Repulsion Linkage Research Articles

Designing an optimal marker-based pedigree selection strategy for parent building in barley in the presence of repulsion linkage, using computer simulation

Pyramiding multiple desirable genes is an important method for the development of improved breeding materials and/or new cultivars. When the number of genes to be pyramided is many, or the genes are tightly linked in repulsion, it is practically impossible to recover the desirable recombinants in a single generation using a realistic population size, and repeated selection at several generations is required. The availability of markers tightly linked to the desirable genes makes it possible to conduct effective individual selection at early generations. This reduces the number of lines tested in the later generations and increases the desirable genotype frequency in the selected progeny. Computer simulation was used to develop such a marker-based pedigree selection strategy for the development of a barley line that contains 6 desired genes from 3 parental breeding lines (HS078 (H): 221222; PI366444 (P): 212222; Sloop Vic. (S): 122111; with 1 and 2 representing desirable and undesirable alleles, respectively), using the top cross H/P//S. The 6 genes targetted contribute to photoperiod sensitivity, Russian wheat aphid resistance, leaf rust resistance, boron tolerance, earliness per se, and cereal cyst nematode resistance. Under the assumption that perfect markers were available for all the 6 genes, a TC1 population of 300 plants was required to obtain 3 or more lines of the best genotype ‘211222/122111’, in which 3 loci were fixed for the desirable alleles, while the remaining 3 were kept as heterozygous. When single seed descent was used from the TC2 generation until complete homozygosity, the probability of obtaining lines of the desirable genotype (fixed for the desirable alleles at all 6 loci) was low due to the tight repulsion linkage between some of the genes. About 4000 individuals would be required to ensure with 99% probability the recovery of at least 1 line with the desirable genotype. The total number of lines that would need to be genotyped would be at least 5000. When the pedigree method was used in all test-cross generations, many schemes resulted in more lines of the fixed desirable genotype by genotyping fewer lines. The various options were compared using the genetic simulation software module QuLine, based on the QU-GENE simulation platform. The optimum scheme in terms of high success rate and relatively low genotyping costs consisted of the following steps: (1) in TC1 genotyping of 300 individuals allows for 3 or more individuals with the genotype ‘211222/122111’ to be identified; (2) in the TC2 individuals that are fixed for 3 loci and segregating for the remaining 3, loci can be selected from among 500 TC2 plants; (3) in the TC3, 50 or more individuals per TC3 line are genotyped for the 3 segregating loci, and individuals fixed for 5 loci and segregating for the 6th locus can be detected (genotyping is only needed for the segregating loci); (4) 25 individuals per TC4 line are genotyped for the single remaining segregating locus and several individuals of the desirable genotype (111111/111111) are finally selected. The desirable line is then obtained by collecting selfed seed from the selected TC4 plants. Using this scheme, on average, 320 desired TC5 lines were obtained by genotyping fewer than 2000 lines. When markers were tightly linked to the target genes but not diagnostic (perfect), not only was more genotyping required, but also appropriate phenotyping at the end of the marker selection process was necessary to confirm the presence of all the target genes. Under the assumption that recombination between marker and target gene was 5%, the best selection scheme identified, on average, 30 fixed desirable lines by genotyping 8000 lines and phenotyping 700 TC5 lines. If double haploid lines were produced from the F1 generation between H and P, and marker and phenotypic screening were conducted, followed by crossing of the individual with the target 2 loci in desired homozygous allelic status with parent S, the total amount of genotyping and phenotyping could be halved. This study showed that genetic simulation allows for numerous strategies to be compared using real data, and to develop an optimal crossing and selection strategy to combine desired alleles in the most effective and efficient way. This approach could likewise be used in other marker-assisted breeding programs.

