Selection under negative linkage disequilibrium. Random mating versus inbreeding.

A population resulting from the diallel cross of a set of elite inbred lines was selected under two strategies: (i) inbred strategy (IS) under brother-sister mating; and (ii) random strategy (RIS) under random mating. The final lines in both cases were completely inbred. RIS populations clearly responded better than IS populations. Although most of the RIS advantage was achieved in the second generation, the average response under the RIS strategy increased with respect to that of the IS strategy from the beginning to the end of the experiment. In general terms and on theoretical grounds this RIS advantage is expected only if the initial disequilibrium is negative. One of the final inbred lines performed significantly better than the sum of the two inbred ancestors, strongly suggesting a heterotic epistatic combination fixed in homozygosity. Strong negative disequilibrium and partial epistatic control of quantitative characters are to be expected in breeding programmes of self-pollinating crops. In all likelihood, recurrent selection under forced random mating in such crops would result in better responses.

Genetic and environmental contributions to bread-wheat flour quality using the SDS sedimentation test as an index.

The contribution of a locus to the genotypic variance depends not only on the effects of its genes but also on their frequency and on the genetic background in which it segregates. In two synthetic populations, involving common cultivars of our collection, estimates were made of the contributions of alleles at the homoeologous high-molecular-weight glutenin (HMW) loci, Glu-A1, Glu-B1, and Glu-D1, to the variation in flour quality using SDS sedimentation as an index. These estimates were of the magnitude of the contributions relative to each other, relative to the residual genetic variance, and relative to the environmental variance. The first population was a synthetic formed from ten bread-wheat cultivars known for their good quality, and selected under forced random mating for high SDS sedimentation. The second was the selfed progeny of a cross of Ribereño, a very poor quality bread-wheat of genotype (Null, 7-8,2-12), with line 7681, a very good quality bread-wheat with the genotype (2(*), 7-9, 5-10). Slightly over one-half of the phenotypic variance is under genetic control and over one-half of this was accounted for by HMW contributions. The initial response to selection was very rapid, as is expected when genes with large effects are involved. In addition, the frequencies of good HMW alleles increased so quickly that their contribution to the genetic variance was exhausted by the fourth generation of selection. If our estimates are correct, over one-half of the maximum possible advance in quality in heterogeneous populations similar to ours can easily be achieved in 2 years, or less, of marker-assisted selection.

Effect of selection intensity and population size on percent oil in maize, Zea mays L.

The effect of selection intensity and population size on the response to selection for percent oil in the grain of maize (Zea mays L.) was evaluated in a replicated experiment over ten cycles of selection. An open-pollinated variety, Armel's Reid Yellow Dent, was divided into subpopulations of 6,10 and 50 plants. Selection proportions of 17% and 5% were imposed upon each subpopulation. Selection was based on the percentage of oil in individual kernels as determined by wide-line nuclear magnetic resonance spectroscopy. As expected, total response to selection increased with larger population sizes and selection intensities. The concave shape of the response curves suggested that an appreciable part of the genetic variance can be attributed to additive genes at high initial frequencies, dominance genes at low initial frequencies, or to the generation of negative linkage disequilibrium due to selection. The consistently greater loss of vigor experienced by the more intensely selected populations reflects the enhancement of inbreeding due to artificial selection, an effect that increases with the intensity of selection. The results indicate that combined selection, based on kernels and using within- and amongfamily information, will be more efficient than other conventional selection procedures, including the normal combined scheme where selection is based on plants.

Genetic changes with generations of artificial selection.

Using conditional probabilities and moment-generating matrices, I derived approximate algebraic equations that give expectations of gene frequency, population mean, gene frequency variance within lines, or heterozygosity, and gene frequency variance between lines, or drift, for repeated cycles of recurrent selection in populations of finite size. For genes of large effect, the responses to selection differ substantially from the classical expectations, and equations are derived that give quantitative estimates of asymmetry of response when selection is done in opposite directions. Particular cases of the derived formulae yield equations given by other authors. The error involved in the approximations is discussed in the appendix.