Improving linkage analysis in outcrossed forest trees - an example from Acacia mangium

Mapping in forest trees generally relies on outbred pedigrees in which genetic segregation is the result of meiotic recombination from both parents. The currently available mapping packages are not optimal for outcrossed pedigrees as they either cannot order phase-ambiguous data or only use pairwise information when ordering loci within linkage groups. A new package, OUTMAP, has been developed for mapping codominant loci in outcrossed trees. A comparison of maps produced using linkage data from two pedigrees of Acacia mangium Willd demonstrated that the marker orders produced using OUTMAP were consistently of higher likelihood than those produced by JOINMAP. In addition, the maps were produced more efficiently, without the need for recoding data or the detailed investigation of pairwise recombination fractions which was necessary to select the optimal marker order using JOINMAP. Distances between markers often varied from those calculated by JOINMAP, resulting in an increase in the estimated genome length. OUTMAP can be used with all segregation types to determine phase and to calculate the likelihood of alternative marker orders, with a choice of three optimisation methods.     

Construction of a genetic linkage map in tetraploid species using molecular markers

This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.     

三点自交法和两点最大似然法构建水稻F2群体分子标记连锁图谱的比较

根据连锁遗传的原理,列出了三点自交法和两点自交最大似然(ML)法估算显性标记遗传距离的具体步骤和算法,将水稻F2群体含香味基因Aro及其连锁的RFLP数据转变为显性标记数据后,用上述两种方法构建的连锁图谱与用MAPMAKER软件计算共显性数据得到的图谱排序相同、标记间距离相近．但是标记数据存在较大程度偏分离时,由三点自交法构建的图谱中标记间图距有增大趋势．作者为提高作图精确性,简化计算过程,讨论了三点自交法对估算重组值的影响及其在分子标记作图中的应用价值,并建议将共显性标记转变为显性标记时进行两次自交ML法估算。     

Comparing the distribution of RAPD and RFLP markers in a high density linkage map of sugar beet.

The distribution of RAPD markers was compared with that of RFLP markers in a high density linkage map of sugar beet. The same mapping population of 161 F2 individuals was used to generate all the marker data. The total map comprises 160 RAPD and 248 RFLP markers covering 508 cM. Both the RAPD and the RFLP markers show a high degree of clustering over the nine linkage groups. The pattern is compatible with a strong distal localization of recombination in the sugar beet. It leads generally to one major cluster of markers in the centre of each linkage group. In regions of high marker density, dominant RAPD markers present in either linkage phase and codominant RFLP markers are subclustered relative to each other. This phenomenon is shown to be attributable to: (i) effects of the mapping procedure when dominant and codominant data are combined, (ii) effects of the mapping procedure when dominant data in both linkage phases are combined, and (iii) genuine differences in the way RAPD and RFLP markers are recruited.     

Maximum-likelihood models for mapping genetic markers showing segregation distortion. 2. F2 populations

In F₂ populations, gametic and zygotic selection may affect the analysis of linkage in different ways. Therefore, specific likelihood equations have to be developed for each case, including dominant and codominant markers. The asymptotic bias of the classical estimates are derived for each case, in order to compare them with the standard errors of the suggested estimates. We discuss the utility and the efficiency of a previous model developed for dominant markers. We show that dominant markers provide very poor information in the case of segregation distortion and, therefore, should be used with circumspection. On the other hand, the estimation of recombination fractions between codominant markers is less affected by selection than is that for dominant markers. We also discuss the analysis of linkage between dominant and codominant markers.     

Constructing genetic linkage maps under a tetrasomic model

An international consortium has launched the whole-genome sequencing of potato, the fourth most important food crop in the world. Construction of genetic linkage maps is an inevitable step for taking advantage of the genome projects for the development of novel cultivars in the autotetraploid crop species. However, linkage analysis in autopolyploids, the kernel of linkage map construction, is theoretically challenging and methodologically unavailable in the current literature. We present here a theoretical analysis and a statistical method for tetrasomic linkage analysis with dominant and/or codominant molecular markers. The analysis reveals some essential properties of the tetrasomic model. The method accounts properly for double reduction and incomplete information of marker phenotype in regard to the corresponding phenotype in estimating the coefficients of double reduction and recombination frequency and in testing their significance by using the marker phenotype data. Computer simulation was developed to validate the analysis and the method and a case study with 201 AFLP and SSR markers scored on 228 full-sib individuals of autotetraploid potato is used to illustrate the utility of the method in map construction in autotetraploid species.     

