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Assignment 10.7 Falconer & Mackay, chapter 10

Assignment 10.7 Falconer & Mackay, chapter 10. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this?.

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Assignment 10.7 Falconer & Mackay, chapter 10

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  1. Assignment 10.7Falconer & Mackay, chapter 10

  2. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this?

  3. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75

  4. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw

  5. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw μLB μ μL μN

  6. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS μLB μ μL μN

  7. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP μLB μ μL μN

  8. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW= VP(1 – .75) μLB μ μL μN

  9. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW= VP(1 – .75) VW = .25VP μLB μ μL μN

  10. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw μLB μ μL μN

  11. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw μLB μ μL μN

  12. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: μLB μ μL μN

  13. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS= .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP μLB μ μL μN

  14. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. μLB μ μL μN

  15. From last lecture: • to estimate genotypic variance, we ask how much less alike are DZ than MZ twins • VEc = variance due to common environment • VEw = variance due to unique environment (i.e., within-pair environmental variance) • twice the difference between the MZ and DZ correlation = (VA + 1.5VD)/VP

  16. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. μLB μ μL μN

  17. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP μLB μ μL μN

  18. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (because corFS=corDZ, and VD=0) μLB μ μL μN

  19. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ– 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 μLB μ μL μN

  20. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1

  21. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1

  22. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP

  23. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP

  24. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1

  25. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1 VA/VP + VEc/VP = 1

  26. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1 VA/VP + VEc/VP = 1 .5+ VEc/VP = 1

  27. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1 VA/VP + VEc/VP = 1 .5+ VEc/VP = 1 VEc/VP = 1 - .5

  28. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1 VA/VP + VEc/VP = 1 .5+ VEc/VP = 1 VEc/VP = 1 - .5 VEc/VP = .5

  29. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .75 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .75VP VW = VP (1 – .75) VW = .25VP .25VP = ½VA + ¾VD + VEw ½VA = .25VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .25VP VA = .5VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.75 = VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .5 + 1.5 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1 VA/VP + VEc/VP = 1 .5+ VEc/VP = 1 VEc/VP = 1 - .5 VEc/VP = .5 So: VA/VP = .5 VEc/VP = .5 VD/VP = 0 VEw/VP = 0

  30. 10.7. Show that if the correlation of full sibs is .75, the heritability of the character cannot be greater than .5. The full-sib correlation of weaning weight in mice is .8; what is the maximum heritability compatible with this? corFS = .8 VW = ½VA + ¾VD + VEw VW = VP – covFS VW = VP – .8VP VW = VP (1 – .8) VW = .2VP .2VP = ½VA + ¾VD + VEw ½VA = .2VP - ¾VD– VEw h2 is max here if VD = VEw= 0: ½VA = .2VP VA = .4VP , if VD = VEc= 0. 2(corMZ - corDZ) = (VA + 1.5VD)/VP 2corMZ – 2*.8= VA/VP (becausecorFS=corDZ, and VD=0) 2corMZ = .4 + 1.6 corMZ = 1 corMZ = (VA + VD + VEc)/VP corMZ = (VA + VEc)/VP (VA + VEc)/VP = 1 VA/VP + VEc/VP = 1 .4+ VEc/VP = 1 VEc/VP = 1 - .4 VEc/VP = .6 So: VA/VP = .4 VEc/VP = .6 VD/VP = 0 VEw/VP = 0

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