Estimate Of Recombination Fraction Research Articles

New statistical methods for estimation of recombination fractions in F2 population

BackgroundDominant markers in an F2 population or a hybrid population have much less linkage information in repulsion phase than in coupling phase. Linkage analysis produces two separate complementary marker linkage maps that have little use in disease association analysis and breeding. There is a need to develop efficient statistical methods and computational algorithms to construct or merge a complete linkage dominant marker maps. The key for doing so is to efficiently estimate recombination fractions between dominant markers in repulsion phases.ResultWe proposed an expectation least square (ELS) algorithm and binomial analysis of three-point gametes (BAT) for estimating gamete frequencies from F2 dominant and codominant marker data, respectively. The results obtained from simulated and real genotype datasets showed that the ELS algorithm was able to accurately estimate frequencies of gametes and outperformed the EM algorithm in estimating recombination fractions between dominant loci and recovering true linkage maps of 6 dominant loci in coupling and unknown linkage phases. Our BAT method also had smaller variances in estimation of two-point recombination fractions than the EM algorithm.ConclusionELS is a powerful method for accurate estimation of gamete frequencies in dominant three-locus system in an F2 population and BAT is a computationally efficient and fast method for estimating frequencies of three-point codominant gametes.

Genetic mapping of 15 human X chromosomal forensic short tandem repeat (STR) loci by means of multi-core parallelization

Typing of X chromosomal short tandem repeat (X STR) markers has become a standard element of human forensic genetic analysis. Joint consideration of many X STR markers at a time increases their discriminatory power but, owing to physical linkage, requires inter-marker recombination rates to be accurately known. We estimated the recombination rates between 15 well established X STR markers using genotype data from 158 families (1041 individuals) and following a previously proposed likelihood-based approach that allows for single-step mutations. To meet the computational requirements of this family-based type of analysis, we modified a previous implementation so as to allow multi-core parallelization on a high-performance computing system. While we obtained recombination rate estimates larger than zero for all but one pair of adjacent markers within the four previously proposed linkage groups, none of the three X STR pairs defining the junctions of these groups yielded a recombination rate estimate of 0.50. Corroborating previous studies, our results therefore argue against a simple model of independent X chromosomal linkage groups. Moreover, the refined recombination fraction estimates obtained in our study will facilitate the appropriate joint consideration of all 15 investigated markers in forensic analysis.

Editorial: Doubled Haploidy in Model and Recalcitrant Species.

Doubled haploid (DH) technology is a powerful tool in plant breeding to reduce the time and costs needed to produce pure lines, the cornerstone of hybrid seed production. This biotechnological alternative to classic methods allows for a reduction of the typical 7–8 inbreeding generations needed to fix a hybrid genotype to only one in vitro generation. It is therefore much faster and cheaper, being the principal advantage of DH technology in plant breeding, but not the only. Indeed, DHs are also useful for genetic mapping of complex qualitative traits, for linkage studies and estimation of recombination fractions, to unmask recessive mutants, to avoid transgenic hemizygotes, or for reverse breeding, among others (Forster et al., 2007; Dunwell, 2010; Dwivedi et al., 2015). These are some of the advantages that make DH technology one of the most exciting fields of present and future plant biotechnology.

Haplotype phasing after joint estimation of recombination and linkage disequilibrium in breeding populations

A novel method for haplotype phasing in families after joint estimation of recombination fraction and linkage disequilibrium is developed. Results from Monte Carlo computer simulations show that the newly developed E.M. algorithm is accurate if true recombination fraction is 0 even for single families of relatively small sizes. Estimates of recombination fraction and linkage disequilibrium were 0.00 (SD 0.00) and 0.19 (SD 0.03) for simulated recombination fraction and linkage disequilibrium of 0.00 and 0.20, respectively. A genome fragmentation phasing strategy was developed and used for phasing haplotypes in a sire and 36 progeny using the 50 k Illumina BeadChip by: a) estimation of the recombination fraction and LD in consecutive SNPs using family information, b) linkage analyses between fragments, c) phasing of haplotypes in parents and progeny and in following generations. Homozygous SNPs in progeny allowed determination of paternal fragment inheritance, and deduction of SNP sequence information of haplotypes from dams. The strategy also allowed detection of genotyping errors. A total of 613 recombination events were detected after linkage analysis was carried out between fragments. Hot and cold spots were identified at the individual (sire level). SNPs for which the sire and calf were heterozygotes became informative (over 90%) after the phasing of haplotypes. Average of regions of identity between half-sibs when comparing its maternal inherited haplotypes (with at least 20 SNP) in common was 0.11 with a maximum of 0.29 and a minimum of 0.05. A Monte-Carlo simulation of BTA1 with the same linkage disequilibrium structure and genetic linkage as the cattle family yielded a 99.98 and 99.94% of correct phases for informative SNPs in sire and calves, respectively.

