Genetic Statistical Model to Estimate Epistasis, Additive and Dominance Genetic Effects Using Advanced Populations

Document Type : Original Article

Authors

1 Agronomy Dept., Plant Breeding Section, Faculty of Agriculture, Fayoum Univ., Fayoum, Egypt.

2 Genetics Dept.,Plant Breeding Section, Faculty of Agriculture, Fayoum Univ., Fayoum, Egypt.

Abstract

Most investigations for estimating gene effects contributing to metric traits has been exclusively focused on means of earlier filial (¯F_1 and ¯F_2) and backcross populations (¯BC_11 and ¯BC_12). In this paper a novel approach is suggested using data generated from advanced filial (¯F_(3 ),¯F_(4 )….¯F_(n )) and backcross populations)¯( BC)_n1 and ¯( BC)_n2). The following set of equations is derived by algebraic solution of ¯P_1,¯P_2,¯F_3,¯F_4,¯BC_31 and ¯BC_32 means:
Mean (M) = 1/98 (4 9 ( P) ̅_1+49 P ̅_2 - 64 (BC) ̅_31-64 (BC) ̅_32+ 128 F ̅_4 ),
Additive effect (D) =□(□(□(1/(2 ))) ) (P ̅_1- P ̅_2 ),
Dominance effect (H) =1/49 (384 (BC) ̅_31+384 (BC) ̅_32 -196 F ̅_3-294 ( P) ̅_1-294 P ̅_2+ 16F ̅_4 ),
Three types of epistasis
Additive x additive effect (I) = 32/49 ( (BC) ̅_31+ (BC) ̅_32-2 F ̅_4 ),
Additive x dominance effect (J) = 1/7 (32 (BC) ̅_31-32 (BC) ̅_32-28 ( P) ̅_1+28 P ̅_2 ) and
Dominance x dominance effect (L) =16/49 (98 F ̅_3-68F ̅_4+49 ( P) ̅_1+49 P ̅_2-64 (BC) ̅_31-64 (BC) ̅_32 )
The proposed equations have been proved mathematically via theoretical working example.

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