Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection.

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination.     

Power analysis for quantitative trait locus mapping in populations derived by multiple backcrosses

 Populations derived by multiple backcrosses are potentially useful for quantitative trait locus (QTL) mapping studies. Comparisons of relative power to detect QTL using populations derived by multiple back-crosses are needed to make decisions when mapping projects are initiated. The objective of this study was to theoretically compare the power to detect QTL in populations derived by multiple backcrosses relative to mapping in a recombinant inbred population of equal size. Backcrossing results in a reduction in genetic variance with each generation and also results in an increasing frequency of the recurrent parent marker genotype. The relevant outcome for QTL mapping is a reduction in genetic variance to partition between marker genotype classes and increasing unbalance of the number of individuals contributing to the mean of the marker genotypes. Both of these factors lead to a decrease in the power to detect a QTL as the number of backcross generations increases. Experimental error was held constant with the populations compared. From a theoretical standpoint, backcross-derived populations offer few advantages for QTL detection. If, however, a backcrossing approach is the most efficient method to achieve a desired breeding objective and if QTL detection is an objective of equal or less importance, backcross-derived populations are a reasonable approach to QTL detection. Received: 4 August 1996 / Accepted: 4 April 1997     

Simultaneous marker-assisted selection for multiple traits in autogamous crops

A method is presented for the selection of parents with the aim of obtaining improved genotypes in the progeny of a cross. The procedure is designed to select in several unrelated traits simultaneously and is based on the selection of molecular markers that are linked to QTLs. The method was compared with conventional phenotypic selection in simulation experiments for a number of genetic structures underlying the traits and several types of parental populations. Although the method in general provides good results, some of the underlying assumptions may be violated quite easily, thereby reducing the applicability of the procedure in practice. Received: 10 September 1999 / Accepted: 24 August 2000     

AFLP mapping of quantitative trait loci for yield-determining physiological characters in spring barley

 An amplified fragment length polymorphism (AFLP) map covering 965 cM was constructed using 94 recombinant inbred lines of a cross between the spring barley varieties Prisma and Apex. This map was employed to identify quantitative trait loci (QTLs) controlling plant height, yield and yield-determining physiological characters using an approximate multiple-QTL model, the MQM method. The seven physiological traits were parameters used in a process-based crop-growth model that predicts barley biomass production as affected by daily temperature and radiation. The traits were measured in experiments conducted over 2 years. Except for the relative growth rate of leaf area, all traits examined had at least one QTL in each year. QTLs and their effects were found to vary with developmental stages for one trait, the fraction of shoot biomass partitioned to leaves, that was measured at several stages. Most of the traits were associated, though to different extents, with the denso dwarfing gene (the height-reducing allele in Prisma) located on the long arm of chromosome 3. Some of the QTLs were mapped to similar positions in both years. The results in relation to effects of the dwarfing gene, the physiological basis for QTL×environment interaction, and the relative importance of the parameter traits with respect to yield, are discussed. Received: 17 September 1998 / Accepted: 28 December 1998     

Analysis of quantitative trait loci (QTLs) and quantitative trait alleles (QTAs) for potato tuber yield and starch content

 Using RFLP markers, QTLs for tuber starch-content and tuber yield were mapped in two F₁ populations derived from crossing non-inbred di-haploid potato breeding lines. QTLs were identified and mapped, based on both single-marker tests and interval analyses. A model specifically developed for interval QTL analysis in non-inbred plant species was successfully applied for the first time to experimental data. Results of both methods of QTL analysis were similar but not identical. QTLs for tuber starch-content and tuber yield were analysed in segregating populations K31 and LH in five and two environments, respectively. Population K31 was fully genotyped whereas population LH was selectively genotyped according to high and low tuber-starch content. Eighteen putative QTLs for tuber starch-content were identified on all 12 potato linkage groups and eight putative QTLs for tuber yield were identified on eight linkage groups. Twenty of twenty six putative QTLs were reproducibly detected in at least two environments and/or mapping populations. Few major QTLs for tuber starch-content were highly stable across environments but were detected in only one of the two mapping populations analysed. Most QTLs for tuber yield were linked with QTLs for tuber starch-content suggesting that the effects on both traits are controlled by the same genetic factors. The results are discussed with respect to marker-assisted selection in potato. Received: 9 March 1998 / Accepted: 29 April 1998     

