Allelic configuration and polysomic inheritance of highly variable microsatellites in tetraploid gynodioecious Thymus praecox agg.

Polyploidy plays a pivotal role in plant evolution. However, polyploids with polysomic inheritance have hitherto been severely underrepresented in plant population genetic studies, mainly due to a lack of appropriate molecular genetic markers. Here we report the establishment and experimental validation of six fully informative microsatellite markers in tetraploid gynodioecious Thymus praecox agg. Sequence data of 150 microsatellite alleles and their flanking regions revealed high variation, which may be characteristic for polyploids with a reticulate evolutionary history. Understanding the patterns of mutation (indels and substitutions) in microsatellite flanking-sequences was a prerequisite for the development of co-dominant markers for fragment analyses. Allelic segregation patterns among progeny arrays from ten test crosses revealed tetrasomic inheritance in T. praecox agg. No evidence of frequent double reduction was detected. Polymerase chain reaction (PCR) based dosage effects allowed for precise assignment of allelic configuration at all six microsatellite loci. The quantification of allele copy numbers in PCR was verified by comparisons of observed and expected gametic allele frequencies and heterozygosities in test crosses. Our study illustrates how PCR based markers can provide reliable estimates of heterozygosity and, thus, powerful tools for breeding system and population genetic analyses in polyploid organisms.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Analysis and Optimization of Bulk DNA Sampling with Binary Scoring for Germplasm Characterization

The strategy of bulk DNA sampling has been a valuable method for studying large numbers of individuals through genetic markers. The application of this strategy for discrimination among germplasm sources was analyzed through information theory, considering the case of polymorphic alleles scored binarily for their presence or absence in DNA pools. We defined the informativeness of a set of marker loci in bulks as the mutual information between genotype and population identity, composed by two terms: diversity and noise. The first term is the entropy of bulk genotypes, whereas the noise term is measured through the conditional entropy of bulk genotypes given germplasm sources. Thus, optimizing marker information implies increasing diversity and reducing noise. Simple formulas were devised to estimate marker information per allele from a set of estimated allele frequencies across populations. As an example, they allowed optimization of bulk size for SSR genotyping in maize, from allele frequencies estimated in a sample of 56 maize populations. It was found that a sample of 30 plants from a random mating population is adequate for maize germplasm SSR characterization. We analyzed the use of divided bulks to overcome the allele dilution problem in DNA pools, and concluded that samples of 30 plants divided into three bulks of 10 plants are efficient to characterize maize germplasm sources through SSR with a good control of the dilution problem. We estimated the informativeness of 30 SSR loci from the estimated allele frequencies in maize populations, and found a wide variation of marker informativeness, which positively correlated with the number of alleles per locus.     

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.     

Recent progress and challenges in population genetics of polyploid organisms: an overview of current state‐of‐the‐art molecular and statistical tools

Despite the importance of polyploidy and the increasing availability of new genomic data, there remain important gaps in our knowledge of polyploid population genetics. These gaps arise from the complex nature of polyploid data (e.g. multiple alleles and loci, mixed inheritance patterns, association between ploidy and mating system variation). Furthermore, many of the standard tools for population genetics that have been developed for diploids are often not feasible for polyploids. This review aims to provide an overview of the state‐of‐the‐art in polyploid population genetics and to identify the main areas where further development of molecular techniques and statistical theory is required. We review commonly used molecular tools (amplified fragment length polymorphism, microsatellites, Sanger sequencing, next‐generation sequencing and derived technologies) and their challenges associated with their use in polyploid populations: that is, allele dosage determination, null alleles, difficulty of distinguishing orthologues from paralogues and copy number variation. In addition, we review the approaches that have been used for population genetic analysis in polyploids and their specific problems. These problems are in most cases directly associated with dosage uncertainty and the problem of inferring allele frequencies and assumptions regarding inheritance. This leads us to conclude that for advancing the field of polyploid population genetics, most priority should be given to development of new molecular approaches that allow efficient dosage determination, and to further development of analytical approaches to circumvent dosage uncertainty and to accommodate ‘flexible’ modes of inheritance. In addition, there is a need for more simulation‐based studies that test what kinds of biases could result from both existing and novel approaches.     

