Simulation of marker-assisted selection utilizing linkage disequilibrium: the effects of several additional factors

Use was made of our published model and methods to investigate the effects of several additional factors on marker-assisted selection (MAS) utilizing linkage disequilibrium. The additional factors were: size of the sample used to estimate the marker quantitative trait locus (MQTL) association effects, the method used to estimate the MQTL effects, use of the average of the top MQTL estimates in selection rather than individual estimates, size of the selection population, and the crossing of duplicate selection lines to generate further linkage disequilibrium and further selection response. The average map distance between the quantitative trait loci (QTLs) and their nearest marker was 0.15 Morgans. Use of estimates of MQTL effects derived by least squares yielded smaller selection responses than estimates derived by mixed-model methods. Selection responses were also reduced by using a smaller sample for estimating the associations because MQTL effects were less well estimated. This applied to selection on the MQTL effects themselves and to selection combining the MQTL with phenotypic information. Thus, poorly estimated MQTL effects added noise to the system and reduced selection response in combined selection. Using the average of the top MQTL estimates, rather than individual estimates, also reduced selection response. New linkage disequilibrium, generated by crossing two lines selected from the same population, did not lead to additional selection response in the cross line. These results show limitations to MAS using linkage disequilibrium until close linkages of markers and QTLs are available.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

Effect of selection on genetic parameters of correlated traits

Summary Changes in genetic parameters of correlated traits due to the buildup of linkage (gametic phase) disequilibrium from repeated truncation selection on a single trait are studied. After several generations of selection, an equilibrium is approached where there are no further changes in genetic parameters and limiting values are reached. Formulae are derived under an infinitesimal model for these limiting values of genetic variances and covariances, heritabilities, and genetic correlations between traits directly and indirectly selected. Changes from generation zero to the limit in all these parameters become greater as heritability of the trait under direct selection increases and, to a lesser extent, as intensity of selection increases. Change in heritability of a trait under indirect selection also increases as the absolute value of the correlation between the trait under indirect and the trait under direct selection increases. The change is maximum when the initial value of heritability is close to 0.5 and insignificant when the initital value is close to zero or one. Change in the genetic correlation between the trait under direct selection and the trait under indirect selection is maximum when its initial value is close to ±0.6 and insignificant when its initial value is close to zero or ±1. Heritability of the trait indirectly selected and genetic correlation between that trait and the trait directly selected always decrease in absolute value, whereas genetic correlation between two traits indirectly selected can either decrease or increase in absolute value. It is suggested that use be made of formulae at selection equilibrium in the prediction of correlated responses after several generations of selection.     

Genetic polymorphism at two linked loci,Sod and Est-6, in Drosophila melanogaster

We have examined the patterns of polymorphism at two linked loci, Sod and Est-6, separated by nearly 1000 kb on the left arm of chromosome 3 of Drosophila melanogaster. The evidence suggests that natural selection has been involved in shaping the polymorphisms. At the Sod locus, a fairly strong (s>0.01) selective sweep, started ≥2600 years ago, increased the frequency of a rare haplotype, F(A), to about 50% frequency in populations of Europe, Asia, and the Americas. More recently, an F(A) allele mutated to an S allele, which has increased to frequencies 5–15% in populations of Europe, Asia and North America. All S alleles are identical (or very nearly) in sequence and differ by one nucleotide substitution (which accounts for the F→S electrophoretic difference) from F(A) alleles. At the Est-6 locus, the evidence indicates both directional and balancing selection impacting separately the promoter and the coding regions of the gene, with linkage disequilibrium occurring within each region. Some linkage disequilibrium also exists between the two genes.     

Dynamics of linkage disequilibrium in bacterial genomes undergoing transformation and/or conjugation

Bacteria may undergo recombinational exchange either by conjugation followed by crossing over, or by transformation of small segments of DNA into the cell followed by incorporation into the chromosome by gene conversion. These two forms of recombination may have very different consequences on the patterns of linkage disequilibrium seen within bacterial genomes. In this paper deterministic recursions are obtained for three linked loci in populations having these two forms of recombination. Both neutral genetic variation and the case of one selected gene are considered. It is shown that the two forms of exchange have identical consequences on two-locus linkage disequilibria, but that three-locus disequilibria can have different behaviors. Hitchhiking also has different consequences on the pattern of disequilibrium seen between linked neutral genes in the region of the selected locus. Inference of the relative importance of these two modes of recombination from static samples of DNA sequences will hinge on the relationship between linkage map distance and disequilibria.     