A framework linkage map of bermudagrass (Cynodon dactylon × transvaalensis) based on single-dose restriction fragments

This study describes the first detailed linkage maps of two bermudagrass species, Cynodon dactylon (T89) and Cynodon transvaalensis (T574), based on single-dose restriction fragments (SDRFs). The mapping population consisted of 113 F1 progeny of a cross between the two parents. Loci were generated using 179 bermudagrass genomic clones and 50 heterologous cDNAs from Pennisetum and rice. The map of T89 is based on 155 SDRFs and 17 double-dose restriction fragments on 35 linkage groups, with an average marker spacing of 15.3 cM. The map of T574 is based on 77 SDRF loci on 18 linkage groups with an average marker spacing of 16.5 cM. About 16 T89 linkage groups were arranged into four complete and eight into four incomplete homologous sets, while 15 T574 linkage groups were arranged into seven complete homologous sets, all on the basis of multi-locus probes and repulsion linkages. Eleven T89 and three T574 linkage groups remain unassigned. In each parent consensus maps were built based on alignments of homologous linkage groups. Four ancestral chromosomes were inferred after aligning T89 and T574 parental consensus maps using multi-locus probes. The inferred ancestral marker orders were used in comparisons to a detailed Sorghum linkage map using 40 common probes, and to the rice genome sequence using 98 significant BLAST hits, to find regions of colinearity. Using these maps we have estimated the recombinational length of the T89 and T574 genomes at 3,012 and 1,569 cM, respectively, which are 61 and 62% covered by our maps.

Linkage Analysis between Gametophytic Restorer Rf 2 Gene and Genetic Markers in Cotton

In heterozygous fertility restored F 1 plants of the CMS-D8-Rf 2 gametophytic restoration system of cotton (Gossypium hirsutum L.), only the pollen grains with the Rf 2 allele are functional; consequently, all F 2 plants are fertile. Our objective was to develop a statistical method to estimate the recombination fraction (r) between Rf 2 and genetic markers linked in repulsion or coupling phases in fertile F 2 populations. Alleles linked to Rf 2 are preferentially transmitted through pollen, whereas the transmission of alleles linked to rf 2 is reduced. Thus, linked genes give distorted segregation ratios depending on the linkage strength. Genes independent of Rf show normal segregation. The traditional 3:1 or other appropriate ratios can be used to test the linkage between a marker and the Rf locus in an F 2 population. Examples are given for two crosses: (D8R × T586) F 2 for repulsion linkage and (D8R × T582) F 2 for coupling phase linkage. The morphological data confirmed that Rf 2 is not linked to nine dominant genes in T586 or to five recessive genes in T582. However, a RAPD marker, UBC188 500 , present in D8R and absent in nonrestoring lines, exhibited extremely skewed segregation in the D8R × T586 F 2 population with only two plants without UBC188 500 in a population of 76 plants. The recombination frequency between Rf 2 and this marker is 5.26%, which agrees with our previous estimate from a testcross, (D8R × T586) × H1330. This indicates that the proposed method is a valid alternative for mapping gametophytic Rf 2 . Its advantages and limitations are discussed.

Marker-based Selection as a Tool for Enhancing the Efficiency of Two Conventional Breeding Methods of Self-fertilizing Crop Plants, the Generation-accelerated Bulk Breeding and Doubled Haploid Breeding

The effectiveness of marker-based selection (MBS) for enhancing the efficiency of two conventional breeding methods of self-fertilizing crop plants, i.e., generation-accelerated bulk breeding (GAB) and doubled haploid breeding (DHB), is evaluated. When incorporated into GAB, MBS is assumed to be applied in F2 and F3 generations based on DNA markers that are linked with desirable trait genes. The effectiveness of MBS is evaluated based on its contribution to increasing the probability of obtaining the desired genotype. Our calculations of the probability show that the effectiveness of MBS depends on the number of trait genes involved in the breeding objective as well as the number of available markers; MBS will produce a great increase in the probability when more than about 12 genes are involved in the breeding objective and markers are available for several or more of these trait genes. In such a case, MBS is useful even when as few as 100 plants are tested in F2 and F3 generations, compared to conventional GAB in which 2000 plants are grown for generation acceleration. The effectiveness of MBS increases in the presence of repulsion linkage between desirable trait genes, whereas it decreases in the presence of coupling linkage. Although codominant markers are superior under most practically possible conditions, dominant markers (linked with desirable trait genes) could be superior when relatively few, roughly fewer than 12, genes are involved in the breeding objective and desirable trait genes are linked prevalently in the coupling phase. When MBS is based on more than several codominant markers, it is important to widen the range of the marker genotypes to be selected; not only the best but also the second and third best, partially heterozygous genotypes should be selected. Linkage between trait genes and markers needs not to be perfect; when many markers are available, the advantage of MBS is not lost even with a map distance as long as 10 cM. When desirable trait genes are linked prevalently in the repulsion phase, MBS could effectively be combined with DHB for eliminating unpromising doubled haploid genotypes prior to field test, or for selecting from an F2 population, plants that should be treated for doubled haploidization.