Estimation of unbiased recombination values in the presence of misclassification of a trait using RFLP maps

The effect of misclassification of phenotypes of a trait on the estimation of recombination value was investigated. The effect was larger for closer linkage. If a locus is dominant and linked with the misclassfied trait locus in the repulsion phase, then the effect on the recombination value between the two loci is largest. A method for estimating the unbiased recombination value and the misclassification rate using maximum likelihood associated with an EM algorithm is also presented. This method was applied to a numerical example from rice genome data. It was concluded that the present method combined with the metric multi-dimensional scaling method is useful for the detection of misclassified markers and for the estimation of unbiased recombination values.     

Construction of a genetic linkage map in celery using DNA-based markers.

A F2 population of two celery cultivated types (Apium graveolens L. var. rapaceum and A. graveolens L. var. secalinum) was used to construct a linkage map consisting of 29 RFLP (restriction fragment length polymorphism), 100 RAPD (random amplified polymorphic DNA), four isozyme, one disease resistance, and one growth habit markers. The map contains 11 major groups and 9 small groups and has a total length of 803 cM with an average distance of 6.4 cM between two adjacent loci. Ten percent of the RAPDs segregated as codominant markers and their allelic homologies were tested by Southern hybridization. One-quarter of the dominant RAPDs were linked in repulsion phase, whereas the majority of them were linked to either codominant or dominant markers in coupling phase. About 10% of the markers showed significant segregation distortion. The detectable level of duplications in the celery genome was relatively low.     

Intensive Linkage Mapping in a Wasp (Bracon Hebetor) and a Mosquito (Aedes Aegypti) with Single-Strand Conformation Polymorphism Analysis of Random Amplified Polymorphic DNA Markers

The use of random amplified polymorphic DNA from the polymerase chain reaction (RAPD-PCR) allows efficient construction of saturated linkage maps. However, when analyzed by agarose gel electrophoresis, most RAPD-PCR markers segregate as dominant alleles, reducing the amount of linkage information obtained. We describe the use of single strand conformation polymorphism (SSCP) analysis of RAPD markers to generate linkage maps in a haplodiploid parasitic wasp Bracon (Habrobracon) hebetor and a diploid mosquito, Aedes aegypti. RAPD-SSCP analysis revealed segregation of codominant alleles at markers that appeared to segregate as dominant (band presence/band absence) markers or appeared invariant on agarose gels. Our SSCP protocol uses silver staining to detect DNA fractionated on large thin polyacrylamide gels and reveals more polymorphic markers than agarose gel electrophoresis. In B. hebetor, 79 markers were mapped with 12 RAPD primers in six weeks; in A. aegypti, 94 markers were mapped with 10 RAPD primers in five weeks. Forty-five percent of markers segregated as codominant loci in B. hebetor, while 11% segregated as codominant loci in A. aegypti. SSCP analysis of RAPD-PCR markers offers a rapid and inexpensive means of constructing intensive linkage maps of many species.     

Joining genetic linkage maps using a joint likelihood function

We present an efficient method to join genetic maps derived from different crosses, which is especially appropriate for dominant markers. In contrast to the JoinMap algorithm, which estimates information about recombination in a given cross from the LOD values and then combines estimates among crosses assuming a binomial sampling distribution, we construct a joint likelihood function that combines information across all crosses, to obtain a joint estimate of recombination. Simulations indicate that the difference between these two approaches is small when codominant markers are used, but that the joint likelihood approach shows substantially improved estimates when dominant or a mixture of dominant and codominant markers are used. This is because the joint likelihood implicitly finds the optimal weights among different classes of data, while the former method does not accurately predict the information from crosses involving dominant markers. Application of our method is illustrated by the construction of a linkage map for Linanthus using both backcrosses and the F₂ of a cross between Linanthus jepsonii and L. bicolor, assayed with amplified fragment length polymorphisms (AFLP).     