Linkage disequilibrium and gametophytic self-incompatibility

Summary The approach to linkage equilibrium of a locus linked to the locus determining gametophytic self-incompatibility (S) is considered. For the simplest case of three alleles at the S locus and two at the linked locus it is necessary to consider 3 measures of linkage disequilibrium. These are found to approach their equilibrium value of zero in one of three ways: 1) steadily declining to zero; 2) oscillating as decline proceeds; 3) a combination: 2) followed by 1). Linkage equilibrium may be established before genotype frequencies reach their expectation under random crossing. Earlier studies (Li 1951; Moran 1962) of the approach to S allele equilibrium have been based on the assumption that all types of pollen take part in fertilizations equally frequently. Such an assumption leads to simpler expressions for changes in S gene frequencies but is extremely unrealistic and, in particular, leads to a different rate of approach to equilibrium from the more comprehensive model. It is shown that even in the absence of selection it is not possible to predict the equilibrium gene frequency of a linked locus until S allele equilibrium is reached. This frequency may be either higher or lower than that calculated from a gene count in the starting genotype pool. However, these two gene frequencies may stabilize long before linkage equilibrium is achieved. An examination of selection against one genotype at the linked locus is undertaken. If linkage is complete, lethality can be less effective at reducing the gene frequency than is less intense selection (in only a few generations of selection). Here too linkage equilibrium may be established with selection still effective in bringing about a decline in gene frequency. An examination of the analysis and conclusions of Rasmuson (1980) shows that because these were based on the inadequate formulae previously discussed and exclude phenomena discussed above, they are misleading. The possibility of a gametophytic self-incompatibility system providing a sufficient condition for the sheltering of lethals in the absence of the condition of complete linkage to the S locus (r=0) is shown to be unlikely.     

Patterns of polymorphism detected in the chloroplast and nuclear genomes of barley landraces sampled from Syria and Jordan

In order to examine how molecular polymorphism in barley landraces, sampled from five different ecogeographical regions of Syria and Jordan, is organised and partitioned, genetic variability at 21 nuclear and 10 chloroplast microsatellite loci were examined. Chloroplast polymorphism was detected, with most variation being ascribed to differences between the five regions (F_st 0.45) and to within sites within each region (F_st 0.44). Moreover, the distribution of chloroplast polymorphism is structured and not distributed randomly across the barley landraces sampled. From a total of 125 landrace accessions (five lines from each of five sites from each of five regions) genotyped with 21 SSRs a total of 244 alleles were detected, of which 38 were common to the five regions sampled. Most nuclear variation was detected within sites. Significant differentiation between sites (F_st 0.29) was detected with nuclear SSRs and this partially mirrored polymorphism in the chloroplast genome. Strong statistical associations/interaction was also detected between the chloroplast and nuclear SSRs, together with non-random association (linkage disequilibrium) of alleles at both linked and unlinked SSR loci. These results are discussed in the context of adaptation of landraces to the extreme environment, the concept of 'adapted gene complexes' and the exploitation of landraces in breeding programmes.Communicated by P. Langridge     

Analytical results concerning linkage disequilibrium in models with genetic transformation and conjugation

Expressions are obtained for the expected levels of linkage disequilibrium under three different equilibrium neutral models that make different assumptions about how recombination takes place. A transformation model is considered in which exchange events involve only one locus at a time. Two conjugation models are considered one with a linear genome and one with a circular genome. In the conjugation models large blocks of genes can be transferred with each conjugation. Consistent with published simulation results, it is found that if the transformation rate per locus is more than twenty times the mutation rate per locus, then the levels of linkage disequilibrium are quite low. If the number of loci being sampled is greater than 10, conjugation with a circular genome can be considerably more effective than transformation in reducing linkage disequilibrium. When recombination rates are high, expected linkage disequilibrium is shown to be proportional to the inverse of the transformation rate (or conjugation rate.)     

Linkage disequilibrium in Bougainville Island

Linkage disequilibria are estimated for three 2-locus systems in 18 samples from Bougainville Island, Solomon Islands. The systems are haptoglobin, acid phosphatase and MN blood group. The disequilibria are estimated two ways: by maximum likelihood (ML) and by the covariance between the non-alleles. Though seven of the 52 ML estimates are statistically different than zero, none of the covariance estimates are significant. We conclude that because linkage disequilibrium for loosely linked loci is a small quantity and because the sample sizes for most populations studied by anthropologists are small, linkage disequilibrium will not be a useful parameter for the study of natural selection in these populations.     

