Meiosis at three loci in autotetraploids: Probabilities of gamete modes and genotypes without and with preferential cross-over formation

A long-standing goal in the field of polyploid biology has been the derivation of mathematical models of gamete mode formation. These models form the basis of statistical inference and evolutionary theory. Here, we present 3-locus models of gamete mode formation in autotetraploids without and with preferential cross-over formation. The three loci are assumed to occur on one arm of the same chromosome. For preferential cross-over formation, one of the three loci affects the tendency for sets of sister chromatids to pair and therefore affects rates of recombination. The models are derived such that the process of double reduction is a function of rates of synaptic partner switches and recombination, as opposed to being independent of these processes. We assume potentially one synaptic partner switch per meiosis. We also assume the coefficient of coincidence is one, such that cross-over events are independent, given a set of cross-over rates. Illustrative cases are examined demonstrating differences in the gamete mode probabilities without and with preferential cross-over formation. Lastly, we explore the accuracy of maximum likelihood estimates of the probability of synaptic partner switches and preferential cross-over formation when the locus controlling preference is at a proximal, middle, or distal location on the chromosome arm. All Supplementary Information is available at https://github.com/ckgriswold/3-locus-autotetraploid-meiosis .

A tetrasomic inheritance model and likelihood-based method for mapping quantitative trait loci in autotetraploid species

Dissecting the genetic architecture of quantitative traits in autotetraploid species is a methodologically challenging task, but a pivotally important goal for breeding globally important food crops, including potato and blueberry, and ornamental species such as rose. Mapping quantitative trait loci (QTLs) is now a routine practice in diploid species but is far less advanced in autotetraploids, largely due to a lack of analytical methods that account for the complexities of tetrasomic inheritance. We present a novel likelihood-based method for QTL mapping in outbred segregating populations of autotetraploid species. The method accounts properly for sophisticated features of gene segregation and recombination in an autotetraploid meiosis. It may model and analyse molecular marker data with or without allele dosage information, such as that from microarray or sequencing experiments. The method developed outperforms existing bivalent-based methods, which may fail to model and analyse the full spectrum of experimental data, in the statistical power of QTL detection, and accuracy of QTL location, as demonstrated by an intensive simulation study and analysis of data sets collected from a segregating population of potato (Solanum tuberosum). The study enables QTL mapping analysis to be conducted in autotetraploid species under a rigorous tetrasomic inheritance model.

Computational characterization of double reduction in autotetraploid natural populations

Population genetic theory has been well developed for diploid species, but its extension to study genetic diversity, variation and evolution in autopolyploids, a class of polyploids derived from the genome doubling of a single ancestral species, requires the incorporation of multisomic inheritance. Double reduction, which is characteristic of autopolyploidy, has long been believed to shape the evolutionary consequence of organisms in changing environments. Here, we develop a computational model for testing and estimating double reduction and its genomic distribution in autotetraploids. The model is implemented with the expectation-maximization (EM) algorithm to dissect unobservable allelic recombinations among multiple chromosomes, enabling the simultaneous estimation of allele frequencies and double reduction in natural populations. The framework fills an important gap in the population genetic theory of autopolyploids.

Letter to the Editor: Methods for mapping quantitative trait loci in autotetraploid species

Mapping quantitative trait loci (QTL) in autotetraploid species represents a timely and challenging task. Two papers published by Wu and his colleagues proposed statistical methods for QTL mapping in these evolutionarily and economically important species. In this Letter to the Editor, we present critical comments on the fundamental conceptual errors involved, from both statistical and genetic points of view.

High-Resolution Linkage Map With Allele Dosage Allows the Identification of Regions Governing Complex Traits and Apospory in Guinea Grass (Megathyrsus maximus)

Forage grasses are mainly used in animal feed to fatten cattle and dairy herds, and guinea grass (Megathyrsus maximus) is considered one of the most productive of the tropical forage crops that reproduce by seeds. Due to the recent process of domestication, this species has several genomic complexities, such as autotetraploidy and aposporous apomixis. Consequently, approaches that relate phenotypic and genotypic data are incipient. In this context, we built a linkage map with allele dosage and generated novel information of the genetic architecture of traits that are important for the breeding of M. maximus. From a full-sib progeny, a linkage map containing 858 single nucleotide polymorphism (SNP) markers with allele dosage information expected for an autotetraploid was obtained. The high genetic variability of the progeny allowed us to map 10 quantitative trait loci (QTLs) related to agronomic traits, such as regrowth capacity and total dry matter, and 36 QTLs related to nutritional quality, which were distributed among all homology groups (HGs). Various overlapping regions associated with the quantitative traits suggested QTL hotspots. In addition, we were able to map one locus that controls apospory (apo-locus) in HG II. A total of 55 different gene families involved in cellular metabolism and plant growth were identified from markers adjacent to the QTLs and APOSPORY locus using the Panicum virgatum genome as a reference in comparisons with the genomes of Arabidopsis thaliana and Oryza sativa. Our results provide a better understanding of the genetic basis of reproduction by apomixis and traits important for breeding programs that considerably influence animal productivity as well as the quality of meat and milk.

