Synthetic varieties(SVs)are populations generated by randomly mating their parents.They are a good alternative for low-input farmers who grow onions,maize,and other allogamous crops since the seed produced by a SV doe...Synthetic varieties(SVs)are populations generated by randomly mating their parents.They are a good alternative for low-input farmers who grow onions,maize,and other allogamous crops since the seed produced by a SV does not change from one generation to the next.Although SV progenitors are commonly pure lines,in this case a synthetic(Syn_(TC))whose parents are t three-way line crosses,a very common type of maize hybrid grown in Mexico,is studied.The aim was to develop a general and exact equation for the inbreeding coefficient of a Syn_(TC)eF_(m)^(f)Syn_(TC)T because of its relationship with the mean of economically important traits.This objective arose due to the need for a more advanced study in terms of determining whether F_(m)^(f)Syn_(TC)can be applied specifically and accurately for any number of parents(t),plants per parent(m)and inbreeding coefficient(IC)of the initial lines(F_(L)).A formula for the IC of the Syn_(TC)was derived that,given any values of F_(L)(0≤F_(L)≤1)and t,is specific for any value of m,not just for“large”numbers associated with the context in which the Hardy-Weinberg law is stated.It was found that F_(m)^(f)Syn_(TC)is very sensitive to changes in m when m is not greater than eight,after which it tends to stabilize very quickly.In summary,unlike previously derived formulas,F_(m)^(f)Syn_(TC)is exact for any values of t,m and F_(L).展开更多
文摘Synthetic varieties(SVs)are populations generated by randomly mating their parents.They are a good alternative for low-input farmers who grow onions,maize,and other allogamous crops since the seed produced by a SV does not change from one generation to the next.Although SV progenitors are commonly pure lines,in this case a synthetic(Syn_(TC))whose parents are t three-way line crosses,a very common type of maize hybrid grown in Mexico,is studied.The aim was to develop a general and exact equation for the inbreeding coefficient of a Syn_(TC)eF_(m)^(f)Syn_(TC)T because of its relationship with the mean of economically important traits.This objective arose due to the need for a more advanced study in terms of determining whether F_(m)^(f)Syn_(TC)can be applied specifically and accurately for any number of parents(t),plants per parent(m)and inbreeding coefficient(IC)of the initial lines(F_(L)).A formula for the IC of the Syn_(TC)was derived that,given any values of F_(L)(0≤F_(L)≤1)and t,is specific for any value of m,not just for“large”numbers associated with the context in which the Hardy-Weinberg law is stated.It was found that F_(m)^(f)Syn_(TC)is very sensitive to changes in m when m is not greater than eight,after which it tends to stabilize very quickly.In summary,unlike previously derived formulas,F_(m)^(f)Syn_(TC)is exact for any values of t,m and F_(L).