Linkage analysis using direct and indirect counting and relative efficiencies for codominant and dominant loci1

A method based on direct and indirect counting is developed for rapid and accurate linkage analysis for codominant and dominant loci. Methods for estimating gender-specific recombination frequencies are available for cases where at least one of the two loci is multiallelic and for biallelic loci with mixed parental linkage phases where at least one locus is codominant. Most of the estimates of gender-average and gender-specific recombination frequencies required iterative solutions. The new method makes use of the full data set, yields exact estimates of the recombination frequencies when the observed and expected genotypic frequencies are equal, and are computationally efficient. Relative efficiency of various data types is affected by the inheritance mode and by parental linkage phases of biallelic loci, but unaffected by the locus polymorphism when using the full data set for linkage analysis. The ability to determine parental linkage phases is affected by the locus polymorphism as well as inheritance mode. Intercross (or F-2 design) is more efficient for mapping codominant loci, whereas backcross is more efficient if dominance is involved. Mixed parental linkage phases of biallelic loci are less efficient than coupling or repulsion linkage phases. Ignoring noninformative offspring results in biased estimates of recombination frequency for biallelic loci only and reduced LOD scores for all cases.

Linkage analysis using direct and indirect counting and relative efficiencies for codominant and dominant loci.

A method based on direct and indirect counting is developed for rapid and accurate linkage analysis for codominant and dominant loci. Methods for estimating gender-specific recombination frequencies are available for cases where at least one of the two loci is multiallelic and for biallelic loci with mixed parental linkage phases where at least one locus is codominant. Most of the estimates of gender-average and gender-specific recombination frequencies required iterative solutions. The new method makes use of the full data set, yields exact estimates of the recombination frequencies when the observed and expected genotypic frequencies are equal, and are computationally efficient. Relative efficiency of various data types is affected by the inheritance mode and by parental linkage phases of biallelic loci, but unaffected by the locus polymorphism when using the full data set for linkage analysis. The ability to determine parental linkage phases is affected by the locus polymorphism as well as inheritance mode. Intercross (or F-2 design) is more efficient for mapping codominant loci, whereas backcross is more efficient if dominance is involved. Mixed parental linkage phases of biallelic loci are less efficient than coupling or repulsion linkage phases. Ignoring noninformative offspring results in biased estimates of recombination frequency for biallelic loci only and reduced LOD scores for all cases.

Detecting and mapping repulsion-phase linkage in polyploids with polysomic inheritance

It has been suggested that ratios of coupling- to repulsion-phase linked markers can be used to distinguish between allopolyploids and autopolyploids, because repulsion-phase linkages are much more difficult to detect in autopolyploids with polysomic inheritance than allopolyploids with disomic inheritance. In this report, we analyze the segregation pattern of repulsion-phase linked markers in polyploids without complete preferential pairing. The observed repulsion-phase recombination fraction (R) in such polyploids is composed of a fraction due to crossing-over (Rc) and another fraction due to independent assortment (Ri). Ri is the minimum distance that can be detected between repulsion-phase linked markers. Because Ri is high in autopolyploids (0.3373, 0.4000, 0.4286 and 0.4444) for autopolyploids of 2n=4x, 6x, 8x and 10x), large population sizes are required to reliably detect repulsion linkages. In addition, the default linkage used in mapping-programs must be greater than the corresponding Ri to determine whether a polyploid is a true autopolyploid. Unfortunately, much lower default linkages than the Ris have been used in recent polyploid studies to determine polyploid type, and markers have been incorporated into polyploid maps based on the R values. Herein, we describe how mapping repulsion linkages can result in spurious results, and present methods to accurately detect the degree of preferential pairing in polyploids using repulsion linkage analysis.

