A general polyploid model for analyzing gene segregation in outcrossing tetraploid species

Polyploidy has played an important role in higher plant evolution and applied plant breeding. Polyploids are commonly categorized as allopolyploids resulting from the increase of chromosome number through hybridization and subsequent chromosome doubling or autopolyploids due to chromosome doubling of the same genome. Allopolyploids undergo bivalent pairing at meiosis because only homologous chromosomes pair. For autopolyploids, however, all homologous chromosomes can pair at the same time so that multivalents and, therefore, double reductions are formed. In this article, we use a maximum-likelihood method to develop a general polyploid model for estimating gene segregation patterns from molecular markers in a full-sib family derived from an arbitrary polyploid combining meiotic behaviors of both bivalent and multivalent pairings. Two meiotic parameters, one describing the preference of homologous chromosome pairing (expressed as the preferential pairing factor) typical of allopolyploids and the other specifying the degree of double reduction of autopolyploids, are estimated. The type of molecular markers used can be fully informative vs. partially informative or dominant vs. codominant. Simulation studies show that our polyploid model is well suited to estimate the preferential pairing factor and the frequency of double reduction at meiosis, which should help to characterize gene segregation in the progeny of autopolyploids. The implications of this model for linkage mapping, population genetic studies, and polyploid classification are discussed.     

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.     

A bivalent polyploid model for linkage analysis in outcrossing tetraploids

Polyploids can be classified as either allopolyploids or autopolyploids based on their presumed origins. From a perspective of linkage analysis, however, the nature of polyploids can be better described as bivalent polyploids, in which two chromosomes pair at meiosis, multivalent polyploids, in which more than two chromosomes pair, and general polyploids, in which bivalent and multivalent formations occur simultaneously. In this paper, we develop a statistical method for linkage analysis of polymorphic markers in bivalent polyploids. This method takes into account a unique cytological pairing mechanism for the formation of diploid gametes in tetraploids-preferential bivalent pairings at meiosis during which two homologous chromosomes pair with a higher probability than two homoeologous chromosomes. The higher frequency of homologous over homoeologous pairing, defined as the preferential pairing factor, affects the segregation patterns and linkage analysis of different genes on the same chromosome. A maximum likelihood method implemented with the EM algorithm is proposed to simultaneously estimate linkage and parental linkage phases over a pair of markers from any possible marker cross type between two outbred bivalent tetraploid parents demonstrating preferential bivalent pairings. Simulation studies display that the method can be well used to estimate the recombination fraction between different marker types and the preferential pairing factor typical of bivalent tetraploids. The implications of this method for current genome projects in polyploid species are discussed.     

RFLP Mapping in Cultivated Sugarcane (Saccharum Spp.): Genome Organization in a Highly Polyploid and Aneuploid Interspecific Hybrid

Sugarcane cultivars are polyploid, aneuploid, interspecific hybrids between the domesticated species Saccharum officinarum and the wild relative S. spontaneum. Cultivar chromosome numbers range from 100 to 130 with ~10% contributed by S. spontaneum. We have undertaken a mapping study on the progeny of a selfed cultivar, R570, to analyze this complex genome structure. A set of 128 restriction fragment length polymorphism probes and one isozyme was used. Four hundred and eight markers were placed onto 96 cosegregation groups, based on linkages in coupling only. These groups could tentatively be assembled into 10 basic linkage groups on the basis of common probes. Origin of markers was investigated for 61 probes and the isozyme, leading to the identification of 80 S. officinarum and 66 S. spontaneum derived markers, respectively. Their distribution in cosegregation groups showed better map coverage for the S. spontaneum than for the S. officinarum genome fraction and occasional recombination between the two genomes. The study of repulsions between markers suggested the prevalence of random pairing between chromosomes, typical of autopolyploids. However, cases of preferential pairing between S. spontaneum chromosomes were also detected. A tentative Saccharum map was constructed by pooling linkage information for each linkage group.     