Linkage Analysis and Haplotype Phasing in Experimental Autopolyploid Populations with High Ploidy Level Using Hidden Markov Models

Modern SNP genotyping technologies allow measurement of the relative abundance of different alleles for a given locus and consequently estimation of their allele dosage, opening a new road for genetic studies in autopolyploids. Despite advances in genetic linkage analysis in autotetraploids, there is a lack of statistical models to perform linkage analysis in organisms with higher ploidy levels. In this paper, we present a statistical method to estimate recombination fractions and infer linkage phases in full-sib populations of autopolyploid species with even ploidy levels for a set of SNP markers using hidden Markov models. Our method uses efficient two-point procedures to reduce the search space for the best linkage phase configuration and reestimate the final parameters by maximizing the likelihood of the Markov chain. To evaluate the method, and demonstrate its properties, we rely on simulations of autotetraploid, autohexaploid and autooctaploid populations and on a real tetraploid potato data set. The results show the reliability of our approach, including situations with complex linkage phase scenarios in hexaploid and octaploid populations.

Linkage Analysis and Haplotype Phasing in Experimental Autopolyploid Populations with High Ploidy Level Using Hidden Markov Models

Modern SNP genotyping technologies allow measurement of the relative abundance of different alleles for a given locus and consequently estimation of their allele dosage, opening a new road for genetic studies in autopolyploids. Despite advances in genetic linkage analysis in autotetraploids, there is a lack of statistical models to perform linkage analysis in organisms with higher ploidy levels. In this paper, we present a statistical method to estimate recombination fractions and infer linkage phases in full-sib populations of autopolyploid species with even ploidy levels for a set of SNP markers using hidden Markov models. Our method uses efficient two-point procedures to reduce the search space for the best linkage phase configuration and reestimate the final parameters by maximizing the likelihood of the Markov chain. To evaluate the method, and demonstrate its properties, we rely on simulations of autotetraploid, autohexaploid and autooctaploid populations and on a real tetraploid potato data set. The results show the reliability of our approach, including situations with complex linkage phase scenarios in hexaploid and octaploid populations.

Quantifying the Power and Precision of QTL Analysis in Autopolyploids Under Bivalent and Multivalent Genetic Models

New genotyping technologies, offering the possibility of high genetic resolution at low cost, have helped fuel a surge in interest in the genetic analysis of polyploid species. Nevertheless, autopolyploid species present extra challenges not encountered in diploids and allopolyploids, such as polysomic inheritance or double reduction. Here we investigate the power and precision of quantitative trait locus (QTL) analysis in outcrossing autopolyploids, comparing the results of a model that assumes random bivalent chromosomal pairing during meiosis to one that also allows for multivalents and double reduction. Through a series of simulation studies we found that marginal gains in QTL detection power are achieved using the double reduction model when multivalent pairing occurs. However, when exploring the effect of variable genotypic information across parental homologs, we found that both QTL detection power and precision require high and uniform genotypic information contents. This effect far outweighed considerations regarding bivalent or multivalent pairing (and double reduction) during meiosis. We propose that autopolyploid QTL studies be accompanied by both marker coverage information and per-homolog genotypic information coefficients (GIC). Application of these methods to an autotetraploid potato (Solanum tuberosum L.) mapping population confirmed our ability to locate and dissect QTL in highly heterozygous outcrossing autotetraploid populations.

CH. QTL analysis reveals quantitative resistant loci for Phytophthora infestans and Tecia solanivora in tetraploid potato (Solanum tuberosum L.)

Late blight and Guatemalan potato tuber moth caused by Phytophthora infestans and Tecia solanivora, respectively, are major phytosanitary problems on potato crops in Colombia and Ecuador. Hence, the development of resistant cultivars is an alternative for their control. However, breeding initiatives for durable resistance using molecular tools are limited due to the genome complexity and high heterozygosity in autotetraploid potatoes. To contribute to a better understanding of the genetic basis underlying the resistance to P. infestans and T. solanivora in potato, the aim of this study was to identify QTLs for resistance to P. infestans and T. solanivora using a F1 tetraploid potato segregant population for both traits. Ninety-four individuals comprised this population. Parent genotypes and their progeny were genotyped using SOLCAP 12K potato array. Forty-five percent of the markers were polymorphic. A genetic linkage map was built with a length of 968.4 cM and 1,287 SNPs showing good distribution across the genome. Severity and incidence were evaluated in two crop cycles for two years. QTL analysis revealed six QTLs linked to P. infestans, four of these related to previous QTLs reported, and two novel QTLs (qrAUDPC-3 and qrAUDPC-8). Fifteen QTLs were linked to T. solanivora, being qIPC-6 and qOPA-6.1, and qIPC-10 and qIPC-10.1 stable in two different trials. This study is one of the first to identify QTLs for T. solanivora. As the population employed is a breeding population, results will contribute significantly to breeding programs to select resistant plant material, especially in countries where P. infestans and T. solanivora limit potato production.

AlloMap6: an R package for genetic linkage analysis in allohexaploids

Allopolyploids are a group of polyploids with more than two sets of chromosomes derived from different species. Previous linkage analysis of allopolyploids is based on the assumption that different chromosomes pair randomly during meiosis. A more sophisticated model to relax this assumption has been developed for allotetraploids by incorporating the preferential pairing behavior of homologous over homoeologous chromosomes. Here, we show that the basic principle of this model can be extended to perform linkage analysis of higher-ploidy allohexaploids, where multiple preferential pairing factors are used to characterize chromosomal-pairing meiotic features between different constituent species. We implemented the extended model into an R package, called AlloMap6, allowing the recombination fractions and preferential pairing factors to be estimated simultaneously. Allomap6 has two major functionalities, computer simulation and real-data analysis. By analyzing a real data from a full-sib family of allohexaploid persimmon, we tested and validated the usefulness and utility of this package. AlloMap6 lays a foundation for allohexaploid genetic mapping and provides a new horizon to explore the chromosomal kinship of allohexaploids.