

●

●●●

●

●●

●

●

●

●

●

●

●●

●

●

●●● ●

●

●

●●

●

●●●

●●

● ●

●●●●

●

●

●

●

●●●●●

●●●●●●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●●

●

●●●

●●●●

●

●●

●●●●●

●

●

●

●

●●

●

●●

● ●●

●

●

●

●

●●●

●

●●

●

●

●●

●●

●●

●●●

●●

●

●●●

●

●

●●●●

●●

●●

●●

●

●

●

●

●●●

●●●

●●

●

●●●●●

●●●●

●●●

●

●

●

●●

●●

●

●

●●●

●

●

●●

●

●

●

●

●●

●

●●●●●●

●●●

●●●

●

●●

●

●●

●

●●●

●

●

●

●●

●

●●●

●

●●

●

●

●●●

●

●

●●

●●●

●

●

●●

●●●

●

● ●

●●●

●●

●●●

●

●●●●

●●

●●

●●

●

●●

●●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●●●●

●

● ●●●●●●●

●●●

●●●●

●

●

●●

● ●

●

●● ●●

●

●●●●

●●

●

●● ●●

●●●●●

●●

●

●●●

●●

●●●

●●●●●●

●

●●●●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●●●

●●●●

●

●●

●● ●

●

● ●

●●

●

●●●●

●

●

●●

●

●

●●●

●

●●

●

●●●

●

●●

●

●●●

●●

●

●●●●

●

●●

●●●

●● ●

●●●

●

●

●

●●

●●

●●

●●

●

●

●

●

●

● ●

●●

●

●

●

●

●

●●●

●●

●

●

●●●●

●

●●●●

●

●●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●●

●●●

●●●●●●

●

●

●●●

●

●●

●

●

●●

●●

●●●●

●

●

●●

●

●●

●

●●

●

●●●●●

●●

● ●

●●

●●

●●

●●●

●

●

●

●

●●●

●

●

●

●

●●

●

●●●

●

●●

●●●

●●●●

●

●

●

●●●

●

●

●

●● ●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

● ●●

● ●●

●

●

●

●●

●●

●

●●

●

●●

●

●

●●

●●●●

●

●●●

●●

●●

●●●●

●●●

●●●

●

●

●

●●

●●●

●

●

●

●

●●

●

●

●

● ●

●●

●●

●

●

●

●

●

●●●

●●

●

●

●

●●●

●

●●

●

●●●

●●●

●

●

●●

●●●●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●●●●

●

●

●●●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●●

● ●

●●

●

●●

●●

●

●

●●●●●

●

●

●●

●

●

●●●

●

●

●●

●

●●

●● ●

●●

●

●

●

● ●●

●

●

●

●

●●

●●

●●

●●●

●

●

●

●

●●●

●●

●●

●●

●

●●●●

●●●

●

●●

●●

●●●●

●●

●

●

●

●●

●●

●●●

●

●

●

●●●

●

●

●

●

●●

●●●

● ●●

●

●●●

●

●●●

●

●●

●●●●●

● ●●

●

● ●

●

●●

●●

● ●●

●

●●

●●

●● ●●

●

●

●●●●

●

●●

●

●

●

●

●●

●

●

●●●

●●

●●●●

● ●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●●●

●●

●

●●

●

●●●● ●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●●

●●

●

●

●

●

●

●●

●

●●●

●●

●

●

●

●●

●

●●●●

●

●●●

●

●

●●●

●●●●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

● ●

●

●●●

●

●●

●

●

●

●● ●

●

●

●

●

●

●●●

●

●●●

●

●●

●

●

●●

●

●

●●●●

●

●

●●●

●●

●

●●

●

●●●●●

●●●●

●

●●●

●

●●●

●●

●●

●●●

●

●●

●

●

●

●●

● ●

●●

●●●

●●

●

●

●

● ●

●

●●

●

●

●

●●

●

●●●●

●

●●

●●

●●

●

●●●

●

●

●

●●●●●●

●● ●●●

●

●●

●●

●

●

●●●

●

●●●●●

●

●

●●

●●

●

●●

●

●●

●

●

●●

●

●●●●

●

●●

●

●●

●

●

●●

●

●●●

●

●

●

●●●● ●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●●●

●

●●

●●●

●

●

●

●●●●

●

●

●●●

●

●

●●

●●●

●●

●●

●

●

●●●●

●●●●

●

●

●

●●

●●

●●●●

●

●●●

●

●●

●

●●

●●●●

●●

●●●●

●

●

●

●

●● ●●●

●● ●

●●●

● ●●

●

●

●

●●

●

●

●

● ●●

●

●

●

●●

●●●

●

●●

●

●●●

●

●

●

●●

●●●●●

●●

●

●

●●

●

●

●●●

●●

●

●●●●●

●●

●●●

●●●

●●●●

●

●●

●

●

●●

●●

●

●●

●

●●

●●

●●●●

●

●

●●● ●●

●

●

●

●

●

●

●●●

●●

●

●●

●

●

●●

●

●●●

●●

●●

●●

●●

●●

●

●

●●

●

●●●●

●

●

●●

●

●

●●●

●●

●

●

●

●●

●●

●●

●●

●

●

●●

●

●

●

●

●●

●

●

●●●

●

●●

●

●●●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

● ●

●●

●

●

●

●

●●

●●

●●

●

●

●●

● ●●

●●

●●●●

●

●●

●

●●●

● ●●●●

●

●● ●●

●●●

●●

●●●

●●

●

●●●

●

●

●

●●●

●

●

●

●

●

●

●●●

●

●●●●

●●

●

●●●● ●

●

●●

●●●●●

●

●

●●

●● ●

●

●

●

●

● ●

●●

●

●●

●

●●

●●●

●

●●

●

●●

●

●

●

●●●

●

●●●

●●

●

●

●●

●

●

●●

●●

●

●●●

●

●●

●

●● ●●●

●

●

●●

●

●●●

●

●

●

●

●

●

● ●

●●●●

●

●●

●

● ●●

●

●

●●●

●●

●

●●

●

●

●

●

●●

●●●

●

●●

●●●

●●● ●

●●●●

●●●

●

●

●

●●

●●

●●●●

●

●

●●●

●●●

●●

●●●

●●●

● ●

●

●●●

●

●

●

●●●

●●

●

●

●●●

●●●●

● ●●●● ●

●

●

●●●●

●

●●●

●

●

●

●

●●

●

●●

●

●●●●●

●

●

●

●●

●●●●●

●●

●

●● ●

●●●

●

●

●●

●

●● ●●

●

●

●

●

●

●●●●

●

●

●

●● ●●

●●

●●

●●●

●

●●●●

●●●

●●

●

●●●

●●

●●

●

●

●● ●●

●

●

●

●●

●●●

●

●

●●

●●●

●

●

●

●

●

●

●●●●

●

●●●●

●

●

●● ●●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

● ●●

●

●●

●●●

●

●

●

●●

●

●●●●

●●

●●

●●●●

●●●●

●

●●

●

●

● ●●●●

●

●●

●●●

●●●

●●

●●●●

●

●●

●

●

●

●

●

●●

●

●●●

●●

●●

●

●●●●●●

●●●

●

●

●●

●

●

●● ●●

●●●

●

●●

●

●●

●●

●

●●●

●

●

●

●

●● ●●●●

● ●●

●

●●●●

●

●

●

●

●

●

●

●●●

●●

●●●

●

● ●●

●●

●●●●

●●

●●●

●

●●

●

●●●●

●●

●

●●●

●

● ●

●

●●●

●●●

●

●

●

●

●

●

●●●●

●

●●●

●

●

●

●●

●

●●

●

●●

●

●

●●●

●●●

●

●

●

●●

●

●

●●

●

●●●

●●

●

●●

●●

● ●

●

●●

●

●●

●

●

●

●●●●

●

●

●

●●

●●

●

●

●●

●

●

●●●●●●●

●

●

●

●

●●

●●●

●●●

●●●●

●●

●●

●●

●

●●●

●

●

● ●●●

●●

●

●

●

●●

●

●

●

●●

●●●

●●●●

●

●

●

●

●●

●

●

●●● ●● ●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●●

●●

● ●

●

●●● ●

●●●

●

●●●

●●●

●●

●

●

●●●

●

●

●

●●

●

●●

●●●●

●●●

● ●●

●●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●●●

●●●● ●●●●

●

●●

●

●

●

●

●●

● ●

●●●●● ● ●

●

●●

●●●●●

●●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●●

●

●●●

●●●●

●

●

●●

● ●

●

●●

●●

●●●

●●●

●

●●●

●

●●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

● ●●●●

●

●●

● ●

●

●●●

●

●●●

●●●

●

●●

●●●

●●● ●●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

● ●●●

●●

●●

●●

●

●●

● ●

●●●●

●●●

●

●●

●

●

●●

●

●

●

●

●●

●

●●● ●●●●●

●●

●●

●●

●

●

●

●

●●

●●

●

●

●

●●

●●

●

●

●

●●●

●

●●

●●●●●

●●●

●●

●●●●●●●

●● ●

●

● ●●●

●●

●

●●

●

●

●

●

●●●

●

●●

●●●●●●●●

●

●●●

●

●

●●●●

●●●

●

●

●

●●

●●

●

●

●

●

●●

●●

●●

●

●

●●

●

●●

●

●

●●●●

●

●●

●●●

●

●●

●●

●●

●●

●

●●

●

●

●●●●

●

●

●

●

●

●●

●

●

●●●

●●

●●

●

●

●●

●

●

●

●●●●●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●●

●

●●●●●

●

●●●

●

●●●

●

●

●●

●●●

●●●●

●

●

●●●●

●

●●

●

●●

●●

●

●

●●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

● ●●

●

●

●

●●

●●

●

●●● ●●

●

●

●●

●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●●

●●●●

●●

● ●

●

●

● ●

●

●

●●

●

● ●

●●●●

●

●

●

●●

●●●●

●●

●●

●

●●

●

●●

●

●

●●

●

●

●●●●●● ●

●

●●●●●

●●●

●●

●

●

●● ●

●

●●

●●

●

●

●

●●●

●

●

●

●

●

●

●

● ●

●

●

●

● ●

●

●

●●

●

●●

●

●●●●

●

●●●

●●●

●● ●

●

●

●●●●●

●

●

●●

●●●

●●●

●

●●●

●

●

●●

●

●●

●

●

●● ●

●

●●●●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●●

●

●

●

●●

●●

●

●

●●

●●●

●

●●●

●●●●●

●

●●

●

●●●

●

●●● ●

●

●

●●

●

●●●●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●

●

●

●●

●

●●

●

●●

●●●

●●●

●●

●

●

●●

●●

●

●

●●

●

●

●

●●

●●

●●

●●

●●●

●

●

●●

●

●●●

●

●

●

●

●

● ●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●●●●

●●

●

●

●

●

● ●●●

●

●

●

● ●●

●

●

●

●

●

●

●●●●

●

●●

●

●

●●

●

●●●

●●

●

● ●

●

●

●

●

●

●

●

● ●●●

●

●

●● ●●●

●

●

●●

●

●

●

●●

●

●

● ●

●●

●●

●●

●

●●● ●

●●

●●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●

●

●

●

●

●

●●●●●

●

●

●●●

●●

●●●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●● ●

●● ●

●●

●

●

●●

●●●●●

●

●

●

● ●●

●

●

●

●● ●●● ●●

●●●

●

●● ●

●

●●●

●

●

●●●

●

● ●

●●

●

●●

●●●●

●

●●

●

●●●

●●●

●●●

●

●

●

●

●●

●●●●●●●

● ●●

●●●

●

●●●

●●

●

●●

●

●●

●

●

●●

●

●●

●●

●

●●

●

●●●●

●

●●

●

●●●

●

●

−0.05 0.10 0.25

−0.

040.

020.