Partial preferential chromosome pairing is genotype dependent in tetraploid rose

It has long been recognised that polyploid species do not always neatly fall into the categories of auto‐ or allopolyploid, leading to the term ‘segmental allopolyploid’ to describe everything in between. The meiotic behaviour of such intermediate species is not fully understood, nor is there consensus as to how to model their inheritance patterns. In this study we used a tetraploid cut rose (Rosa hybrida) population, genotyped using the 68K WagRhSNP array, to construct an ultra‐high‐density linkage map of all homologous chromosomes using methods previously developed for autotetraploids. Using the predicted bivalent configurations in this population we quantified differences in pairing behaviour among and along homologous chromosomes, leading us to correct our estimates of recombination frequency to account for this behaviour. This resulted in the re‐mapping of 25 695 SNP markers across all homologues of the seven rose chromosomes, tailored to the pairing behaviour of each chromosome in each parent. We confirmed the inferred differences in pairing behaviour among chromosomes by examining repulsion‐phase linkage estimates, which also carry information about preferential pairing and recombination. Currently, the closest sequenced relative to rose is Fragaria vesca. Aligning the integrated ultra‐dense rose map with the strawberry genome sequence provided a detailed picture of the synteny, confirming overall co‐linearity but also revealing new genomic rearrangements. Our results suggest that pairing affinities may vary along chromosome arms, which broadens our current understanding of segmental allopolyploidy.     

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 (R_c) and another fraction due to independent assortment (R_i). R_i is the minimum distance that can be detected between repulsion-phase linked markers. Because R_i 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 R_i to determine whether a polyploid is a true autopolyploid. Unfortunately, much lower default linkages than the R_is 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. Received: 29 February 2000 / Accepted: 17 July 2000     

Further evidence for the presence of meiotic pairing control genes in Alopecurus L. (Gramineae)

Mathematical equations applied to data on the meiotic chromosome behaviour of diploid, triploid and tetraploid Alopecurus species, their hybrids and synthesised autopolyploids confirm that chromosome pairing among homologues does not occur at random. The genotypic control of preferential bivalent formation is demonstrated and its role in natural populations discussed.     

A mixed polyploid model for linkage analysis in outcrossing tetraploids using a pseudo-test backcross design.

Based on how chromosomes pair at meiosis, the nature of polyploids can be described by bivalent polyploids, multivalent polyploids, and mixed polyploids. In bivalent polyploids, only two chromosomes pair, during which two more similar chromosomes have a higher pairing probability (preferential pairing) than two less similar chromosomes, whereas in multivalent polyploids more than two chromosomes pair at a time, which results in double reduction. Preferential chromosome pairings and double reduction affect the frequencies of gamete formation and, therefore, linkage analysis of polymorphic markers in bivalent and multivalent polyploids, respectively. For mixed polyploids, in which both bivalent and multivalent formations occur simultaneously, linkage analysis is affected by both preferential pairings and double reduction. In this study, we develop a hierarchical maximum likelihood model for discerning gamete genotypes derived from different pairing mechanisms and different formation modes. The first-stage model in the hierarchy is formulated to characterize the relative frequencies of bivalent and multivalent pairing configurations in terms of the preferential pairing factor. The second-stage model is derived to rule out identical gamete genotypes into their different formation modes with relative probabilities determined by the recombination fraction. The first-stage pairing mechanism and second-stage formation mode are integrated to provide the simultaneous maximum likelihood estimates of the preferential pairing factor, the frequency of double reduction, and the recombination fraction, by implementing the EM algorithm. We performed extensive simulation studies to demonstrate the statistical properties of our hierarchical model for linkage analysis in tetraploids. The implications of our model for polyploid linkage mapping are discussed.     

A general framework for statistical linkage analysis in multivalent tetraploids

In multivalent polyploids, simultaneous pairings among homologous chromosomes at meiosis result in a unique cytological phenomenon-double reduction. Double reduction casts an impact on chromosome evolution in higher plants, but because of its confounded effect on the pattern of gene cosegregation, it complicates linkage analysis and map construction with polymorphic molecular markers. In this article, we have proposed a general statistical model for simultaneously estimating the frequencies of double reduction, the recombination fraction, and optimal parental linkage phases between any types of markers, both fully and partially informative, or dominant and codominant, for a tetraploid species that undergoes only multivalent pairing. This model provides an in-depth extension of our earlier linkage model that was built upon Fisher's classifications for different gamete formation modes during the polysomic inheritance of a multivalent polyploid. By implementing a two-stage hierarchical EM algorithm, we derived a closed-form solution for estimating the frequencies of double reduction through the estimation of gamete mode frequencies and the recombination fraction. We performed different settings of simulation studies to demonstrate the statistical properties of our model for estimating and testing double reduction and the linkage in multivalent tetraploids. As shown by a comparative analysis, our model provides a general framework that covers existing statistical approaches for linkage mapping in polyploids that are predominantly multivalent. The model will have great implications for understanding the genome structure and organization of polyploid species.     