A statistical method for genetic mapping of sterility genes that exhibit epistasis in remote hybridization of plants using molecular markers in an F2 population

Estimation of the position and effect of sterility genes is an important problem to be solved to understand the sterility mechanism in remote hybridization in plants. In this study, a maximum likelihood (ML) method was used for estimation of the position and effect of sterility genes that exhibit epistasis in an F2 population using the distorted segregation of markers. The ML solutions for recombination fraction and viability were obtained via an expectation-maximization algorithm. The results of Monte Carlo simulations showed that the estimates of recombination fraction and viability were consistent with their true values. The bias and standard deviation of parameters indicated that a larger sample size, closer linkage and lower viability of sterile genes led to better estimates of the parameters involved. A subset of marker data of the F2 population derived from a single cross between the rice japonica cultivar Nipponbare and the indica cultivar Kasalath was analyzed using this method. Eight sterility genes were identified on chromosomes 1, 3, 6, 8 and 10, and significant epistasis was detected among four pairs of sterility genes.

Collaborative genetic mapping of 12 forensic short tandem repeat (STR) loci on the human X chromosome

A large number of short tandem repeat (STR) markers spanning the entire human X chromosome have been described and established for use in forensic genetic testing. Due to their particular mode of inheritance, X-STRs often allow easy and informative haplotyping in kinship analyses. Moreover, some X-STRs are known to be tightly linked so that, in combination, they constitute even more complex genetic markers than each STR taken individually. As a consequence, X-STRs have proven particularly powerful in solving complex cases of disputed blood relatedness. However, valid quantification of the evidence provided by X-STR genotypes in the form of likelihood ratios requires that the recombination rates between markers are exactly known. In a collaborative family study, we used X-STR genotype data from 401 two- and three-generation families to derive valid estimates of the recombination rates between 12 forensic markers widely used in forensic testing, namely DXS10148, DXS10135, DXS8378 (together constituting linkage group I), DXS7132, DXS10079, DXS10074 (linkage group II), DXS10103, HPRTB, DXS10101 (linkage group III), DXS10146, DXS10134 and DXS7423 (linkage group IV). Our study is the first to simultaneously allow for mutation and recombination in the underlying likelihood calculations, thereby obviating the bias-prone practice of excluding ambiguous transmission events from further consideration. The statistical analysis confirms that linkage groups I and II are transmitted independently from one another whereas linkage groups II, III and IV are characterised by inter-group recombination fractions that are notably smaller than 50%. Evidence was also found for recombination within all four linkage groups, with recombination fraction estimates ranging as high as 2% in the case of DXS10146 and DXS10134.

A new strategy for estimating two-locus recombination fractions under some natural inequality restrictions

Linkage analysis is now being widely used to map markers on each chromosome in the human genome, to map genetic diseases, and to identify genetic forms of common diseases. Two-locus linkage analysis and multi-locus analysis have been investigated comprehensively, and many computer programs have been developed to perform linkage analysis. Yet there exists a shortcoming in traditional methods, i.e., the parameter space of two-locus recombination fractions has not been emphasized sufficiently in the usual analyses. In this paper, we propose a new strategy for estimating the two-locus recombination fractions based on data of backcross family in the framework of some natural and necessary parameter restrictions. The new strategy is based on a restricted projection algorithm, which can provide fast reasonable estimates of recombination fraction, and can therefore serve as a superior alternative algorithm. Results obtained from both real and simulated data indicate that the new algorithm performs well in the estimation of recombination fractions and outperforms current methods.