Power analysis of QTL detection in half-sib families using selective DNA pooling

Individual loci of economic importance (QTL) can be detected by comparing the inheritance of a trait and the inheritance of loci with alleles readily identifiable by laboratory methods (genetic markers). Data on allele segregation at the individual level are costly and alternatives have been proposed that make use of allele frequencies among progeny, rather than individual genotypes. Among the factors that may affect the power of the set up, the most important are those intrinsic to the QTL: the additive effect of the QTL, and its dominance, and distance between markers and QTL. Other factors are relative to the choice of animals and markers, such as the frequency of the QTL and marker alleles among dams and sires. Data collection may affect the detection power through the size of half-sib families, selection rate within families, and the technical error incurred when estimating genetic frequencies. We present results for a sensitivity analysis for QTL detection using pools of DNA from selected half-sibs. Simulations showed that conclusive detection may be achieved with families of at least 500 half-sibs if sires are chosen on the criteria that most of their marker alleles are either both missing, or one is fixed, among dams.     

A multivalent pairing model of linkage analysis in autotetraploids.

Polyploidy has been recognized as an important step in the evolutionary diversification of flowering plants and may have a significant impact on plant breeding. Statistical analyses for linkage mapping in polyploid species can be difficult due to considerable complexities in polysomic inheritance. In this article, we develop a novel statistical method for linkage analysis of polymorphic markers in a full-sib family of autotetraploids. This method is established on multivalent pairings of homologous chromosomes at meiosis and can provide a simultaneous maximum-likelihood estimation of the double reduction frequencies of and recombination fraction between two markers. The EM algorithm is implemented to provide a tractable way for estimating relative proportions of different modes of gamete formation that generate identical gamete genotypes due to multivalent pairings. Extensive simulation studies were performed to demonstrate the statistical properties of this method. The implications of the new method for understanding the genome structure and organization of polyploid species are discussed.     

Parentage and sibship inference from markers in polyploids

Many plants and some animal species are polyploids. Nondisomically inherited markers (e.g. microsatellites) in such species cannot be analysed directly by standard population genetics methods developed for diploid species. One solution is to transform the polyploid codominant genotypes to pseudodiploid‐dominant genotypes, which can then be analysed by standard methods for various purposes such as spatial genetic structure, individual relatedness and relationship. Although this data transformation approach has been used repeatedly in the literature, no systematic study has been conducted to investigate how efficient it is, how much marker information is lost and thus how much analysis accuracy is reduced. More specifically, it is unknown whether or not the transformed data can be used to infer parentage and sibship jointly, and how different sampling schemes (number and polymorphism of markers, number of individuals) and ploidy level affect the inference accuracy. This study analyses both simulated and empirical data to examine the effects of polyploid levels, actual pedigree structures and marker number and polymorphism on the accuracy of joint parentage and sibship assignments in polyploid species. We show that sibship, parentage and selfing rates in polyploids can be inferred accurately from a typical set of microsatellite loci. We also show that inferences can be substantially improved by allowing for a small genotyping error rate to accommodate the distortion in assumed Mendelian inheritance of the converted markers when large sibship groups are involved. The results are discussed in the context of polyploid data analysis in molecular ecology.     

Insights into population genetics and evolution of polyploids and their ancestors

We have developed the first comprehensive simulator for polyploid genomes (PolySim) and demonstrated its value by performing large‐scale simulations to examine the effect of different population parameters on the evolution of polyploids. PolySim is unlimited in terms of ploidy, population size or number of simulated loci. Our process considered the evolution of polyploids from diploid ancestors, polysomic inheritance, inbreeding, recombination rate change in polyploids and gene flow from lower to higher ploidies. We compared the number of segregating single nucleotide polymorphisms, minor allele frequency, heterozygosity, R² and average kinship relatedness between different simulated scenarios, and to real data from polyploid species. As expected, allotetraploid populations showed no difference from their ancestral diploids when population size remained constant and there was no gene flow or multivalent (MV) pairing between subgenomes. Autotetraploid populations showed significant differences from their ancestors for most parameters and diverged from their ancestral populations faster than allotetraploids. Autotetraploids can have significantly higher heterozygosity, relatedness and extended linkage disequilibrium compared with allotetraploids. Interestingly, autotetraploids were more sensitive to increasing selfing rate and decreasing population size. MV formation can homogenize allotetraploid subgenomes, but this homogenization requires a higher MV rate than previously proposed. Our results can be considered as the first building block to understand polyploid population evolutionary dynamics. PolySim can be used to simulate a wide variety of polyploid organisms that mimic empirical populations, which, in combination with quantitative genetics tools, can be used to investigate the power of genomewide association, genomic selection or breeding programme designs in these species.     

