Estimation of allele frequencies in polyploids under certain patterns of inheritance

Allele frequencies have long been studied by biologists interested in evolution and speciation. More recently, with the application of molecular markers in human DNA profiling we have also seen the need for reliable population allele frequency estimates for making probabilistic inferences. There is now interest in applying the same DNA profiling technology to identification of plant varieties. HortResearch maintains a large germplasm of horticultural plant species. It is becoming evident that accurate identification of these accessions through DNA fingerprinting is essential for effective utilisation and maintenance of this germplasm. Microsatellites are the markers of choice for this fingerprinting. However, such markers do not reveal the dosage of alleles in a polyploid. Polyploidy is common amongst horticultural plants. Estimating allele frequencies in a polyploid population is, therefore, complicated because of some marker genotypes being phenotypically indistinguishable. For example, in a tetraploid, with four alleles at a locus showing polysomic inheritance, although 35 genotypes are possible, these will fall into only 15 marker phenotypic classes. Furthermore 'null' individuals are rarely detected in polyploids. Furthermore, some polyploids can be cryptic exhibiting disomy, instead of the polysomic inheritance. We will discuss the implications of these factors and present an EM-type algorithm for estimating allele frequencies of a polyploid population under certain patterns of inheritance. The method will be demonstrated on simulated data. We also discuss the nature of some of the additional problems that may be encountered with estimating allele frequencies in polyploids for which other solutions still need to be developed.     

Inferring the mode of origin of polyploid species from next‐generation sequence data

Many eukaryote organisms are polyploid. However, despite their importance, evolutionary inference of polyploid origins and modes of inheritance has been limited by a need for analyses of allele segregation at multiple loci using crosses. The increasing availability of sequence data for nonmodel species now allows the application of established approaches for the analysis of genomic data in polyploids. Here, we ask whether approximate Bayesian computation (ABC), applied to realistic traditional and next‐generation sequence data, allows correct inference of the evolutionary and demographic history of polyploids. Using simulations, we evaluate the robustness of evolutionary inference by ABC for tetraploid species as a function of the number of individuals and loci sampled, and the presence or absence of an outgroup. We find that ABC adequately retrieves the recent evolutionary history of polyploid species on the basis of both old and new sequencing technologies. The application of ABC to sequence data from diploid and polyploid species of the plant genus Capsella confirms its utility. Our analysis strongly supports an allopolyploid origin of C. bursa‐pastoris about 80 000 years ago. This conclusion runs contrary to previous findings based on the same data set but using an alternative approach and is in agreement with recent findings based on whole‐genome sequencing. Our results indicate that ABC is a promising and powerful method for revealing the evolution of polyploid species, without the need to attribute alleles to a homeologous chromosome pair. The approach can readily be extended to more complex scenarios involving higher ploidy levels.     

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 .     

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.     

Accounting for genotype uncertainty in the estimation of allele frequencies in autopolyploids

Despite the increasing opportunity to collect large‐scale data sets for population genomic analyses, the use of high‐throughput sequencing to study populations of polyploids has seen little application. This is due in large part to problems associated with determining allele copy number in the genotypes of polyploid individuals (allelic dosage uncertainty–ADU), which complicates the calculation of important quantities such as allele frequencies. Here, we describe a statistical model to estimate biallelic SNP frequencies in a population of autopolyploids using high‐throughput sequencing data in the form of read counts. We bridge the gap from data collection (using restriction enzyme based techniques [e.g. GBS, RADseq]) to allele frequency estimation in a unified inferential framework using a hierarchical Bayesian model to sum over genotype uncertainty. Simulated data sets were generated under various conditions for tetraploid, hexaploid and octoploid populations to evaluate the model's performance and to help guide the collection of empirical data. We also provide an implementation of our model in the R package polyfreqs and demonstrate its use with two example analyses that investigate (i) levels of expected and observed heterozygosity and (ii) model adequacy. Our simulations show that the number of individuals sampled from a population has a greater impact on estimation error than sequencing coverage. The example analyses also show that our model and software can be used to make inferences beyond the estimation of allele frequencies for autopolyploids by providing assessments of model adequacy and estimates of heterozygosity.     

Molecular karyotyping and aneuploidy detection in Arabidopsis thaliana using quantitative fluorescent polymerase chain reaction

Certain cellular processes are sensitive to changes in gene dosage. Aneuploidy is deleterious because of an imbalance of gene dosage on a chromosomal scale. Identification, classification and characterization of aneuploidy are therefore important for molecular, population and medical genetics and for a deeper understanding of the mechanisms underlying dosage sensitivity. Notwithstanding recent progress in genomic technologies, limited means are available for detecting and classifying changes in chromosome dose. The development of an inexpensive and scalable karyotyping method would allow rapid detection and characterization of both simple and complex aneuploid types. In addition to the problem of karyotyping, genomic and molecular genetic studies of aneuploids and polyploids are complicated by multiple heterozygous combinations possible at loci present in more than two copies. Quantitative scoring of allele genotypes would enable large-scale population genetic experiments in polyploids, and permit genetic analyses on bulked populations in diploid species. Here, we demonstrate that quantitative fluorescent-polymerase chain reaction (QF-PCR) can be used to simultaneously genotype and karyotype aneuploid and polyploid Arabidopsis thaliana. Comparison of QF-PCR with flow cytometric determination of nuclear DNA content indicated near perfect agreement between the methods, but complete karyotype resolution was only possible using QF-PCR. A complex karyotype, determined by QF-PCR, was validated by comparative genomic hybridization to microarrays. Finally, we screened the progeny of tetraploid individuals and found that more than 25% were aneuploid and that our artificially induced tetraploid strain produced fewer aneuploid individuals than a tetraploid strain isolated from nature.     