On the bias of recombination fractions, Kosambi's and Haldane's distances based on frequencies of gametes

The estimation of recombination frequencies is a crucial step in genetic mapping. For the construction of linkage maps, nonadditive recombination fractions must be transformed into additive map distances. Two of the most commonly used transformations are Kosambi's and Haldane's mapping functions. This paper reports on the calculation of the bias associated with estimation of recombination fractions, Kosambi's distances, and Haldane's distances. I calculated absolute and relative biases numerically for a wide range of recombination fractions and sample sizes. I assumed that the ratio of recombinant gametes to the total number of gametes can be adequately represented by a binomial function. I found that the bias in recombination fraction estimates is negative, i.e., the estimator is an underestimate. However, significant values were only obtained when recombination fractions were large and sample sizes were small. The relevant estimates of recombination fractions were, therefore, nearly unbiased. Haldane's and Kosambi's distances were found to be strongly biased, with positive bias for the most interesting values of recombination fractions and sample sizes. The bias of Kosambi's distance was considerably smaller than the bias of Haldane's distance.

A hidden Markov model approach to multilocus linkage analysis in a full-sib family

Statistical packages for constructing genetic linkage maps in inbred lines are well developed and applied extensively, while linkage analysis in outcrossing species faces some statistical challenges because of their complicated genetic structures. In this article, we present a multilocus linkage analysis via hidden Markov models for a linkage group of markers in a full-sib family. The advantage of this method is the simultaneous estimation of the recombination fractions between adjacent markers that possibly segregate in different ratios, and the calculation of likelihood for a certain order of the markers. When the number of markers decreases to two or three, the multilocus linkage analysis becomes traditional two-point or three-point linkage analysis, respectively. Monte Carlo simulations are performed to show that the recombination fraction estimates of multilocus linkage analysis are more accurate than those just using two-point linkage analysis and that the likelihood as an objective function for ordering maker loci is the most powerful method compared with other methods. By incorporating this multilocus linkage analysis, we have developed a Windows software, FsLinkageMap, for constructing genetic maps in a full-sib family. A real example is presented for illustrating linkage maps constructed by using mixed segregation markers. Our multilocus linkage analysis provides a powerful method for constructing high-density genetic linkage maps in some outcrossing plant species, especially in forest trees.

Maximum likelihood estimates of two-locus recombination fractions under some natural inequality restrictions

BackgroundThe goal of linkage analysis is to determine the chromosomal location of the gene(s) for a trait of interest such as a common disease. Three-locus linkage analysis is an important case of multi-locus problems. Solutions can be found analytically for the case of triple backcross mating. However, in the present study of linkage analysis and gene mapping some natural inequality restrictions on parameters have not been considered sufficiently, when the maximum likelihood estimates (MLEs) of the two-locus recombination fractions are calculated.ResultsIn this paper, we present a study of estimating the two-locus recombination fractions for the phase-unknown triple backcross with two offspring in each family in the framework of some natural and necessary parameter restrictions. A restricted expectation-maximization (EM) algorithm, called REM is developed. We also consider some extensions in which the proposed REM can be taken as a unified method.ConclusionOur simulation work suggests that the REM performs well in the estimation of recombination fractions and outperforms current method. We apply the proposed method to a published data set of mouse backcross families.

A New Strategy for Estimating Recombination Fractions Between Dominant Markers From an F2 Population

Although most high-density linkage maps have been constructed from codominant markers such as single-nucleotide polymorphisms (SNPs) and microsatellites due to their high linkage information, dominant markers can be expected to be even more significant as proteomic technique becomes widely applicable to generate protein polymorphism data from large samples. However, for dominant markers, two possible linkage phases between a pair of markers complicate the estimation of recombination fractions between markers and consequently the construction of linkage maps. The low linkage information of the repulsion phase and high linkage information of coupling phase have led geneticists to construct two separate but related linkage maps. To circumvent this problem, we proposed a new method for estimating the recombination fraction between markers, which greatly improves the accuracy of estimation through distinction between the coupling phase and the repulsion phase of the linked loci. The results obtained from both real and simulated F2 dominant marker data indicate that the recombination fractions estimated by the new method contain a large amount of linkage information for constructing a complete linkage map. In addition, the new method is also applicable to data with mixed types of markers (dominant and codominant) with unknown linkage phase.