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     

Experimental population design for estimation of dominant molecular marker effect on egg-production traits

A potential limitation of the use of a dominant molecular marker system such as DNA fingerprinting (DFP) is the inability to distinguish homozygous from heterozygous allele state in an individual, and a resulting inaccuracy in estimating effects of the marker alleles. The objective of this study was to accurately estimate the effect of DFP markers on egg-production traits. A BC1 population was produced from two distinct layer lines. Four DFP bands, each originating predominantly in one of the two parental lines, were evaluated for linkage with egg-production quantitative trait loci in the BC1 population. The egg-production traits consisted of eight early period and seven late period measurements. Eight marker-trait linkages were identified out of 60 total statistical tests. By utilizing information on frequency of DFP bands in two parental lines, selecting F1 sires with DFP bands present, and backcrossing to the line lacking these bands, the population design allowed definitive identification of the DFP zygosity in the BC1 resource population hens. In this manner, accurate estimates of marker allele effects on egg-production traits were obtained from the dominant marker system of DNA fingerprinting.     

Genetic characterization and diversity among avocado (<Emphasis Type="Italic">Persea americana</Emphasis> Mill.) genotypes from INIA-CENIAP,Venezuela

Studies on Persea americana have been addressed in different ways with biochemical and molecular techniques. Microsatellites are able to detect multiple alleles for particular loci and are therefore a useful tool to study genealogical relationships, population structures and genetic mapping. Ninety-six samples from 49 cultivars including three horticultural groups and hybrids were collected from the avocado germplasm bank at INIA-CENIAP (Venezuela). A modified DNA extraction protocol was performed. Forty microsatellites were selected from previous references, PCR amplifications were performed, and presence/absence, size, and number of alleles were evaluated on polyacrylamide gels. Attributes for polymorphic alleles were analyzed with POPGENE, and genetic diversity was calculated by effective sample size, number of alleles per locus (Na), effective number of alleles (Ne), Shannon information index (In), observed heterozygosis (H), expected heterozygosity (He), Wright’s fixation index (Fis), and allele frequencies. Only 14 primers were amplified, and AVT106 primer resulted monomorphic. Unique genotypes for each sample were obtained. Nine loci showed allele patterns that can be useful for taxonomic identification of cultivars or varieties. Comparing values of Fis with Ho and He, we found a direct relationship where low heterozygosis alleles identified in the population may affect the expected level. Allele frequencies ranged from 0.5632 to 0.0105. For all loci, at least one rare allele was observed. With the available information from genetic analysis, an identifying system was implemented for selected avocado cultivars maintained at the INIA-CENIAP Venezuelan germplasm bank on the basis of molecular data.     

Inference of individual ploidy level using codominant markers

A significant portion of plant species are polyploids, with ploidy levels sometimes varying among individuals and/or populations. Current techniques to determine the individual ploidy, e.g., flow cytometry, chromosome counting or genotyping‐by‐sequencing, are often cumbersome. Based on the genotypic probabilities for polysomic inheritance under double‐reduction, we developed a model to estimate allele frequency and infer the ploidy status of individuals from the allelic phenotypes of codominant genetic markers. The allele frequencies are estimated by an expectation‐maximization algorithm in the presence of null alleles, false alleles, negative amplifications and self‐fertilization, and the posterior probabilities are used to assign individuals into different levels of ploidy. The accuracy of this method under different conditions is evaluated. Our methods are freely available in a new software package, ploidyinfer , for use by other researchers which can be downloaded from http://github.com/huangkang1987/ploidyinfer .     

Assessment of genetic variation and differentiation of hop genotypes by microsatellite and AFLP markers.

Microsatellites have many desirable marker properties and have been increasingly used in crop plants in genetic diversity studies. Here we report on the characterisation of microsatellite markers and on their use for the determination of genetic identities and the assessment of genetic variability among accessions from a germplasm collection of hop. Thirty-two polymorphic alleles were found in the 55 diploid genotypes, with an average number of eight alleles (3.4 effective alleles) for four microsatellite loci. Calculated polymorphic information content values classified three loci as informative markers and two loci as suitable for mapping. The average observed heterozygosity was 0.7 and the common probability of identical genotypes was 3.271 x 10(-4). An additional locus, amplified by one primer pair, was confirmed by segregation analysis of two crosses. The locus discovered was heterozygous, with a null allele in the segregating population. The same range of alleles was detected in nine triploid and five tetraploid hop genotypes. Cultivar heterozygosity varied among all 69 accessions, with only one cultivar being homozygous at four loci. Microsatellite allele polymorphisms distinguished 81% of all genotypes; the same allelic profile was found mainly in clonally selected cultivars. Cultivar-specific alleles were found in some genotypes, as well as a specific distribution of alleles in geographically distinct hop germplasms. The genetic relationship among 41 hop accessions was compared on the basis of microsatellite and AFLP polymorphisms. Genetic similarity dendrograms showed low correlation between the two marker systems. The microsatellite dendrogram grouped genetically related accessions reasonably well, while the AFLP dendrogram showed good clustering of closely related accessions and, additionally, separated two geographically distinct hop germplasms. The results of microsatellite and AFLP analysis are discussed from the point of view of the applicability of the two marker systems for different aspects of germplasm evaluation.     