A genetic map of tetraploid <Emphasis Type="Italic">Paspalum notatum</Emphasis> Flügge (bahiagrass) based on single-dose molecular markers

Paspalum notatum Flügge is a warm-season forage grass with mainly diploid (2n = 20) and autotetraploid (2n = 40) representatives. Diploid races reproduce sexually and require crosspollination due to a self-incompatible mating system, while autotetraploids reproduce by aposporous apomixis. The objectives of this work were to develop a genetic linkage map of Paspalum notatum Flügge at the tetraploid level, identify the linkage/s group/s associated with apomixis and carry out a general characterization of its mode of inheritance. A pseudo test-cross F₁ family of 113 individuals segregating for the mode of reproduction was obtained by crossing a synthetic completely sexual tetraploid plant (Q4188) as female parent with a natural aposporous individual (Q4117) as pollen donor. Map construction was based on single-dose markers (SDAFs) segregating from both parents. Two linkage maps (female and male) were constructed. Within each map, homologous groups were assembled by detecting repulsion-phase linked SDAFs. Putative Q4188 and Q4117 homolog groups were identified by mapping shared single dose markers (BSDF). The Q4188 map consisted of 263 markers distributed on 26 co-segregation groups over a total genetic distance of 1.590.6 cM, while the Q4117 map contained 216 loci dispersed on 39 co-segregation groups along 2.265.7 cM, giving an estimated genome coverage of 88% and 83%, respectively. Seven and 12 putative homologous chromosomes were detected within Q4188 and Q4117 maps, respectively. Afterward, ten female and male homologous chromosomes were identified by mapping BSDFs. In the Q4117 map, a single linkage group was associated with apospory. It was characterized by restriction in recombination and preferential chromosome pairing. A BPSD marker mapping within this group allowed the detection of the female homolog and the putative four male groups of the set carrying apospory.     

A major QTL located on chromosome V associates with in vitro tuberization in a tetraploid potato population

The cultivated potato (Solanum tuberosum L.) is an autotetraploid species. The complexity of tetrasomic inheritance and the lack of pure lines increase the difficulty of genetic analysis of the inherited characteristics. Tuberization is the determinant step for economic yield of potato. To understand the complex genetic basis of tuberization of the cultivated potato, we developed linkage maps for a tetraploid population (F1) of 237 genotypes and mapped QTLs for the percent of in vitro tuberized plantlets (% IVT). The paternal map for E108 (well tuberized) covered 948 cM and included 12 linkage groups, all of which contained all four homologous chromosomes. The maternal map for E20 (nontuberized) covered 1,286 cM and included 14 linkage groups, 12 of which contained all four homologous chromosomes. All 12 chromosomes of potato were tagged using the SSR markers. A major QTL (MT05) with additive effect was detected on chromosome V of E108 which explained 16.23 % of the variation for % IVT, and two minor QTLs (mt05 and mt09) displaying simplex dominant effects were located on chromosome V and chromosome IX of E20 which explained 5.33 and 4.59 % of the variation for % IVT, respectively. Based on the additive model of MT05, the segregation ratio of the gametic genotypes (Q?: qq = 5:1) matched the ratio of the tuberized genotypes to the nontuberized genotypes in the population suggesting that the segregation of in vitro tuberization in this population is controlled by a major-effect gene or genes. The mapping results of three important candidate genes indicated that the QTL causal genes detected in our study are new. In this study, we developed the almost complete linkage maps of a tetraploid population, identified a major QTL on chromosome V affecting in vitro tuberization, suggested a major-effect gene with minor modifiers model controlling this trait and found that the QTLs identified here correspond to new tuberization genes. Our work provides new and useful information about the genetic basis for tuberization of this autotetraploid crop.     

Genetic segregation in relation to chromosome pairing in tetraploid hybrids between Lolium perenne and L. multiflorum

Summary Segregation at one of the loci controlling tiller-base pigmentation was studied to determine the mode of inheritance in tetraploid hybrids between Lolium perenne and L. multiflorum. The results could be explained by tetrasomic inheritance and thus did not support previous reports of a degree of preferential chromosome pairing in this material. However, double reduction and aneuploidy may to some extent have masked any tendency to disomic segregation brought about by preferential pairing. Moreover, there was significant heterogeneity between families in the segregation ratios which may indicate genetically controlled differences in pairing behaviour. The results are related to previous cytological and genetic studies.     