06

animal2

Additive relationship

Dom

inan

ce r

elat

ions

hip

●

●

●●

●

●●●

●

● ●

●

●

●●●

●●●

● ●●

●

●

●

●●

●

●●

●●

●

● ●

● ●

●●● ●●

●●

● ●●●

●

●

●●●

●●

●●

●●● ●

●

●

●

●

●

●●

●●

●

●●● ●

●●

●●

●●●●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●●

●●

●●

●

●

●

●

●

●

●●

●

● ●

●

● ●

●

●

●

●

●

●●●● ●

●

●

●●●●

●

●●

●

●●

●●

●

●

●

●

●●●

●●●

●●

●●●

●●

●●●

●

●

●●●

●

●● ● ●●

●●

●●

●

●

●●

●

●● ●●●●

● ●●

●●

●

●

●●●●

●

●●

●●

●●

●

●●

●

●●

●●

●●●

●

●

●

●●●

●●●●

●

●●

●●

●●●●●

●●●●

●●

●● ●

●●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●●

●●

●●

●●● ●●

●●

●●●

●

●

●

●●●●●

●

●

●●

●●

●

●

●

●●●

●●

●

●●

●●● ●

● ●●● ●●

●

●

●●●

●●

●

● ●

●●

●

●●

●●

●●

●

●

●●●●

●

● ●●

●●

●●

●●●

●

●

●● ●●●

● ●

●

●●

●

●

●

●●●

●●

●●●●

●●●

●●

●● ●

●

●

●●

● ●

●●

●

● ●●

●

●

●

●

●●●●

●●●●

●●●●●●

●

●

●●

●

●

●●

●●

●●

●●●●●

●●

●

●

●

●

●●●

●

●

● ●●

●

● ●●●

●●●●●

●

●

●●●

●

●

●●

●●

●

●●

●●●●

●●

●

●

●●● ●

●

●

●●●

●●

●●● ●

●

●●

●

●●

●

●

●●

●

●●

●

●

●●●●

●●

●

●●

●●●

●●●● ●●●

●●●

●

●●●●●●

●●

●

●●

●

●

●●

●●

● ●

●

●●●

●

● ●

●

●●●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●●

●

●●

●

●●●

●●

●

●●

●

●● ●●

●●●

●●

●●●

●●

●●

●●

●

●●●●

●●

●●●

●

●

●●

●

●●

●●

●

●

●

●

●

●●●

●

●

●●●

●●

●

●

●●●●

●

●

●

●

●

●

●●

●

●●●

●●

●● ●

●

●●

●

●

●

●

●●●

●●

●●

●●

●●●

●●●●●

●

●

●

●

● ●●

●●●

●● ●

●

●●●●

●●●

●●

●

●

●

●

● ●●●●●

●●

●

●●●

●

●●

● ●

●

●●●

●

●●●

●●●

●

●

●

●●●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●●●●

●

●

●

●●●●

●●

●●●

●●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●● ●

●●

●

●

●●

●

●

●●

●

●●●

●●

●

●●

●

●●●●

● ●

●●

●

●●

●

●

●●

●

●

●●●●●●●

●

●●

●

●●

●

●●●

●

●●

● ●●●●

●●●

●●

● ●

●

●

●

●

●●

●

●

●● ●●

●

●●

●●

●●

●●●●

●●

●

●●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●●

●●

●●

●

●● ●

●●●

●

●

●

●●

●

●

●

●●●

●●●

●●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●●

●●

●

●

●●●●●●

●

●●

●

●

●

●●●

●●

●●

● ●●●●●●

●●

●

●●

●

●●●●

●

●

●●

●

●●●

● ●●●

●

●●●

●

● ●●●●

●●●●

●

●●

●

●

●●

●●

●

●● ●●

●

●

●

●● ●●

●●●

●●

●

●●

●

●●●

●

●●●

●

●●●●

●

●

●

●

●● ●● ●●

●

●●

●● ●

●

●

●

●●

●

●●

●●

●●●●

●

●

●

●

●●●●

●●●

●

●

●●

●

●

●

●

●●

●●

●

●●

●●●●

●●

●●

●

●

●

●●●

●

●

●●

●●

●

●●

● ●●

●

●

●● ●●●

●

●

●

●●

●

●●

●

●

●

●● ●

●●

●

●

●●

●

●●●

●

●

●

●●

●●

●●

●

●

●●

●●●●

●

● ●

●●

●

●●

●

●●

●●

●●

●●

●

●

●●

●

●●

●●●●

●●

●●●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●

●● ●

●●

●

●

●

●

●●

●●

●

●●● ●●●

●●

●●

●●

●●

●●

●●● ●●●

●

●●

●●● ●

●●

●

●

●●●●●●●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●● ●●

●

●●

●●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●

●

●

●●● ●

●

●●

●

●

●

●

●●●

●●●●●

●

●●

●●●

●

●

●

●● ●●●●●

●●

●

●

●

●

●●

●●

●●

●

●●●

●

●

●●●

●●●●

●●

●●●

●

●

●●

●

●

● ●●●

●

●●

●●

●●

●●●●

●

●

●●

●

●●●

●●

●

●● ●●

●●●●

●

●●●

●

●●●

●

●

●●

●●

● ●●●

●

●●

●

●●●●

●●

●

●

●

●

●

●●●

●●●

●

●

●●

●●

●

●

●●

●

●●

●●

●●

●●●

● ●●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●●●●

●●

●●

●

●

●

●●● ●

●

●●

●

●

● ●●●●

●●

●●

●

●●

●

●

●

●● ●●●

●

●

●

● ●●

●●

● ●

●

●●

●●

●●●●●

●

●

●●●●●

●

●●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●●

●●

●●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●●●

●

●●

●●●

● ●

●

●●

●●●

●

●● ●

●

●●●

●

●●●●

●

●

●●●

●

●●●

●

●●

●

●

●

●

●

●●●

●

●

●

●

● ●

●

●●

●

●

●

●

●●●●●

●

●

●●●●

●

●

●

●

●

●●

●●●

●●

●

●●

●

●●●●

●

●●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●●●●

●

●●

●

●●●

●

●

●

●● ●

●

●●

●

●●●

●

●

●

●●

●●●

●●

●

●

●●

●

●

●

●●

●

●

●●

●

● ●●

●

●●

●●●

●

●●

●

●●●

●

●●

●

●●●●●●

●

●●

●

●

●●

●●

●

●

●●●●●

●

●●●●●

●●

●

●●●

●●●

● ●

●

● ●●

●

●●

●●

●●●

●●

●

●●●●

●

●

●

●●

●

●

●

●●●

●●

● ●

●●

●

●

●● ●

●●

●

●

●

●●

●

●● ●

●

●●

●

●

●

●●●

●●

●

●●

●

●

●●●

●

●

●●

● ●●●●

●

●●●●●

●

●●

●●

●

●

●●●●

●●

●

● ●●

●

●●

●●

●

●●

●●

●●

●

●

●

●

●

●

●●●

●

●

●●

●●●

●●

●● ●

●

●

●

●●

●●

●●● ●●

●●

●

●

●●

●

●

●

●●●●

●

●

●●

●●

● ●

●

●●

●

●

●●●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

● ●

●

●

●

●●

●

●

●

●

●

●

●●

●●●

●●●●●

●

●

●

●●

●

●

●

●●

●

●

●● ●

●

●

●●

●

●●

●●

●●●●●

●●●

●

●●

●

●

●

●

●

●

● ●●

●

●●

●

●●

●

●

●●●

●

●●

●●

●●

●●

●

●

●●●

●

●●●●

●●●●●●

●

● ●●

●●

●

●

● ●

●

●

●

● ●●

●●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●●●

●●

●●●

●●

●●

●

●

●

●●

●

● ●

● ●●

●

●

●

●

●

●

●

●

● ●●

●

●●●●

●

●●

●

●●

●●

●● ●●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

● ●

●

●●

●●

●

●

●

●

●

● ●

●

●

●●

●

●

●

●

●

●

●●

●

●●●●●

●●● ●

●

●

● ●●●

●

●●

●

●●

●●●

●●●

●●

●

●

●

●● ●

●●

●

●●

●

●

●

●

●

●●●

●

●

●●

●

●

●●● ●

●

●●

●

●

●

●

●

● ●●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●●

●

●●

●●

●

●

●●

●●●

●

●

● ●

●

●

●

●●

●

●

●●

●

●

●●●●

●●

●

●●

●

●●●

●

●

●

●

●

●

●● ●

●●●

●

●

●●

●

●

●

●●●

●●

●● ●

●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●

●●

●

●●●●

●

●●

●●

●●

●●

●

●●

●

●●

●●●

●●●

●

●●

●●

●●

●●

●●

●●

●

●

●

●●

●●●●●

●

●●●

●

●

●

●●

●

●●

●

●

●

●●

●●●●●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

● ●●

●

● ●

●●

●

●

● ●●

●

●

●

●●●

●

●

●●

●●

●

●

●●●●

●●●

●

●●●●

●●

●

●

●

●●

●●

●

●● ●

●●

●

●●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●

●●

●

●●●●

●

●●

●

●●

●

●

●●●

●●●●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

● ●

●●

●●

● ●

●

●

●●●

●●

●

●

●

●

●●

●●●

●●●

●● ●

●

●

●

●●●

●●

●

●●●

●●●

●

●●●

●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●●●●

●●

● ●

●●

●

●

●●

●●● ●

● ●

●

●●

●●

●

●

●●

●

●●

●●●

●

●

●

●

●●●

●●

●●

●

●

●●

●●●●●

●

●●●●

●●

●

●

● ●●

●

●●

●

●●

●

● ●●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●●

●●

●●●

●

●

●

●

●●●

●

●

●●

●

●●●●●●

●

●

●

●●

●

●

●

●

●

●●●

●

● ●

●

●●

●●

● ●●●●

●●

●●

●

● ●

●

●

●

● ●

●

●●●●

●

●●

●

●●

●●●

●

●●●

●

●

●●●

●●●

●●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●●

●

●●

●●

●

●●●

●

●●

●

●

●● ●

●

●

●

●●●●

●●●

●●

●

●

●●

●●

●● ●●●

●●

● ●●

●●●●

●

●●

●●

●●●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●

●

●

●●

●

●

●●

●●●

●

●● ●●

●

●

●●●●

●● ●

●

●

●●

●

●●●●●

●●

●●●

●

●●●

●●

●●

●●

●

●●●●

●

●

●●●●●●●●●●

●● ●●

●●

●●

●●

●

●

●

●●

●

●●●●

●

●●●

●●●

●

●

●

●

●

●●●

●●●●

●● ●●●

●

●●

●

●●

● ●●

●

●

●●●

●●●●

●

●

● ●

●

●

●●

●

●

●●●

●

●●

● ●●●

●

●

●● ●

●●●●

●

●●●

●●●

●●

●●●

●●

●

●

●

●●

●

●

● ●●●

●

●●●

●

●●

● ●●

●●

●

●

●●

●●

●●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●●

●

●

● ●

●

●

●●

●●●

●●

●

●

●●●●

●●●

●

●

●

●

●

●●

●

●

●

●●●

●●

●

●●

●●● ●●

●●

●

●●●

●

●

●

●●

●

●

●●●

●●

●●●

● ●

●●

●● ●

●●

●

●

●

●●

●

●

●●●

●●

● ●

●

●●●

●

●

●●●●

●●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●●

●●

●●●

●●

●●●

●

●

●

●●

●

●

●●

●

●●●

●

●●

●●

●

●● ●●●

●

● ●

●

●

●

●

● ●

●

●

●

●

●●●●

●●

●

●●

●

●●

●

●●

●●●

●

●●●

●

●

●●

●

●

●●●

●

●●

●

●●●●

●●● ●

●●●●

●

●●●●

●●●

●

●●

●

●

●

●

●

●●●

●●

●

●

●●

●

●●

●●

●●

●●

●

●●

●●

●

●●

●

● ●●● ●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●●●

●

●●

●

●

●

●●

●●●

●

●●

●

●

●●

●

●●

● ●●●

●

●●

●●●

●

●

● ●

●●●

●●

●●

●

●●

●

●

●

●

●

●●

●

●

●● ●

●

●

●

●

●

●●●

●

●●●●

●●

●

●●

●

●

●●

●●●●●

●●

●

●

●●●

●●

●

●● ●●

●

●●●

●●

●

●●

● ●

●●

●●

●●●

●

●●

●

●●

●●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

● ●

●

●●

●

●●

●

●● ●●●

●

●●

●

●●●

●●

●

●

●

●

●

●● ●

●

●

●

●

● ●●●●

●●

●●

●

●●●●●

●

●●●●

●

●●

●●

●

●●●●●

●

●●

●● ●

●● ●

●

●

●●

●

●●

●●●●●●

●●

●

●

●●

●

●

●

●●

●

●●

●

● ●

●

●●●● ●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

● ●●●

●

●

●●●

●●●

●●

●●●●

●

●

● ●●

●●

●●●

●

●

●

●

●●

●

●

●●●

●

●

●●●●

●

●●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●●● ●●

●

●

●

●●

●

●

●●

●●

●●

●●

●●

●

●●●

●

●●●

●●

●●

●

●

● ●●

●

●●

●

●

●

●●

●

●

●●

●●●

●

●

●

●

●●●●

●

●●●

●

●

●

●●

●●

●● ●

●

●

●

●●

●

●●

●

●●

●●

●●●

●

●

●

●

●●●

●●●

●

●

●●●● ●

●

●●

●

●

●●

●●●●

●

●

●

●●

●●●●●●

●

● ●●

●●

●

●●

●

●●

●

●

●●

●●●●

●●●●

●●●●

●●

●

●

●

●

●●●

●

●●●●●

●

●●

●●●●●

●

●●

●● ●

●

●

●

●

●●

●

●

●●●

●

●

●●●

●

●●

● ●●●

●

●●

●●

●

●

●●

●

●

●●

●●

●●●

●

●●

●

●

●●

●

●●●

●●

●●

● ●

●

●

●

●●●●

●

●●

●

●

●●●●

●●

●●●●

●

●●●●●

●●● ●

●●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●●●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●●●

●●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●●●

●●

●●●●

●

●●

●

●●●

●●

●

●

●

●

●●

●

●●

●

●●

●● ●● ●

●●●

●

●

●●

●●

●●●● ● ●●

●●●

●●

●●

●●●●

●●

●

●

●●

●

●●●

●●

●

●

● ●

●

●

●

●● ●●

●

●

●

●

●●

●

●●●

● ●

●●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●●●●

●

●

●

●●●

●●

●

●

●

●

●

●

●

● ●

●

●

●●

●●

●

●●

●●

●

●●

●

●

●●●

●

●

●●

●●

●● ●

●●●

●●

●

●

−0.05 0.10

−0.

020.

020.

06

animal3

Additive relationship

Dom

inan

ce r

elat

ions

hip

●●

●

●

●●

●●●

●

●

●●●

●● ●●

●

●●

●

●

●●

●●

●

●●

●

●●

●●●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●

●●●●

●● ●

●

●●●●

●●

●

●●●

●

●●

●

● ●

●●

●●●●

●●●●

●●

●●●●

●●

●●●●

●

●

●●

●

●●●

●●

●●

●

●●

●●

●

●●●

●●

●●●●

●●

●●

●

●

●●●●

●● ●

●

●●

●

●● ●●

●

●●

●●

●

●●●

●●●

●

●

●

●●

●

●●●

●●

●●

●

●●●

●

●●●●●

●

●

●●

●

●●●

●

●

●

●

●● ●●●

●

●

●

●

●

●●

●

●●●

●

●●

● ●

●●

●●●

●●

●

●●

●●●●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●●●

●

●

●● ●

●●

●●●

●●●●●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●●

●●

●

●●●

●●

●

●●

●

●●

●●●

●● ●●●● ●●

●●

●

●●

●

●●

●●

●●●●

●

●

●●●

●

●

●●

●

●●●●●

●

●●

●

●

●●●

●

●

●

●●

●

●

●

●●●●●●

●

●●

●

●●●

●

●●

●

●●

●●●●

●

●●

●●

● ●●●

●●

●

●

●

●

●

●

●

●●

●●●

●

● ●

●

●●●

●●

●●

●

●

● ●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●●●

●●●

●

●

●●●● ●●

●●●

●●

●●●

●

●●●

●

●●●● ●

●

●

●

●●●●

●●● ●

●

●●

●

●●

●

●

●●

●

●

●●●●

●

●

●

●

●●●●●

●●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

● ●●

●● ●

●

●

●●

●●

●

●●

●●

●

●●

●

●

● ●●

●

●

●

●●●

●

●

●●●

●●

●

●

●●

●●

●●●●●

●

●●

●●

●

●●

●●●●● ●●●●

●

●

●

●●

●

●●

●●●●

●

●

●

●●●

●●● ●

●●

●●

●

●

●

●

●●●

●●

●

●●●●

●●

●

●●

●●

●

●

●

●●

●●●

●●●

●

●

●

●●

●

●

●●●

●

●●

●

●●●

●●●

●

●

●●●●

●

●

●

●●

●

●●●●●

●

●

●●

●

●●● ●

●

●

●

● ●●

●

●

●

●●●●●

●● ●●

● ●●

●

●●

●

●●

●●●●●

●●

●●●

●●

●

●

●

●

●●

●

●●

●

● ●●

●

●●

●●

●●●

●●

●●

●

●

●

●●

●●

●●●

●●

●

●

●●● ●

●●

●●●●

●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●●● ●●

●●●

●●●

●

●

●

● ●

●

●●

●●

●●

●●●

●

●●

●●●●

●●

●●●

●●

●

●

●

●

●

●

●●

●

●

●

● ●●●●

●● ●

●

●●

●●

●●

●

●

●●●

●

●●

●

●

●●●●

●

●● ●●

●●

●

●●

●

●

●●

●●

●●

●● ●●

●

●●

●

●

●

●●●●●●●●

●

●●

●●

●●

●

●

●●●●

●

●●

●●

●

●●●

●●

●

●

●●

●

●●●

●

●

●

●

●●

● ●●

●●

●●

●●●

●

●●

●●●

● ●

●

●●●

●● ●●

●

●

●●

●●

●●

●

●●●

●●

●

●●● ●● ●●

●●●●

●

●●●●●●●

●●

●●●●

●●

● ●●●

●●●●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●●

● ●●●

●●

●●●●●●

●

●

●

●

●●●

●

●●●

●

● ●● ●

●

●●●● ●

●

●

●

●●

●●

●●

●●

●

●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●●

●

●●●

● ●●

●●

●●

●

●

●●

●●●

●

●●

●

●●●

●

●

●●

●●

●

●●

●●●●●

●●

●

●●●

●

●●

●

●●

●

●● ●

●●●●

●

●●●●

●

●●

●●●

●

●●●

●

●●

●●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●●

●●

●●●

●

●●

●

●

●●

●●

●●●●

●● ●

●●

●●●

●●

●

●●

●●●●

●

●●●●●●

●

●

●●

●●

●●●

●

●●

●●●

●●

●●●●

●●

●● ●

●

●●●

●

●

●●●

●●●

●●

●

●

●

●

●●●

●●●

●●

●●●

●

●●●

●

●

●

●

●●

●

●

●●

●●●

●●

●

●

●●

●●●●

●●●

●●

●●●●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●●●

●

●

●●●

●

●●

●

●●

●

●

●● ●

●●

● ●●

●

●● ●

●

●●

●● ●

●

●

●●

●●●●

●

●●

●●

●●●●●

●●●●●●

●●

●

●●●

●

● ●●

●●●

●

●●●

●

●●

●

●

●

●

●● ●

●

●●

●●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

● ●●

●●●

●

●●●●●●● ●●

●

●

●●●

●

●●

● ●●●

●

●

●

●●

●

●

●●

●

●●●

●

●

●●●

●

●●

●●●●

●●●

●

●

●●

●

●●

●

●

●

●

●●

●

● ●

●

●●● ●

●

●

●

●

●● ●●●

●●

●●

●

●● ●

●●

●●

●●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●●●

●

●

●

●●●

●●

●●

●●●

●●

●

●

●●

●●●●

●●●

●

●

●

●

●●

●

●

●●●

●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●●

●

●

●●

●●

●●

●

●●

●

●●●●

●

●

●

●

●

●●●●●

●

●

●●

●●● ●

●

●

●

●● ●●●

●

●

●

●

●●

●

●●

●●●●●●

●●●

●

●

●

●●●

●

●

●●●●

●

●

●

●

●

●●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●

●●●●

●●●●

●

●

●●

●

●

●●

● ●●●

●

●●●

●●●

●●

●●

●

●●

●●

●●

●● ●●●

●●

●

●

●●

●●●●

●

●

●

●●●

●●

●●●

●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●●

●●

●

●●

●●●

●

●● ●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●●●●

●

●●

●

●●●

●

●

●●●

●

●●

●

●●●

●

●●

●

●●

●●

●●

●●●

● ●

●

●●

●

●

●●

●●●

●

●●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●●

●●

●

●●●

●●●

●

●

●

●

●

●

●●●

●

●

●●

●●

●

●●●

●●●

●

●

●

● ●

●

●

● ●●

●●●

●

●

●

●●

●●

●●

●

●● ●●●●

●●●●●●

●

●

●●●

●

●

●

●

●

●

●●

●

●

● ●●

●

●●●●

●●●●●

●●

●●●

●

● ●●

●

●

●●● ●●

●●●●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

● ●

●●

●●

●●●●

●

●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●●

●●

●●●

●●●

●●

●

●●

●

●●

●●●● ●

●

●●●

●

●

●

●

●

●

●

●●

●●●●

●●●

●

●

●●●

●●●●

●●

●

●

●●

●

●

●

●

●

●

●●

●●●

●

●●

●●●

● ●●●●●●●●●

●●

●●

●

●●

●●

●

●

●

●

●● ●●●●

●●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●●●●

●

●●●

●

●

●

●

● ●●●

●●

● ●

●●

●●

●●

● ●●●

●

●●●●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●●●

●●

●●●

●

●●

●●

●●

●●●

●

●● ●●

●

●

●

●

● ●●●

●●

●

●

●● ●

●

●●●

●

●

●

●●

●●

●

●

●●

●

●●

●

●●

●●●

●●

●●

●●

●●●

●

●● ●

●●

●●

●

●●

●

●

●●●

●

●●

●

●●●

●

●●

●●●

●●●

●

●●

● ●●

●●●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●●●●●●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●●●●●

●

●

●

●

●●●

●

●

●

●●

●● ●●

●

●●

●

●

● ●

●

●●

●

●

●

●

●

●●●

●

●

●●●

●

●

●●

●

●● ●

●●

●

●

●●

●

●

●● ●

●

●●

●

●●●

●

●●

●

●●

●●●●●

●

●

●

●

●

●●●

●

●

●

●●●

●●

●●

● ●●

●

●

●●●

●

●

●

●●●

●●●

●●●

●●●

●

●

●●●

●

●●●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●●

● ●

●

●●

●●●

●●●

●

●●

●●

●●

●

●●

●

●

●●●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●●●

●

●

●

●●●●●

● ●

●●●

●

●●●●

● ●●

●

●

●

●● ●

●

●●

●

●●●

●●●

●

●●

●● ●●

●●●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●●●●●

●●

●●

●●●

●●

●

●●

●●

●●●

●

●

●●●

●●

●●

●

●●

●●

●●

●

●●

●●

●

●●●

●

●

●

●●

●●

●●

●●

●

●

●

●●

●●

●

● ●

●

●●

●

●

●

●●● ●●

●●

●●

●

●

●●●

●●

●

●●●●●●

●●

●

●

●

●●

●

●●

●

●

●

●

●●

●●●

●

●

●●

●●●●●

●●●

●●●

● ●

●●

●●

●

●●●

●

●

●●

●

●

●

●

●●

●

●●●

●

●●●●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●●●

●●

●● ●

●

●

●●●●●●

●●

●

●●●

●

●

●●

●

●

● ●●●●

●●

●

●

●

●●

●

●

●

●● ●

●

●

●●●

●

●

●●

●●

●●

●

●●

●●●

●

●

●●

●●

●

●

●

● ●●●

●

●

●●

●●

●●

●●●● ●

●

●● ●●● ●

●

●●

●●

●●

●

●

●●

●●●●●●●

●●●●

●

●●

●

●●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

● ●●

●

●

●

●

●●●●●●

●●

●

●

●●●●

●

●

●●

●●

●

●●●●

● ●●●●

●

●●●●

●

●●

●● ●

●

●●●●

●● ●●●●●●●

●

●

●

●●

●●

●●●

●

●

●

●●●

●

●●

●

●●

●

●●

●●●

● ●●

●●●

●●

●

●●

●

●

●

● ●

●●●●

●●●● ●●●●

●●

●●● ●●

●●

●

●

●

●●

●

●●

●

●

●

●

●●●●

● ●●

●●● ●

●

●

●

●

●●

●

●●●

●

●

●●

●

●●●●

●●●●

●

●●

●●●

●

●

●●

●●

●●

● ●

●

●●

●

● ●

●●

●●

●●

●● ●

●●● ●

●●

●●●

●

●●

●

●

●

●●

●

●

●●

●

●●

●●●●

●

●● ●

●●

●

●

● ●●●●

●●

●

●

●●

●

●

●

●

●●

●

●●●

●●

●●

●

●●●

●●

●

●

●●●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

● ●●●

●

●●

●

●

●●

●●

●●

●●

●●●●●

●● ●●●

●

●

●●●

●

●

●

●●

●

●

●

●●

●

●●

●●●

●●

● ●●

●

● ●●

●●●

●● ●

●

● ●

●●

●●

●

●

●

●●

●

●

●

●●

●●●

●

●

●

●

● ●

●●

●●

● ●

●

●●

●● ●

● ●

●

●

●

●● ●

●●

●●

●

●

●●●

●

●

●●●●

●

●

●

●

●

●

●●

●●●

●●

●

●●

●

●

●●●

●

●●●

●●

●● ●●

●

●●●●

●●●

●●

●●●●●●● ●

●

●

●

●

●

●●●●●●

●●

●●

●

●●

●

●●

●

●

●●

●

●●●

●

●

●

●●●●

●●●●● ●

●

●

●

●

●

●●●●

●●●

●●●●

●

●

●

●

●

●

●

●

●

●●

● ●●

●●●● ●

●

●

●●

●●●●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●●

●●

●●

●

●●●●

●

●

●

●

●

●●

●

●

●●

●●●

●

●

●

●

●●●● ●●

●●

●

●●●●

●

●

●●

●●

●●●

●●

●●

●

●●

●

●●●

●●

●●●

●●

●●●

●●

●●●

●●●●

●

●

●

●●

●●

●

●

●

●

●●

●

●●●

●●

●

●

●●●●●

●●

●● ●

●

●

●

●

●●

●

●●●

●

●●

● ●●●●●

●

●●●

●●●

●

●●

●●

●

●● ●

●●

●●

●

●

●

●●

●●●●

●

●●

●

●●

● ●

● ●

●

●

●

●

●●

●●

●

●

●●●

●

●●●

●

●

●

●●●

●●

●●

●

●

●

●

●●

●●

●●

●

●●

●●

●

●

●●

●

●●●

●●●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●●

●

●

●●

●

●

●●●●

●●

●●●

●

●●● ●

●●●●

●●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●

●

●●

●

●●

●● ●●

●●●

●

●

●

●●

●

●●

●

●●

●●●

●●

●●

●●

●

●

●

●●

●

●

●●●

●

●●●

●

●

●

●●●

● ●●

●●

●●●●●●

●

●●●●

●●

●

●●

●

●

●

●

●

●

●

●●●●

●●

●●

●

● ●

●

●●●

●●

●

●●●●

●●

●

●●

●●●

●

●●

●

●

●

●●●

●

●●

●

●

●●●●●

●

●

●

●●

●●●

●

●

●

●●●●

●●

●

●

●●

●

●●

●●

●●●

●

●●●

●●

●●

●

●

●●●●●●●●●

●●

●●

●

●

●●●

●

●●

●

●●●

●

●

●

●

●●

●

●●●●

●●

●●

●●●

●

●

●●

●●

●

●

●●

●

●●

●●

●

●●●●

●●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●●

●●

●●

●

●

●●●●

●

●●

●

●

●●●

●

●

●●

●●

●

●

●

●

● ●

●

●●

●

●

●

●

●●

●●●

●

●

●

●●

●●

●

●

●

●●●●

●

●

●

●●

●

●

●●

●●

●

● ●●

●

●●●

●●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●● ●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●●●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●●

●

●●●●●

●●●

●●

●

●●

●●●

●

●●

●●●

●● ●

●

●

●●

●● ●

●●

0.0 0.2

−0.

