Vol. 32, Special Issue, S 1 S 17 (2011)
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1 Vol. 32, Special Issue, S 1 S 17 (2011) luke154@jcom.home.ne.jp
2 S Herman Nilsson-Ehle F 2 F E. M. East 1.3 Wilhelm Ludwig Johannsen , , gene genotype phenotype
3 S Ronald Aylmer Fisher The correlation between relatives on the supposition of Mendelian inheritance Biometrika 1918 epistasis population genetics A 3 A 1A 1, A 1A 2, A 2A 2 f 11, 2f 12, f 22 (f 11 +2f 12 + f 22 =1) g 11, g 12, g 22 A 1, A 2 2 A 1 : p = f 11 + f 12 A 2 : q = f 12 + f 22 (1) (p + q =1) ḡ ḡ = f 11g 11 +2f 12g 12 + f 22g 22 (2) ḡ y 11 = g 11 ḡ y 12 = g 12 ḡ
4 S4 y 22 = g 22 ḡ (3) y 11, y 12, y 22 A 1, A 2 θ 1, θ 2 A 1A 1, A 1A 2, A 2A 2 2θ 1, θ 1 + θ 2,2θ 2 dominance A 1A 1 y 11 2θ 1 2 Q = f 11(y 11 2θ 1) 2 +2f 12(y 12 θ 1 θ 2) 2 + f 22(y 22 2θ 2) 2 (4) Q θ 1, θ 2 θ 1, θ 2 A 1, A 2 average effect y 11, y 12, y 22 θ 1 + θ 1, θ 1 + θ 2, θ 2 + θ 2 A 1 1 Q θ 1, θ 2 (4) θ 1, θ θ 1, θ 2 g 11 = 100, g 12 = 90, g 22 =60 f 11 =0.25, f 12 =0.25, f 22 =0.25 ḡ = 85, θ 1 = 10, θ 2 = 10. f 11 =0.50, f 12 =0.25, f 22 =0.00 ḡ = 95, θ 1 =2.5, θ 2 = 7.5
5 Q = 4f 11(y 11 2θ 1) 4f 12(y 12 θ 1 θ 2) = 0 θ 1 Q = 4f 12(y 12 θ 1 θ 2) 4f 22(y 22 2θ 2)=0 θ 2 S5 (5a) (5b) pθ 1 + qθ 2 =0 (6) θ = θ 1 θ 2 (7) θ 1 = qθ θ 2 = pθ (8a) (8b) θ A 1 A 2 A 1 A 2 p = q a A 1A 1, A 1A 2, A 2A 2 2θ 1, θ 1 + θ 2,2θ 2 A 1 δ 11 = y 11 2θ 1 δ 12 = y 12 θ 1 θ 2 δ 22 = y 22 2θ 2 (9a) (9b) (9c) A 1A 1, A 1A 2, A 2A 2 population genetics A 1 A 2 p,q A 1A 1, A 1A 2, A 2A 2 p 2,2pq, q 2 HW HW HW
6 S6 V g V g = f 11y f 12y f 22y22 2 (10) V a = f 11(2θ 1) 2 +2f 12(θ 1 + θ 2) 2 + f 22(2θ 2) 2 = p 2 (2θ 1) 2 +2pq(θ 1 + θ 2) 2 + q 2 (2θ 2) 2 =2pqθ 2 (6) (11) The genetical interpretation of statistics of the third degree in the study of quantitative inheritance F. R. Immer Olof Tedin d,h, d d h F 2 F 3 F F 2 F d h F 2 2
7 S7 2 Kenneth Mather DNA g e p p = g + e (12) g e 0 σ 2 a i d i e 2 P 1 P 2 F 1,F 2,F 3 2 (12) A 2 A 1 A 2 3 A 1A 1 A 1A 2 A 2A 2 g 11, g 12, g 22 (g 11 g 22)/2 A a A A 1 A 2 A 1 A 2
8 S8 2.. a d g 11 = 100, g 12 = 90, g 22 =60. u = 80, a = 20, d =10 2 A 1 A 1 A 2 a i A 1 A 2 a i g 12 1 (g11 + g22) A 2 d A 0 d A =0 A d A < a A d A = a A d A > a A 2 P 1 P 2A, B 2 A, B a A, a B d A, d B F 1 A 1A 1B 1B 1 u + a A + a B (13a) A 1A 2B 1B 2 u + d A + d B (13b) A 2A 2B 2B 2 u a A a B (13c) u u
