Estimation of the proportion of genetic variance explained by molecular markers

estimation of the proportion of genetic variance explained by molecular markers (p) plays an important role in basic studies of quantitative traits, as well as in marker-assisted selection (mas), if the selection index proposed by lande and thompson (genetics 124: 743-756, 1990) is used. frequently, the coefficient of determination (r2) is used to account for this proportion. in the present study, a simple estimator of p is presented, which is applicable when a multiple regression approach is used, and progenies are evaluated in replicated trials. the associated sampling distribution was obtained and compared with that of r2. simulations indicated that, when the number of evaluated progenies is small, the statistics are not satisfactory, in general, due to bias and/or low precision. coefficient r2 was found adequate in situations where p is high. if a large number of progenies is evaluated (say, a few hundreds), then the proposed estimator appears to be better, with acceptable precision and considerably lower bias than r2. a normal approximation to the sampling distribution of is given, using taylor's expansion of the expectation and variance of this statistic. approximate confidence intervals for p, based on normal distribution, are reasonable, if the number of progenies is large. the use of in mas is illustrated for estimation of the weight given to the molecular score, when a selection index is used.