Cytogenetic studies in wheat XIX. Chromosome location and linkage studies of a gene for leaf rust resistance in the Australian cultivar ‘Harrier’

AbstractMonosomic analysis indicated that a seedling leaf rust resistance gene present in the Australian wheat cultivar ‘Harrier’(tentatively designated LrH) is located on chromosome 2A. LrH segregated independently of the stripe rust resistance gene Yr1 located in the long arm of that chromosome, but failed to recombine with Lr17 located in the short arm. LrH was therefore designated Lr17b and the allele formerly known as Lr17 was redesignated as Lr17a. The genes Lr17b and Lr37 showed close repulsion linkage. Tests of allelism indicated that Lr1 7b is also present in the English wheats ‘Dwarf A’(‘Hobbit Sib’), ‘Maris Fundin’ and ‘Norman’. Virulence for Lr17b occurs in Australia, and pathogenicity studies have also demonstrated virulence in many western European isolates of the leaf rust pathogen. Despite this, it is possible that the gene may be of value in some regions if used in combination with other leaf rust resistance genes.

Identification of AFLP and SSR markers associated with quantitative resistance to Globodera pallida (Stone) in tetraploid potato (Solanum tuberosum subsp. tuberosum) with a view to marker-assisted selection

Seventy eight clones from the cross between SCRI clone 12601ab1 and cv Stirling were used to explore the possibility of genetical linkage analysis in tetraploid potato (Solanum tuberosum subsp. tuberosum). Clone 12601ab1 had quantitative resistance to Globodera pallida Pa2/3 derived from S. tuberosum subsp. andigena. The strategy adopted involved identifying single- (simplex) and double- (duplex) dose AFLP markers in the parents from segregation ratios that could be unambiguously identified in their offspring, detecting linkage between a marker and a putative quantitative trait locus (QTL) for resistance, and placing the QTL on the linkage map of markers. The numbers of scorable segregating markers were 162 simplex ones present only in 12601ab1, 87 present in Stirling, and 32 present in both; and 72 duplex markers present only in 12601ab1 and 45 present in Stirling. The total map length was 990.9 cM in 12601ab1 and 484.6 cM in Stirling. A QTL with a resistance allele present in double dose (QQqq) in 12601ab1 was inferred from the associations between resistance scores (square root of female counts) and two duplex markers linked in coupling, which, in turn, were linked in coupling to four simplex markers also associated with resistance, but to a lesser degree. The largest marker class difference was the one for the duplex marker P61M34=15. It accounted for 27.8% of the phenotypic variance in resistance scores, or approximately 30% of the genotypic variance. Subsequently, this duplex marker was found to be linked in coupling with a duplex SSR allele Stm3016=a, whose locus was shown to be on chromosome IV in a diploid reference mapping population. The other QTLs for resistance segregating in the progeny were not identified for one or more of the following reasons: the markers did not cover the whole of the genome, there were unfavourable repulsion linkages between the QTLs and markers, or the gene effects were not large enough to be detected in an experiment of the size conducted. It is concluded that prospects appear good for detecting QTLs and using marker-assisted selection in a tetraploid potato breeding programme, provided that, in future, the population size is increased to over 250 and more SSR markers are used to complement the AFLPs; the same is likely to be true for other autotetraploid crops.