Gluten,a lectin with oligomannosyl specificity and the causative agent of gluten-sensitive enteropathy

The pathogenesis of gluten-sensitive enteropathy or coeliac disease is as yet unknown. We can demonstrate by laser nephelometric measurements that gluten has lectin-like properties. Gluten binds ‘high-mannose type’ glycoproteins and the complex formation is inhibitable by mannan. As known for other lectins the reaction is absolutely Ca-dependent. Glycoproteins from the immature crypt cells from the small intestine are highly more reactive than glycoproteins from the mature villous zone. The possibility of a genetically determined deficiency of the growth-dependent N-acetyl-glucosaminyltransferase-1 as the pathogenic factor of the gluten-sensitive enteropathy is discussed.     

Development of sequence-specific PCR markers linked to the Tardus gene that reduces pod shattering in narrow-leafed lupin (Lupinus angustifolius L.)

Seed pods of wild-type narrow-leafed lupins (Lupinus angustifolius L.) shatter upon maturity, dispersing their seeds. Recessive alleles of the genes Tardus and Lentus that confer reduced pod shattering have been incorporated into domesticated cultivars to facilitate harvesting. Tardus was mapped in an F₈ recombinant inbred population of a cross between domesticated and wild lupins. A microsatellite–anchored fragment length polymorphism marker (TaM1), which mapped 2.1 cM from Tardus, was converted to a locus-specific PCR assay. Marker TaM2, a restriction fragment length polymorphism marker was converted to a PCR assay and mapped to 3.9 cM on the other side of Tardus. Marker TaM3, a cleaved amplified polymorphic sequence marker, was positioned along-side marker TaM1 at 3.9 cM from Tardus. One or more markers was polymorphic in 70% of possible pairwise crosses between Australian domesticated lines and wild accessions tested, indicating wide applicability of the markers in crosses between wild and domesticated germplasm.     

Doubled haploids for estimating genetic variances in presence of linkage and gene association

Summary The effect of gene association (or dispersion) and linkage on the estimation of genetic variances in a diallel experiment involving doubled haploid lines is evaluated. It is shown that the estimates of the additive and the additive X additive genetic variances, as obtained by Choo et al. (1979), are biased if genes are linked or are not independently distributed in the parents. However, this bias only occurs in the presence of interaction between homozygous loci. Gene association (or dispersion) and linkage, if present, can be detected by comparing the parental vs the crosses mean, the parental vs the doubled haploid lines variance, and the among vs the within crosses variance.     

Antigen and haplotype frequencies at three human leucocyte antigen loci (HLA-A, -B, -C) in the Pawaia of Papua New Guinea

The genetic profile of the Pawaia, a seminomadic, linguistic isolate from the highlands fringe of Papua New Guinea, is described in terms of antigen and haplotype frequencies at three class I human leucocyte antigen loci (HLA-A, -B, and -C). The Pawaia, like other Papua New Guinea populations, exhibit restricted polymorphisms at all three loci studied, both in the number of alleles segregating and in the level of average heterozygosity. An extremely high frequency (52.9%) of HLA-B27, the antigen implicated in the pathogenesis of seronegative arthropathies, was found. A novel HLA-C locus specificity, CNG, resulting probably from a gene duplication event, was also observed in significant numbers. Although the gene frequency comparisons suggest their strong affinities with the highlanders, the Pawaia haplotypes reveal significant admixture from other neighbouring groups as well. The usefulness of HLA haplotypes in tracing the movements of human populations in the New Guinea area is discussed.     

Linkage disequilibrium and the genetic distance in livestock populations: the impact of inbreeding

Genome-wide linkage disequilibrium (LD) is subject to intensive investigation in human and livestock populations since it can potentially reveal aspects of a population history, permit to date them and help in fine-gene mapping. The most commonly used measure of LD between multiallelic loci is the coefficient D''. Data based on D'' were recently published in humans, livestock and model animals. However, the properties of this coefficient are not well understood. Its sampling distribution and variance has received recent attention, but its expected behaviour with respect to genetic or physical distance remains unknown. Using stochastic simulations of populations having a finite size, we show that D'' fits an exponential function having two parameters of simple biological interpretation: the residual value (rs) towards which D'' tends as the genetic distance increases and the distance R at which this value is reached. Properties of this model are evaluated as a function of the inbreeding coefficient (F). It was found that R and rs increase when F increases. The proposed model offers opportunities to better understand the patterns and the origins of LD in different populations and along different chromosomes.     