Multilocus dynamics under haploid selection

 A general haploid selection model with arbitrary number of multiallelic loci and arbitrary linkage distribution is considered. The population is supposed to be panmictic. A dynamically equivalent diploid selection model is introduced. There is a position effect in this model if the original haploid selection is not multiplicative. If haploid selection is additive then the fundamental theorem is established even with an estimate for the change in the mean fitness. On this basis exponential convergence to an equilibrium is proved. As rule, the limit states are single-gamete ones. If, moreover, linkage is tight, then the single-gamete state with maximal fitness attracts the population for almost all initial states. Received 27 November 1995; received in revised form 17 January 1996     

Comparison between marker-assisted selection and phenotypical selection in a set of Arabidopsis thaliana recombinant inbred lines

 Parents were selected from a well-characterised Arabidopsis recombinant inbred line (RIL) population based on (1) their phenotype for flowering time or (2) marker and QTL information that had been assessed previously. The F₂ offspring obtained from pairs of selected RILs was analysed for these traits, and the results obtained with these two methods of selection were compared. Selection based on marker and QTL information gave approximately the same result as selection based on phenotype. The relative high heritability of flowering time in Arabidopsis facilitated successful phenotypical selection. The difference in selection result that was anticipated to be in favour of the marker-assisted approach was therefore not observed. Received: 29 November 1997 / Accepted: 8 June 1998     

Computing the selection gradient and evolutionary response of an infinite-dimensional trait

 Following the results developed in a previous paper, an equation describing the evolutionary response to selection is extended from finite- to infinite-dimensional traits. The selection gradient and evolutionary response are then computed for a large class of infinite-dimensional traits of broad biological interest. In this framework, traits are modeled as Gaussian processes, and reproducing kernel Hilbert spaces constitute a primary tool. Received 12 September 1996     

Mapping of quantitative trait loci affecting Drechslera teres resistance in barley with molecular markers

 Resistance loci for seedling-stage resistance to net blotch disease (Drechslera teres) in barley were mapped with molecular markers in an F₂ population derived from a cross between the susceptible barley cultivar ‘Arena’ and the resistant Ethiopian landrace ‘Hor 9088’. Disease reactions were scored with first and second leaves of 2-week-old plants 7 and 9 days after inoculation with a single spore-derived isolate. For linkage analysis, 22 RFLP markers and 284 AFLP markers were used. The seven linkage groups covered 1153.3 cM with an average marker interval of 3.76 cM. The resistance was determined to be inherited in a quantitative manner. Altogether, 12 QTLs were mapped with positions depending on the leaf used for testing and the time period after infection. Heritability in the broad sense ranged between 0.21 and 0.37. Received: 26 May 1998 / Accepted: 9 June 1998     

Identification of quantitative trait loci controlling developmental characteristics of Brassica oleracea L

A segregating population of F₁-derived doubled haploid (DH) lines of Brassica oleracea was used to detect and locate QTLs controlling 27 morphological and developmental traits, including leaf, flowering, axillary bud and stem characters. The population resulted from a cross between two very different B. oleracea crop types, an annual cauliflower and a biennial Brussels sprout. A principal component analysis (PCA), based on line means, allowed all the traits to be grouped into distinct categories according to the first five Principal Components. These were: leaf traits (PC1), flowering traits (PC2), axillary bud traits (PC3 and 5) and stem traits (PC4). Between zero and four putative QTL were located per trait, which individually explained between 6% and 43% of the additive genetic variation, using the multiple-marker regression approach to QTL mapping. For lamina width, bare petiole length and stem length two QTL with opposite effects were detected on the same linkage groups. Intra- and inter-specific comparative mapping using RFLP markers identified a QTL on linkage group O8 accounting for variation in vernalisation, which is probably synonymous with a QTL detected on linkage group N19 of Brassica napus. In addition, a QTL for petiole length detected on O3 of this study appeared to be homologous to a QTL detected on another B. oleracea genetic map (Camargo et al. 1995). Received: 28 March 2001 / Accepted: 25 June 2001     

Homoclinic chaos in a model of natural selection

 We modify a simple mathematical model for natural selection originally formulated by Robert M. May in 1983 by permitting one homozygote to have a larger selective advantage when rare than the other, and show that the new model exhibits dynamical chaos. We determine an open region of parameter space associated with homoclinic points, and prove that there are infinite sequences of period-doubling bifurcations along selected paths through parameter space. We also discuss the possibility of chaos arising from imbalance in the homozygote fitnesses in more realistic biological situations, beyond the constraints of the model. Received 3 February 1995; received in revised form 1 November 1995     