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.     

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.     

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.     

Perspectives on polyploidy in plants – ancient and neo

It is timely to re-examine the phenomenon of polyploidy in plants. Indeed, the power of modern molecular technology to provide new insights, and the impetus of genomics, make polyploidy a fit, fashionable and futuristic topic for review. Some historical perspective is essential to understand the meaning of the terms, to recognize what is already known and what is dogma, and to frame incisive questions for future research. Polyploidy is important because life on earth is predominantly a polyploid phenomenon. Moreover, civilization is mainly powered by polyploid food – notably cereal endosperm. Ongoing uncertainty about the origin of triploid endosperm epitomizes our ignorance about somatic polyploidy. New molecular information makes it timely to reconsider how to identity polyploids and what is a polyploid state. A functional definition in terms of a minimal genome may be helpful. Genes are known that can raise or lower ploidy level. Molecular studies can test if, contrary to dogma, the relationship between diploids and polyploids is a dynamic two-way system. We still need to understand the mechanisms and roles of key genes controlling ploidy level and disomic inheritance. New evidence for genome duplications should be compared with old ideas about cryptopolyploidy, and new views of meiosis should not ignore premeiotic genome separation. In practice, new knowledge about polyploidy will be most useful only when it reliably predicts which crops can be usefully improved as stable autopolyploids and which genomes combined to create successful new allopolyloids.  © 2004 The Linnean Society of London, Biological Journal of the Linnean Society , 2004, 82 , 411–423.     

Resolving allele dosage in duplicated loci using genotyping‐by‐sequencing data: A path forward for population genetic analysis

Whole‐genome duplications have occurred in the recent ancestors of many plants, fish and amphibians. Signals of these whole‐genome duplications still exist in the form of paralogous loci. Recent advances have allowed reliable identification of paralogs in genotyping‐by‐sequencing (GBS) data such as that generated from restriction‐site‐associated DNA sequencing (RADSeq); however, excluding paralogs from analyses is still routine due to difficulties in genotyping. This exclusion of paralogs may filter a large fraction of loci, including loci that may be adaptively important or informative for population genetic analyses. We present a maximum‐likelihood method for inferring allele dosage in paralogs and assess its accuracy using simulated GBS, empirical RADSeq and amplicon sequencing data from Chinook salmon. We accurately infer allele dosage for some paralogs from a RADSeq data set and show how accuracy is dependent upon both read depth and allele frequency. The amplicon sequencing data set, using RADSeq‐derived markers, achieved sufficient depth to infer allele dosage for all paralogs. This study demonstrates that RADSeq locus discovery combined with amplicon sequencing of targeted loci is an effective method for incorporating paralogs into population genetic analyses.     

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.     

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 .     

Gene trees and species trees – mutual influences and interdependences of population genetics and systematics

Both population genetics and systematics are core disciplines of evolutionary biology. While systematics deals with genealogical relationships among taxa, population genetics has mainly been based on allele frequencies and the distribution of genetic variants whose genealogical relations could for a long time, due mainly to methodological constraints, not be inferred. The advent of mitochondrial DNA analyses and modern sequencing techniques in the 1970s revolutionized evolutionary genetic studies and gave rise to molecular phylogenetics. In the wake of this new development systematic approaches and principles were incorporated into intraspecific studies at the population level, e.g. the concept of monophyly which is used to delineate evolutionarily significant units in conservation biology. A new discipline combining phylogenetic analyses of genetic lineages with their geographic distribution ('phylogeography') was introduced as an explicit synthesis of population genetics and systematics. On the other hand, it has increasingly become obvious that discordances between gene trees and species trees not only result from spurious data sets or methodological flaws in phylogenetic analyses, but that they often reflect real population genetic processes such as lineage sorting or hybridization. These processes have to be taken into account when evaluating the reliability of gene trees to avoid wrong phylogenetic conclusions. The present review focuses on the phenomenon of non-phylogenetic sorting of ancestral polymorphisms, its probability and its consequences for molecular systematics.     