Identification of a QTL decreasing yield in barley linked to Mlo powdery mildew resistance

A molecular marker map, including Mlo mildew resistance, of the spring barley cross Derkado (Mlo-resistant) × B83-12/21/5 (Mlo-susceptible) was scanned for yield QTLs to determine whether the association of Mlo resistance with reduced yield was due to linkage or pleiotropy. Over the mapped portion of the genome of the cross, the QTL with the greatest effect upon yield was located within a 22 cM region between mlo and the simple sequence repeat HVM67 on chromosome 4(4H). The association of Mlo resistance with lower yield was therefore due to a repulsion linkage. Analysis of yield component characters revealed QTL alleles for reduced grain number and earlier heading date in the same region, also associated with Mlo resistance. Genotyping of a range of cultivars and sources of Mlo resistance with the HVM67 simple sequence repeat showed that the Derkado HVM67 allele was rare as it was found only in one other cultivar and four land-races or sources of disease resistance. Grannenlose Zweizeilige, the source, and Salome, the carrier of Mlo resistance in Derkado, have the same HVM67 genotype, although Salome was a mixture of two genotypes. The entire mlo-HVM67 chromosomal segment from Grannenlose Zweizeilige is therefore thought to have been transmitted to Derkado, possibly through joint selection for Mlo resistance and early heading. L92, synonym EP79, was another source of Mlo resistance with the same HVM67 allele as Derkado but recombination must have occurred during the breeding of Atem as it possesses a different HVM67 allele which is present in all the other Mlo sources and cultivars surveyed. Abbreviations: GN, grains per main stem ear; HD, heading date; MSTGW, thousand grain weight derived from GN and MSY; MSY, yield of grain on the main stem; PY, yield of grain from the whole plot; sCIM, simplified compound interval mapping; SIM, simple interval mapping; SPY, single plant yield; S-SAP, sequence-specific amplification polymorphism; TGW, thousand grain weight derived from bulk of plot seed; TN, number of fertile stems per plant.

Genetic analysis using trans-dominant linked markers in an F2 family

Trans-dominant linked markers pairs (trans referring to the repulsion linkage phase) provide a model for inferring the F2 progeny genotype based upon both the conditional probabilities of F2 genotypes, given the F2 phenotype, and prior information on marker arrangement. Prior information of marker arrangement can be readily obtained from a linkage analysis performed on marker segregation data in a family resulting by crossing the F1 individual to a "tester" parent or else can be obtained directly from the gametes of the F1, or from recombinant inbred lines. We showed that a trans-dominant linked marker (TDLM) pair can be recoded as a "co-dominant megalocus" when the recombination fraction, r1, for apair of TDLMs is less than 0.05. We obtained a maximum-likelihood estimator (MLE) of the recombination frequency, r2, between a TDLM pair and a co-dominant marker in an F2 family using the EM algorithm. The MLE was biased. Mean bias increased as r1 and r2 increased, and decreased as sample size increased. The information content for r2 was compared to the information content of dominant and co-dominant markers segregating in an F2 family. It was almost identical with two co-dominant markers when r1≤0.01 and r2≥0.05. For larger values of r1, (0.05≤r1≤0.15) a TDLM pair provided 75%-66% of the information content of two co-dominant markers. Although dominant markers can be converted to co-dominant markers by a laborious process of cloning, sequencing, and PCR, TDLM pairs could easily substitute for co-dominant markers in order to detect quantitative trait loci (QTLs) and estimate gene action in an F2 family.

