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CROP BREEDING, GENETICS & CYTOLOGY

Variance of Marker Estimates of Parental Contribution to F₂ and BC₁-Derived Inbreds

^a Laboratory Center, Henan Academy of Agricultural Sciences, Zhengzhou, Henan 450002, P.R. People's Republic of China
^b Dep. of Agronomy, Purdue Univ., 1150 Lilly Hall of Life Sciences, West Lafayette, IN 47905-1150 USA

bernardo{at}purdue.edu

An Essentially Derived Variety is a cultivar or inbred that largely retains the characteristics of an ancestral cultivar or inbred. The parental contribution to F₂-derived inbreds (p_F2) and BC₁-derived inbreds (p_BC1) can be estimated with molecular markers. A recombinant inbred (RI) with p_F2 or p_BC1 greater than a specified threshold is then considered essentially derived. Our objectives were (i) to derive the variance of p_F2 and p_BC1, and (ii) to determine the probability of obtaining an essentially derived RI for different numbers of marker loci in different species. The variances of p_F2 and p_BC1 are a function of the number of chromosomes, length of each chromosome, and number of marker loci on each chromosome. The standard errors (SE) of p_F2 and p_BC1 were smallest when the two marker loci closest to the ends of each chromosome were included. The minimum values of SE(p_F2) and SE(p_BC1) are useful for setting minimum values of thresholds for declaring essential derivation. Suppose selfing from the BC₁ is permissible and the maximum error rate for falsely declaring an RI is essentially derived is set at 2.5%. The minimum value of the threshold for these conditions is 0.881 in maize (Zea mays L.). For a threshold of 0.90, the probabilities of an essentially derived RI from the BC₁ generation were >6% in rye (Secale cereale L.), >3% in barley (Hordeum vulgare L.), <3% in tomato (Lycopersicon spp.), rice (Oryza spp.), and maize, and <1% wheat (Triticum aestivum L.). These results suggest that the thresholds used to declare essential derivation should differ among species.

Abbreviations: cM, centimorgans • RI, recombinant inbred

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