A simple note on how to save money in linkage analysis

Genetic linkage maps are often based on maximum-likelihood estimates of recombination fractions which are converted into map units by mapping functions. This paper presents a cost analysis of linkage analysis for a segregating F2␣population with codominant or dominant molecular markers and a qualitative monogenic dominant–recessive trait. For illustration, a disease-resistance trait is considered, where the susceptible allele is recessive. Three sub-populations of the F2 can be used for linkage analysis [susceptible (= recessive) individuals, resistant (= dominant) individuals, complete F2]. While it is well-known that recessive individuals are more informative than dominant individuals, it is not obvious a priori, which of the three sub-populations should be preferred, when costs of phenotyping and genotyping are taken into consideration. A comparative economic analysis of alternative procedures of linkage detection based on these three sub-populations does exhibit a clear economic superiority of the sub-population of susceptible (= recessive) individuals, when costs of genotyping are high. This cost-effectiveness is due to the higher information content of this sub-population compared to the sub-population of dominant (= resistant) individuals and also compared to the complete F2. Our final conclusion/recommendation is as follows: If the cost to genotype an individual is sufficiently large compared with the cost to phenotype an individual, then linkage analysis and genetic mapping should be only based on susceptible (= recessive) individuals. Conversely, if the cost of phenotyping exceeds that for genotyping, it may be preferable to genotype all plants. The exact conditions under which a strategy is preferable are described in the paper.

Two- and Three-Locus Tests for Linkage Analysis Using Recombinant Inbred Lines

We consider fixed recombinant inbred lines (RILs) derived either by selfing or by full-sib mating; when applicable, we also consider intermated recombinant inbreds (IRIs). First, we show that the usual estimate of recombination fraction based on RIL data is biased, and we provide an estimate where the major part of that bias is removed. Second, we derive simple formulas to compute the frequencies of genotypes at three loci in RILs. We describe the nonindependence of multiple recombinations arising in RIL recombination data even though there may be no interference in each meiosis. Finally, we give formulas for interference tests, gene mapping, or QTL detection in RIL populations.

Constructing the Parental Linkage Phase and the Genetic Map Over Distances <1 cM Using Pooled Haploid DNA

A new statistical approach for construction of the genetic linkage map and estimation of the parental linkage phase based on allele frequency data from pooled gametic (sperm or egg) samples is introduced. This method can be applied for estimation of recombination fractions (over distances <1 cM) and ordering of large numbers (even hundreds) of closely linked markers. This method should be extremely useful in species with a long generation interval and a large genome size such as in dairy cattle or in forest trees; the conifer species have haploid tissues available in megagametophytes. According to Mendelian expectation, two parental alleles should occur in gametes in 1:1 proportions, if segregation distortion does not occur. However, due to mere sampling variation, the observed proportions may deviate from their expected value in practice. These deviations and their dependence along the chromosome can provide information on the parental linkage phase and on the genetic linkage map. Usefulness of the method is illustrated with simulations. The role of segregation distortion as a source of these deviations is also discussed. The software implementing this method is freely available for research purposes from the authors.

Bayesian Statistics-Based Method for Genetic Linkage Analy-sis

Bayesian School as one of the important statistical schools is different from the Classical Statistics, and the Bayesian methods have been widely used in many fields of modern sciences. In the present paper, we discussed the application of Bayesian method in linkage analysis, including the Bayesian estimation of recombination fraction, linkage testing based on the Bayes Factor and the Bayesian approach for genetic linkage map construction via Markov chain Monte Carlo algorithm. Simulation study and real data analysis were performed using SAS/IML software, and the validity and practicability of Bayesian method in genetic linkage analysis were thus verified.