Population estimators or progeny tests: what is the best method to assess null allele frequencies at SSR loci?

Nuclear SSRs are notorious for having relatively high frequencies of null alleles, i.e. alleles that fail to amplify and are thus recessive and undetected in heterozygotes. In this paper, we compare two kinds of approaches for estimating null allele frequencies at seven nuclear microsatellite markers in three French Fagus sylvatica populations: (1) maximum likelihood methods that compare observed and expected homozygote frequencies in the population under the assumption of Hardy-Weinberg equilibrium and (2) direct null allele frequency estimates from progeny where parent genotypes are known. We show that null allele frequencies are high in F. sylvatica (7.0% on average with the population method, 5.1% with the progeny method), and that estimates are consistent between the two approaches, especially when the number of sampled maternal half-sib progeny arrays is large. With null allele frequencies ranging between 5% and 8% on average across loci, population genetic parameters such as genetic differentiation (F _ST) may be mostly unbiased. However, using markers with such average prevalence of null alleles (up to 15% for some loci) can be seriously misleading in fine scale population studies and parentage analysis.     

Sequence characterization of microsatellites in diploid and polyploid Ipomoea

 The objectives of the present study were to evaluate the inheritance and nucleotide sequence profiles of microsatellite genetic markers in hexaploid sweetpotato [Ipomoea batatas (L.) Lam.] and its putative tetraploid and diploid ancestors, and to test possible microsatellite mutation mechanisms in polyploids by direct sequencing of alleles. Sixty three microsatellite loci were isolated from genomic libraries of I. batatas and sequenced. PCR primers were designed and used to characterize microsatellite loci in two hexaploid I. batatas populations, a tetraploid Ipomoea trifida population, and a diploid I. trifida population. Nine out of the sixty three primer pairs tested yielded a clearly discernible, heritable banding pattern; five showed Mendelian segregation. All other primer pairs produced either smeared banding patterns, which could not be scored, or no bands at all in I. batatas. All of the primers which produced discernible banding patterns from I. batatas also amplified products of similar size in tetraploid and diploid I. trifida accessions. The sequence analysis of several alleles in the three species showed differences due to mutations in the repeat regions consistent with small differences in the repeat number. However, in some cases insertions/deletions and base substitutions in the microsatellite flanking regions were responsible for polymorphisms in both polyploid and diploid species. These results provide strong empirical evidence that complex genetic mechanisms are responsible for SSR allelic variation in Ipomoea. Four I. batatas microsatellite loci showed polysomic segregation fitting tetraploid segregation ratios. To our knowledge this is the first report of segregation ratios for microsatellites markers in polyploids. Received: 4 January 1999 / Accepted: 4 January 1999     

Characterization of microsatellite loci and reliable genotyping in a polyploid plant, Mercurialis perennis (Euphorbiaceae)

For many applications in population genetics, codominant simple sequence repeats (SSRs) may have substantial advantages over dominant anonymous markers such as amplified fragment length polymorphisms (AFLPs). In high polyploids, however, allele dosage of SSRs cannot easily be determined and alleles are not easily attributable to potentially diploidized loci. Here, we argue that SSRs may nonetheless be better than AFLPs for polyploid taxa if they are analyzed as effectively dominant markers because they are more reliable and more precise. We describe the transfer of SSRs developed for diploid Mercurialis huetii to the clonal dioecious M. perennis. Primers were tested on a set of 54 male and female plants from natural decaploid populations. Eight of 65 tested loci produced polymorphic fragments. Binary profiles from 4 different scoring routines were used to define multilocus lineages (MLLs). Allowing for fragment differences within 1 MLL, all analyses revealed the same 14 MLLs without conflicting with merigenet, sex, or plot assignment. For semiautomatic scoring, a combination of as few as 2 of the 4 most polymorphic loci resulted in unambiguous discrimination of clones. Our study demonstrates that microsatellite fingerprinting of polyploid plants is a cost efficient and reliable alternative to AFLPs, not least because fewer loci are required than for diploids.     