Chromosome pairing in female and male diploid and polyploid anurans (Amphibia) from South America

Chromosome pairing in females and males of diploid (2n = 22) and tetraploid (2n = 44) Odontophrynus americanus and diploid Ceratophrys cranwelli (2n = 26) and tetraploid C. ornata (2n = 104) showed that diploid females formed more chiasmata per paired arm than diploid males and polyploids of both sexes. There was a reduction in the level of recombination in female polyploids by forming multivalents with terminal chiasmata. The reduction reflected a change in the genetic control of pairing in females after polyploidization.     

Estimation of preferential pairing in tetraploid x diploid hybridizations

Summary Crosses made between tetraploid and diploid, 2n pollen-producing species directly transfer from one-half to the entire diploid genome from the diploid to the tetraploid level, depending on the mechanism of 2n pollen formation and the amount of crossing-over that occurs. Tetraploid plants that result from tetraploid x diploid hybridizations can be further utilized in a breeding program. It is postulated that preferential pairing between homologous chromosomes derived from the original tetraploid or diploid parent occurs in the tetraploid x diploid hybrid. Depending on the genetic divergence of the species involved, preferential pairing of homologous chromosomes may range from zero to one. Theoretical estimates of the amount of preferential pairing and the standard errors of these estimates are derived for cases where the diploid parent produces 2n gametes by either a first division or a second division restitution mechanism.     

Chromatin structure and physical mapping of chromosome 6 of potato and comparative analyses with tomato

Potato (Solanum tuberosum) has the densest genetic linkage map and one of the earliest established cytogenetic maps among all plant species. However, there has been limited effort to integrate these maps. Here, we report fluorescence in situ hybridization (FISH) mapping of 30 genetic marker-anchored bacterial artificial chromosome (BAC) clones on the pachytene chromosome 6 of potato. The FISH mapping results allowed us to define the genetic positions of the centromere and the pericentromeric heterochromatin and to relate chromatin structure to the distribution of recombination along the chromosome. A drastic reduction of recombination was associated with the pericentromeric heterochromatin that accounts for ~28% of the physical length of the pachytene chromosome. The pachytene chromosomes 6 of potato and tomato (S. lycopersicum) share a similar morphology. However, distinct differences of heterochromatin distribution were observed between the two chromosomes. FISH mapping of several potato BACs on tomato pachytene chromosome 6 revealed an overall colinearity between the two chromosomes. A chromosome inversion was observed in the euchromatic region of the short arms. These results show that the potato and tomato genomes contain more chromosomal rearrangements than those reported previously on the basis of comparative genetic linkage mapping.     

Pairing Competition between Identical and Homologous Chromosomes in Autotetraploid Rye. I. Submetacentric Chromosomes

Meiotic pairing preferences between identical and homologous but not identical chromosomes were analyzed in ten induced tetraploid/diploid chimaeral rye plants (Secale cereale) heterozygous for telomeric heerochromatin C-bands in both arms of chromosome 1R. These plants were the progeny of two crosses between only one plant of cv. Petkus, used as male, and two plants of the inbred lines E and R, respectively. Different pairing preferences for chromosome 1R were found: (1) between plants, (2) between chromosome arms within the same plant and (3) between bivalents and multivalents within the same plant. The possible influence in the preferences of several factors such as differences in C-heterochromatin content in the chromosomes analyzed, specific genetic control and independence in pairing behavior between both arms and partner exchange is discussed.     

The recombination landscape and multiple QTL mapping in a Solanum tuberosum cv. ‘Atlantic’-derived F1 population

There are many challenges involved with the genetic analyses of autopolyploid species, such as the tetraploid potato, Solanum tuberosum (2n = 4x = 48). The development of new analytical methods has made it valuable to re-analyze an F₁ population (n = 156) derived from a cross involving ‘Atlantic’, a widely grown chipping variety in the USA. A fully integrated genetic map with 4285 single nucleotide polymorphisms, spanning 1630 cM, was constructed with MAPpoly software. We observed that bivalent configurations were the most abundant ones (51.0~72.4% depending on parent and linkage group), though multivalent configurations were also observed (2.2~39.2%). Seven traits were evaluated over four years (2006–8 and 2014) and quantitative trait loci (QTL) mapping was carried out using QTLpoly software. Based on a multiple-QTL model approach, we detected 21 QTL for 15 out of 27 trait-year combination phenotypes. A hotspot on linkage group 5 was identified with co-located QTL for maturity, plant yield, specific gravity, and internal heat necrosis resistance evaluated over different years. Additional QTL for specific gravity and dry matter were detected with maturity-corrected phenotypes. Among the genes around QTL peaks, we found those on chromosome 5 that have been previously implicated in maturity (StCDF1) and tuber formation (POTH1). These analyses have the potential to provide insights into the biology and breeding of tetraploid potato and other autopolyploid species.Subject terms: Polyploidy in plants, Genetic linkage study, Quantitative trait, Plant breeding     