040.

020.

06

animal4

Additive relationship

Dom

inan

ce r

elat

ions

hip

●● ●

●

●●●

●

●●

● ●●

● ●● ● ●●●

●●

●●●●

● ●

●

●●●

●●●●● ● ●

●

● ●

●

●●

●

●●

●●● ●

●●

●●

●●

● ●● ●● ●●●●

●●●●● ●●●

●

●●

●●

●●

●●● ● ●●●

●●●

●

●●● ●●

●●●●

● ●●●●● ●●●

●

● ●●●

●

● ●

●

● ●●

●●

●

●●●

●● ●

●●

●●●

●

●● ●●●●

●●

●●●

●●

●●●●

● ●●●●●

●●● ●●●

●●●

●●● ●●

●●●

●●

●

●

●●●

●●●●●

●●

●

●● ●●●

●

●●

●

●●●●● ●● ● ●●● ●

●●

●●●●● ●

●

●

● ● ●●●

●●

●●●● ● ●●●

●

●●● ●●

●●●

●●●● ●

●●●●

●●● ●●●●● ●

●●●●

●● ●●

●

●●● ●

●

● ●●●● ●● ●●●●●

●●

●

● ●●

● ●●

●●●●

●

●●●●

●

●● ●● ●●●●●

●●

● ●●●●●

●● ● ●●●

●● ●●●●

●●●

●●●●

●●●

●●●

●●●● ●●● ●

●●●●●●● ● ●● ●●● ●●

●● ●● ●●●

●●● ●●●●

●

●

●●●●

●●● ●● ●●

●

●●●

●●

●

●● ●●●●

●●●●●

●●●●

●●●

●●●

●●●● ●●●

●

●

● ●●●●● ●●●

●● ●● ●●● ● ●●●●

●

● ●●●●●●●

●●●

●●●

●●●● ●● ●● ●

●● ●

●●●

●

●●●

●●● ●●

●

● ●●

●

●●●●

●●●●

● ●●●●●●

●●●

●

●●●

●

●●

●●●●● ●●

●

●●

●●●

●

● ●● ● ●●

●●●

●

● ● ●

●

●●●

●●●●● ●●●●●●● ●● ●●●●●● ● ●

● ●●●● ●●●●

●●●

●

●●●

●● ● ●●● ●● ●● ●●●● ● ●●●●●●●●●●● ●● ●●

●

●● ●● ●

●●●●

●

●●●

●

● ●●●

●

●

●●●●●

● ●●●

●●●●

●● ●● ●●● ●●

●● ●●● ●●●●● ●

●● ●●

●● ●●●

●●● ●● ●●● ●

●● ●●●

●●●● ●●●

●●●

●●

●

● ●●●

●

●● ●●●●● ● ●

●

●●● ●●●●●●●●●● ●●●

●

●●●

●

●●

●● ●●●

●●

●●●

●●●

●

●●●

●●● ●●●●●

●● ●●● ● ●●●●●

●●● ●●●

●●●

●● ●●●●● ● ●●● ●●●●●●

● ●●●

●

● ●●●●●● ●●

●●● ●●●●●

● ●●●●●●●●

●●

●●

●●

●●●

●

●

●●● ●●●●● ●●●●●● ●●● ● ●

●

● ●●

●

●●●●●

●

●●

●

●

●

●●●●●●

● ●

●●●

●● ●●

● ●●●●●●●

●●● ●●● ●

● ●●●●

●

●●●● ●● ●● ●●

●●●●● ●●●

●

●●●● ●●● ●

●●

●● ●●●●● ●● ●●● ●

●

●●●●●●

●●●

●

●●●●● ●●● ●●● ●

●●●

● ●●●

● ●●●●

●●● ●

●

●● ●●●●●

●● ●●●●

●● ●●

●●

●●●●●

●●

●

●● ●●●●

●

●● ●●●●●●●●●●●

●

●●

●

●

●● ●

●

●●●●●

●●

●●

●●●

●

●●●

●● ●● ●●●● ●●●●

●

●●●● ●●●●●

●

●●●●●●

●

● ●●●●●● ● ●●

● ●●●●

●●●● ●● ●

●

●●●●● ●●

●●● ●● ●●

●●●●● ●

●●●●● ●●●

●

●●●●●● ●●●● ●

●

●●

●●● ●

●●●●

●●●●●●●●●●●●

●

●●●

●● ●

●● ●●● ●●●●●

●●●●●

●

●

●●●

●● ●

●●●●●

●

●●●●

●●

●●●

●

●●●●●

● ●●●●●●

●

●●●

●

●

●

●

●

●

●

● ●●

●●

●●●● ● ●●●

●

●

●●

●●●● ●●●

●●

●

●

●●●●

●●●

●

●

●●

●

●● ●

●●●

●●

●

●●

●●●●

●● ●●●

●

●

●●

● ●●● ●

●

●● ●●●●

● ●●

●

● ● ●●

●●●●

●●● ●

●●

●●

●

●●●●●●●

● ●●●

●

●

●● ●●●

●●● ●●●

● ●●● ●●●

●●● ●●● ●●●● ●●●●

●●

●

● ●● ●●●●

●

●●

● ●●●●

●●

●● ●●●●●●●●●●●

●●

●

●

●●●●● ●

●●●●

●● ●●●

●●●● ●●

●●

●● ●●● ●

●

●●

●●

●●

●●

●

●

●

●●●

●

●● ●●●●

●●●●

●●●●

●●

●

●●●● ●●

● ●●●

●● ● ●● ●●●●●●●●

●

●

●●

●●

●●

● ●● ● ●●

●

●●●●● ● ●● ●●●●

●●

●

●●●●● ●● ●●●●●●●●

●●● ●

● ●●

●● ●●

●●●

●●●●

●●

●●● ●● ●

●

●

●

●

●

●

●● ●

●●●●

●

●●

●

●●

●●●●●● ●●●●

●

●●●

●●● ●

●

●●●

●

● ● ●●●● ●●●

●

● ●● ●● ●●

●●

●

●●●

●●

●

●●

● ●

●

●●● ●●●●

●

●●

●

●●●

●●●

●

●

●

●

●●●

● ●● ●●● ●●

●

●● ●●●

●

●●

● ●●● ●●●

●

●●●

●

●●

●

●●●●●

●●●

●

● ● ●●

●

●●●●● ●● ●●● ●

●●●●

●●●● ●●

●

●●● ●●

●

●●

● ●●●●●

●

●

●●●

●

●

●

●●●

●●●

●●●●

●●●●

●●● ●●●

●●

●

●● ●

●● ●●

●

●●●●●●●●

●●

● ●

●●

●● ●●

●●

●●●● ●●●

●

●●●●●

●

● ●● ●●●

● ●●●●●

●● ●●●●●●●

●

●●●● ●●●●

●●●●● ● ●●●●

●●

● ●●

●●

●●

●●●

● ●●●●

●

●●●●●

●● ●

●

●● ●●

●

●●

●

●

●

● ●●

●

●●●

● ●●●

●

●

●

●

● ●●●

●●●●● ●●

●●●●●

●●●● ●●●●● ●● ●● ●●●●●●●●

●

● ●● ●●●●●

●●

●

●●●●●●

●●● ●● ●●●●● ●●●●

●● ●● ●

●

●●

●●● ●●

●●●●●●●●●●●●●●●

●

●●●

●

●●

●

● ●

●

●●

●●●

●

● ●

●●●●●●●

● ●● ●●●● ●

●

●● ●●

●●

●● ●●

●●

●

●●●●●

●●●

●●●●●●

●●●● ●●●●

●●●

●

●

●●●●

●●●●

●●

●● ●

●●● ●●● ●●●●

● ●●●

●

●●

●● ●●

●●●

●●

●●

● ●●

●

●●

●●

●● ●● ●●●●

●

●●

●

●

●●●

●

●●●

●

● ●● ●●●

●● ●●

●● ●●●●●

●●

●●

●●●

● ●●●●●● ●●●●

●●

● ●● ●●● ●●●

●

●● ●

● ●

●

●●●●

●●

● ●

●●●

●●

●●●● ●

●

●●

●● ● ●●●●●

●●

●● ● ●

●●

●● ●●● ●

●

●●●

● ●●● ●●●● ●

●

●●

●●●●●●●●● ●

●

●●●● ●●

●●

●

● ●● ●●●●●●●

●

●●●●●

●●

●● ●●

●

●●●●

●

●●●●●

●●●●● ●●●●●

●●●●● ● ●

●●

● ●●●

● ●●● ●

●

●●●

●● ●● ●●● ●●●●●

●

●● ● ●●●●●●

●●

● ●●

●

●● ● ●●

●

●● ● ●● ●●● ●●●●●●●●●●●●

● ●●●●

●● ●● ●●●●

●●●●● ●●●

●

●●● ●●●●●● ●●

●●●●● ●●●● ●●●● ●●● ●

●

●●●

●●●● ●

●●● ●●

●● ●●●●●

●●●

●● ●● ●●●●●

●●● ●●

●

●●

●●

●● ●●

●●●●

●●● ● ●

●●

●

●●

●

●●

●

●●●●

● ●●●●● ●

●●

●●● ● ●●

●●●●●●●●● ●

●●

●●● ●●●●

●●● ●●●

●●

● ●●●

●

●

●

●● ●●●● ●

●●

●

●

●

●●●

● ●●

●●●●

●●

●

●●

●

●●● ●●●

● ●●● ●●●●●● ●●●●●●

●●●●

●

●● ● ●● ●

●● ●●

●

●●

●

●● ●

●

● ●●● ●

●

●●●

● ●●●●● ●●

●●●

●●●●

● ●●●

● ●●

●●●●

● ●●

●● ●● ●

●●●● ●●

●

●●

●

●

●●

●

●

●

●●

●●●● ●●● ●

● ●

●● ●● ●●

●●

●●●● ●

●●

●● ●

●●●●●●●●●●

●●● ●●

●● ●●●●●●●

●● ●●● ●● ●●●●●

●● ●●● ●●

●● ●●

● ●●

●

●●●

●

●●●

●

●

●

●● ●●●●

●

●●●

●

●●●

●●●

●●●

●●●●●●●●●●● ●

●

●●

●

●●●●● ●●● ●

●●

●● ●●●

●●

●●

●

●● ●●● ●●

● ●●●●●● ●●

●

●

●● ●●

●

● ●●● ●●

●●●●

●●● ●●●

●●●● ●●

●●●●

●● ●

●●●

●

●●●●

●●● ●●●

●

●●● ●●●●

●

●●

●● ●●

●

● ●●●●●●

●●● ●●● ●

●●

●

●●●●●

●●

●●● ●● ●● ●●

●

●

●●

●●● ●● ●●●● ●●●●●●●●● ●●●●●

●

●●●

●●

●● ●● ●●●●●● ●●●●●

●

●●●

●●●●●●

●●

●

●●●●●●

●

●●●●●●●●

●●●

●●●● ●● ●●

●●●● ●

●● ●●●

●● ●●●●●●

●

●

● ●●●

●

●

● ●●●● ●●● ●● ●●●●

● ●●● ●● ●●

●

●●

●●

●●●● ●● ●● ●

●

●

●

●●● ●● ●●

●●●●

●

● ●●●●

●●●

●●

●●●

●●

●● ●●

●●●●●● ●

●● ●●●●

●

●●●●●

● ●●●●●

●●●●

●●● ●●●●● ●●

●●●

●

●●●●

●●●

●●●●

●●● ●●●

●

●●

● ●●● ●●

●

●●● ●● ●●

●● ●●

●●

●●● ●●●

●●●

●●●

● ●● ●● ●●

●

●

●●●

●●●●●

●●

●

●●●●● ●

●● ● ●●

●●● ●

●●●●●●●●● ●●●

●

●●

●

●●

● ●● ●

●●● ●●●●

●

●●●

●

●

● ●●●●●●●● ●

●

● ●●●

● ●●●●

●

●●●● ●

●●●●●

●● ●●●● ●

●●●●

●

●●● ●●●

● ●● ●●●

●●●

●● ●●●●● ●●●● ●●

● ●

●●●

● ●●●●●●

●●● ●●●

●●●●

●

●●●●● ●

●

●

●●

●

●

●●●

●●●●●● ●●

●

● ●

●

●● ●●

●●●

●●

●●●

●●

●

●●●●

●●

●●●●

●

●●●●

●

● ●●

●●● ●●●

●●●●● ●● ●

●

●● ●●

●

● ●●

●

● ● ●●●●●

●

●

●●

●

● ●●●

●●

●●

● ●● ●

●●

●

●

●●

●●●● ●●

●

●●

●

●

●● ●●●●● ●

●●●

●●

● ●●●●● ●●●●

●

●●●

●

●

●●●

●●●

●

●

●●

●●

●

●●

●

●●●

●●●

●●

●

●●●●●●●

●●

●

●

●●

●●●●●● ●●

● ●●●●

●● ●●

●●

●● ●●●

●

●●

●

●●●●

●●

●

●●

●

●●

●

●

●

●● ●

●

●●●●● ●●

●●

●●

●

●

●

●● ● ●

●

●●● ●●●●●

●●

●●

●●

●

●

●●● ●

●●

●●●

●●

●

●●

●●●

●

●●●●●●●

●

●●

●

●●●●

●

●●

●

●●

●

●●●●

●●●

●

● ●●●●●

●●●●●● ●●

●

●●

●●

●●● ●●

●●●

●●

● ●●● ●●●●

●●●●●● ●● ●●●● ●●

●●●●●●●

●●

●

●

●

●●●●●●● ●●

●

●

●● ●●

●

●●

●●

●

●●● ●●

●●

●●●●● ●●

●●●

●●●

●

●●

●●●● ●●●●●●

●● ●● ●●● ●●● ●● ●●● ●●● ●●●●● ●●●●●

●

●●●

●

●●

●●●● ●● ●●●●● ●●●

●

●●● ●●● ● ●

●●●● ●● ●●● ●●●●●●

● ●● ● ●●●●

●

●●●

●

● ●● ●●●

●●

●

●● ●●● ●●● ●

●

● ● ●● ●●● ●●●

● ●●

●●●●● ●●

●● ●●●●● ●● ●●● ●●

●●● ● ●●

●● ●●●●●

●● ●

●

● ●●● ●● ●● ●

● ●●●

●● ● ●●●●● ● ●●● ●●●

●●

●

●●●●●●●

●●● ●●●● ●● ●●

●●●●●●

●●● ●●

●

●

●

●

●

●●●

● ●

●

●● ●● ●● ●

●

●●●

●●●

●●● ●●

●● ● ●●

● ●● ●

●

●

●● ●

●● ●● ● ●●● ●●●● ●●●●● ●●●●● ●

●

●

●●●●

●●●

●● ●●●● ●●

●●● ●●● ●●

●●●● ●

●●

●●●●

●●

●●●●

● ● ●●●

●

●●●● ●●●●●● ●●●

●●●●● ●●●● ●●●●

● ●●●● ●●●●● ●●

●● ● ●● ●●●

●●●

●

●

●●●

●●●● ●●●●●●●

●●● ●

●●

●● ●● ●●

●●● ●●● ●●●

●

●

●●●●●●●

● ● ●●●

●●

●

●

●

● ●●

●●● ●●●

●●●

●●

●●●● ● ●●●●●●●● ●●●●● ●●●

●● ●●●

●●● ●●●●●● ●● ●● ●●●●

●●●●

● ●●

●

●

●●●●●

●●

●●●

●

●

●● ●●

●● ●●

●●● ● ●●●●

●

● ●●●●

●●

●●●●

● ●●●●●●

●

●●●●

●

●

● ●●

●●

●●

●

● ●●

●

●● ●●

●●●● ●●●● ●●

●

●●●● ●

●

●

●●●

−0.05 0.05

0.00

00.