Marker-assisted selection in autogamous RIL populations: a simulation study

 Molecular markers may enable plant breeders to select indirectly for genes affecting quantitative traits by selecting for molecular markers closely linked to these genes (marker-assisted selection, MAS). We have assessed the effectiveness of MAS compared to phenotypic selection. Key variables in this assessment were: trait heritability, selection intensity, genetic architecture and uncertainty in QTL mapping. Simulation studies showed that the application of MAS in autogamous crops, with the objective of obtaining transgressive genotypes, can improve selection results when compared to conventional selection procedures. Marker-assisted selection appears particularly promising when dominant alleles at quantitative trait loci are present and linked in coupling phase. Uncertainty in estimated QTL map positions reduces the benefits of marker-assisted selection, but this reduction remains limited in most cases. Received: 5 September 1997 / Accepted: 6 October 1997     

Identification of quantitative trait loci influencing annual height- and diameter-increment growth in loblolly pine (Pinus taeda L.)

 Quantitative trait loci (QTLs) for annual height- and diameter-increment growth were estimated in each of two three-generation loblolly pine pedigrees. Annual height-increment was measured in three consecutive years in the BASE pedigree and in four consecutive years in the QTL pedigree. Annual diameter-increment was measured only in the QTL pedigree for two consecutive years. An interval mapping-approach was used to estimate the number of QTLs, the magnitude of QTL effects, and their position on genetic linkage maps. Thirteen different height-increment and eight different diameter-increment QTLs were detected, suggesting that the these traits are, at least in part, controlled by a few genes of large effect. Little evidence was found for the expression of individual QTLs in multiple years or in multiple genetic backgrounds. These results were discussed in terms of the power of the experiment and their consequences for marker-assisted breeding. Received: 12 July 1998/Accepted: 5 August 1998     

Quantitative trait loci associated with traits determining grain and stover yield in pearl millet under terminal drought-stress conditions

Drought stress during the reproductive stage is one of the most important environmental factors reducing the grain yield and yield stability of pearl millet. A QTL mapping approach has been used in this study to understand the genetic and physiological basis of drought tolerance in pearl millet and to provide a more-targeted approach to improving the drought tolerance and yield of this crop in water-limited environments. The aim was to identify specific genomic regions associated with the enhanced tolerance of pearl millet to drought stress during the flowering and grain-filling stages. Testcrosses of a set of mapping-population progenies, derived from a cross of two inbred pollinators that differed in their response to drought, were evaluated in a range of managed terminal drought-stress environments. A number of genomic regions were associated with drought tolerance in terms of both grain yield and its components. For example, a QTL associated with grain yield per se and for the drought tolerance of grain yield mapped on linkage group 2 and explained up to 23% of the phenotypic variation. Some of these QTLs were common across stress environments whereas others were specific to only a particular stress environment. All the QTLs that contributed to increased drought tolerance did so either through better than average maintenance (compared to non-stress environments) of harvest index, or harvest index and biomass productivity. It is concluded that there is considerable potential for marker-assisted backcross transfer of selected QTLs to the elite parent of the mapping population and for their general use in the improvement of pearl millet productivity in water-limited environments. Received: 15 November 2000 / Accepted: 12 April 2001     

Methods for quantitative sampling of epiphytic microinvertebrates in lake vegetation

 Two methods were developed for the quantitative sampling of rotifers and cladocerans attached to aquatic macrophytes while separating them from plankton. We named them the “covering method” and the “picking-up method.” We consider the covering method to be better for estimating the abundance of animals on plants, but it requires hard work on a boat. In contrast, the picking-up method is simple and easy to perform, but it seems to estimate animal abundance with some errors. The densities of rotifers and cladocerans on emergent and submerged plants in two Japanese lakes were estimated by the two methods, and the results were compared. The densities of most animals (e.g., the rotiferans Brachionus, Mytilina, Lepadella, and Colurella, and the cladoceran Alona) estimated by the picking-up method did not differ from those estimated by the covering method. In contrast, the densities of the rotiferans Monostyla, Euchlanis, and Trichocerca estimated by the picking-up method tended to be lower than those estimated by the covering method. These suggest that the picking-up method is suitable for estimating many densities, except for some rotiferan genera. Received: August 29, 2001 / Accepted: February 15, 2002     

Introgression of quantitative trait loci (QTLs) determining stripe rust resistance in barley: an example of marker-assisted line development

