Variance of marker estimates of parental contribution to F₂ and BC₁-derived inbreds

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.