004

0.00

8

animal1

Additive relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

●●●●● ●● ●● ●●●●●●

● ●●●●● ●●●●●●● ●●

●

●

●●●● ●● ●●●●●●●●●●●●● ●●●●●●●●●●●●

●●●●● ●●●●●●●●● ●●●●

●● ●● ●●●●●●●● ●●●●● ●●●●●● ● ●●●●●●●●● ●●●●● ●● ●●●● ●●

●

●●●● ●●●●●● ●●●●●●●●●●●

●●●●●●●●●●●●●●● ●●●●●●● ●● ●●●

●●●●●●●● ●●

●●

●●●●●●● ●● ●●●●●●●

● ●●●●●●● ●●●●●●●● ●●●● ●●●

●●●●● ●●●● ●●●●●●●●●

●●●●●●●● ●●● ●●●●●●●●●● ●●●●●●●●●

●●

●●●●●

●●● ●●● ●●●● ●●●

●●●●●●●

●

●●● ●●● ●

●●

●

●●● ●●●●●●

●●●●

●●●●●●●●● ●●●●●● ●●●●●

●●●●●● ●●● ●●

●● ●●●● ●●

●●● ●

●

● ●●●●●●● ●●●●●● ●● ●●●●● ●●● ●●●

●●● ●●●●●●●●●● ●●●● ●● ●●●●●●

●●●●●

●●●● ●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●

●

●●●●● ●●●●● ●●●● ●●●●●●● ●●●●● ●●● ●●●●●●●● ●●●●● ●●●●● ●●●● ●●● ●●

●●● ●●● ●● ●●● ●●●●●● ●●●● ●●

●●●●

●●●●●● ●●●

● ●●●● ●●●●● ●●●●●●

●● ●●●●●●

● ●● ●●●●●●●● ●●●●●●●●●●●●●●● ●●●●●●●● ●●●● ●●

●● ●

●

●● ●●

●

●●●

● ●● ●●●●●● ●●●●●●● ●●●●●●●●

●●●●● ●●●● ●●● ●●●● ●●●●●●●

● ●●● ●●●●●● ●● ●●●●●●●●●● ●●●● ●●●●●●●●●● ●●● ●●●●●●●●●●●●● ●●●●

● ●● ●●●●●●●●●●●●●● ●●●●● ●●●●●●●●●●●● ●●●●●●●●●● ●●●●●●●●●● ● ●●●● ●●●●●● ●●●●●● ●●● ●●●● ●●●●● ●●●

●●●●

●

●● ● ●●●●● ●●● ●● ●

●●●●● ●●●●●● ●●●●●●●● ●●●● ●●●● ●●

●●●● ●●●●●● ●●●● ●●● ●● ●●●●● ●●●●●●

●● ●●

●● ● ●●● ●●●●

●●●● ●● ●●●●●●●●●●● ●●●●●●● ●● ●●● ●● ●●● ●●●●

●●●●●●●●● ●● ● ●

●●●●●●●●●●●●● ●●●● ●●●●

● ●● ●●●●● ●●● ●●●●●●●●●●●● ●● ●●●

●●●●●●●●

●●● ●● ●●

●●●●●●●●●●●●●● ●●

●●●● ●

●●●●● ●●●●● ● ●●●

●

●●

●

●●●●● ●●●●●●●●

●● ●●●● ● ●●●●● ●●●●●●●●●● ●●● ●● ●●● ●●●●●● ●●●●●● ●●●

●●●●● ●

●● ●●● ●●●●●● ●●●●● ●● ●●●●●●●

●●● ● ●●●● ● ●● ● ●●●● ●● ●●●●●●●● ●● ●● ●●●● ●●● ●●●●●●●●●●●●●●●● ●●●●●

●●●●●

●●●

●

●

● ●●●

●●● ●●●●●●●●●●●●● ●●● ●● ●●●●●●●

●

●●● ●●●● ●●●●●●● ●●●●●●● ●●●●●●●●

●●●●● ●●●

●●●●●●●●●●●●●●●●●● ●● ●●●● ●●● ●●●●●●●●●●●●●●●●●● ●●●

●●●●●● ●●● ●

●●●●●

●●● ●●●●●●●●●

●●●●● ●●● ●●●●● ● ●●●●●

●●●

●●● ●●●●●●●● ●●●● ●●●●● ●●●●● ●●● ●●●●●●● ●●●● ●●● ●●●●● ●●●●● ●●●●●●●● ●●

● ● ●●●●● ●●●●●●●●●●● ●● ●● ● ●●●● ●●●●●●●● ●● ●●● ●●●●●● ●●●● ●●●●●●●● ●●●●●●●● ●●● ●●●●

●●●●● ●●●● ●●●●● ●● ● ●●●●● ●●●● ●●●● ●●●● ●●●●●●

●

●●● ●●●●●● ●●● ●●●●●●●● ●● ●●●●●●●● ●●●●●

●●●●●●● ●

●● ●●●●●● ●● ●●●● ●●●●

●● ●●●●●

●

●

●●● ●●●●

●●●● ●●●●● ● ●●● ●●● ●● ●● ●● ●●●●● ●●●●●● ●●●●●●●●● ● ●●●● ●●●●●

●

●●●● ●●●●●● ●● ●●●●●●●●●●●●●●●● ●●●● ●●●● ●●● ●●●● ●●●●●●●●●●●● ●●●● ●●

●● ●●● ●●●●●●●●● ●●●●●●●●●●●●●●●●● ●●●●●●●●●●●● ●● ●●●●● ●●●●●●●●● ●● ●●● ●●●● ●●●●●●●● ●●● ●●●●● ●●● ●●●●● ●●●●●●● ● ●●●●●●●

●

●●● ●●●●●●

●●●●●●●●● ●●●● ●●●● ●●●●●●● ●●●●●●●

● ●●● ●●

●

●●●●●● ● ●●●● ●●●

●

● ●●● ●● ●●●●

●●● ●●●● ●● ●●●●●●●●●●● ●●●●●●● ●●●●●●●●●●●●●● ●●● ●● ●● ● ●●●

●●●● ●●●●● ●●● ●●●●●●●●●

●

● ● ●●●● ●●●●●●●●●● ●●●●● ●●●●●●● ●●●●●●●●●● ●●●● ●●● ● ●● ●●●●

●●●●●● ●●● ●●●●●●

●●● ●●●● ●●●● ●●●●

● ● ●●●●●

●●●● ●●● ●●● ●●●● ●●

●●●●●●● ●●

●●●●● ●●

●●● ●●●●●●●●● ●●● ●● ●● ●●●●● ●●●●● ●●●● ●●●●●●●●●●●●● ●●

●●● ●●●●●●●●●●●● ●●●●● ●●●●● ●●●●● ●●●●● ●●● ●

●

●●● ●●● ●●● ●

●

●●●●● ●●● ●●●● ●● ●●● ●●●●●●● ●●●●● ●● ●●●● ●●●●●●●● ●●●●●● ●●●● ●●● ●● ●●●

●●●●●●● ●●●●●●●● ●●● ●●●

● ●●●●●●●●●

● ●● ●●● ●●●●●●●●●● ●●● ●●●●●●●●●●●● ●● ●●● ●●●●●

●● ●●●●●●● ●●● ●●●●● ●● ●●●●● ●●●

●●● ●●●●●● ●●●●●● ● ●●●

●●●●●●● ●●● ●●●●●● ●●●●●

●●●

●●●

● ● ●●●●●●●●● ●●● ●● ●●● ●● ●● ●●●●●● ●●●● ●●●●●● ●● ●●● ●● ●● ●●●●●●● ●●●●●

●●●● ●●●●●●●●●●●●●

●● ●● ●●●

● ●●●●● ● ●●● ●●●●● ●●

●● ●●●

●●●●●●●●●●● ● ●●●●●●●●

●● ●●●●●

●● ●●●●● ●●●●●● ● ●●●● ●● ●●● ●●●●●● ● ●●●●

●●● ●●●●●●● ●●●●● ●● ●●●●●●●●● ●●●●●● ●●● ●●● ●●●●● ●●● ●●●●●●●●●●● ●●●●● ●●●●●●● ●●●●● ●

● ●●●● ●●● ●● ●●●● ●●●●●●● ●●●●●●●●●● ●●●

●●●● ●●●● ●●● ●●●●●●●● ●● ●●●● ●●●●●●● ●●● ●● ●● ●●●● ●●●●● ●●●●●●●●●●●●●● ●●●●● ●●●●●●

●● ●●●● ●● ●●●● ●●●●● ●● ●●●● ●●● ●●

●

●●●● ●●● ●●●●●● ●●●● ●● ● ●● ●●● ●●

●●●●●● ●●●

● ●● ●●●

● ●●●

●

●●●●● ●● ●●●●●●●●●●

● ●● ●● ●●●● ●●●● ●●●●●●●●● ●●●●●●●●● ●●●

●●●●●●●● ●●●●●●●●●● ●●

●●●●●● ●●●●●●

● ●● ●●●●●

●●●●●

●●●● ●●●●● ●●●

●●●●●●●● ●

●● ●●●

● ●●●●●

● ●● ●●●●●●●●●●●●●●● ●●●●●●●●●●● ● ●● ●●● ●●●● ●●●●●●●●● ●●●●●● ●●●●

●●●

●●● ●●●●●●●●●●●●●● ●●● ●●● ●●●●●●●● ●●●●

●

●●●●●● ●●●●

●

●●●●● ●● ●●● ●●●●●●●● ●●●● ●●●●●● ●●●●●●●●●● ●● ●●●● ●●● ●●●●●●● ●●●● ●●●●●●●●●●●

●●●●●●●●●●● ●● ●

●●● ●●●●●●

●●● ●● ●●● ●●●●●● ●●● ●● ●●● ●●●●●● ●●●●●● ●●●●●●●● ●

●● ●●● ●●●●●●●● ●●●●●●●●●● ●●● ●●●●●●●●●●●●●● ●●●●● ●●●

●●

●

●●● ●●●●●● ● ●●●

●●●●●● ●●●●●

●●● ●●● ●●●● ●●● ●●●● ●●●●●●●●●● ●● ●● ●● ●● ●●●●● ●●●●●●●● ●●● ●

●●● ●●● ●●●

● ●●

●●●

●●● ●● ●● ●●● ●●● ●●● ●● ●●●● ●●●

●●

●●●●● ●● ●●●● ●●●●●

●●● ●●

●●●●●●● ●●●●●●

●●●●●● ●● ●●●●●●

●

●

●●●●● ●● ●●●●●●● ●●●● ●●● ●●●●●● ● ●●●● ●●●●

●●●● ●● ●●● ●●●●● ●● ●●●●●●●●●●●

●

●●● ●● ●●●

● ●●●●

●●●

● ●●●● ● ●●●●●●●●● ●●●●●●●●●●● ●●● ●●●●

●● ●●● ●●● ●●●

●

●● ●●●●●●●●

●

●● ●●

●

●●●●●●●●●●

●●● ●

●●● ●●● ●● ●●●●●●

●

●● ●● ●●●●●● ●●●● ●●● ●●●●●●●●●

● ●● ●●●●●●● ●●●●● ●●●●●● ●●●

●●●●●

●●●●●●●

●● ●● ●●●●●●●●● ●●●●

● ●●● ●●●●● ●●● ● ●● ●●●●●●●● ●●●●●●●

●●●●● ●●●●

●●●

●●

●●●●●●

●

●●● ●● ●

●●

●● ●●●●

●

● ● ●●●● ●●●●●●●●● ●●●●●●●●●●

●● ●● ●

●

●●●● ●●● ●●●●●● ●●●●●●●●●●●●● ●● ●● ●

●●

●●● ● ●●●●●● ●● ●● ●●●●●●●●● ●●● ●●●●● ●●●●●●●●● ●

●●●●●●●● ●●●●●●● ●●●●●●●●

●

●●●

●

●●●●

●

●

●●

●●●● ●●

●

●●●●● ●●●●● ●●●● ●●●●● ●●

●●●●●●●● ●● ●●● ●●●●● ●●●

●●●●●●●●●● ●●●●●●●●●●● ●●

●●●●●●●●●●●

●

●●

●● ●●●●●●●●●●●●●●●●●●●●●●●●●● ●●● ●●●●●●● ●●●●●● ●●●● ●● ●●●● ●●●● ●●●●●●● ●● ● ●●●● ●●● ●●●●● ●●●●● ●●● ●●●●●●●●●●●●●●●● ●

● ●●●●● ●●●●●●●●

●● ●●●

●● ●●●●●●● ●●●● ●●●●●●●●●●● ●●●●

●●●●●●●●●●●●●

●●● ● ●●●●

●●

● ●●●●

●

●

●●●●● ●●●●●●●●●●●●●●●●●

●●

●●●●●●●

●●●●●● ●

●●●

●●●●●●

● ● ●●● ●● ●●●● ●●●● ● ●●● ●●●●●●

●●

●●●

●

● ●●

●●●●●●●●●●

●●● ●● ●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●●●●●●●●●●●● ●● ●●●● ●●●●●

●●● ●●●●● ●●● ●●● ●●●

●●●●●●●●

●● ●●●

●●●● ●●● ●●●●●●●● ●●●●●●● ●●●●●

●●●

●● ●● ●●●

●●●

●●●●

●●●●●●●●●●●●●●●●●●●● ●●●●● ●●● ●●●●●●●

●●●●

●●●●●● ●● ●●●

●●●●●

●●●●●

● ●●

−0.05 0.10 0.25

0.00

00.

010

0.02

0

animal2

Additive relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

● ●●●●

●●● ●● ●●●●●●●●

●●●●

● ●●●● ●●● ●● ●● ●● ●●●● ●●●●● ●

●● ●●●●● ●●●●●●● ●●

●●● ●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●● ●●●●

●●●● ●● ●●●●●●● ●●●●●●●●●

●● ●●●●

●●● ●● ●●●● ●●●●●●●● ●●●

●●●●●●● ●●●●●●●● ●●●●●

●

●●●●●●●●●●● ● ●●● ●●●●

●● ●●●●

●●●● ● ●●

●●●

●

●●● ●● ●●●●●●●●●

●●●●●●●●●●

●●

●● ●●●● ●●● ●●●●●●●● ●●●●●●● ●●●● ●● ●●●●●● ●●●●● ●●●●● ●●●●●● ●● ●● ●●●● ●●●●●●●

●●●●●● ●●●●●●● ●● ●●●●● ●

● ●●● ●●●●

●● ●●●● ● ●●●●●●●●●●●●●●●●●●

●●● ●●● ●●●

●●

●●

●●●● ●● ●●

●●●

●●●●●●●●●●●●●●●●

●●●●●● ●●● ●● ● ●●●

●

●●●●

●

●●● ●●

●●●●●●● ● ●●●●● ●●●●

●●●

●●●●●●●

●●●●●●● ●●●● ●●●● ●●●●●●●●●● ●●●● ●

● ●●●●●●●●●●● ●● ●●●●●●●●●●● ●●●●●●●●● ●● ●●

●●● ●● ●●● ● ●●● ●●●●●●● ●●●●●●●●●●●●●● ●● ●●●

●● ●●●● ●●●●●●● ●●●●●●●●● ●●● ●●●●●

●●●●● ●●●●●● ●●●●●●●

●● ●●● ●●●● ●●●●●●●● ●●●●●●●●● ●●●●● ●●●●●●● ●●●●●

●

●●

●●● ●●●● ●●●● ●●● ●●● ●●●●●●● ●●●●●●● ● ●●●●●●

●●●●●● ●●● ●●●●●●●●●●●● ●● ●●●●●●● ● ●●●●●●●●●●●

●● ●● ●●●●●●●●●● ●●●●● ● ●● ●●● ●●●●●●● ●●●●●● ●● ●●● ●●●●●●● ●●●●●●●●

● ●●●●●●●

●●● ●●●●●●●●● ●●●●●●●●●●● ●●● ●● ●●●● ●● ●●●●● ●●

●●●●

●● ●●●● ●●●●●●●●● ●●●● ●●● ●●● ●● ●●● ●●●●●●●●● ●●●●●●●●● ●●●●●● ●●●● ●● ●●●●●●● ●● ●●●

●●●●●●●● ●● ●●●●●● ●

●

● ●● ●●●●●●●

●●●●●●● ●● ●●●●● ●●●●

●

●●●●●●●●● ● ●●●●●●

●● ●●●● ●●●●●●

●●●●●●● ●●●●●●● ●●●●●●●●●● ●●●●●●●●● ●●●●●●●●●

●●●●●●●●●●●● ●●●● ●●● ●● ●●●● ●●●●●●●●●●●●

●●● ●●●● ● ●●●● ●●● ●●● ●●●●● ●●●●●●

●

●●●● ●●●●●●● ●●● ●● ●●●●●●● ●● ●● ●● ●●● ●●●●● ●● ●● ●●●●●● ●●●●●●● ●●●● ●●●● ●●●●● ● ●●●● ●●●●●●●●●●●●

●●●● ●●●●●● ●●●●

●● ●●

●● ●● ●●●● ●●●●●

●●●●●● ●●●●

●●●●●

●●●●●●●●●

● ●●●●●● ●● ●●● ●●●●●●●●● ●● ●●●●●●●●●●● ●● ●●●●●●● ●●

●●● ●●● ●●●●

●●●● ●●●

●●●● ●●●● ●●● ●●●●● ●●● ● ●●●●●●●●● ●●●●● ●●●●●●●●●●●●● ●●●●●●●● ●●●● ●● ●●●

●●●●●● ●● ●●●●

● ●●●●

●●●● ●●●● ●●●● ●●

●● ●● ●●●●●●●● ●●●●●●● ●● ●●●●● ●●● ●●●●●●●●●● ●●●●●●●● ●●●●● ●●●●●●●●●●● ●●● ●●●●●●●●●●●●

●●● ●●●●●● ●●● ●●●●●● ● ●●●● ●●●●●●●●●● ●●●●●●

● ●●●●●●●●●● ●●●● ●●●● ●●●● ●●●●

● ●●●●

●● ●●●●● ●●●●●● ●●

●●●●●●●

●● ●●●●● ●●●●

●

● ●●●● ●●●●● ●● ●●●● ●●● ●

● ●●●●●●● ●●●● ●●● ●● ●●● ●●●●●●● ●●●●●

●●●●●●● ●● ●● ●●

●● ● ●●●● ●●●● ●●●● ●●●●●●● ●●●●●●●●●

● ●●● ●●●●●●●●●● ●●●●●●●●●● ●●●●●● ●● ●● ●●●●●●

●●●● ●●●● ●● ●●●●●●●

●

● ●● ●●●● ●● ●● ●●●●●●●●●● ● ●●●

●●●●●●● ●●●● ●●●●

●●●●

●● ●● ●●●● ●●●●● ●●●●● ●●●●● ●●●● ●● ●● ●●●●●●●●●●●●●●●●

●●●● ●●●●

● ●●●● ●● ●● ●●● ●●●●● ●●●●●●●●●●● ●●●●●● ●●●

●●● ●●

●● ●●●●●●●●●●●●●● ●●●● ●●●● ● ●● ●●●●●●●●● ●●● ●●●●●●●

●●● ●● ●●●● ●●●●●●● ●●● ●●●●

●●●●●●● ●●●●

●

● ●●●●●● ●●●●●●●●● ●● ●● ● ●● ●●●●●●●●●●●●●●●●●●●●●● ●● ●● ● ●●●●● ●●● ●

●● ●●

●● ●●● ●●●● ●●●● ●●● ●● ●●●

●●● ●●● ●●●●● ●●● ●●● ●●●●● ●●●●●● ●●

●●●

●●●●●● ●● ●●●●●

●●●

●●● ●● ●● ●●●

●●●● ●● ● ●

●●●●●● ●●●●● ●● ●●● ●●●●●●●●● ●●●

●●● ●●●● ●●●● ●●●●● ●●●

●●●●●

● ●●●●●●●●●● ●●●● ●●● ●● ●●●●●●●●

●● ●●● ●●●●●●● ● ●●●●● ●●

●● ●● ● ●●● ●●

●●●●

●● ●●● ●●●

●●●●● ●●●

●● ●●●● ●●●●●●●

●

●●●

●●● ●● ●● ●

●

●●

●● ●●● ●●●●●●●● ●●● ●●●●●● ●●●●●● ●●

●● ●●●

●● ●●●● ●●● ●●●● ●●● ●●●●● ●●● ●●●●●

●●●●●●●●●●●●●● ●●●● ●●●●●●●●● ●●●●●●●●

●●

● ●● ●● ●●●●●●●●●●●●●●●●●●●●● ●●● ●

●

●● ●●● ●●●● ●●●● ●●●●●●

●●

● ●●●●●● ●●●

●●●●●● ●● ●●●● ●●●●●● ●

●●●●●●●●●●●

●●●●●

●● ●●●● ●●●●●●●● ●●●

●●●●●●● ●●●●●● ●●●●●●●●●●●●●●● ●●●●●●● ●●●●●●●●●●●● ●● ●●●●●●●●● ●●● ●●

●● ●●●●● ●●●●● ●●● ●●●●●●●●●●● ●●●●●

●●●●●●● ●●●●●●●●● ●●●●●●●●● ●●●●

●●●

●

●● ●●●●

●●●●● ●

●

●●●●●● ●●●●●●●●●●●●● ●●●●● ●● ●●● ● ●●●

●●

●●●●●●●●● ●●● ●●● ●● ●●●

●

●● ●● ●● ●● ●●●●●●●● ●●● ●●●●●●● ●●●●●●●●●●● ●

● ●● ●●●● ●● ●●●●●●● ●●●●●●●● ●● ●●● ● ●●

●●●●

●●●

●●●●●●●●● ●●●●● ●●●

● ●●● ●●●

●● ●● ●●●● ●● ●●●●●●●●●● ●● ●● ●● ●●●●●●●

●●●● ●●●●●●●●●● ●●●

●●●●●●●●●●●●●●● ●●● ●●

●

●●●

●●●

● ●●●●●●

●●●●●●● ●●

●●●●●● ●●●● ●●●● ●

●●● ●●●●●●●●●● ●●●●●

●●● ●●●●●●●●●

●●●● ●●●●●●●●● ●● ●●●●● ●●●● ●● ●●●● ●●●●● ●● ●●●●●

●● ●●● ●●●●●●● ●●●●●

●●●●●●●●●● ●● ●● ●●●● ●●● ●●●●●

●● ●●● ●●●● ●●●●●● ●●●●●● ●

●●●●●●●●●● ●●●

●●●●●●● ●●●●●● ●● ●●●●● ●●●●●●●●● ●●●●●●● ●

●●●●●●●

●●●●●●●● ●●●

●●

●●●●

●●●●●●●●

●●● ●●●●●●● ●●●●●● ●●●●●● ●● ●●

●

●●●● ●●● ●●●●● ●●● ●●●●●●●●●●● ●● ●●●●

●● ● ●● ●●●●

●

●●● ●●●

●●●●● ●●●●●

●●●●●●● ●● ●●●●●● ●●● ● ●●●●● ●● ●●●● ●●● ●●

●●●● ●●●●●● ●● ●●●● ●●● ●●●●●● ●●●●●● ●●●●● ●●●●● ●●● ●● ●●●● ●●●

●● ●● ●●●●

●● ●●●●●● ●

●

●●

●● ●●●●

●●●●●● ●●●●●●● ●● ●●●● ●●●●●●●●●●● ●●● ●●

●●●● ●●● ●●● ●●●● ●●●● ●● ●●● ●●● ●●●●●●●●●●●●● ●●● ●●●●● ●●●●

●

●●●● ●●●●●●● ●●● ●●●●●● ●●●●● ●●● ●●

●● ●●●● ●●●●●●●●●●●●●● ●●●●●

●●●●●●●●●●●●

●●●●●●● ●●●● ● ●● ●●●● ●●●● ●●●●● ●●●●● ●● ●● ●●

●●● ●●●● ●●●● ●● ●●●●●●● ●●●●●●● ●●●●● ●●●●●●●●●●●

●●●●

●●●●● ●●● ●●● ●● ●● ●●●●●

●● ●●●●●●● ●●● ●

●●● ●●●●● ●● ●●●●●●●●●●●● ●●

●●● ●●●● ● ●●●●●●● ●● ●●●●●●●● ●●●● ●●●●●● ●●●

●●●●●

●●

●●●●●● ●●●●● ●●●●●●●●●●●●●● ●●●●●●●●●●●●● ●●●●● ●●● ●●

●● ●●●●● ●●● ●●●●●●●● ●

●●● ●●●●●●● ●●

●● ●●●●●●● ●●●

● ●●

● ●● ●●●●● ●● ●● ●●● ●●●● ●●●● ●●●● ●●●● ●● ●●●●●● ●●● ●●●●●● ●●●●● ●●●●● ●●●●●● ● ●●● ●●● ●●●● ●●● ●●●●●●● ●●● ●●● ●●● ●●