Genetic studies of self-fertility in rye (Secale cereale L.). 2. The search for isozyme marker genes linked to self-incompatibility loci

The segregation of several isozyme marker genes has been studied in F₂ inbred families from hybrids between self-sterile and five self-fertile inbred lines (nos. 2, 3, 4, 5, and 8) as well as from interline hybrids. Self-pollination of F₁ hybrids between self-sterile forms and lines 5 and 8 gave an F₂ segregation ratio of 1 heterozygote:1 homozygote for the gene Prx7 (chromosome 1R) against the allele from the line. This is interpreted as a result of tight linkage of the Prx7 gene with the S1 gene in chromosome 1R (recombination at a level of 0–1%). The self-pollination of such hybrids with lines 2,3 and 4 gave normal segregation for the Prx7 gene (1:2:1). This means that these lines carry a self-fertility allele which is not on chromosome 1R. Interline hybrids 5×2, 5×3 and 5×4 had self-fertility alleles for the two S genes and in inbred F₂ progenies gave the expected deviating segregation for the Prx7 gene in a ratio of 2:3:1. The segregation of interline hybrid 5×8 was normal, 1:2:1, as expected. Highly-deviating segregation in an inbred F₂ family of a hybrid with line 5 has also been obtained for another gene from chromosome 1R — Pgi2 (recombination with the S1 locus of 16.7%). By using the same method it has been estimated that line 4 has a self-fertility allele of the S2 locus from chromosome 2R and that the genes -Glu and Est4/11 are linked with it (recombination 16.7% and 17.5–20% respectively). Lines 2 and 3 have a self-fertility allele of the S5 locus from chromosome 5R which is linked with the Est5-7 gene complex (recombination at a level of 28.8–36.0%).     

The dynamics of interlocus associations in the three-locus hitchhiking model

The hitchhiking effects of a selected locus upon the dynamics of the pairwise association,D _nn between two neutral loci is examined analytically for the special case where at least one of the neutral loci is in linkage equilibrium with the selected locus. The results apply approximately whenever the product of the pairwise associations between the selected locus and each neutral locus is negligible with respect to the three-way linkage disequilibrium. It is shown that precisely four broad classes of trajectories are possible, whether the selected locus is between (nsn) or to one side (snn) of the neutral loci, and whatever the mode of selection operating.D _nn may: (1) decay rapidly to zero, at a rate faster in each generation than that expected for two isolated neutral loci; (2) monotonically decay to zero at a rate which is slower in every generation than under the usual neutral regime; (3) increase initially and/or in intermediate periods before eventually slowly decaying to zero; or (4) exhibit type 1 behavior in the first segment of the trajectory and either type 2 or 3 behavior in the subsequent generations, with the transition marked by a change in sign. The nature of a given trajectory is largely determined by the direction of gene frequency change at the selected locus, and the initial signs of bothD _nn and the three-way linkage disequilibrium.The single most important consequence of these results is that there is no simple relation between the amount of pairwise association between two neutral markers and the recombination fraction between them. Several factors influencing the magnitude of the hitchhiking effect are also examined. It is shown that, all else being equal, the greater the three-way linkage disequilibrium, the greater the departure ofD _nn from the expected neutral dynamic. Increased recombination among the loci reduces the hitchhiking effect onD _nn . The dependence of the behavior upon the exact position of the selected locus is also determined both within and betweennsn andsnn chromosomal systems. An interesting discovery is that given equivalentnsn andsnn systems, with each having the same recombination between their two neutral loci,D _nn will deviate more from the standard neutral dynamic in thesnn system if its selected locus is sufficiently tightly linked to the neutral loci.     

SNP detection and population structure evaluation of Salix gordejevii Y. L. Chang et Skv. in Hunshandake Sandland,Inner Mongolia,China

Single nucleotide polymorphisms (SNPs) are the most abundant and richest form of genomic polymorphism and, hence, are highly favorable markers for genetic map construction and genome-wide association studies. Based on the DNA specific-locus amplified fragment sequencing (SLAF-seq) for large-scale SNP detection, the genetic diversity and population structure of Salix gordejevii Y. L. Chang et Skv., a valuable sand-fixing shrub, was assessed in 199 accessions from 20 populations in Hunshandake Sandland of northern China. A total of 623.15 M reads resulted in 30.49 × sequencing depth on average and a mean Q30 of 95.70%, and 2,287,715 SNPs in 178,509 polymorphic SLAF tags were obtained. By discarding minor allele frequency > 0.05 and integrity > 0.8, a total of 93,600 SNPs were retained for population genetic analyses, which revealed that 199 individuals could be divided into six groups based on cross-validation errors. However, this grouping pattern did not match the geographical distribution, indicating that there is no apparent geographic barrier in the blank areas where S. gordejevii was not distributed in Hunshandake Sandland. In addition, the physical distance of linkage disequilibrium decay in the analyzed S. gordejevii individuals was 18.5 kb when r² = 0.1. The linkage disequilibrium decay distances for different chromosomes varied from 4.6 kb (chromosome 16) to 37.8 kb (chromosome 3). The obtained SNPs offer suitable marker resources for further genetic and genomic studies and will benefit S. gordejevii breeding programs.