Selective Mapping of QTL Conditioning Disease Resistance in Common Bean

Genetic markers linked with quantitative trait loci (QTL) may enable indirect selection of complex disease resistance. Construction of separate linkage maps to identify QTL for each complex disease resistance trait of common bean (Phaseolus vulgaris L.) is unfeasible, however. We investigated whether selective mapping could be used to hasten identification of random amplified polymorphic DNA (RAPD) associated with QTL conditioning bean golden mosaic virus (BGMV) or common bacterial blight (CBB) resistance. The mapping population (‘Dorado’ × XAN 176) consisted of 79 F5:7 recombinant inbred lines. A bulked segregant analysis (BSA) of as few as three individuals and selective genotyping was used. The 101 RAPDs identified between the parents were tested across resistant vs. susceptible bulks for BGMV reaction, combined greenhouse (leaf) and field reactions to CBB, and pod (greenhouse) reaction to CBB. Fourteen of 22 RAPDs selectively mapped because they cosegregated among lines within bulks, were linked with seven of the nine QTL conditioning resistance as identified by QTL mapping using all 101 RAPDs. The two QTL not identified by this approach had minor effects. BSA and selective genotyping required only about one‐third the cost and labor of completely classifying the whole population with each marker and was similarly effective for identifying RAPD markers associated with major‐effect QTL that condition disease resistance in common bean. Two‐locus models (R2), for select environments, explained 60% of the phenotypic variation in BGMV reaction, and 65, 58, and 46% of the phenotypic variation in greenhouse‐leaf, ‐pod, and field reactions to CBB. Repulsion linkages between QTL for BGMV and CBB may complicate the combination of resistance alleles for these two traits.

A RAPD Genetic Map of Saccharum officinarum

Saccharum officinarum L. is the major contributing species to modern sugarcane varieties. It is a polyploid where 2n = 80, although the basic chromosome number and level of ploidy have not been conclusively determined. A genetic map in S. officinarum could benefit breeding programs through marker‐assisted selection and could provide information about the genetic structure of sugarcane. The objective of this research was to develop a genetic linkage map by means of random amplified polymorphic DNA (RAPD) single‐dose markers in S. offcinarum. The map was constructed with 84 F1 progeny from the cross ‘La Purple’ (S. officinarurn) × ‘Molokai 5829’ (S. robustum Brandes and Jeswiet ex Grassl.). Single‐dose markers should segregate in a 1:1 fashion in the progeny of this cross. Primers were first screened in the parental genotypes, and those revealing polymorphisms were then tested in six progeny selected at random to identify putative single‐dose markers. All resulting markers were then tested in 84 progeny and those showing a 1:1 segregation pattern were considered single‐dose markers and were used for mapping. Among 279 singledose markers identified from initital screening with 1840 primers, 161 markers were linked in 50 linkage groups with a minimum LOD of 5.0 and a maximum recombination value of 0.28. The detection of 12 repulsion linkages suggested the occurrence of limited preferential chromosome pairing in this species. Linkage of eyespot susceptibility to a RAPD marker identified an additional linkage group and indicated that linkages identified in this map could potentially be used for marker‐assisted selection.

Genetic linkage of the Yr1 and Pm4 genes for stripe rust and powdery mildew resistances in wheat

Genes Yr1 for resistance to stripe rust and Pm4a for resistance to powdery mildew showed linkage of 2.0±0.6 cM. Close repulsion linkage probably accounts for the absence in European wheats of genes Yr1 and Pm4b in combination.

Effects of selection and opportunities for recombination in doubled‐haploid populations of barley (Hordeum vulgare L.)

AbstractDoubled‐haploid breeding systems are typically based on sampling gametes from F1 plants. However, in the case of repulsion linkages, additional recombination could be advantageous. Pre‐selection of gamete donors might also shift progeny performance in a desired direction. The objectives of this study were to quantify the effects of an additional round of recombination and assess the effectiveness of pre‐anthesis selection in the production of barley doubled haploids. Assessments were conducted on: 1. 100 F1‐derived lines representing a subset of lines used in previous genome‐mapping studies; 2. 100 random F2‐derived lines; and 3. 50 F2‐derived lines from gamete donors selected for early heading. An additional round of recombination had only a modest effect on generating more favourable genotypes. Pre‐anthesis selection was ineffective in generating an earlier heading population. According to published quantitative‐trait locus (QTL) analyses based on the F1 ‐derived population, there are few repulsion linkages between QTL determining the traits measured in this experiment. Any advantages to be gained from postponing the generation of derivation of doubled haploids must be weighed against the delay and additional cost.