●●●● ● ●●

●●●● ●

●

●●●●●● ●●● ●●

●●●● ●●●●●●● ●●●● ●●● ●●●●●●●●●●●●●

●●● ●●●●

●●●●●●

●●●●●●●●●●● ●● ●●

●

● ●●●●●●●●●● ●●

●●●●●● ●● ●●

●● ●●●●●●●

●●●● ●

●

●

●●●

●

●●●●●●

●●●

● ●●●●●●

●●

● ●●●●●●●●

●●●●●

●●●●● ●●

●●

●

●●●●●●●●●●●●●●●●●●●

●●●●● ● ●●●●

●●●● ●●●●●● ●● ●●●

● ●● ●●●●●●●●●●●●●●●●● ●●●

●●

●●●●●●●●●●●●●●●●●●●●●●●●● ●●● ●●●●●●●● ●●●●●●●●●●●

●● ●●●● ●●

●●●●●●●●●●

●●●●●●●●●●●●

●●●●●●● ●●●●●●● ●●●●●

●●●●●● ●●●

●● ●●●●●●●●●●●●●●●●●●●●● ●● ●●

●●●●●●● ●●● ●●●●

●●●●●●●●●●●●●●●●●●●●●●●

●●●●

●● ●●●●●

● ●● ●●●●●●●● ●●●

●●

●●● ●● ●●

●●●●● ●●●●●●●●●●●●● ●●●●

●●●●●●●● ●●●●●●● ●●●

● ●●●●

●●●●● ●●●●●●● ●●●●●●● ●● ●●●●

●● ●●

●● ●●●● ● ●● ●●●●●●

●●● ●●●● ●● ●●

●● ●●●●● ●● ●

●●

●●●●●●●●

●● ●●● ●●●

●●●●

●●● ●● ● ●●● ●●●●

●●●●●● ●●

●

●●●●●●●●●●

● ●●●● ●●●●●

●●●●

●● ●

●

● ●●

●●●●●

●

●●●

● ●●●● ●●● ●●●● ●●●● ●●●●

−0.05 0.10

0.00

00.

010

animal3

Additive relationshipA

dditi

ve b

y do

min

ance

rel

atio

nshi

p

●●

●

●●●●●●●●

● ●● ●● ●●●●●● ●●● ●●● ●●●●●●●●

●

●●●●●● ●●●● ●●●●●●●●●●●●●● ●● ●●●●●●● ●●● ●●●●●●● ●●● ●●●●●●●●●● ●●●●●● ●●●●●● ●●●●●●●●●

●● ●●●●●●●●●● ● ●●●

●●●●● ●

● ●●●●● ●●●●● ●● ●●●●●

●●●●●●●●●●●●

●●●●●●●●●●

●

● ●●●●●●●●● ●●●●●● ●●● ●●●● ●●●●●●●

●●●● ●●●●●●●

●

●●●●● ●●●

● ●●●●●● ●●●●●● ●●●●●●● ●●

● ●●● ●

●

●●● ●●● ●●●

●●●●●●●● ● ●●●●

●

●● ●●

●●●● ●●●●●●● ●●●●●● ●● ●

●

●● ●●●●●

●

●●●● ●●●●● ●●●●●●●● ●●●● ●●●● ●● ●●●● ●●●●● ●●●●●● ●●●●●●●●●●

●

●●●●●●●●●

●

●●●●●●●

● ●● ●●●●●●●●●●●● ●●●

●●●●●● ●●●●● ●●●●● ●●● ●●●●●●●

●●

●●●● ●●●● ●● ●●●●● ●●●●

●

●● ●●

●

●● ●●●●

●● ●●●●

●●

●

●●● ●●●●●●●●●●●●●●● ●●● ●● ●●●●●● ●●●●●●●● ●●●●●●●● ●●● ●● ●●●●●●● ●●●●●●● ●

●●

●

●

●●●●●●●●●●● ●●●●●● ●● ●●●

●● ●●●● ●● ●●● ●●●●

●●● ●●● ●●● ●●●

●

●

●●●● ●●●● ●●● ●●●● ●● ●●●●●●●●●

●

●●●●●●● ●●●●●●●

● ●● ●● ●●●●●

●

● ●● ●● ●● ●●●●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●● ●●● ●● ●●●●●●● ●●●●●●● ●●●●●● ●●●●●●●●

●●●●●●●● ●●●●

●● ●● ●●●●● ●●●● ●●●●●●●● ●●● ●●

●●●●●●●●●●●●● ●●●●●

● ●●●

● ●●●●

●● ●●●●●●●●●● ●● ●●●●

●●● ●●●●●●● ●●●●● ●●●●●●●●●●● ●●●●●●

●● ●●● ●● ●●●

●●●● ●●●● ● ●● ●●●●● ●●●●●

●

● ●● ●● ●●●●●● ●● ●●●●●●●● ●●●● ●●●

●●●●

●● ●●●

● ●●●● ●● ●●●●●●●●● ● ●●●●●●● ●●● ●●●●● ●●●● ●●● ●●

●● ●●

●●

●● ●●●

● ●●●

●

●●●●●●●●●●●

●●

●●●

● ●●●● ●●●●●●●●●●●●● ●● ●●●● ●● ●●●●● ●●● ●●●●●●●●● ●●●●●●●●●● ● ●●●●●●●●●●●●●●●●

●●●● ●● ●● ●● ●●●●●●●●●●●●●●●● ●●● ●●●●●●●●● ●●●● ●●● ●●●

●●

●●●●● ●●●● ●● ●●● ●● ●●●●●●●●● ●●●●●●●● ●● ●● ●●●●●● ●●●●●●●●●

●●●●●●● ●

●●●● ●● ●●●●● ●●●●● ●●●● ●●●●●●●●●●●●●● ●●● ●●●●● ●●●●●

●●●●●●●● ●●●●● ●●● ●●● ●●● ●● ●●●●●●●●●

●● ●●●● ●●● ●●● ●●●

●●●●●●

● ● ●●●●●●●●●● ●●●●●● ●● ●●●●● ● ●●● ●● ●●●●●●●● ●●●●●●● ●●●●●●●● ● ●● ●●●●● ● ●●●●● ●●●●●●●●●● ●● ●●●●●● ●●● ●●●●●●

●● ●●● ●●●●●●●●●●●●●

●●●

●●●

●

●●●● ●●●●●●●●●●●● ●●●● ●●●●● ●

●●

●

●●

●

●●●●●● ●●●●●

●

●● ●●●●● ●●●● ●●●

●

● ●●

●

●● ●●● ● ●●● ●● ●

●

●● ●● ●●●●●●●●● ●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

● ●●

●

●●●● ●● ●●● ●●●

●

● ●

●

● ●

●

●●●●●●●

●

●

●●●●●

●

●

●● ●●●●●●

●●●●●●● ●●●

●

●●●

●

●●● ●●●

●

●●

● ●●

●

●●● ●●● ●●●●●●

●● ●●●● ●●●●● ●●●

●●●

●

●

●●● ●● ●

●

●●● ●●● ●

●

●● ●●● ●●●●

●

●● ●●● ● ●●●●●●● ●● ●●

●

●●● ●●●● ●●●●●●●●●●

●●●●●● ●●● ●●●● ●●

●

●●●●●●●● ●●● ●●●

● ●

●

●●●● ●●●●●●●●●●●●●●

●

●

●●● ●●●● ● ●●●● ●●

●

●●●●●● ●●●●●●●●●●

● ●● ●●●●● ●●●●●●● ●

●

●

●●● ●● ●●●

●●●●

●

● ●●●●●●● ●●●●

●

●

●●● ●● ●●●●●●● ●●●●● ●●●●●●●●● ● ●●● ●●●●●●●● ●●● ●●●●● ●●●● ●●●● ●●●●●● ●●●● ●●●●●●●●● ●●●● ●● ●●● ●●●●●

●● ●●●●

● ●●●●

●●●●

●●● ●●●●●●

●●●●●●●●●●●●● ●●● ●●●

●● ●●●●●●●●● ●●●●●●●● ●●●●● ●●●● ●●●●● ●●●●●● ●●●●●● ●●● ●●●●● ●●●● ●● ●●● ●●●●● ●●●●●●● ●●

●●●● ●●●●●●●● ●●●●●● ●●●● ●●●●●●●●●●●●●● ● ●●●● ●●● ●●●● ●● ●●●●●

●

●●●●●●●

●● ●●●●●●●●●●

●

●●●●

●

●

●●● ●●●●●● ●● ●●● ●●●●●●●●●●●● ●● ●●●●●●● ●●● ●●●●●●●●●●●●

●●

●● ●●● ● ●● ●●●●●● ●●

●● ●● ●●● ●●●●●●●● ●●●●● ●●●● ●●●●●●●● ●●●

●●●●●●● ●● ●

●●● ●● ●●●● ●● ●● ●●●●●●● ●●●●●●●● ●●●● ●●●●●●●●●● ●●●●●●●●● ●● ●●●●●●● ●●●●●● ●●●●●●●●●●● ●●●●●●● ●● ●●●● ●●● ●●● ●●●●●●●●● ●●●● ●●● ●● ●●●● ●●●

●●●●● ●● ●●●●●●● ●● ●●● ●●●

●

●● ●●●●

●●●●●● ●●● ●●●● ●● ●●●● ●●● ●● ●●●

●●●●●●● ●●

●● ●●●●●●●●●●●● ●●●●● ● ●●●●●●●●●●●

●●●●●● ●● ●●●●● ●●●● ●●●●

●

●●● ●●●●●● ●●●●

●●●

● ●● ●● ●●●●●● ●●●●

●

●●● ●

●

●●●

●

●●

●

●●● ●

●

●

●

● ●● ●●●●●●●●●●

●●●●●

●●●

●●

● ●●●

●● ●●●●●●●●●●

●

●●

●

● ●●●●●

●

●●●●●●●●●●●●●●●●● ●●● ●● ●●● ●●

●●● ●●●●●●

●●

●

●●●● ●●●●●●

●●

●

●● ●●

● ●●●●●●●● ●●●●●●●●●●●●

●● ●●●●●●●●● ●●●●●● ●●●●●●●●● ●●●●●●●●●●●●●●●● ●●●● ●●●●●●●●●●●●●

●

●●●●● ●●●●

●

●

●

●

●

●●

●

●

●

●●●●●● ●●●●●●●●●●●●●●● ●●● ●●●●●●●● ●●●● ●● ●●●●●●●●●●●●●● ●● ●●●

●●●●● ●●●●●●●● ●●●●●●●●●● ●●●●

● ●● ●●●●

●●●●● ●●●● ●●● ●●●●● ●●●●●●●●●●●●●●

● ● ●● ●● ●●●●●● ●●●● ●●●●●●●●●●●●●●●●●●●●● ●●● ●●●●●●●●●●●●●●● ●●●●●● ●●●● ●●●●●●●●● ●●●●●●●●●● ●●●●●●

●●●● ●●● ●● ●●●●● ●●●●● ●●●●● ●● ●●●●●●●●●●●● ●●●● ●● ●●●●● ●●●●●●●●●●●●●●●

●● ●●●●● ●●●●●●●●

●●● ●●●●●●●●●●● ●●●●●●● ●●● ●●●●●●●

●●●●●●●●● ●●● ●● ●●● ●

●

●●

●●●●●●● ●●●

●●●●

●●● ●●●●●●● ●● ●●

● ●●●●●●

●● ●●●● ●●●●●●●●●●●●

●● ● ●●● ●●●● ●●●●●● ●● ●●●●●●●●●●● ●●●●●● ●●

●●● ●●●●●

●●

●●●

● ●●●

●●●●●● ●●●●● ●●●● ●●●●●●●●●●●● ●●●●● ●●●●● ●●●●●● ●●● ●●●●●● ●● ●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●●● ●● ●●●●● ●●●● ●●● ●●●●● ●●●● ●●●●●●●●● ●●

●●

●●●●●

●

● ●●●●●●●●●● ●●● ●● ●●●●●●●● ●●●●●●●●●●●● ●●● ●●● ●●●●●●●●

●●●●● ●●● ●

●● ●● ●●●●●●● ●●●● ● ●●●●● ● ●●●● ●

●●●●●●●●●●●●●●●● ●●●●

●

● ●● ●● ●●●●●●● ●●●

●●

●

●●● ●●● ●●●●●●●●● ●●●●●● ●● ●●●●●● ●●● ●●●●

●●●● ●●●

●●●●●●●●●●●●● ●●●●●●● ●●●●

●

●●● ●● ●●●● ●●●●●

●●●●●●●● ●● ●● ●● ●●●●● ● ●● ●●●●●● ●●●● ●●●●●●●●●●●●● ●●● ●●● ●●●●●●

●●●●

●●●● ●● ●●●

●

●

●●●●●●● ●●●● ●● ●●●●●●●● ●●●●●●

●● ●●●●●● ●●● ●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●● ●● ●●● ●●●

●●●●●●●● ●●●●●●●●●●● ●●●●●●● ●●● ●●● ●●●●●●●

●●●● ●● ●●● ●●●●●● ●●

●● ●●●●● ●●●●●●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●●●●

●

●● ●●●●

●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● ●●

●●●●● ●●●●● ●●●●●●●●● ●●● ●●

●● ●

●

●●

●

●●●●● ●● ●●●●●●●

●● ●●●●●●●●●●●●●●● ●●●●●●●●●● ●● ●●●● ●● ●● ●●●●●● ● ●●●●●●●

●

●●

●

●●● ●● ●●

●

●

●●●●● ●●●●●

●●●●● ●● ● ●●●●●●●●●●●●●●●●● ●●●● ●●●●●●●●●●●

●

●

●

●●●●●●●●●●

●●●●● ●●●●● ●●●

●●●

●

●●●●●●●●●● ●●● ●●●●●

●●●● ●●●●●●●●● ● ●●●●● ●●●●●●●

●●●●●●●●

●●●● ●●●●●●●

●

●●●

● ●●● ●● ●● ●● ●●● ●●●● ●●●● ●●●●●●●●●●●

●● ●●●●●●●●●● ●● ●●●● ●●●●●●●● ●●●●●●●●●

●●●●●●● ●●●

●●●●●●● ●● ● ●● ●●● ●● ●●●●●●● ●●●●●●● ●●●● ●●●●●●●●●●●●●●●● ●● ●●●●● ●●●●●● ●●●● ●●●●●●●●●●●● ●●●●●● ●● ●●●●●●●●●●● ●●●● ●●●●●●● ●●●●●●●●●●●●●● ●●●●

●● ●●●●● ●● ●●●●●● ●●●●●●●●●● ●●●● ●●●●● ●●●●●●●●●●●●●●●●●●●●●●● ●● ●●●●● ●●●

●●●

●● ●● ●● ●●

●

●●● ●●●●●●●●●● ●● ●●● ●●●●

●

●

●●●●●●●●●●● ●●●●●● ●●

●

●●●●●●●●●●

●

●

●●

●●

●

●

●

●●●●●●● ●●

●

●

●●● ●●●●●●●

●

● ●

●

●●●

●

●●●

●●●●

●

● ●●●●●●

●●●●

●● ●●● ●●

●

●●●●●

●

●●●●● ●●●●●

●●●●●●●●●●● ●●● ●● ●●●●●● ●● ●

●

●●● ●● ●●●

0.0 0.2

0.00

00.