Investigation of genomic organization in switchgrass (Panicum virgatum L.) using DNA markers

We report an early investigation into genomic organization and chromosomal transmission in switchgrass based on restriction fragment length polymorphism (RFLP) markers. The segregation of 224 single dose restriction fragments (SDRF) in 85 full-sib progeny of a cross between the genotypes Alamo (AP13) and Summer (VS16) was used to determine linkage associations in each parent. In the seed parent AP13, 11 cosegregation groups were identified by 45 SDRF markers with a cumulative recombination length of 412.4 cM. In the pollen parent VS16, 57 SDRF markers were assigned to 16 cosegregation groups covering a length of 466.5 cM. SDRF markers identified by the same probes and mapping to different cosegregation groups were used to combine the two maps and identify homology groups. Eight homology groups were identified among the nine haploid linkage groups expected in switchgrass. The high incidence of repulsion phase associations indicates that preferential pairing between homologous chromosomes is predominant in switchgrass. Based on marker distribution in the paternal map (VS16), we estimated the recombinational length of switchgrass genome to be 4,617 cM. In order to link 95% of the genome to a marker at a 15-cM distance, a minimum of 459 markers will be required. Using information from the ratio of repulsion to coupling linkages, we infer that switchgrass is an autotetraploid with a high degree of preferential pairing. The information presented in this study establishes a foundation for extending genetic mapping in this crop and constitutes a framework for basic and applied genetic studies.Electronic Supplementary Material Supplementary material is available for this article at     

Linkage analysis for mapping genes of sex-influenced traits

Abstract Statistical methods are developed to estimate gender-specific and gender-average recombination frequencies between a biallelic or multiallelic marker and a sex-influenced gene. Iterative solutions are developed for intercross (or F-2 design). For biallelic markers, two iterative solutions are required, one for coupling and repulsion parental linkage phases and one for mixed parental linkage phases. For multiallelic markers, one set of iterative equations applies to all possible parental linkage phases. The resulting formulae for estimating recombination frequency use the full data set and yield estimates that are exactly the same as the true parameters if the observed and expected phenotypic distributions are equal. When one parent is homozygous for the sex-influenced gene as is expected with the backcross design, simple solutions exist for estimating recombination frequencies. However, offspring of one gender (male or female) do not have linkage information depending on whether the homozygous parent has two male-dominant or male-recessive alleles. Consequently, an F-2 design is more efficient than a backcross design for mapping a sex-influenced gene. Knowing each parental linkage phase is important to apply the methods developed in this article. It is shown that an individual's linkage phase of the sex-influenced locus can be determined based on allele transmission from the parents for all crosses except under the mating between an expressed male and an unexpressed female.     

Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species

With the advent of new molecular marker technologies, it is now feasible to initiate genome projects for outcrossing plant species, which have not received much attention in genetic research, despite their great agricultural and environmental value. Because outcrossing species typically have heterogeneous genomes, data structure for molecular markers representing an entire genome is complex: some markers may have more alleles than others, some markers are codominant whereas others are dominant, and some markers are heterozygous in one parent but fixed in the other parent whereas the opposite can be true for other markers. A major difficulty in analyzing these different types of marker at the same time arises from uncertainty about parental linkage phases over markers. In this paper, we present a general maximum-likelihood-based algorithm for simultaneously estimating linkage and linkage phases for a mixed set of different marker types containing fully informative markers (segregating 1:1:1:1) and partially informative markers (or missing markers, segregating 1:2:1, 3:1, and 1:1) in a full-sib family derived from two outbred parent plants. The characterization of linkage phases is based on the posterior probability distribution of the assignment of alternative alleles at given markers to two homologous chromosomes of each parent, conditional on the observed phenotypes of the markers. Two- and multi-point analyses are performed to estimate the recombination fraction and determine the most likely linkage phase between different types of markers. A numerical example is presented to demonstrate the statistical properties of the model for characterizing the linkage phase between markers.     

Linkage mapping of sex-specific differences

Most current linkage analyses assume identical fractions of meiotic recombination between homologous marker loci of the two sexes. This assumption is not realistic, because considerable sex-related differences have been observed in recombination fraction. In this paper, a general EM-based algorithm is presented to estimate sex-specific recombination fractions for a mixed set of molecular markers segregating differently in a full-sib family derived from two heterozygous parents. The asymptotic variances of the estimates of linkage specifically for each of the parents are evaluated using a numerical analysis based on information functions. This approach will have important implications for precise gene mapping based on sex-specific linkage maps.     