The HLA‐B landscape of Africa: Signatures of pathogen‐driven selection and molecular identification of candidate alleles to malaria protection

Human leukocyte antigen (HLA) genes play a key role in the immune response to infectious diseases, some of which are highly prevalent in specific environments, like malaria in sub‐Saharan Africa. Former case–control studies showed that one particular HLA‐B allele, B*53, was associated with malaria protection in Gambia, but this hypothesis was not tested so far within a population genetics framework. In this study, our objective was to assess whether pathogen‐driven selection associated with malaria contributed to shape the HLA‐B genetic landscape of Africa. To that aim, we first typed the HLA‐A and ‐B loci in 484 individuals from 11 populations living in different environments across the Sahel, and we analysed these data together with those available for 29 other populations using several approaches including linear modelling on various genetic, geographic and environmental parameters. In addition to relevant signatures of populations’ demography and migrations history in the genetic differentiation patterns of both HLA‐A and ‐B loci, we found that the frequencies of three HLA alleles, B*53, B*78 and A*74, were significantly associated with Plasmodium falciparum malaria prevalence, suggesting their increase through pathogen‐driven selection in malaria‐endemic environments. The two HLA‐B alleles were further identified, by high‐throughput sequencing, as B*53:01:01 (in putative linkage disequilibrium with one HLA‐C allele, C*04:01:01:01) and B*78:01 in all but one individuals tested, making them appropriate candidates to malaria protection. These results highlight the role of environmental factors in the evolution of the HLA polymorphism and open key perspectives for functional studies focusing on HLA peptide‐binding properties.     

Current status and future possibilities of molecular genetics techniques in <Emphasis Type="Italic">Brassica napus</Emphasis>

As PCR methods have improved over the last 15 years, there has been an upsurge in the number of new DNA marker tools, which has allowed the generation of high-density molecular maps for all the key Brassica crop types. Biotechnology and molecular plant breeding have emerged as a significant tool for molecular understanding that led to a significant crop improvement in the Brassica napus species. Brassica napus possess a very complicated polyploidy-based genomics. The quantitative trait locus (QTL) is not sufficient to develop effective markers for trait introgression. In the coming years, the molecular marker techniques will be more effective to determine the whole genome impairing desired traits. Available genetic markers using the single-nucleotide sequence (SNP) technique and high-throughput sequencing are effective in determining the maps and genome polymorphisms amongst candidate genes and allele interactions. High-throughput sequencing and gene mapping techniques are involved in discovering new alleles and gene pairs, serving as a bridge between the gene map and genome evaluation. The decreasing cost for DNA sequencing will help in discovering full genome sequences with less resources and time. This review describes (1) the current use of integrated approaches, such as molecular marker technologies, to determine genome arrangements and interspecific outcomes combined with cost-effective genomes to increase the efficiency in prognostic breeding efforts. (2) It also focused on functional genomics, proteomics and field-based breeding practices to achieve insight into the genetics underlying both simple and complex traits in canola.     

Induction,rapid fixation and retention of mutations in vegetatively propagated banana

Mutation discovery technologies have enabled the development of reverse genetics for many plant species and allowed sophisticated evaluation of the consequences of mutagenesis. Such methods are relatively straightforward for seed‐propagated plants. To develop a platform suitable for vegetatively propagated species, we treated isolated banana shoot apical meristems with the chemical mutagen ethyl methanesulphonate, recovered plantlets and screened for induced mutations. A high density of GC‐AT transition mutations were recovered, similar to that reported in seed‐propagated polyploids. Through analysis of the inheritance of mutations, we observed that genotypically heterogeneous stem cells resulting from mutagenic treatment are rapidly sorted to fix a single genotype in the meristem. Further, mutant genotypes are stably inherited in subsequent generations. Evaluation of natural nucleotide variation showed the accumulation of potentially deleterious heterozygous alleles, suggesting that mutation induction may uncover recessive traits. This work therefore provides genotypic insights into the fate of totipotent cells after mutagenesis and suggests rapid approaches for mutation‐based functional genomics and improvement of vegetatively propagated crops.     

Critical review of NGS analyses for de novo genotyping multigene families

The genotyping of highly polymorphic multigene families across many individuals used to be a particularly challenging task because of methodological limitations associated with traditional approaches. Next‐generation sequencing (NGS) can overcome most of these limitations, and it is increasingly being applied in population genetic studies of multigene families. Here, we critically review NGS bioinformatic approaches that have been used to genotype the major histocompatibility complex (MHC) immune genes, and we discuss how the significant advances made in this field are applicable to population genetic studies of gene families. Increasingly, approaches are introduced that apply thresholds of sequencing depth and sequence similarity to separate alleles from methodological artefacts. We explain why these approaches are particularly sensitive to methodological biases by violating fundamental genotyping assumptions. An alternative strategy that utilizes ultra‐deep sequencing (hundreds to thousands of sequences per amplicon) to reconstruct genotypes and applies statistical methods on the sequencing depth to separate alleles from artefacts appears to be more robust. Importantly, the ‘degree of change’ (DOC) method avoids using arbitrary cut‐off thresholds by looking for statistical boundaries between the sequencing depth for alleles and artefacts, and hence, it is entirely repeatable across studies. Although the advances made in generating NGS data are still far ahead of our ability to perform reliable processing, analysis and interpretation, the community is developing statistically rigorous protocols that will allow us to address novel questions in evolution, ecology and genetics of multigene families. Future developments in third‐generation single molecule sequencing may potentially help overcome problems that still persist in de novo multigene amplicon genotyping when using current second‐generation sequencing approaches.