010

0.02

0

animal4

Additive relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

●●●

●

●●●

●

●●

●●●

●●●● ●●●

●●

●●●●

●●

●

●●●

● ●● ●● ●●

●

●●

●

●●

●

●●

●●●●

●●

●●●●

● ●●●●

●●●●●●

●●●● ● ●

●

●●

●●

●●

●●●●●●●

●● ●

●

●● ●●●

● ●●●

● ●●● ●●● ●●

●

●●●

●

●

●●

●

● ●●

●●

●

●●●

●●●

●●

●●●

●

●●● ● ●●

●●

● ●●

●●

●●●●

●●● ●●●

●●●●●●

●●

●●●

● ●●●●●

●●●

●

●●●

●●● ●●●

●

●

●●●●●

●

●●

●

●●●●●●●●●●● ●

●●

●●●●● ●

●

●

● ●●●●

●●

●●●●●● ●●

●

●●●●●

●●●

●●●● ●● ●

●●

●●● ●●●●●●

●●●●

●●● ●

●

●●● ●

●

● ● ●●●●● ●●●● ●

●●

●

●●●

●●●

● ●●●

●

●● ● ●

●

●●●●●●●●●

●●

●●●●

●●● ● ●●● ●●● ●●●

●●

●●●

●●●●

●●●

● ●●

●●● ●●●●●

●● ●●●●●●●●●● ●● ●●●●●●●

●●● ●●●●

●

●

●●●●

●●●●● ●●

●

●●●

●●

●

● ● ●●●●

● ●● ●●

●●●●

●●●

●●●●

●●● ●●●

●

●

●●●●●● ●●●

●● ●● ●●● ● ●● ●●

●

●●● ●●● ●●

●●●

●●●

●● ●● ●● ●●●

●●●

●●

●

●

● ●●●● ● ●●

●

●●●

●

● ●●●

●●●●

●●● ●●●●

● ●●

●

●●●

●

●●

●●●●●● ●

●

●●●●●

●

● ●●●●●

●●

●

●

●●●

●

●●●

● ●● ●● ●● ●● ●●●● ●●●● ●●●●●

●●●●● ●● ●

●●● ●

●

●●●

●●● ●● ● ●● ●●● ●●● ●● ●●●●● ● ●●●●●● ● ●

●

●● ●● ●

● ● ●●

●

●●●

●

●●●●

●

●

●●●●

●

● ●●●

●●●●

●●● ●● ●●●●●

● ●●●● ●●●● ●●● ●

●●●●●●●●●● ●●●●●

●● ●●●

● ●●● ●●●

●●●

●●

●

● ●●●

●

●●●●●●●●●

●

●●● ●● ●●●● ● ●●● ●●

●

●

●● ●

●

●●

●●●●●

●●

● ●●

●●●

●

●●●

● ●● ●●●●●●● ●●●● ●●● ●

●●●● ●

●●●

● ●●●●● ●●●● ● ●●●● ●●●

●●● ● ●

●

●● ●●●●●●●●

●●● ●●● ●● ●●

●●● ●●●●●

●●

●●

●●●

●

●

●●●●●●●●● ● ●●●●●●●● ●

●

● ●●

●

●●●●●

●

●●

●

●

●

●●● ●

●●●●

●●

●●● ●

●

●●● ●● ●●●●

●● ●●● ●●● ●●●

●

● ●●●●● ●● ●●

●●

● ●● ●●●

●

●● ●● ●●

●●

●●

●●●●●●●●● ●●● ●

●

●●●●●●

●●●

●

●●●●● ●● ● ●● ●●

●●●

●●●●

●●●●●

●●●●

●

●● ●●●●●

●●●●●●

●● ●●

●●

●●●

●●●

●

●

●● ●●●●

●

●● ●●●● ●● ●●●●●

●

●●

●

●

●●●

●

●●● ●

●●

●●●

●●

●

●

●●

●●●●● ●●●● ●●●●

●

●●●● ●

●●●●

●

●●● ●●●

●

●●●●●●●● ●●

● ●●●●

●●●●●● ●

●

●●● ●● ●●

● ●● ●●●●

●●●●● ●

●●●● ● ●●●

●

●● ●●●●●●●●●

●

●●●

●● ●

●●●

●● ●● ●●●●●● ●●

●

●

●●

●●●●

●● ●●●●●●●●

●●●● ●

●

●

●● ●

●●●

●● ●●●

●

●● ●●

●●

●●●

●

●●●●●● ●●

●●● ●

●

●●

●

●

●

●

●

●

●

●

●●●

●●

● ●●● ●●●●

●

●

●●

● ●●● ●●●

●●●

●

●●●●

●●●

●

●

●●

●

●●●

●●●

●●

●

●●●

● ●●●

● ● ●●●

●

●●

● ●●●●

●

●●●● ●●

●●●

●

●●●●

●●●●

●●●●

●●

●●

●

● ●●● ●●●

●●●●

●

●

●● ●●●

●●● ●●●

●● ●●●●●

●●●● ●● ●●●●●●● ●

●●

●

● ●●● ●●●

●

●●

●●●●●

●●

● ●● ●●● ●●

● ●●●●

●●

●

●

●●● ●●●● ●

●●

●● ●●●

● ●●● ●●

●●

●●●●● ●●

●●●●

●●

● ●

●

●

●

●●●

●

● ●●●●●

●● ●●

●●●●

●●

●

●●

●● ●●●●

●●●● ●●● ●●●●●●●●

●

●

●●●●

●●

●●● ●●●

●

●● ●● ●●●●●●●●

●●

●

● ●●●●● ●● ● ●● ●● ●●

●●● ●

●●●

●●●●

●●●

●●●●

●●

●●●●●●

●

●

●

●

●

●

● ●●

●●●●

●

● ●

●

●●

●●●● ●● ●●●●

●

●●●

●●●●

●

●● ●

●

●● ●● ●●● ●●

●

●●●●●●

●●●

●

● ●●

●●

●

●●

●●

●

●●● ● ●●●

●

●●

●

●●●

●●●

●

●

●

●

●●●

● ●● ●●●● ●

●

●●●●●

●

●●● ●●● ● ●●

●

● ●●

●

●●

●

●●● ●●

●●●

●

●● ●●

●

●●●●●●●● ●● ●

●●●●● ●●● ●●

●

●● ●● ●

●

●●

●● ●● ●●

●

●

●●●

●

●

●

●●●

●●●

●●●●●●●●

●●●●● ●

●●

●

●● ●

●●●●

●

● ● ●●●●●●

●●

●●

●●

● ●●●

●●

●●●● ●●●

●

● ●●● ●

●

●●●●●●

●●●●●●

●● ●●● ●● ●●

●

●●● ●●●●●

●●● ● ●●● ●●●

●●

● ●●

●●

●●

● ●●

●●●●●

●

●●●●●

●● ●

●

●● ●●

●

●●

●

●

●

● ● ●

●

● ●●● ●●●●

●

●

●

●●● ●

● ●●●●●●

●●●●●

● ●●● ● ●●●●● ●●●● ●● ● ●●●●

●

● ●●●●●●●

●●

●

●●●●

●●

●●●●●● ●●●●●●●●

●●●●●

●

●●

●●● ●●

●●●● ●● ●● ●

● ●● ●●●

●

●●●

●

●●

●

●●

●

●●

● ●●

●

● ●

● ●●●●●●

● ●● ●●●●●

●

●● ●●

●●

●● ●●

●●

●

●● ●●●

● ●●

●●●● ●●

●●●● ●●● ●

●●●

●

●

● ●●●

●●● ●

●●

●●●

●●● ●●●

● ●● ●● ●

●●●

●●

●●●●

●●●

●●

●●

● ●●

●

●●

●●

●●●●●●●●

●

●●

●

●

●●●

●

●●

●●

●●●● ●●

●● ●●

●● ●●●●●

●●

●●●●

●●●

●● ●● ●●●●●

●●

● ●●● ● ●●● ●

●

●●●

● ●

●

●●●●

●●

● ●

●● ●

●●

●●

●● ●

●

●●

●●●●●●●●

●●

●● ●●

●●

●●●●●●

●

●●●

● ●●● ●●●●●

●

●●

●●●●●● ●●●●●

●●●● ●●

●●

●

● ●●●●●●● ●●

●

● ●●●●

●●

●●● ●

●

●●● ●

●

●● ●●●

●● ●● ●●● ● ●●

●●●●●● ●

●●

●● ●●●●●●●

●

●● ●

●● ●

●●● ●●● ●●●

●

●● ●●●●●●● ●●

● ●●●

●●●

●●●

●●● ● ●●●● ● ●● ●●●●

● ●● ●●

●●●●●

● ●●●●● ●●● ●●●● ●●

●

●

●●●●●●●●●● ●●

● ●●●● ●●● ●● ●● ●●● ●

●

●●●

●● ●● ●●● ●●

●●● ●●●

●●

●●●

●●● ●● ●● ●●

●●●

● ●●

●●

●●

●●● ●●

● ●●●●●●●

●●

●

●●

●

●●

●

●●●●

● ●●●●●●

●●

●●● ●●●

●●●●● ●●●● ●

●●

●●●●● ●

●●●●● ●

●●

●●●●

●●

●

●

●●●● ●● ●

●●

●

●

●

●●●

●●●

●●●●

●●

●

●●

●

●●● ●●●● ●●●●

●●●●● ●●●●●●

●● ●●

●

●●●●● ●

●● ●●

●

●●

●

●● ●

●

●●●● ●

●

●●●

● ●●●●●●●

●●●

●●●●

●●●● ●●

●● ●● ●● ●●

●●●●●

● ●●●● ●

●

●●

●

●

●●

●

●

●

●●

●● ●●●●● ●

● ●

●● ●●●●

● ●

●●●●●

●●

●● ●● ●

●● ●● ●●●●●●● ●●

●●● ●●●●

●●

●●●●

●●●●● ●●●

●●●

● ●● ●●● ●●

●●●

●

●●●

●

●●●

●

●

●

●● ●●●●

●

●● ●

●

●●●

●●●

●●●●● ●● ●●●●●●●●

●

●●

●

●●●●● ●●●●

●●

●●● ●●

●●

●●

●

●●●● ●●●

● ●●●

● ●●●●

●

●

●●●●

●

●●●● ●●

●●●●

●● ● ●●●

●●●●●●

●●● ●

●● ●

●●●

●

●●●

●

●● ●●●●

●

● ●●●●●●

●

●●

●●●●

●

● ●●●● ●●

●●● ●●●●

●●

●

●●●●●

●●

●●● ●●●●●● ●

●

●●

●●● ●●●●●● ●●●●●●● ●● ●●● ●●

●

● ●●

●●

●● ●●● ●● ●●● ●●●●●

●

● ●●

● ●●●● ●

●●

●

●●●●●●

●

●●●● ●●●●

● ●●

●●●● ●●●●

●●●●●

●●● ●●

●●● ●●● ● ●

●

●

●●●●

●

●

●●●●● ●●● ●● ●●●●● ●●● ●●●

●

●

●●●

●● ●●●●

● ●● ●

●

●

●

●● ●●● ●

●● ●●●

●

●●●●●

●●●

●●

●●●

●●

●●●●

●●●●●● ●

●●●●●●

●

●●●●

●

●●● ●●●

●●●●

●●●● ●●●● ●●

●●●

●

●●●●

● ●●

● ●● ●

●●●●● ●

●

●●

●●●●●●

●

● ●● ●●●●●

●● ●●

●

● ●● ●●●● ●

●●●

●● ●

● ●●●●●

●

● ●●

●●● ●●

●●

●

●●●●●●

●● ●● ●

●●● ●

●● ●

●●●●●●●●●

●

● ●

●

●●

●●● ●

●●●● ●●●

●

●●●

●

●

●● ●● ●● ●●● ●

●

● ●●●

● ●●●●

●

●●●●●

●●●

●●●

● ●●●● ●●●

●●

●

●● ●●●●

●●●●●●

● ●●

●●● ●●●● ●●●

●● ●

●●

●●●

● ●●●● ●●●

● ●●●●●●●●

●

● ●●●● ●●

●

●●

●

●

●●●

●●

● ●● ● ●●

●

● ●

●

●●● ●

●●●

●●

●● ●

●●

●

●●●●

●●

●●●●

●

●●●●

●

●●●

● ●● ●●●

●●●●● ●● ●

●

●●● ●

●

●●●

●

●●●●●●●

●

●

●●

●

●●●●

●●●

●●●● ●

● ●

●

●

●●●● ●● ●●

●

●●

●

●

●● ●●●●●●

●●●

●●

● ●●● ●●● ● ●●

●

●●●

●

●

●●●

●●●

●

●

●●

●●

●

●●

●

●●●●●

●●

●●

●●●● ●●

●

●●

●

●

●●

●●

● ●● ●●●

●● ●●●

●●●●

●●●

●● ●●

●

●●

●

●● ●●

●●

●

●●

●

●●

●

●

●

●● ●

●

● ●●●● ●●

●●

●●

●

●

●

●● ●●

●

●●● ●●●● ●

●●

●●

●●

●

●

●●● ●

●●

●●●

●●

●

●●

● ●●

●

●● ●

●●●●

●

● ●

●

●● ●●

●

●●

●

●●

●

●●●

●●

●●

●

● ●●●●●

●●●● ● ●●●

●

●●

●●● ●● ●

●● ●●

●●

● ●●● ●●●●

● ●●

●●● ●●●●●●●●

●●●●●● ●

●●

●

●

●

●●●● ●●● ●●

●

●

●●●●

●

●●

●●

●

●●●● ●

●●●●

●●● ●●●

●●● ●

●●

●●

●●●●● ●●●●

●●●●● ●●●● ●● ●● ●●●●

●● ●● ●●●●● ● ●●

●

●●●

●

●●

●●●● ●● ●●● ●● ●●●

●

●●● ●●

●● ●●

●●● ●●●●●●●●● ●●●●●●●●

●●

●

●●●

●

●●● ●●

●●●

●

●●●●● ●●● ●

●

●●●●●●●●●●

●●●

●●● ●●●●●●●●●●● ●● ●●● ●●

●●●● ●●

●● ●●●●●

●●●

●

●●●●●● ●

● ●

●●●●

●●●●●● ●● ●●●●●●

●●●

●

●●● ●●●●●●●●●●● ●

● ● ●●

●●●●●●

●●● ●

●

●

●

●

●

●●●

●●

●

●●●●●● ●

●

●●●

●●●

●●● ●●

●●●●●

●●●●●

●

●●●

●● ●●● ●●●● ●●●●● ●●●

●●●●●●

●

●

● ●●●

●●●

●●●● ●●●●

● ●●●●● ●●

●●●●●

●●

●●●●

● ●

●●●●

●● ●●●

●

●● ●● ●●●● ●● ●●●

●●●●● ●●●● ●●●●●● ●

● ●● ●● ●● ●●●● ●●● ●●

●●

●● ●

●

● ●●●●●● ●●●●●●● ● ●

● ●

●●

●●●●●●

● ●●●● ● ●●●

●

●

●●●●● ●●

●● ●●●

●●

●

●

●

● ●●

●● ● ●●●

●●●

●●

●●●●● ●●

●●●●●● ●●●●●●●●●

●● ●●●

●●●●●●●● ●● ●●●●●●

●●●●

●● ●

●

●

●●●●●

●●

●●●

●

●

●● ●●

●● ●●

●● ●●● ●●●

●

● ●●●●

●●

●●●●

● ●●●● ●●

●

●●● ●●

●

●● ●

●●

●●

●

● ●●

●

●● ●●

●●●● ●● ●●●●

●

●● ●●●

●

●

●● ●

−0.04 0.02 0.06

0.00

00.

004

0.00

8

animal1

Dominance relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

●●●● ● ●●●● ●●●● ●

●● ●●●●● ●● ●●● ●● ●

●●

●

●●●●● ●●● ●●●●●● ●●●●● ●●●● ●●●●●●●●

● ●●●● ●●● ●● ●● ●● ●●●●

●●● ●●●● ●● ●●● ●● ●●●● ●●●●● ●●●●● ●●●●● ●● ●●●●● ●●● ●●●

●

●●●●●● ●●●● ●●●●●●●● ●●●

●● ●●●●●● ●● ●● ●●●● ●●●●●● ●●●●●

●● ●●● ● ●●● ●

●●

● ●●●● ●● ●● ●●●●●●●

●●●●●●●● ●●● ●●●● ●●● ●● ●●●

● ●● ●●●●●● ● ●● ●●●●●

●●●●●● ●●●●●●●● ●●● ●● ●●●● ●● ●●● ● ●

●●

●

●● ●●●

● ●● ●●● ●●●●● ●●●● ●● ● ●●

●

●●● ●● ●●

●●

●

●●● ●● ●● ●●

● ●●●

●●●●● ●●●● ● ●●●●●●●●●●

●●●●●● ●●● ●●

●● ●●●● ●●●●● ●

●

●●●●●●●●●●●●●● ●●●● ●●● ●●●●●●

●●● ●● ●●●●●●●● ●●●●●● ●● ●●●●

● ●●●●

●● ●● ●● ●

●●●● ●●●●● ●●● ●●● ● ●●●●●●●● ●●●

●●●●●●●● ●● ●●●● ●●● ●●●●

●

●●●●● ● ●●●● ●●● ●●● ●●●● ●●●● ●●●● ●●●●●●●●●●● ●●●●● ●●● ●●●●● ●●●

●● ●● ●●● ●● ●●● ●●●●●● ●●●●●

●● ●●

●● ●● ●●● ●●

●●●●●● ●●● ●●● ●●●●

●●●●●

●●●●

●●●●●●●●● ●●● ●● ●●●●●●●●●● ●● ●●●●●●●● ●●●●●●

●● ●

●

●● ●●

●

●●●

●●●● ●●●●●● ●●●●●●●●●● ●●●●●● ●●● ●●●● ●● ●●● ●● ●●

●●●● ●● ●●● ●●●●●●●● ●● ●●●●●●● ●●●●● ● ●●● ●● ●● ●●●●●●● ●●●●●● ●● ●● ● ●●●

●●●● ●●●●●●●●●●●●●● ●●● ●●● ●●●● ●●● ●●●● ●● ●●●●●●●●●● ●●● ●●●●● ●●●●● ●●●●●● ●●●● ●● ●● ●●●●● ●●● ●●● ●●

●●●●

●

●● ●●●● ●● ●●●●●●

●●●●● ●●● ●●● ●●● ●●● ●● ●●●● ●● ●●●●

●●●● ●●●●● ●● ●●●● ●● ●● ●●●●● ●●●●●●

●● ● ●●● ● ●●● ●●

● ●●●

●● ●●●●●●●● ●●●●●●●●● ●● ●●● ●●●●●● ●● ● ●●●●

●●● ● ●●●● ●● ●●●●● ●●●● ● ●●●●●●●●● ●●●

●● ●●●●●●●●●● ●●●●●●●●● ●●●●● ●

●●●●●●●●● ●

●●● ●● ●●

●●● ●●●●●● ●●●●●●●

●● ●●●

●●●●● ●● ●●● ●●●●

●

●●

●

●●● ●● ●●●●● ●●●

●●●●●●● ●●●●● ●●● ●●●●●●● ●●●●● ●● ●●● ●●●●● ●●●●● ●●●

●● ●●● ●

●● ●●● ●●●●●

●●●●●● ●●●●●●●●●

●●● ● ●●●● ●●● ●●● ●●●● ●●●●●●●● ●●●● ●●●●●●● ●●●●●● ●●●●●●●●●● ●●●●●

●●●●●

●●●

●

●

●●●●

●●● ●●●●●●●●●●● ●●●●●● ●●● ●●●● ●

●

●●● ●●●● ●●●● ●●● ●●● ●●● ●●●●

●●●●●

●●●●● ●●●

●●●● ●●●● ●●●●●● ●●● ● ●●●● ●● ● ●● ●●●●●● ●●●● ●●● ●●●●● ●●●

●● ●●●● ●●● ●

●●●●●

●●● ●●●●●●●●●

●● ●●● ●●● ●● ●●●● ●●●●●

●●●

●●● ●●●● ●●●●●●● ●●●● ●● ●●●●● ●●● ●●●● ●● ● ●●● ●●●● ●●●●●●●●●● ●● ●●●●● ● ●●

●● ● ●● ●● ●● ●●● ●●● ●●● ●●●● ●●●●● ●●●● ●● ●●●●●●● ●●●●●●●●●●●● ●●●●●● ●●●●●● ●● ●●● ●●● ●

●●●●● ●●● ●● ●●●● ●● ●●● ●●● ●●● ● ●●●● ●●● ●●●●●●●

●

●●● ●●●●●● ● ●● ●●● ● ●●●● ●● ●●●●●●● ● ●●●●●

●●● ● ●●● ●

●● ●● ●●● ●●●● ●●● ●●●●

●● ●●● ●●●

●

●●● ●●●●

●●●● ●●●●●● ●●● ●● ●●● ●● ●● ●●●● ●●●●● ●● ●● ●●●●● ●●●● ●●● ●●●●●

●

●●●●●●●●●● ●● ●●● ●● ●●● ●●● ●●● ●● ●● ●● ●●● ●●●● ●●●● ●●●● ●●●●● ●●●●●●●●●

●● ●●●●● ●●●●●●●●●● ●●●●● ●●●● ●● ●●● ● ●●●●●● ●●●●●●● ●●● ●● ●● ●● ● ●●●● ●● ● ●●●● ●●●●● ●●●●● ●●● ●●●●●●●● ●● ●● ● ● ●●● ●●● ● ●●●●● ●●

