Modeling population genetic data in autotetraploid species

Model-based genotype and ancestry estimation for potential hybrids with mixed-ploidy

Non-random mating among individuals can lead to spatial clustering of genetically similar individuals and population stratification. This deviation from panmixia is commonly observed in natural populations. Consequently, individuals can have parentage in single populations or involving hybridization between differentiated populations. Accounting for this mixture and structure is important when mapping the genetics of traits and learning about the formative evolutionary processes that shape genetic variation among individuals and populations. Stratified genetic relatedness among individuals is commonly quantified using estimates of ancestry that are derived from a statistical model. Development of these models for polyploid and mixed-ploidy individuals and populations has lagged behind those for diploids. Here, we extend and test a hierarchical Bayesian model, called entropy, which can use low-depth sequence data to estimate genotype and ancestry parameters in autopolyploid and mixed-ploidy individuals (including sex chromosomes and autosomes within individuals). Our analysis of simulated data illustrated the trade-off between sequencing depth and genome coverage and found lower error associated with low-depth sequencing across a larger fraction of the genome than with high-depth sequencing across a smaller fraction of the genome. The model has high accuracy and sensitivity as verified with simulated data and through analysis of admixture among populations of diploid and tetraploid Arabidopsis arenosa.

Estimation of Molecular Pairwise Relatedness in Autopolyploid Crops

A suitable pairwise relatedness estimation is key to genetic studies. Several methods are proposed to compute relatedness in autopolyploids based on molecular data. However, unlike diploids, autopolyploids still need further studies considering scenarios with many linked molecular markers with known dosage. In this study, we provide guidelines for plant geneticists and breeders to access trustworthy pairwise relatedness estimates. To this end, we simulated populations considering different ploidy levels, meiotic pairings patterns, number of loci and alleles, and inbreeding levels. Analysis were performed to access the accuracy of distinct methods and to demonstrate the usefulness of molecular marker in practical situations. Overall, our results suggest that at least 100 effective biallelic molecular markers are required to have good pairwise relatedness estimation if methods based on correlation is used. For this number of loci, current methods based on multiallelic markers show lower performance than biallelic ones. To estimate relatedness in cases of inbreeding or close relationships (as parent-offspring, full-sibs, or half-sibs) is more challenging. Methods to estimate pairwise relatedness based on molecular markers, for different ploidy levels or pedigrees were implemented in the AGHmatrix R package.

Genotypic Frequencies at Equilibrium for Polysomic Inheritance Under Double-Reduction

Polyploids are organisms whose genomes consist of more than two complete sets of chromosomes. Both autopolyploids and allopolyploids may display polysomic inheritance. A peculiarity of polysomic inheritance is multivalent formation during meiosis resulting in double-reduction, which occurs when sister chromatid fragments segregate into the same gamete. Double-reduction can result in gametes carrying identical-by-descent alleles and slightly increasing homozygosity. This will cause the genotypic frequencies to deviate from expected values and will thus bias the results of standard population genetic analytical methods used in molecular ecology and selective breeding. In this study, we extend existing double-reduction models to account for any even level of ploidy, and derive the symbolic expressions for genotypic frequencies via two methods. Inbreeding coefficients and heterozygosity under double-reduction and inbreeding are also calculated. Numerical solutions obtained by computer simulations are compared with analytical solutions predicted by the model to validate the model.

Population assignment in autopolyploids

Understanding the patterns of contemporary gene dispersal within and among populations is of critical importance to population genetics and in managing populations for conservation. In contrast to diploids, there are few studies of gene dispersal in autopolyploids, in part due to complex polysomic inheritance and genotype ambiguity. Here we develop a novel approach for population assignment for codominant markers for autotetraploids and autohexaploids. This method accounts for polysomic inheritance, unreduced gametes and unknown allele dosage. It can also utilise information regarding the origin and genotype of one parent for population assignment of maternal or paternal parents. Using simulations, we demonstrate that our approach achieves high levels of accuracy for assignment even when population divergence is low (F_ST~0.06) and with only 12 microsatellite loci. We also show that substantially higher accuracy is achieved when known maternal information is utilised, regardless of whether allele dosage is known. Although this novel method exhibited near identical levels of accuracy to Structure when population divergence was high, it performed substantially better for most parameters at moderate (F_ST=0.06) to low levels of divergence (F_ST=0.03). These methods fill an important gap in the toolset for autopolyploids and pave the way for investigating contemporary gene dispersal in a widespread group of organisms.

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.

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.

Extending coalescent theory to autotetraploids

We develop coalescent models for autotetraploid species with tetrasomic inheritance. We show that the ancestral genetic process in a large population without recombination may be approximated using Kingman's standard coalescent, with a coalescent effective population size 4N. Numerical results suggest that this approximation is accurate for population sizes on the order of hundreds of individuals. Therefore, existing coalescent simulation programs can be adapted to study population history in autotetraploids simply by interpreting the timescale in units of 4N generations. We also consider the possibility of double reduction, a phenomenon unique to polysomic inheritance, and show that its effects on gene genealogies are similar to partial self-fertilization.

Evolutionary consequences of autopolyploidy

Autopolyploidy is more common in plants than traditionally assumed, but has received little attention compared with allopolyploidy. Hence, the advantages and disadvantages of genome doubling per se compared with genome doubling coupled with hybridizations in allopolyploids remain unclear. Autopolyploids are characterized by genomic redundancy and polysomic inheritance, increasing effective population size. To shed light on the evolutionary consequences of autopolyploidy, we review a broad range of studies focusing on both synthetic and natural autopolyploids encompassing levels of biological organization from genes to evolutionary lineages. The limited evidence currently available suggests that autopolyploids neither experience strong genome restructuring nor wide reorganization of gene expression during the first generations following genome doubling, but that these processes may become more important in the longer term. Biogeographic and ecological surveys point to an association between the formation of autopolyploid lineages and environmental change. We thus hypothesize that polysomic inheritance may provide a short-term evolutionary advantage for autopolyploids compared to diploid relatives when environmental change enforces range shifts. In addition, autopolyploids should possess increased genome flexibility, allowing them to adapt and persist across heterogeneous landscapes in the long run.

Segregation models for disomic, tetrasomic and intermediate inheritance in tetraploids: a general procedure applied to Rorippa (yellow cress) microsatellite data

Tetraploid inheritance has two extremes: disomic in allotetraploids and tetrasomic in autotetraploids. The possibility of mixed, or intermediate, inheritance models has generally been neglected. These could well apply to newly formed hybrids or to diploidizing (auto)tetraploids. We present a simple likelihood-based approach that is able to incorporate disomic, tetrasomic, and intermediate inheritance models and estimates the double-reduction rate. Our model shows that inheritance of microsatellite markers in natural tetraploids of Rorippa amphibia and R. sylvestris is tetrasomic, confirming their autotetraploid origin. However, in F(1) hybrids inheritance was intermediate to disomic and tetrasomic inheritance. Apparently, in meiosis, chromosomes paired preferentially with the homolog from the same parental species, but not strictly so. Detected double-reduction rates were low. We tested the general applicability of our model, using published segregation data. In two cases, an intermediate inheritance model gave a better fit to the data than the tetrasomic model advocated by the authors. The existence of inheritance intermediate to disomic and tetrasomic has important implications for linkage mapping and population genetics and hence breeding programs of tetraploids. Methods that have been developed for either disomic or tetrasomic tetraploids may not be generally applicable, particularly in systems where hybridization is common.

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.

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.

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.