The backcross breeding method is often used to transfer recessive traits controlled by one or a few genes from one pure line to another. Guidelines are needed to help plant breeders to use backcrossing cost-effectively. In a backcrossing program, a plant breeder may choose between methods with two or three stages per cycle. The two-stage method utilizes alternate backcrossing and selfing to identify BCiSj plants with the recessive trait while the three-stage method uses two sequential crosses followed by selfing. In the three-stage method, n(min), the minimum number of plants required to recover at Least one or two BCiSj plants in the i(th) cycle with a given probability (1 - alpha), is obtained by growing only one BCiSij plant for each of n(min), BCiSo. Alternative values for the number of BCiSo plants (n(b)) and BCiSj plants per BCiSo (n(s)) are present for alpha = 0.05 and alpha = 0.01 for traits controlled by one, two, three, or four recessive genetic loci. A method to compare the cost-effectiveness of alternative values is presented for cases where the relative costs of crossing, selfing, and evaluation of S-j progeny are known. Unless time is the paramount concern, it is only in cases where the ressive trait is controlled by a single locus that it can be more cost-effective to make two sequential crosses to the recurrent parent before selfing than to cross and self and then only if the cost of evaluating BCiSj plants is high relative to the cost of producing BCiSo plants. When using the three-stage backcross method, the breeder can reduce the n(b) and increase n(s) if the cost of evaluating BCiSj plants is low relative to the cost of producing BCiSo plants.