●

●● ●●●● ●●●

●● ●●●● ●●●●● ●●●● ●● ●●● ●●●●●●●●●●●

● ● ●● ●●

●

●● ● ●● ●● ●●●● ●●●

●

● ● ●●●● ●● ●●

● ●● ●●●● ●●●● ●●●●● ●●●● ● ●●●●●● ●●● ●●●●●● ●●●●● ●●● ●●●●●●●●

●●●● ●●● ●● ●● ●●●● ●●●●●●

●

● ●●● ●●● ● ●●●● ●●●●●●●●● ●●● ●●●● ●● ●●●●●●●●●●●● ●● ●● ●● ●●●●

●●●●●● ●●● ●●● ●●●

●●●● ●●● ●●●●●●●●

● ● ●●●●

●●●●● ●

●●●●●● ●●● ●●●

●● ●●●●● ●●

● ●●● ●●●●● ●●● ●●●●●● ●●● ●● ●●●●●●● ●●●● ●●●●●●●●● ●● ●●●●●●●●●

●●● ●●● ●●●● ●●●●●●●●●● ●● ●●●●●●●●●●● ●●●●● ●

●

●●● ●● ●●●● ●

●

●●●●● ●●● ●●●● ●● ●●●●●●●●●● ●● ●● ● ●●●●● ●● ●●●●●●●●●●●●● ●●●● ●●● ●● ●●●

● ●●● ●●●●●●●●● ●● ●●●●●●

● ●●● ●●●●●● ●●● ●● ●●● ●●●●● ●● ●●●● ●● ●● ●●● ●●●●● ●●●●● ●●●●●

●● ●●● ●●●● ●●● ●●●●● ●● ●●● ●●●●●

●●● ●●●●●● ●●● ●●● ● ●●●

● ●●● ●● ●●●● ●●●●●● ●●●●●

●●●

●●●

●● ●●●●● ●● ●●●● ●●●●●● ●●●● ●●●●●●●●●● ●●●● ●● ●●●●● ●● ●● ●●● ●●●●●● ●●●

●●●●●● ●●●●●●● ●●●● ●●●● ● ●●

●● ●●● ●● ●●● ●●●●●●●

●● ●●●

●●●● ●●●●● ●● ●●● ●●●●●●

●●● ●●●●

●●●●● ●● ●●● ●●● ● ●● ●● ●●●●●●●●●●● ●●●●

●

●●● ●● ●●● ●● ●● ●●● ●● ●●● ●●●●● ●●●●●● ●●●● ●● ●●●●●●●●● ●●●● ●●● ●●●●●●●● ●●● ●●● ●● ●●●●●●

● ●● ●● ●●●●●●●●●●● ●●●●● ●●●● ●● ●●

●●● ●●●

●●●●●● ● ●●● ●● ●●●●●● ●●●●●●● ●●●● ●●●●● ●● ●● ●●●●●●● ●●● ●●●●●●●● ●●●●●●●●●● ●●●● ●●

●●● ●●●●● ●●●

●●● ●●● ●●●●●● ●● ● ●●●

●●●● ●●●●●● ●●●●●●● ●● ● ●● ●●● ●●

● ●●●● ●●●●

●●●●●●

● ●●●

●

●●●●●● ●●●●●●●●●●●

●●● ●●●●●● ●●●●●●●●●●● ●●●●●●●● ● ●●● ●●●

●●● ●●●● ●●●●●●●●●● ●●●● ●● ●●●● ●●●

●●●● ●●●●

●●●●●

●● ●●●●●●●●●●

●●●●●●

●● ● ●●

● ●●●●● ●●●

●●●● ●●●●●●●●●●●●●●● ●●●●●● ●●●●● ●●● ●●●●●●● ●● ●● ●●●●● ●●●● ●● ●●●

●●●

●●●● ●●●●●●●● ● ●●●●● ●●● ●●●●● ●●●

●●●● ●●●

●

●●● ● ●●●●●●

●

● ●●●● ●● ●●●● ●●●●●●● ●● ●● ●●●●●●●● ●●●●●● ●●● ● ●●●● ●● ●●●●●● ●● ●● ●● ● ●●● ●●●●●●●

●●● ●●● ●● ●●●●●●

●●● ●●● ●● ●

●●● ●● ●●● ●● ●●●● ●●●●● ●●●●●●●● ●●●●●● ●●●● ●●● ●● ●

●●●●●●●●● ●●●●●●●● ●●●● ●●●●● ●●●● ●● ●●●●●●●●●●●●● ●●●

●●

●

●● ●●●●●●●●● ●●●

●●●●●●●● ●●

●●● ●● ● ●● ●●●●● ●●●● ●●●●●●● ●●●● ●●● ●

●●● ●●●●●● ●●●● ●●● ●●● ●●

●● ●●● ●●●● ●

●●●

●●●● ●● ●● ●●● ● ●● ●● ● ●● ●●●● ●●

●●

●●●● ●● ●● ●

●●●●●●●●

●● ●●●

●●●● ●●● ●●●● ●●

●●● ●●●●● ●● ●●●●

●

●

● ●● ●● ●●●● ●●●● ●●●● ● ●●● ●●●●● ●● ●●●● ●●●●

●●●● ●● ●●● ●●●● ●●●●●●●● ●●●●●●

●

●● ●●● ●●●

●● ●●●

●●●

● ●●● ●●●●●●●●●●● ● ●●●●●●●●●●●● ●●●●●

●● ●●● ●● ● ●●●

●

●● ●●●●●●●●

●

●●●●

●

●●●●● ●● ●●●

●● ●●

●●● ●●●●● ●●● ●●●

●

●● ●● ●●●●● ●●●●● ●●● ●●●●●●● ●●

● ●●●●●● ●● ● ●●●● ● ●●●●●●●●●

●● ●●●

●●●●●●●

●●●● ●●●● ●●● ●● ●●●●

●●●● ●●●●● ●●●●●●●●● ●●● ●●●●●●●●●

●●●●● ●● ●●

●●●

●●

●●● ●●●

●

●● ●●●●

●●

● ● ●●●●

●

● ●●● ●● ●●● ●● ●●●●●●● ●●●●●●●

●● ●● ●

●

●● ●●● ●● ●● ●●●● ●●● ●●●●●●● ●● ●●● ●●●

● ●

●●● ●●● ●●●● ●● ●● ●●●●●● ●●● ●●● ●●● ●●●● ● ●●●●●●●

●●●●●●●● ●●● ●● ●●●● ●●●● ●●

●

●●●

●

● ●●●

●

●

●●

● ●●●●●

●

●● ●●● ●●●●● ●●●●●●●●●●●

● ●●●●●●● ●●●●●●●●● ●●●●●

●● ●●●● ●●●●● ●●●● ●● ● ●● ●●●●●●●●●● ●●●

●

●●

●●●●●● ●●● ●●●●●● ●●●●●●●●● ●●●● ●●●● ●● ●● ●●●●●● ●● ●● ●● ●● ●● ●● ●● ●● ●● ●●●●● ●●● ●●●● ●●● ●●●●●●●●●● ●●●●●●●● ●● ● ●●●● ●●● ● ●

●●●● ●● ●● ●●●●●●

●● ● ●●

● ● ●●●●● ●● ● ●●● ●

●●●●●● ●●● ●●●●

●● ●● ●● ●●●●●●● ●

●●● ●●●●●

●●

●●●●●

●

●

●●●●●●● ●●●●

●●●●●●●● ● ●

●●

●●● ●●

● ●●●●●

● ●●●

●●●

● ●●●●●

●●●● ●●●●●●●●● ●●●●●● ●●●●●●●

●●

● ●

●

● ●●

●● ● ●●●●● ● ●● ●● ●● ●● ●●●●● ●●● ●●●● ●●●●●● ●● ●●●●●●●●●●●●● ●●

●● ●● ●● ●● ●● ●●●●●

●●● ●● ●●●●●●● ●●●● ●

●●● ●●●

●●●

●●●●●

●●●●●●●● ●●●●●●● ●●●● ●● ●●●● ●●

●●●

●●●●●●●

●●●

●●●●● ●

●●●● ●●● ●● ●●●●●●●●●● ●●● ●●●●●● ●●●●

●● ●●

●●●●●●●● ●●●

●●●●●

●●●●●●●●

−0.04 0.02 0.08

0.00

00.

010

0.02

0

animal2

Dominance relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

● ●●●●

●●● ●●● ●●●●●●●

●●●●

● ●●●● ●●● ●●● ●●●● ●●●●●●●●●●● ●● ●●●●●●●●●●● ●

● ●● ●●● ●● ●●●●●●● ●● ●●●●● ●●● ●●● ● ●● ●● ●● ●●● ●

●●●● ●● ●●●●●●●●● ●● ●● ●●●● ●● ● ●

●●●● ●● ●●

●●●● ●●●●●● ●●●●●●●● ●● ● ●●●●● ●●●●●●

●

●

●●●●● ●●●● ●●●●●●● ●●●

●●●● ●●

●●●●●●●●●●

●

●●●●●●● ●● ●●● ●●

● ●●●● ●●●●●

●●

●●●●●● ●●● ●●●●●●●●●●● ●●●●●●●● ●●● ● ●●●●● ●● ●●●●●● ●●●●●●●●● ●●●●●● ● ●●●●●●

●●●●●● ●● ●●● ●●●● ●●●●●●●●●●●●●

●●●●●●

● ●●●● ●●●●●●● ●● ●●●●● ●●●●●●●●● ●●

●●

●●●●●●● ●●

●●●

●●●●● ● ●●●●●●●● ●●●●● ●●●● ●●●●●●● ●

●

●●●●

●

●●●●●

●●●●●●● ●●

● ●●● ●● ●●●●●

●●●● ●●

●●●●● ●● ●●●●●●●● ●●●●●●

●●●●● ●● ●●●● ●●●●●●

●●● ●●●●●●● ●●●●● ●●●●● ●●●●●●● ●●●●

●●● ●●●●●● ●●● ●●●●●●●●●●●●●● ●●●●●●●●● ●●● ●●● ●●●●● ●●●●●● ●●●●●● ●● ●● ● ●●●●

●●

●● ●● ●●● ●● ●●●●● ●●●●●●●●●●●●●●●●●●●●●●●● ●●●●● ●●●●●●● ●● ●●● ●●●● ●

●

●●●●● ●●●● ●● ●● ●●●●●● ●●● ●●● ●●●● ●●●●● ●●●●● ●●●●●●●●● ●●●●●●●●●●●

●● ●●●● ●●●●●● ●●●●●●●●●●●

●● ●●●●●●●●● ●●●●●●●●● ●●●●● ●●● ●●●● ●● ●●●● ●● ●● ● ●●● ●● ●● ●●●● ●●●●

●●●●●●●●

●●● ●●● ● ●● ●●● ●●●● ●● ●●● ●● ●●● ●● ●●●● ●●●●●●● ●●

●●●●

●●●●●● ●●● ●● ●●● ●●● ●● ●●● ●●● ●● ●●●●●●● ●●●● ●● ●●●● ●●●●●●●●●●●●●●● ● ●● ●●● ●● ●●●●●

●●●● ●●●●●● ●● ●●●● ●

●

● ●● ●●●● ●●●

●●● ●●●●●● ●● ●●●●●●●

●

● ●●●● ●●●●●●●●●●●

●● ●● ●● ●●●● ●●

●●●●●●● ●●●● ● ●●● ●●●●●●● ●● ●●●●●● ●● ●●●●●●●●● ●

●●● ●●●●● ● ●●● ●●●●●●●●●●● ●●●●●● ●●●● ●●● ●

● ●● ●●● ●●●●●● ●●●●●● ●●●●● ●● ●●●●

●

●●●● ●●●●● ●● ●●●●●●● ●●● ●●●● ●● ●● ●●● ●●●●●●● ●● ●●●●● ● ●●● ●●●● ●● ●●● ●● ●●● ●●●●●●●●● ●● ●●● ●● ●●●

●●● ●●●● ●

●●●●●●●

●●●●

●●●● ●● ●●●●● ●●

●●●●●● ●● ●●

●●●●●

●● ●●●●●●●

●● ● ●●

●● ●● ●●● ●●●● ● ●●● ●●●●●●●●● ●●● ●●●●● ●●●●●● ●●●

●● ● ●●●●● ●● ●

●●●●●

●●●●●●●●●●●●●●● ●●●●●●●●● ●●●●●●●● ●● ●●●●●●●● ●● ●●● ●● ●●● ●●●● ●●●●● ●●●

●●●●● ● ●● ●●●●

● ●● ●●

●●●●● ●●●● ●●●●●

● ●●●● ●●●●● ●●● ●●● ●●● ●●●●●●● ●●● ●● ●●● ●●●●● ●●●● ●●●●●●●●●●●●● ●● ●●●● ●●●● ●●●●●●●●●●●●

●●● ●●●●●● ●●●●●●●●●● ●●●● ●●● ●● ●●●● ●●●● ●●●● ●●●●●●●● ●● ●●●● ●●● ●●●●●● ●●

●● ●●●

●●●●●●●●●●●● ●● ●

●● ●●● ●●

●●● ●●●●●● ●●●

●

● ●●●●●●●●● ●●●●●● ●●●●

●●●● ●● ●●●●●● ● ●●●● ●● ●●● ●●●●● ●●●● ●●●●●●●● ●● ●● ●

●●● ●●●●● ●● ●● ●●● ● ●●●● ●●● ● ●●●

●●●●●● ●●● ●●● ●●●●●●●●● ●● ●●● ●●●●● ●●●● ●●●●● ●●●●●

● ●●● ●●●

● ●● ●●●● ● ●●

●

●●● ●● ●● ●● ●●●●● ●●●●●●● ● ●●●

●●●●●●● ● ●●● ●●●●

●●●●

●● ●● ●●● ● ●● ● ●● ●●●●●●● ●●● ●●●● ●● ●●● ●●●●●●● ● ●● ●●●●

●● ●● ●●● ●

●● ●●●●

●●●●●●● ●●●●● ●●●● ●●●● ●●● ●●●●●●●●●

●●●●●

●● ●●●●●●● ●●●●●●●●●●●●●● ●● ●●●●● ●●●● ●●●●● ●●●●●● ●

●●● ●● ●●●● ●●●● ●● ●● ●●● ●●●

●●●● ●● ●●● ●●

●

● ●●●●●●● ●●● ●● ●●● ●●●●●●● ●● ●●●●●●●● ●●●● ●●●● ●●●●●● ●●● ●●● ●●●● ●●

●● ●●

●● ●●● ●● ●● ●●●●●●●●● ●●●● ●● ●●●●● ●●● ●●● ●● ●●●●●● ●●● ●●●●

●●●

●●●●●●● ●●●● ●

●●●

●●●

●● ●● ●●●● ●●

●●● ●● ●●●

●● ●●●●●●●● ●● ●●● ●● ●●● ● ●●●●● ●● ● ● ●●●● ●●●●●●●●● ●●●

●● ●●●

●●●● ●●● ●●●● ●●●● ●●●●●●●●● ●● ●●

●●●●●●●●●●●● ●●●●●● ● ●

●● ●● ●●●●●● ●

●●●●

● ● ●●●●●●

●●● ●●● ●● ●●● ●●●●●●● ●●

●

●●●

● ●●●●●● ●

●

●●

●● ●● ●●● ●●●●●● ●●● ●●● ●●●●●● ●● ●●●

●● ●●●

● ●● ●●● ●● ●● ●●●●●● ● ●●●●● ●● ●● ●● ●

● ●● ●● ●●●●●●●●●● ●● ●●●● ●●●● ●● ●●●●●●●●

●●

● ●●●●● ●●● ●● ●●● ●●● ●● ●●● ●●●●● ●●●

●

●● ●● ●●● ●● ●● ●●●●● ●●●

●●

● ●● ●●● ●●●●

●● ●●●● ● ●●●● ● ●●● ●●●●

●●●●● ●●● ●●●

●●●●●

●● ●● ●●● ●●●● ●●● ●●●

●●●●● ●●●● ●●●● ●● ●● ● ●●● ●●●●● ●●● ●●●●●● ●●●● ●●●●● ●●● ● ●●●●●●● ●●● ●●●●●●●● ●●● ● ● ●●

●●●●● ●●●●●● ● ●● ●●● ●● ● ●●●●●●●● ●

●● ●●● ●●● ●● ● ●● ●● ●●●● ●●● ●●

●

● ●●● ●●

●●●●● ●

●

●●●● ●●●●● ●●●● ●●●●●● ●● ●● ● ●●●●●● ●●●

●●

●●● ●● ●●●● ●●● ●●● ●●● ●●

●

●●●● ●● ●● ●●●● ●● ●●●●●●●●●●●● ●●● ●●● ●● ●●● ●

●●●●●●●●● ●●●●●●● ●●● ●●●●● ●●●●●● ●●

●●●●

●●●

●●●●●●● ●●●● ●●●●●●

●● ●●● ● ●●● ●●●●●●●●● ●●● ●●●●●●●●● ●●● ●● ●●●●

●●●●●●● ●● ●●●●●● ●●

●● ●●●●●●●● ●●●●●● ●● ●●●

●

●●●

●●●

●●●●●●●

●●● ●● ●● ●●

● ●● ●●● ●●● ● ●●●●●

●●● ●●●●●●● ●● ● ●●●●●

●●● ●●●●●●●● ●

●●●● ● ●● ●●●●● ●●● ●● ●●●●●●●●●●● ● ●●● ●● ●●● ●● ●●

●● ●●●●●●●● ●●● ●● ●●

●●●●●● ●●● ●● ●● ●●●

●●● ●●● ●●●● ●

●● ●● ●●●●●●●●●● ●●●● ●●●●

●● ●●●●●●●● ●●●

●●● ●●●●●●● ●●●●● ●●●●● ●●●●●●● ●●● ●●●● ●● ●

●● ●● ●●●

● ●●●● ●●● ●●●

●●

● ● ●●

●●●●●● ●●●●●● ●●●●●●●●● ●●● ●●●●● ●●● ●●

●

●●●● ●●● ●● ●●●●●● ●●●●●●●●●●●●●●●●●

● ●●●● ●●●●

●

●●●● ●●

●● ●●●● ●●●●

●●● ●●●●●●●●● ●●●●●● ●●● ●● ●●● ●●●●● ●●●●

●●●● ●●●●● ●●●●●●● ●●●● ●●●●● ●●● ●●● ●●●●●●● ●●● ●●● ●●●● ●● ●●●

●●● ●●●●●

●● ●● ●●●●●

●

●●

●●●●●●

●●● ●●

● ●●●●● ● ●●● ●●●●●● ●●● ●●●●●●●●● ●●

●●●●●● ●●●●●●●●●●●●●●●●● ●●●● ●● ●●● ●●●● ●●●●●●● ●●●●● ●●●

●

●●● ● ●● ●●●● ●●● ●●●● ●●●●● ●●● ●●● ●●

●● ●● ●●●●● ●●●●●●●●●●● ●●●●●

●●●● ●●●● ●●●●

●● ●● ●●●●●●● ●●● ● ●● ●●● ●● ●●●●● ●●● ●●●●●● ●●

●●● ●●●● ●● ●● ●● ●●●●●●● ●●●●●●●●●●●● ●●●●● ●●●●●●

● ●●●

●●●● ●●●● ●●● ●●●● ●●●●●

● ●●●● ●●●

●●●●●●●● ●● ●● ●●● ● ●●● ●● ●●● ●●● ●

●●●● ●●●● ●●

● ●●● ●●● ●●●●● ●● ●●● ●● ●●●●●●● ●●●●

●● ●●●

●●

●● ●●●● ●● ●● ●●●● ●●●●● ●●●●●● ●●●●●●●●●●● ●●● ●●● ●●●●●●

●●●●● ●●● ●●●●●● ●●●●●●● ●● ●●● ●● ●●

●● ●● ●● ●●● ●●●

●●●

●●● ●● ●●●●●●● ●●●● ●●●● ●●● ●● ● ●● ●●● ● ●●●●●●● ●●● ●●●●●● ●●●●● ●●●●● ●●●●●● ●●●●●●●● ●● ●● ●●●●●●●●● ●●● ●●● ● ●● ●●

● ●●● ●●●

●●●●●

●

●● ● ●●● ●●● ●●●

● ●● ●●●●● ●●●●●● ●●●●●●●● ●●●●●●● ●

●●●● ●●●

●● ●● ●●

● ●●●● ●● ●●●●● ●●●

●

● ●●●● ●●● ●●● ●●

●● ●●●●●● ●●

●●● ●● ●●●●

●●●● ●●

●

●●●

●

●●●●●●

●●●

●●● ●●●●

●●

●● ●● ●

●●●●●● ●●

●●●●● ●●●

●●

●

●●●● ●●● ●●● ●● ●●● ●●●

●●

●●●●● ●● ●●

●●●● ●●●●●●●●●●●

● ●● ●●●●●● ●●●●●●●●●●●●● ●

●●

●●●●●● ●●●● ●●●●●●●●●●●●●●● ●● ●●●● ●●●●● ●●● ●●●●●● ●●

●●●●●● ●

●●●● ●●●● ● ●●●●●● ●

●●●● ●● ●●● ●●●●● ●●●● ● ●●●

●● ● ●●●● ●●●●●

●●●● ●● ●●●●●● ●●● ●●●●●●●●●●● ●●

●●●●●●●● ●●● ●●●

●● ●●●

●● ●●●● ●

●●●●● ●● ●●●●●● ●●

●● ●● ●●●

● ●● ●●●●● ●●●●●

●●

●● ●●●● ●

●●● ●●● ● ●● ●●

●●●●●●●● ●● ●●●

● ●●● ● ●● ●●●●●●● ●●●● ●●●

●●

●●●●● ●●● ●●● ●● ●●●●●●●● ●

●●●● ●●

●● ●●●●●●●●●●●●

●●●●●●●● ●● ●

●●● ●

●●●● ●●●●

●●

●●●●●● ●

●●●● ●●● ●

●●●●

●●● ●●●●●● ●● ●●

●● ●● ●● ●●

●

●●●● ●●●● ●●

● ●●●●●●● ●●

●●● ●

●● ●

●

●●●

●●● ●●

●

●●●

● ●●●● ●●● ●●●●●●●● ●●●●

−0.02 0.04

0.00

00.