Cytogenetic studies in wheat. XV. Location of rust resistance genes in VPM1 and their genetic linkage with other disease resistance genes in chromosome 2A

Inheritance studies showed that the VPM1-derived seedling resistances to stem rust, stripe rust, leaf rust, and powdery mildew were controlled by single genes; the genes for rust resistance were designated Sr38, Yr17, and Lr37, respectively, whereas the gene for resistance to powdery mildew was postulated to be Pm4b. Sr38, Yr17, and Lr37 were shown to be closely linked and distally located in the short arm of chromosome 2A. They showed very close repulsion linkage with Lr17 and were genetically independent of other genes known to be located in chromosome 2A. Previously unmapped, Yr1 appeared to be distally located in the long arm of chromosome 2A.

Effects of epistasis on tests for linkage in self-pollinated species

Tests for linkage based on covariances among relatives in self-pollinated species are usually based upon an assumption that epistasis is not important. This study was conducted to determine the impact of epistasis on, and to investigate the sensitivity of, such tests. Thirty covariances were calculated for each of ten non-epistatic and ten epistatic genetic models with varying probabilities of recombination between two coupling or repulsion loci. Each set of covariances was tested for linkage by comparing covariances calculated for the model with those expected for an additive-dominance model with no linkage. Results showed that the test for linkage is quite insensitive to the effects of linkage due to the disproportionate influence of inbreeding. Repulsion linkages should be easier to detect than coupling linkages for all models. Epistasis was found to mimic or counteract the effects of linkage. Tests for linkage based on covariances within a hierarchical mating design appear to be insensitive to linkage and may confuse the effects of linkage and epistasis.

Selection for recombination in a polygenic model--the mechanism.

SummaryA polygenic model has been simulated in order to reveal the process whereby selection in an infinite population can lead to an increase in the frequency of alleles causing higher rates of recombination (CHalleles). Directional selection generates repulsion linkage disequilibrium (+ − + −), which is less strong inCHgametes (gametes carryingCHalleles). In consequence,CHgametes contribute greater phenotypic variability, and therefore respond more to directional selection: that is, they accumulate more selectively favoured alleles.CHalleles then increase in frequency by hitch-hiking. In contrast, normalizing selection, or frequent changes in the direction of selection, favour alleles for a low recombination rate.

Estimation of the true additive genetic variance sigma ki = 1 d2i in the presence of linkage disequilibrium.

Accurate estimates of the true additive genetic variance (sigma ki = 1 d2i) of a cross between two pure breeding varieties can be obtained from the additive genetic components of the first three ranks (D1, D2 and D3) when the latter are biased by the presence of linkage. Additive genetic variances of the lower ranks are directly equatable with sigma ki = 1 d2i because they incur minimal bias even when the predominating linkages are strong. More precise estimates of sigma ki = 1 d2i are however obtainable from the asymptotic regression analysis or a weighted least squares analysis. Estimates of sigma ki = 1 d2i when obtained from 784 hierarchically derived F7 families of the V2 X V12 cross of Nicotiana rustica were observed to be considerably larger than the additive genetic variance displayed by the F13 inbreds of the same cross for all the characters that showed significant excess of repulsion linkages. These results lend support to our commonly held view that the prediction procedures generally underestimate the probability of successful recovery of superior recombinant inbreds.

Investigations into the linkage of genes controlling individual quantitative characters in barley

Technical innovations in barley breeding have resulted in the ability to reduce generation times. Single seed descent and doubled haploidy have become practical propositions in barley improvement. These Fx samples are also powerful tools for genetical analyses and have been used in this paper together with conventional generations to investigate the linkage of genes controlling quantitative characters. Such investigations are of relevance to barley breeders since the detection of significant levels of repulsion linkages would indicate that the single seed descent (SSD) technique would be preferable to doubled-haploid (DH) methods. The present study indicated that estimates of D (the additive genetic variance) from DH and SSD sampled did not differ significantly. Thus linkage disequilibrium is not an important component of the genetic architecture of the five crosses investigated. Hence F1-derived doubled haploids or SSD will be equally effective in producing desirable recombinant inbred lines.Key words: Hordeum, doubled haploids, linkage disequilibrium.