Determining the minimum sample size required to obtain sufficient progeny with a desired genotype at two quantitative trait loci

In this paper we determine the minimum progeny sample size n needed to obtain, with probability , at least m individuals of a desired two-locus genotype affecting quantitative traits. The two quantitative trait loci (QTLs) of interest may be linked or independent, with or without epistatic interaction between them. Parental genotypes may be known or unknown, and gene action at either locus may range from additive to overdominance. To reduce the required sample size, mating patterns that will produce a high proportion of desired progeny are suggested for different progeny genotypes and dominance levels. Based on the assumption of normally distributed quantitative trait expression, individuals can be classified into a genotype or genotypic group according to their phenotypic expressions. This technique is used to select both parents and progeny with unknown genotypes. Choice of parental classification criteria for a given quantitative trait affects classification accuracy, and hence the probability of obtaining progeny of the desired genotype. The complexity of this probability depends on the dominance level at each locus, the recombination fraction, and the awareness of parental genotypes. The procedure can be expanded to deal with more than two loci.BU-1168-MB in the Biometrics Unit Technical Report Series, 337 Warren Hall, Cornell University, Ithaca, NY 14853, USAFormerly known as S.-F. Shyu     

Genetic loci associated with field resistance to late blight in offspring of Solanum phureja and S.tuberosum grown under short-day conditions

Field resistance to late blight – a fungal disease caused by Phytophthora infestans – has been genetically characterized by analyzing trait-marker association in a Solanum phureja (phu)×dihaploid Solanum tuberosum (dih-tbr) population. Trait data were developed at three locations over a 3-year period under natural infection pressure. RAPD (random amplified polymorphic DNA) and AFLP (amplified fragment length polymorphism)markers were used to develop anonymous genetic linkage groups subsequently anchored to potato chromosomes using mapped RFLP (restriction fragment length polymorphism), SSR (single sequence repeats) and AFLP markers. RFLP and SSR markers achieved the most-accurate anchoring. Two genetic maps were obtained, with 987.4 cM for phu and 773.7 cM for dih-tbr. Trait-marker association was revealed by single-marker and interval mapping analyses. Two important QTLs (quantitative trait loci) were detected on chromosomes VII and XII as a contribution from both parents, totalling up to 16% and 43%, respectively, of the phenotypic variation (PH). One additional QTL was detected on chromosome XI (up to 11% of the PH) as a contribution from the phu parent, and three others were detected on chromosome III (up to 13% of the PH), chromosome V (up to 11% of the PH) and chromosome VIII (up to 11% of the PH) as a contribution from the dih-tbr parent. Our results reveal new genetic loci of the potato genome that contribute to resistance to late blight. We postulate that some of these loci could be related to plant growth under short-day conditions. Received: 5 July 2000 / Accepted: 17 November 2000     

Using aggregate data to estimate the standard error of a treatment–covariate interaction in an individual patient data meta‐analysis

Subgroup analyses are important to medical research because they shed light on the heterogeneity of treatment effectts. A treatment–covariate interaction in an individual patient data (IPD) meta‐analysis is the most reliable means to estimate how a subgroup factor modifies a treatment's effectiveness. However, owing to the challenges in collecting participant data, an approach based on aggregate data might be the only option. In these circumstances, it would be useful to assess the relative efficiency and power loss of a subgroup analysis without patient‐level data. We present methods that use aggregate data to estimate the standard error of an IPD meta‐analysis’ treatment–covariate interaction for regression models of a continuous or dichotomous patient outcome. Numerical studies indicate that the estimators have good accuracy. An application to a previously published meta‐regression illustrates the practical utility of the methodology.