A Simulated Study on Mapping QTL in a Segregating Sub-population

For mapping QTLs, phenotypes of the traits in segregating population derived from the cross between two isogenic lines of the targeted QTL may reflect its genotype if the effect of the QTL is relatively large. In order to map the QTL, it is necessary to use a large sample under the high density of markers around the QTL. However, it increases experimental costs. In order to save the costs, it is possible to map the QTL using the sub-population that consists of plants with homogenous recessive. In this paper, the sub-population was used to estimate the recombination fraction between the marker and the QTL, and its standard error for F2, backcross (BC), double haploid (DH) and recombinant inbred lines (RIL) populations, respectively. The results from Monte Carlo simulation showed that the estimation of recombination fraction based on the sub-population is consistent with that obtained from the full population, and the precision of the former is same as that of the later under the same sample size.

Estimation of the recombination fraction by the maximum likelihood method in mapping interacting genes relative to marker loci

For mapping nonlinked interacting genes relative to marker loci, the recombination fractions can be calculated by using the log-likelihood functions were derived that permit estimation of recombinant fractions by solving the ML equations on the basis of F2 data at various types of interaction. In some cases, the recombinant fraction estimates are obtained in the analytical form while in others they are numerically calculated from concrete experimental data. With the same type of epistasis the log-functions were shown to differ depending on the functional role (suppression or epistasis) of the mapped gene. Methods for testing the correspondence of the model and the recombination fraction estimates to the experimental data are discussed. In ambiguous cases, analysis of the linked marker behavior makes it possible to differentiate gene interaction from distorted single-locus segregation, which at some forms of interaction imitate phenotypic ratios.

High-resolution gene mapping using admixture linkage dis-equilibrium

This note reports simulation study on the rate of decay in linkage disequilibrium (LD) in mixed populations over multiple discrete generations and explores the usefulness of the LD analysis in highresolution gene mapping. The results indicate that the smaller the recombination fraction and the fewer generations since admixture event, the higher power of the approach in gene mapping. The expected estimate of recombination fraction would give an estimate that is slightly biased upwards, if relevant genes are in tight linkage. The estimated recombination fraction is usually larger than the true value within 2–5 generations. From generations 10–20, the mean estimates are in good agreement with the true value. The method presented here enables estimation of means and corresponding confidence intervals of the recombination fraction at any number of generations.

Biased estimation of the recombination fraction using half-sib families and informative offspring.

A maximum-likelihood method to estimate the recombination fraction and its sampling variance using informative and noninformative half-sib offspring is derived. Estimates of the recombination fraction are biased up to 20 cM when noninformative offspring are discarded. In certain scenarios, the sampling variance can be increased or reduced up to fivefold due to the bias in estimating the recombination fraction and the LOD score can be reduced up to 5 units when discarding noninformative offspring. Comparison of the estimates of recombination fraction, map distance, and LOD score when constructing a genetic map with 251 two-point linkage analyses and six families of Norwegian cattle was carried out to evaluate the implications of discarding noninformative offspring in practical situations. The average discrepancies in absolute value (average difference when using and neglecting noninformative offspring) were 0.0146, 1.64 cM, and 2.61 for the recombination fraction, map distance, and the LOD score, respectively. A method for simultaneous estimation of allele frequencies in the dam population and a transmission disequilibrium parameter is proposed. This method might account for the bias in estimating allele frequencies in the dam population when the half-sib offspring is selected for production traits.

Rate of decay in admixture linkage disequilibrium and its implication in gene mapping

Modeling linkage disequilibria (LD) between genes usually observed in admixed natural populations has been shown an effective approach in high-resolution mapping of disease genes in humans. A prerequisite to obtain accurate estimation of recombination fraction between genes at a marker locus and the disease locus using the approach is a reliable prediction of the proportion of the admixture populations. The present study suggested the use of gene frequencies to predict the estimate of the admixture proportion based on the observation that the gene frequencies are much more stable quantities than the haplotype frequencies over evolution of the population. In this paper, we advanced the theory and methods by which the decay rate of nonlinear term of LD in admixed population may be used to estimate the recombination fraction between the genes. Theoretical analysis and simulation study indicate that, the larger the difference of gene frequencies between parental populations and the more closely the admixture proportion approaches 0.5, the more important the nonlinear term of the LD in the admixed population, and hence the more informative such admixed populations in the high-resolution gene mapping practice.