9 S9 u k (a)= (d)= (13a,b,c) kx i=1 kx i=1 a i d i (14a) (14b) A 1A 1B 1B 1 u +(a) (15a) A 1A 2B 1B 2 u +(d) (15b) A 2A 2B 2B 2 u (a) (15c) A B (k =2)F 2 9 A 1A 1B 1B 1, A 1A 1B 1B 2, A 1A 1B 2B 2, A 1A 2B 1B 1, A 1A 2B 1B 2, A 1A 2B 2B 2, A 2A 2B 1B 1, A 2A 2B 1B 2, A 2A 2B 2B 2 1:2:1:2:4:2:1:2:1 M g[f 2]=(1/16)A 1A 1B 1B 1 +(1/8)A 1A 1B 1B 2 + +(1/16)A 2A 2B 2B 2 =(1/16)(u + a A + a B)+(1/8)(u + a A + d A)+ +(1/16)(u a A a A) = u +(1/2)d A +(1/2)d B = u +(1/2)(d) (16) (a) (d) (12) V P = V G + E (17) V G E F 2 A (1/4)A 1A 1 :(1/2)A 1A 2 :(1/4)A 2A 2 V G[F 2]=(1/4)a 2 +(1/2)d 2 +(1/4)( a) 2 ((1/4)a +(1/2)d (1/4)a) 2 =(1/2)a 2 +(1/4)d 2 (18)
10 S10 i a i d i 2 A,D A = D = F 2 V P [F 2] kx i=1 kx i=1 a 2 i d 2 i (19a) (19b) V P [F 1 2]= 2 A D + E (20) E A D F 3 P 1 BC 1 P 2 BC 2 V P [F 3]=(3/4)A +(3/16)D + E (21) V P [BC 1]+V P [BC 2]=(1/2)A +(1/2)D +2E (22) F 2 F 3 F 2 F 3 F 2 P 1,P 2 F 1 V G =0, V P = E A,D E 3 A D V P A,D,E V P = c 1A + c 2D + E (23) c 1, c 2 F 2 c 1 =1/2, c 2 =1/4 h 2 B =(c 1A + c 2D)/(c 1A + c 2D + E) (24) h 2 N = c 1A/(c 1A + c 2D + E) (25) 2002
11 S11 Anderson and Kempthorne Biometrical Genetics 2 17 polygenic system 1
12 S Jay L. Lush Animal Breeding Plans 1937 Oscar Kempthorne Introduction to Genetic Statistics 1957Douglas Scott Falconer Introduction to Quantitative Genetics1961 Hayman (1954a,b) Griffing (1956) Finlay Wilkinson (1963) DNA QTL 4.1 2
13 S AABB aabb F 1 AB ab Ab ab A B 2 DNA DNA QTL 1980 RFLPRAPD AFLP SSR DNA DNA DNA DNA DNA DNA 1989 Lander Botstein Interval Mapping Quantitative Trait Locus QTL QTL QTL QTL DNA QTL QTL QTL QTL
14 S14 QTL QTL 4.4 QTL QTL F 2 QTL QTL 1 Q 2 A, B A, Q, B 3 AAQQBB, aaqqbb F 1 AQB/aqb / AQB aqb A Q Q B r 1, r 2 A B r 1+2 r 1 r 2 r 1 F 2 AABB, AABb, AAbb, AaBB, AaBb, Aabb, aabb, aabb, aabb Q QQ, Qq, qq 1 3 F 2 i Q j p ij 1 r 1, r 2, r 1+2 Q a,d QQ,Qq,qq 1. 2 i QTL Q 1 Q 1, Q 1 Q 2, Q 2 Q 2 p ij (F 2 ) i: Q 1 Q 1 (p i1 ) Q 1 Q 2 (p i2 ) Q 2 Q 2 (p i3 ) 1: A 1 A 1 B 1 B 1 q1 2 2 q 1 q 2 q2 2 2: A 1 A 1 B 1 B 2 q 1 q 3 q 1 q 4 + q 2 q 3 q 2 q 4 3: A 1 A 1 B 2 B 2 q3 2 2 q 3 q 4 q4 2 4: A 1 A 2 B 1 B 1 q 1 q 4 q 1 q 3 + q 2 q 4 q 2 q 3 5: A 1 A 2 B 1 B 2 z 1 q 1 q 2 + z 2 q 3 q 4 z 1 (q1 2 + q2 2 )+z 2(q3 2 + q2 4 ) z 1 q 1 q 2 + z 2 q 3 q 4 6: A 1 A 2 B 2 B 2 q 2 q 3 q 1 q 3 + q 2 q 4 q 1 q 4 7: A 2 A 2 B 1 B 1 q4 2 2 q 3 q 4 q3 2 8: A 2 A 2 B 1 B 2 q 2 q 4 q 1 q 4 + q 2 q 3 q 1 q 3 9: A 2 A 2 B 2 B 2 q2 2 2 q 1 q 2 q1 2 q 1 =(1 r 1 r 2 + r 12 )/(1 r 1+2 ) q 2 = r 12 /(1 r 1+2 ) q 3 =(r 2 r 12 )/r 1+2 (r 12 =2r 1+2 r 1 r 2 ) q 4 =(r 1 r 12 )/r 1+2 z 1 =(1 r 1+2 ) 2 /{(1 r 1+ ) 2 + r 2 1+2} z 2 =1 z 1 p i1 + p i2 + p i3 =1 (i =1, 2,...,9)