 Genome-analysis tools are useful for dissecting complex phenotypes and manipulating determinants of these phenotypes in breeding programs. Quantitative trait locus (QTL)-analysis tools were used to map QTLs conferring adult plant resistance to stripe rust (caused by Puccinia striiformis f.sp. hordei) in barley. The resistance QTLs were introgressed into a genetic background unrelated to the mapping population with one cycle of marker-assisted backcrossing. Doubled-haploid lines were derived from selected backcross lines, phenotyped for stripe-rust resistance, and genotyped with an array of molecular markers. The resistance QTLs that were introgressed were significant determinants of resistance in the new genetic background. Additional resistance QTLs were also detected. The susceptible parent contributed resistance alleles at two of these new QTLs. We hypothesize that favorable alleles were fixed at these new QTLs in the original mapping population. Genetic background may, therefore, have an important role in QTL-transfer experiments. A breeding system is described that integrates single-copy and multiplex markers with confirmation of the target phenotype in doubled-haploid lines phenotyped in field tests. This approach may be useful for simultaneously producing agronomically useful germplasm and contributing to an understanding of quantitatively inherited traits. Received: 6 May 1997 / Accepted: 1 September 1997     

Identification of a new quantitative trait locus on Chromosome 7 controlling disease severity of collagen-induced arthritis in rats

 Autoimmune diseases, such as rheumatoid arthritis, Crohn's disease, and multiple sclerosis, are regulated by multiple genes. Major histocompatibility complex (MHC) genes have the strongest effects, but non-MHC genes also contribute to disease susceptibility/severity. In this paper, we describe a new non-MHC quantitative trait locus, Cia8, on rat Chromosome (Chr) 7 that controls collagen-induced arthritis severity in F2 progeny of DA and F344 inbred rats, and present an updated localization of Cia4 on the same chromosome. We also describe the location of mouse and human genes, orthologous to the genes in the genomic intervals containing Cia4 and Cia8, and provide evidence that the segment of rat Chr 7 containing Cia4 and Cia8 is homologous to segments of mouse Chr 10 and 15 and human Chr 8, 12, and 19. Received: 1 November 1998 / Revised: 24 January 1999     

Mapping of quantitative trait loci influencing frost tolerance in Eucalyptus nitens

 Regions of the genome influencing frost tolerance in an outbred family of Eucalyptus nitens have been identified. Two QTLs present on the same linkage group, but located 40 cM apart, were identified using single-factor analysis of variance. The QTLs explained between 7.7 and 10.8% of the phenotypic variation for frost tolerance in this family. Analysis of marker loci linked to the QTLs showed one of them to have a simple mode of action with the effect segregating from the male parent in the family. For the other QTL multiple alleles were identified. This QTL showed segregation from the female parent which gave a positive effect on frost tolerance; however, an allele segregating from the male parent was identified which showed a negative interaction with the allele for increased frost tolerance. Received: 10 May 1997 / Accepted: 2 June 1997     

Detection of quantitative trait loci on chromosome 5R of rye (Secale cereale L.)

 Progenies of an F₂ mapping population were analyzed for quantitative traits to detect QTLs by using marker information from F₂ plants for chromosome 5R. The mapping population was segregating for the major dwarfing gene Ddw1 and the gene Hp1 for hairy peduncle. The only QTL determining plant height was located between HP1 and Ddw1 on the distal part of chromosome 5RL. At the same position a QTL for peduncle length was found, and this trait was closely related to plant height (r=0.895). Since Hp1 and Ddw1 are dominant marker loci, no dominance effect could be estimated. The QTLs for spike length and the number of florets were located near the centromere on 5RL. These two traits were correlated with r=0.824 and showed partial dominance, but these traits were not correlated to plant height and peduncle length. Homoeologous relationships between the QTLs mapped for the first time in rye and those mapped in other Triticeae members are discussed. Received: 8 June 1998 / Accepted: 8 October 1998     

Quantitative trait loci for grain quality, productivity, morphological and agronomical traits in sorghum (Sorghum bicolor L. Moench)

 Quantitative trait loci (QTLs) for grain quality, yield components and other traits were investigated in two Sorghum caudatum×guinea recombinant inbred line (RIL) populations. A total of 16 traits were evaluated (plant height, panicle length, panicle compactness, number of kernels/panicle, thousand-kernel weight, kernel weight/panicle, threshing percentage, dehulling yield, kernel flouriness, kernel friability, kernel hardness, amylose content, protein content, lipid content, germination rate and molds during germination and after harvest) and related to two 113- and 100-point base genetic maps using simple (SIM) and composite (CIM) interval mapping. The number, effects and relative position of QTLs detected in both populations were generally in agreement with the distributions, heritabilities and correlations among traits. Several chromosomal segments markedly affected multiple traits and were suspected of harbouring major genes. The positions of these QTLs are discussed in relation to previously reported studies on sorghum and other grasses. Many QTLs, depending on their relative effects and position, could be used as targets for marker-assisted selection and provide an opportunity for accelerating breeding programmes. Received: 14 February 1998 / Accepted: 4 March 1998