偏分离分子标记的作图方法

对取自MAPMAKER软件小鼠F_2群体(含333个体)的5个RFLP连锁标记数据作了共显性分子标记偏分离的分析。先确定选择类型的方程组(配子或合子),随后采用Newton-Raphson迭代法估算标记间的重组值。在构建分子标记遗传图谱时,如果两个相邻标记均存在偏分离,最好采用纳入偏分离因子的估算方法。在估计F_2群体标记间偏分离重组距离上,用连续x~2检测方法比传统x~2检测更为准确。     

Characterization of mixed disomic and polysomic inheritance in the octoploid strawberry (<Emphasis Type="Italic">Fragaria</Emphasis> × <Emphasis Type="Italic">ananassa</Emphasis>) using AFLP mapping

A two-way pseudo-testcross strategy, combined with Single Dose Restriction Fragment (SDRF) marker analysis, was used for genetic mapping in the octoploid cultivated strawberry Fragaria x ananassa (2n = 8 x = 56). Based on a 113 full-sib progeny from a cross between the variety Capitola and the clone CF1116, we generated two parental maps using Amplified Fragment Length Polymorphism (AFLP) markers. Ninety two percent of the markers (727 out of 789) showed ratios corresponding to simplex markers (the majority being SDRF markers), and 8% (62 out of 789) fitted a multiplex ratio. Linkage maps were first established using SDRF markers in coupling phase. The female map comprised 235 markers distributed among 43 co-segregation groups, giving a map size of 1,604 cM. On the male map, 280 markers were assigned to 43 co-segregation groups, yielding a map size of 1,496 cM. Once the co-segregation groups were established, their association was tested using repulsion-phase markers. In total, taking into account associations representing the same linkage groups, 30 linkage groups were detected on the female side and 28 on the male side. On the female map, 68.3% of the pairwise marker linkages were in coupling versus 31.7% in repulsion phase, and the corresponding figures on the male map were 72.2% and 27.8%, respectively. In addition, both groups linked only in the coupling phase and groups linked in the repulsion phase were characterized. The observations suggest that the meiotic behavior of the F. x ananassa genome is neither fully disomic nor fully polysomic, but rather mixed. The genome may not be as completely diploidized as previously assumed.     

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.     

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.     

A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

Molecular linkage maps of the Populus genome.

We report molecular genetic linkage maps for an interspecific hybrid population of Populus, a model system in forest-tree biology. The hybrids were produced by crosses between P. deltoides (mother) and P. euramericana (father), which is a natural hybrid of P. deltoides (grandmother) and P. nigra (grandfather). Linkage analysis from 93 of the 450 backcross progeny grown in the field for 15 years was performed using random amplified polymorphic DNAs (RAPDs), amplified fragment length polymorphisms (AFLPs), and inter-simple sequence repeats (ISSRs). Of a total of 839 polymorphic markers identified, 560 (67%) were testcross markers heterozygous in one parent but null in the other (segregating 1:1), 206 (25%) were intercross dominant markers heterozygous in both parents (segregating 3:1), and the remaining 73 (9%) were 19 non-parental RAPD markers (segregating 1:1) and 54 codominant AFLP markers (segregating 1:1:1:1). A mixed set of the testcross markers, non-parental RAPD markers, and codominant AFLP markers was used to construct two linkage maps, one based on the P. deltoides (D) genome and the other based on P. euramericana (E). The two maps showed nearly complete coverage of the genome, spanning 3801 and 3452 cM, respectively. The availability of non-parental RAPD and codominant AFLP markers as orthologous genes allowed for a direct comparison of the rate of meiotic recombination between the two different parental species. Generally, the rate of meiotic recombination was greater for males than females in our interspecific poplar hybrids. The confounded effect of sexes and species causes the mean recombination distance of orthologous markers to be 11% longer for the father (P. euramericana; interspecific hybrid) than for the mother (P. deltoides; pure species). The linkage maps constructed and the interspecific poplar hybrid population in which clonal replicates for individual genotypes are available present a comprehensive foundation for future genomic studies and quantitative trait locus (QTL) identification.