010

animal3

Dominance relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

●●

●

●●● ●●● ●●

●●●●●●●● ●●● ●●●●●● ●●● ●●●●●

●

●● ●●●● ●●● ●●●● ● ●●● ●● ●●●●● ●●●● ●●●●●●● ●●●● ●●●

●●●● ●●●●●●●● ●●●●●● ●● ●●●●●● ●●● ●●●●● ●

●● ●●●● ●●● ●●●●●●

●●●●

●● ●●●●●●●●● ●●● ●●●● ●●●

●●●●●●●●● ●●●

●● ●●●●●●●●

●

●●●● ●●●●●● ●●●● ●●● ●● ●●● ●●●●● ●●●

●●●●●●● ●●●●

●

●● ●●●●●●

●●●●●●● ●● ●●●● ● ●●● ●●● ●●

●●●●●

●

●●●● ●● ● ●●

●● ●● ● ●● ●● ●●●●

●

●●●●●●●●●●●●●●

● ●● ●●●●●● ●

●

●● ●● ●● ●

●

●●●●● ●●●●●● ●●●●●● ●●● ●●●●● ●●●●●●●●●●● ●●● ●● ●●●●●● ●● ●●●

●

●●● ●●●●●●

●

●● ●● ●●●

●●● ●●● ●● ●●●●●●●●●●

●●● ●●● ●●● ●●●●● ●●●●●●●● ● ●●●●

●● ●● ●●●●● ●●●● ●●● ●●●●

●

● ●●●

●

● ●●●●●

●● ●●●●

● ●

●

● ●●●●●● ●●●●●● ●●●●●●● ●●●●●●●●● ●●●●●●●●●● ●● ●●●● ●●●●● ●● ●●● ●● ● ●●● ●●●●

●●

●

●

●●●●●●●●● ●●● ●● ●●● ●● ●●●

●●●● ●●●● ●●● ●●●●●●● ●●● ●● ●●●

●●

●

●●●● ●●●● ●●● ● ●●●●● ●●●● ●●● ●●

●

●● ●●●●●●●●● ●●●

●●● ●●●● ●●●

●

● ●●●●●●● ●●●●● ●● ●●●●●● ●●●●●●● ●● ● ●●● ●●●● ●●●●●●● ● ●●● ●● ●●●●●● ●●●●●●●● ●●●●●● ●●

●●●●●●●●●● ●●

●●●●● ● ●●●● ●●● ●●●●●●●●●●●●●

●●●●●● ●●●●●●●●●● ●●

● ●●●

●●●●●

●●●●● ●● ●●●●● ●● ●●●● ●●● ●●●●●●● ● ●●●●●●●●●●●●●●● ●●●● ●●

●● ●●● ●● ●●●

●●●● ●●● ● ●●●●●●●●●●●●●

●

●●● ●●●●●●●● ● ●●● ●●●●●●●●●●●●●

● ●● ●●● ●●

●●●●●●●●● ●●● ●● ●●● ●●●●●●●● ●●●●●● ●●●●●● ●●● ●

●●● ●●

●●

●●●●●

●●●●

●

●●●●●●●● ●●●

●●

●●●

● ●●●● ●● ●●●●●●● ●● ●● ●●●●●● ●● ●● ●●●●●● ● ●●●●●●●● ●● ●●●● ●●●●●●● ●● ●●●● ●●● ●●●●●●

●●●●●●● ●●●●● ● ●●●●●●●●●●●● ●●●●●●●●●●●● ●●●● ●●● ● ●●

●●

●●●●●●● ●●●●●●●●●●●●●●●● ●● ●●●●●● ●● ●●●●● ●●●●●●●● ●●● ●● ●

●●● ● ●●● ●●●●● ●● ●●● ●●●● ●●● ●●●●●●●●●● ● ●●●●●●● ●●

● ●●●●● ●●●●●

●●●●●●●●●● ●●● ●●● ●●● ●●●● ●●●●● ●● ●●●

●●●●●● ●●● ●●● ●●

●●●● ●●

●●● ● ●●● ●●●●●●● ●●●● ●●● ●●●●● ●●●●●●●●● ●●●●● ●●● ●●●● ●●●●●●●● ●●● ●●●●●● ●●● ●●●●●●●● ●●●●●● ●●●●● ●●● ●●●●● ●●

●● ●●● ●●●●●●●● ●●●●● ●●●

●●●

●

●●●●●●●●●●●●●●●●●●●● ●●●●● ●

●●

●

●●

●

●● ●● ●●●●● ●●

●

●●● ●●●● ●● ●● ●● ●

●

●● ●

●

●●●●● ●●●● ●●●

●

● ● ●●●● ●●● ●●●● ●●●●●●●●●●●●●●●●●●● ●●●● ●●●●●●● ●●●

●

●●●

●

●● ●●●● ●●●●●●

●

● ●

●

●●

●

● ●●● ●●●

●

●

●●●● ●

●

●

● ●●● ●●●●

●●●●●●●●●●

●

●●●

●

●●●●●●

●

●●

●● ●

●

●●● ●●● ●●●●●●

●● ●●●●●●● ●● ●●●

●●●

●

●

●●● ●●●

●

●●●● ●●●

●

●●●●● ●●●●

●

● ●●●●●● ●●●●●● ●●●●

●

●●● ● ●●● ●●● ● ●●●●●●

●●● ●●● ●●●●●●●●●

●

●●● ●●●●●●●● ●●●

●●

●

●●●●● ●●● ●●●●●● ●●●●

●

●

● ●● ●● ●●● ●●●●●●

●

●● ●●●● ●●● ●●●●● ●●

● ●● ●●●●● ●● ●●●●●●

●

●

● ●●●● ●●●

● ●●●

●

●●●●●●●●●●●●

●

●

●●● ●● ●●●● ●●● ●●●● ●●● ●●●● ●●●● ●●●● ●● ●●●●●●●●●●

●● ● ●●●●●●●● ●●●●●●●

●●●● ●● ●●●● ●●●●●●●● ●●●●●●● ●●

● ●●●●● ●●●

●●●●

●●●● ●● ●●●

●●●●●●●● ●●●●●● ●●●●●

●●●●● ●● ●●● ●● ●●● ●●●●● ●● ●●● ●●●● ●●●●● ●●● ●●●●●● ●●● ●●●●●●● ●● ●●●●● ●●●●● ●●●●● ● ●●●● ●●

●●●●●● ● ●● ●●● ●●●●●● ●● ●● ●●●●●●● ●●●● ●●● ●●●●● ● ●●●

●●●● ● ●●●● ●

●

●●●● ●●●

●●●●●●●●●●●●

●

●●●●

●

●

●●● ●●● ●● ●●● ●●●●●●●●●●● ●●●● ●●●●●● ●●●●●●●●●●● ●●● ●● ●●

●●

● ●● ●● ●●●●●●●●●●●

●● ● ●● ●● ●● ●● ●●●●● ● ●●● ●●●● ●●●●●●●● ●●●

●●●●● ●●●●●

●●●●● ●● ●● ●● ●● ●●●●●●● ● ●●●● ●●●●●●● ●● ●●● ●●● ● ●●●●● ●●●●●● ●●●●●●●●●●●● ●● ●●● ●●●● ● ●●●●●●●●●● ●● ●● ●●●●● ●●●● ●●●●●●●●●● ●● ●● ●●●● ●●●●●●

●●●● ●●●●● ●●●●●● ● ●●● ●● ●

●

●● ●● ●●

●●●●●● ●●● ●●●● ●●● ●●●● ●●●●●●

●● ●●●●●●●

●●●● ●●●●●● ●●●●●● ●●●● ●● ●●●●●● ●●●

●●●●●●● ●●●●● ●● ●●●● ●●●●

●

●● ●●●● ●●● ●●●●●●

●●●●●●●●●

●●● ●● ●●

●

●●● ●

●

●●●

●

●●

●

●● ●●

●

●

●

●●● ●●● ● ●●●●●●

● ●●●●

●●●

●●

● ●●●

● ●●●●●●●●●●●

●

● ●

●

● ●●● ● ●

●

●● ●●● ●●● ●●● ● ●●●●● ●●● ●●●●●●●

●●●● ●●● ●●

●●

●

●● ●● ●●●●●●

●●

●

●●●●●● ●●● ●● ●●● ●●● ●●●●●●●

●●●●●●● ●●● ●● ●●●● ●● ●●●●●●●●●●●● ●●●●● ●● ●●●●●●●●● ●●●● ●●●●●●●● ●●

●

●● ●●● ●●●●

●

●

●

●

●

●●

●

●

●

●●●●● ●●● ●●●●● ●●●● ●●●● ●●● ●●● ●●●●● ●●●● ●● ●●●●●● ● ●● ●●● ●●●● ●●●

●●●●● ●●●●●●● ●●●●● ●●●●● ●●●● ●

● ●●●● ●●

●● ● ●●●● ●●●●●●● ●●● ●●

●● ●● ●● ●●● ●● ●● ● ●● ●● ●●●●●●●●●● ●●●●●● ●● ●●●●●● ●●●● ●●●●●● ●●●●● ● ●

●●● ●●●●● ●● ●●●● ●●●● ●● ● ● ●●● ● ●●● ●● ●● ●●●●●●●●●●

●● ●●●●● ●●●●●●●●● ●●● ●● ●●●

●● ●●●● ●●● ●● ●●●●●●● ●●●●●●●●●● ●●● ●●●●● ●●● ●●

● ●●● ●● ●●●●●●●●

● ●● ●●●● ●● ●●● ●●●●● ●●●●●● ●●●●●●●●

● ●●●●● ● ●● ●● ●●●●●●●

●

●●

●●● ●● ● ●●●●

●●●●

●●● ●●●● ●●●●●●●

● ●●●● ●●

●●●●●● ●●● ●●●●●●●●●

● ●●●●●● ●●● ●●●● ●● ●● ●●●●●●●●●●● ●●● ●●● ●●

● ●● ●●●●●

●●

●● ●● ●●

●●● ●●● ● ●●●●●

●●●● ●●●●●● ●●● ●●● ●●●●●●●●●● ●●●● ●●●●●●● ●●●● ●●●●●●●●●● ● ●●● ●●● ●●●●● ●●●●

●● ●●● ●●● ●●●●●●●●●●● ● ●●● ● ●●● ●●●●●●●●●●●● ●●●●●●●●

●●

●● ●●

●

●●● ●●● ●●● ●●●● ●●●●● ● ●●●●● ●●●● ●●● ●●●●●●●●● ●● ●●●●● ●●●

●●●● ●●● ●●

●●●●●●●●● ●●● ●●●● ●●●●● ● ●●●● ●

●●●●●● ●●● ●●●●● ●●● ●●●

●

●●●●● ●● ●●●● ● ●●●

●●

●

●●● ●●●●●●●● ●●●● ●●●● ●● ●● ●●●● ●● ●●● ● ●●●●

●●●●●●●

●●● ●●●●●●●●● ●●● ●●●●●●●●

●

●●● ●● ● ●●● ●● ●●●

●● ●●●●●●●● ●●●● ●●●●●●●

●●●● ●●● ●● ●● ●● ●● ●●●● ●● ●●●● ●●●●●● ●●● ●●●●

● ●●

●●●●●● ●●●

●

●●● ●● ●●●● ●● ●● ●●●●

●●●●● ●●●●●

●●●● ●●●●● ●●●●● ●●●●●●● ●●●●●●●●●●● ● ●● ●●●●●●●●●●●● ●●● ●●●

●●●● ●●●● ●● ●●●● ●●●●●● ●● ●● ● ●●●●●●● ●●●●●●●

● ●●● ●● ●●●●●●●●●●

●● ●●●●●● ●●●● ●● ● ●●● ●● ●●●●

●●● ●●●● ●●● ●●●● ●● ● ●● ●●●

●

●●●●●●

● ●● ●●●●●●● ●● ●●●●● ●●● ●●●●●●●●● ●

●● ●●●● ●●●●●●●●●●●● ●●●●●●●

●● ●●● ●●●

● ●●

●●

●

●●●●● ●● ●●●●● ●●

●●● ●● ●● ●● ●●●● ●●●●●●●●● ●●● ●●●● ●●●●●● ●●●●●●● ● ●● ● ●●●●●

●

●●

●

●●●● ●●●

●

●

●●●●● ●● ●●●

●●●●● ●● ●●●●●●●● ● ●● ●●●● ●●● ●●●● ●● ●●● ●●● ●●●

●

●

●

●● ●●●● ●●●●

● ●●●● ●● ● ●●● ●●

●●●

●

●●●● ●● ●●●●●●● ●●●●●●●●● ●●●●● ●●●●●●●●● ●●●●●●●

●● ●● ●●● ●

●● ●●● ●●●●● ●●

●

●●●

●●●●●●●●●● ●● ●●● ●● ●●● ●●●●● ●●●● ●●●

●● ●● ●●● ●●●●● ●● ●●●●●● ●●●●●●●● ●●●●●●●

●●●● ●●● ●●●

●●●●●●●●● ●●● ●●●●● ●●●●●●●● ●●●●●● ●● ●● ●●●● ●●● ●● ●●●●●●● ●●●●●●● ●● ●●●●●●●● ●●● ●●●● ●●●● ●●● ●●●● ●● ●●●●●●●●●●● ●●●● ●●●●●● ●●●● ●● ●●●●● ●●●● ●●●●

●●●● ●●●●● ●●●● ●●●●● ●●●●●●●● ●●● ● ●● ●● ●● ●●● ●●● ●●● ●●●● ●● ●●●● ●●●● ●●●●● ●●● ●

●●●

● ●●●● ●●

●

● ●● ●●●●● ●

● ●●●●●● ●● ●●●●

●

●

●●●●● ●●●●● ●●●

●●●● ●●

●

● ●●●● ●●

●●●●

●

●●

●●

●

●

●

●● ● ●●●●●●

●

●

● ●● ●●● ●●● ●

●

● ●

●

● ●●

●

●● ●● ●●●

●

● ●● ●●●●

●●●●

● ●●●●●●

●

●● ●●●

●

● ●● ●● ●●●●●

●●●●●●●● ●●● ●●●●● ●●●●●● ●●●

●

●●●●●● ●●

−0.04 0.02 0.080.

000

0.01

00.

020

animal4

Domiance relationship

Add

itive

by

dom

inan

ce r

elat

ions

hip

Figure 4 : hoge18 / 31

Predictive correlations for six health traits

Traits Types KernelsG GKA GKD GKALL ALL

KETPCP 0.16 0.18 0.16 0.19 0.18EBV 0.85 0.86 0.84 0.87 0.86

DAPCP 0.07 0.08 0.07 0.08 0.07EBV 0.59 0.61 0.53 0.59 0.60

RPPCP 0.03 0.05 0.05 0.06 0.05EBV 0.65 0.67 0.60 0.66 0.65

LAMEPCP 0.07 0.08 0.04 0.07 0.05EBV 0.64 0.66 0.58 0.65 0.64

METRPCP 0.05 0.07 0.04 0.05 0.05EBV 0.48 0.52 0.43 0.50 0.49

CMPCP 0.07 0.08 0.05 0.07 0.07EBV 0.72 0.74 0.68 0.73 0.73

19 / 31

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

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 entiregenomes. The role of non-coding sequences?

21 / 31

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 quantitativegenetics?

22 / 31

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 studyWhich genomic regions play an important role in prediction ofcomplex traits?

23 / 31

Genomic regionsPhysical positions of SNP were mapped to Gallus gallus 4.0assembly• 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

Annotation

Table 1 : Numbers of SNPs assigned to each genomicregion.

Annotation # of SNPs annotated after filteringIGR 299,498 193,970Genes ± 1kb 281,455 184,047Genes 266,947 183,768Exons 29,764 19,511CDS 21,975 14,416

Genomic region specific kernels

• All→ K0

• IGR→ K1

• Genes±1kb→ K2

• Genes→ K3

• Exons→ K4

• CDS→ K525 / 31

Body Weight (BW)All CDS Exons Genes Genes1kb

●

●

●

0.16

0.18

0.20

All

CD

S

CD

S−

IGR

Exo

ns

Exo

ns−

IGR

Gen

es

Gen

es−

IGR

Gen

es1k

b

Gen

es1k

b−IG

R

Genomic regions

Pre

dict

ive

corr

elat

ion

26 / 31

Breast Meat (BM)All CDS Exons Genes Genes1kb

●

●

0.25

0.26

0.27

0.28

0.29

All

CD

S

CD

S−

IGR

Exo

ns

Exo

ns−

IGR

Gen

es

Gen

es−

IGR

Gen

es1k

b

Gen

es1k

b−IG

R

Genomic regions

Pre

dict

ive

corr

elat

ion

27 / 31

Hen House Production (HHP)All CDS Exons Genes Genes1kb

●

●

●

0.19

0.20

0.21

0.22

0.23

0.24

All

CD

S

CD

S−

IGR

Exo

ns

Exo

ns−

IGR

Gen

es

Gen

es−

IGR

Gen

es1k

b

Gen

es1k

b−IG

R

Genomic regions

Pre

dict

ive

corr

elat

ion

28 / 31

3D Chromosome Structure

Figure 19 : Lieberman-Aiden et al. (2009) Science.

29 / 31

Ph.D.-wide Conclusions

No single approach stands out (traits dependent)

Figure 20 : Methods Figure 21 : Kernels

⇓

Functional genomics + quantitative genetics

30 / 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