Genetic linkage mapping in fungi: current state, applications, and future trends

Genetic mapping is a basic tool for eukaryotic genomic research. Linkage maps provide insights into genome organization and can be used for genetic studies of traits of interest. A genetic linkage map is a suitable support for the anchoring of whole genome sequences. It allows the localization of genes of interest or quantitative trait loci (QTL) and map-based cloning. While genetic mapping has been extensively used in plant or animal models, this discipline is more recent in fungi. The present article reviews the current status of genetic linkage map research in fungal species. The process of linkage mapping is detailed, from the development of mapping populations to the construction of the final linkage map, and illustrated based on practical examples. The range of specific applications in fungi is browsed, such as the mapping of virulence genes in pathogenic species or the mapping of agronomically relevant QTL in cultivated edible mushrooms. Future prospects are finally discussed in the context of the most recent advances in molecular techniques and the release of numerous fungal genome sequences.     

Linkage disequilibrium mapping of a<Emphasis Type="Italic"> Verticillium dahliae</Emphasis> resistance quantitative trait locus in tetraploid potato (<Emphasis Type="Italic">Solanum tuberosum</Emphasis>) through a candidate gene approach

We have used the linkage disequilibrium mapping method to test for an association between a candidate gene marker and resistance to Verticillium dahliae in tetraploid potato. A probe derived from the tomato Verticillium resistance gene (Ve1) identified homologous sequences (StVe1) in potato, which in a diploid population map to chromosome 9, in a position analogous to that of the tomato resistance gene. When a molecular marker closely linked (1.5 cM) to the homologues was used as a candidate gene marker on 137 tetraploid potato genotypes (mostly North American cultivars), the association between the marker and resistance was confirmed (P<0.001). The amount of phenotypic variation in resistance explained by the allele of the STM1051 marker was greater than 10% and 25% in two subpopulations that were inferred from coancestry data matrix. Cloning of homologues from the highly resistant potato cv. Reddale indicates that the resistance quantitative trait locus (QTL) comprises at least an eleven-member family, encoding plant-specific leucine-rich repeat proteins highly similar to the tomato Ve genes. The sequence analysis shows that all homologues are uninterrupted open reading frames and thus represent putative functional resistance genes. This is the first time that the linkage disequilibrium method has been used to find an association between a resistance gene and a candidate gene marker in tetraploid potato. We have shown that it is possible to map QTL directly on already available potato cultivars, without developing a new mapping population.Communicated by F. SalaminiAn erratum to this article can be found at     

Mapping of simple sequence repeat (SSR) DNA markers in diploid and tetraploid alfalfa

Cultivated alfalfa (Medicago sativa) is an autotetraploid. However, all three existing alfalfa genetic maps resulted from crosses of diploid alfalfa. The current study was undertaken to evaluate the use of Simple Sequence Repeat (SSR) DNA markers for mapping in diploid and tetraploid alfalfa. Ten SSR markers were incorporated into an existing F₂ diploid alfalfa RFLP map and also mapped in an F₂ tetraploid population. The tetraploid population had two to four alleles in each of the loci examined. The segregation of these alleles in the tetraploid mapping population generally was clear and easy to interpret. Because of the complexity of tetrasomic linkage analysis and a lack of computer software to accommodate it, linkage relationships at the tetraploid level were determined using a single-dose allele (SDA) analysis, where the presence or absence of each allele was scored independently of the other alleles at the same locus. The SDA diploid map was also constructed to compare mapping using SDA to the standard co-dominant method. Linkage groups were generally conserved among the tetraploid and the two diploid linkage maps, except for segments where severe segregation distortion was present. Segregation distortion, which was present in both tetraploid and diploid populations, probably resulted from inbreeding depression. The ease of analysis together with the abundance of SSR loci in the alfalfa genome indicated that SSR markers should be a useful tool for mapping tetraploid alfalfa. Received: 10 September 1999 / Accepted: 11 November 1999