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 .

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.

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.

Landscaping Crossover Interference Across a Genome

The evolutionary success of eukaryotic organisms crucially depends on the capacity to produce genetic diversity through reciprocal exchanges of each chromosome pair, or crossovers (COs), during meiosis. It has been recognized that COs arise more evenly across a given chromosome than at random. This phenomenon, termed CO interference, occurs pervasively in eukaryotes and may confer a selective advantage. We describe here a multipoint linkage analysis procedure for segregating families to quantify the strength of CO interference over the genome, and extend this procedure to illustrate the landscape of CO interference in natural populations. We further discuss the crucial role of CO interference in amplifying and maintaining genetic diversity through sex-, stress-, and age-induced differentiation.

A High-Density Genetic Map of Tetraploid Salix matsudana Using Specific Length Amplified Fragment Sequencing (SLAF-seq)

As a salt-tolerant arbor tree species, Salix matsudana plays an important role in afforestation and greening in the coastal areas of China. To select superior Salix varieties that adapt to wide saline areas, it is of paramount importance to understand and identify the mechanisms of salt-tolerance at the level of the whole genome. Here, we describe a high-density genetic linkage map of S. matsudana that represents a good coverage of the Salix genome. An intraspecific F₁ hybrid population was established by crossing the salt-sensitive “Yanjiang” variety as the female parent with the salt-tolerant “9901” variety as the male parent. This population, along with its parents, was genotyped by specific length amplified fragment sequencing (SLAF-seq), leading to 277,333 high-quality SLAF markers. By marker analysis, we found that both the parents and offspring were tetraploid. The mean sequencing depth was 53.20-fold for “Yanjiang”, 47.41-fold for “9901”, and 11.02-fold for the offspring. Of the SLAF markers detected, 42,321 are polymorphic with sufficient quality for map construction. The final genetic map was constructed using 6,737 SLAF markers, covering 38 linkage groups (LGs). The genetic map spanned 5,497.45 cM in length, with an average distance of 0.82 cM. As a first high-density genetic map of S. matsudana constructed from salt tolerance-varying varieties, this study will provide a foundation for mapping quantitative trait loci that modulate salt tolerance and resistance in Salix and provide important references for molecular breeding of this important forest tree.

High-density SNP-based genetic maps for the parents of an outcrossed and a selfed tetraploid garden rose cross, inferred from admixed progeny using the 68k rose SNP array

Dense genetic maps create a base for QTL analysis of important traits and future implementation of marker-assisted breeding. In tetraploid rose, the existing linkage maps include <300 markers to cover 28 linkage groups (4 homologous sets of 7 chromosomes). Here we used the 68k WagRhSNP Axiom single-nucleotide polymorphism (SNP) array for rose, in combination with SNP dosage calling at the tetraploid level, to genotype offspring from the garden rose cultivar 'Red New Dawn'. The offspring proved to be not from a single bi-parental cross. In rose breeding, crosses with unintended parents occur regularly. We developed a strategy to separate progeny into putative populations, even while one of the parents was unknown, using principle component analysis on pairwise genetic distances based on sets of selected SNP markers that were homozygous, and therefore uninformative for one parent. One of the inferred populations was consistent with self-fertilization of 'Red New Dawn'. Subsequently, linkage maps were generated for a bi-parental and a self-pollinated population with 'Red New Dawn' as the common maternal parent. The densest map, for the selfed parent, had 1929 SNP markers on 25 linkage groups, covering 1765.5 cM at an average marker distance of 0.9 cM. Synteny with the strawberry (Fragaria vesca) genome was extensive. Rose ICM1 corresponded to F. vesca pseudochromosome 7 (Fv7), ICM4 to Fv4, ICM5 to Fv3, ICM6 to Fv2 and ICM7 to Fv5. Rose ICM2 corresponded to parts of F. vesca pseudochromosomes 1 and 6, whereas ICM3 is syntenic to the remainder of Fv6.

A computational approach to developing mathematical models of polyploid meiosis

Mathematical models of meiosis that relate offspring to parental genotypes through parameters such as meiotic recombination frequency have been difficult to develop for polyploids. Existing models have limitations with respect to their analytic potential, their compatibility with insights into mechanistic aspects of meiosis, and their treatment of model parameters in terms of parameter dependencies. In this article I put forward a computational approach to the probabilistic modeling of meiosis. A computer program enumerates all possible paths through the phases of replication, pairing, recombination, and segregation, while keeping track of the probabilities of the paths according to the various parameters involved. Probabilities for classes of genotypes or phenotypes are added, and the resulting formulas are simplified by the symbolic-computation system Mathematica. An example application to autotetraploids results in a model that remedies the limitations of previous models mentioned above. In addition to the immediate implications, the computational approach presented here can be expected to be useful through opening avenues for modeling a host of processes, including meiosis in higher-order ploidies.