Estimation of copy number in polyploid plants: the good,the bad,and the ugly

Genetic studies in polyploid plants rely heavily on the collection of data from dominant marker loci. A dominant marker locus is a locus for which only the presence or absence of an observable (dominant) allele is recorded. Before these marker loci can be used for genetic exploration, the number of copies of a dominant allele carried by a parent (copy number) must be determined for each marker locus. Copy number in polyploids is estimated using a hypothesis testing procedure. The performance of this estimation procedure has never been evaluated. In this paper, I quantify whether the highly sought after single-copy markers can be accurately identified, if the performance of the estimation procedure improves with increasing sample size, and whether the estimation procedure is capable of accurately estimating the copy number of high copy markers. I found that the probability of incorrectly estimating copy number is quite low and that more data can actually reduce the accuracy of the estimation procedure when the testing assumptions are violated. Fortunately, when a significant result is obtained, it is almost always correct. The challenge often is in obtaining a significant result.     

A pairwise relatedness estimator for polyploids

Studies in genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. Many diploid estimators have been developed using either method‐of‐moments or maximum‐likelihood estimates. However, there are no relatedness estimators for polyploids. The development of a moment estimator for polyploids with polysomic inheritance, which simultaneously incorporates the two‐gene relatedness coefficient and various ‘higher‐order’ coefficients, is described here. The performance of the estimator is compared to other estimators under a variety of conditions. When using a small number of loci, the estimator is biased because of an increase in ill‐conditioned matrices. However, the estimator becomes asymptotically unbiased with large numbers of loci. The ambiguity of polyploid heterozygotes (when balanced heterozygotes cannot be distinguished from unbalanced heterozygotes) is also considered; as with low numbers of loci, genotype ambiguity leads to bias. A software, PolyRelatedness , implementing this method and supporting a maximum ploidy of 8 is provided.     

Genomes,multiple origins,and lineage recombination in the Glycine tomentella (Leguminosae) polyploid complex: histone H3-D gene sequences

Relationships among the various diploid and polyploid taxa that comprise Glycine tomentella have been hypothesized from crossing studies, isozyme data, and repeat length variation for the 5S nuclear ribosomal gene loci. However, several key questions have persisted, and detailed phylogenetic evidence from homoeologous nuclear genes has been lacking. The histone H3-D locus is single copy in diploid Glycine species and has been used to elucidate relationships among diploid races of G. tomentella, providing a framework for testing genome origins in the polyploid complex. For all six G. tomentella polyploid races (T1-T6), alleles at two homoeologous histone H3-D loci were isolated and analyzed phylogenetically with alleles from diploid Glycine species, permitting the identification of all of the homoeologous genomes of the complex. Allele networks were constructed to subdivide groups of homoeologous alleles further, and two-locus genotypes were constructed using these allele classes. Results suggest that some races have more than one origin and that interfertility within races has led to lineage recombination. Most alleles in polyploids are identical or closely related to alleles in diploids, suggesting recency of polyploid origins and spread beyond Australia. These features parallel the other component of the Glycine subgenus Glycine polyploid complex, G. tabacina, one of whose races shares a diploid genome with a G. tomentella polyploid race.     

Population genetics of autopolyploids under a mixed mating model and the estimation of selfing rate

Nowadays, the population genetics analysis of autopolyploid species faces many difficulties due to (i) limited development of population genetics tools under polysomic inheritance, (ii) difficulties to assess allelic dosage when genotyping individuals and (iii) a form of inbreeding resulting from the mechanism of ‘double reduction’. Consequently, few data analysis computer programs are applicable to autopolyploids. To contribute bridging this gap, this article first derives theoretical expectations for the inbreeding and identity disequilibrium coefficients under polysomic inheritance in a mixed mating model. Moment estimators of these coefficients are proposed when exact genotypes or just markers phenotypes (i.e. allelic dosage unknown) are available. This led to the development of estimators of the selfing rate based on adult genotypes or phenotypes and applicable to any even‐ploidy level. Their statistical performances and robustness were assessed by numerical simulations. Contrary to inbreeding‐based estimators, the identity disequilibrium‐based estimator using phenotypes is robust (absolute bias generally < 0.05), even in the presence of double reduction, null alleles or biparental inbreeding due to isolation by distance. A fairly good precision of the selfing rate estimates (root mean squared error < 0.1) is already achievable using a sample of 30–50 individuals phenotyped at 10 loci bearing 5–10 alleles each, conditions reachable using microsatellite markers. Diallelic markers (e.g. SNP) can also perform satisfactorily in diploids and tetraploids but more polymorphic markers are necessary for higher ploidy levels. The method is implemented in the software SPAGeDi and should contribute to reduce the lack of population genetics tools applicable to autopolyploids.