15 S15 u + a, u + d, u a u e e 0 σ 2 QQ,Qq,qq y QQ: φ 1 = 1 e (y u a)2 2σ 2 (26a) 2π Qq : φ 2 = 1 e (y u d)2 2σ 2 2π qq: φ 3 = 1 e (y u+a)2 2σ 2 2π (26b) (26c) i Q 1 QQ y p i1ϕ 1 i y Q QQ,Qq,qq z 1,z 2,z 3 z 1 + z 2 + z 3 =1 QQ : z 1 = p i1ϕ 1/(p i1ϕ 1 + p i2ϕ 2 + p i3ϕ 3) Qq : z 2 = p i2ϕ 2/(p i1ϕ 1 + p i2ϕ 2 + p i3ϕ 3) qq : z 3 = p i3ϕ 3/(p i1ϕ 1 + p i2ϕ 2 + p i3ϕ 3) (27a) (27b) (27c) z 1,z 2,z 3 n 9Y Y i L (p i1φ ij1) z ij1 (p i2φ ij2) z ij2 (p i3φ ij3) z ij3 (28) i=1 j=1 z ij1 i j j =1,...,n iq QQ p i1φ ij1,p i2φ ij2,p i3φ ij3 i j QTL Q 1Q 1, Q 1Q 2, Q 2Q 2 (28) Q 3 n 9Y Y i L (p i1φ ij1 + p i2φ ij2 + p i3φ ij3) (29) i=1 j=1 QTL u a d σ 2 4 u QTL 1 QTL QTL QTL L û,â, ˆd, ˆσ 2 log L 1 H 0 :û = u 0,â =0, ˆd =0, ˆσ 2 = σ0 2 log L 0
16 S16 3. QTL LOD 68cM 17 A Q LOD 33cM LOD =log 10 L log 10 L 0 (30) EM QTL 1 cm LOD LOD QTL 3 QTL QTL QTL DNA QTL 5. DNA Anderson, V.L. and Kempthorne, O. (1954). A model for the study of quantitative inheritance. Genetics, 39: Falconer, D.S. (1961). Introduction to Quantitative Genetics. Oliver and Boyd, Edinburgh.
17 S17 Finlay, K.W. and Wilkinson, G.N. (1963). The analysis of adaptation in a plant-breeding programme. Australian Journal of Agricultural Research, 14: Fisher, R.A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh: Earth Sciences, 52: Fisher, R.A, Immer, F.R. and Tedin, O. (1932). The genetical interpretation of statistics of the third degree in the study of quantitative inheritance. Genetics, 17: Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences, 9: Hayman, B.I. (1954a). The analysis of variance of diallel tables. Biometrics, 10: Hayman, B.I. (1954b). The theory and analysis of diallel crosses. Genetics, 39: Kempthorne, O. (1957). Introduction to Genetic Statistics. Iowa State Univ. Press. Iowa. (1960)... Lander, E.S. and Botstein, D. (1989). Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 121: Lush, J.L. (1937). (1 st ), (1943) (2 nd ). Animal Breeding Plans. Iowa State Univ. Press. Ames, Iowa. (1972). 2., 22: (2000)... (2002)...
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