Estimation of gametic frequencies from F2 populations using the EM algorithm and its application in the analysis of crossover interference in rice

The gametes produced in meiosis provide information on the frequency of recombination and also on the interdependence of recombination events, i.e. interference. Using F₂ individuals, it is not possible in all cases to derive the gametes, which have fused, and which provide the information about interference unequivocally when three or more segregating markers are considered simultaneously. Therefore, a method was developed to estimate the gametic frequencies using a maximum likelihood approach together with the expectation maximisation algorithm. This estimation procedure was applied to F₂ mapping data from rice (Oryza sativa L.) to carry out a genome-wide analysis of crossover interference. The distribution of the coefficient of coincidence in dependence on the recombination fraction revealed for all chromosomes increasing positive interference with decreasing interval size. For some chromosomes this mutual inhibition of recombination was not so strong in small intervals. The centromere had a significant effect on interference. The positive interference found in the chromosome arms were reduced significantly when the intervals considered spanned the centromere. Two chromosomes even demonstrated independent recombination and slightly negative interference for small intervals including the centromere. Different marker densities had no effect on the results. In general, interference depended on the frequency of recombination events in relation to the physical length. The strength of the centromere effect on interference seemed to depend on the strength of recombination suppression around the centromere.Electronic Supplementary Material Supplementary material is available for this article at     

Physical distribution of recombination in B-genome chromosomes of tetraploid wheat

Summary Several studies have indicated a noncorrespondence between genetic and physical distances in wheat chromosomes. To study the physical distribution of recombination, polymorphism for C-banding patterns was used to monitor recombination in 67 segments in 11 B-genome chromosome arms of Triticum turgidum. Recombination was absent in proximal regions of all chromosome arms; its frequency increased exponentially with distance from the centromere. A significant difference was observed between the distribution of recombination in physically short and physically long arms. In physically short arms, recombination was almost exclusively concentrated in distal segments and only those regions were represented in their genetic maps. In physically long arms, while a majority of the genetic distance was again based upon recombination in distal chromosome segments, some interstitial recombination was observed. Consequently, these regions also contributed to the genetic maps. Such a pattern of recombination, skewed toward terminal segments of chromosomes, is probably a result of telomeric pairing initiation and strong positive chiasma interference. Interference averaged 0.81 in 35 pairs of adjacent segments and 0.57 across the entire recombining portions of chromosome arms. The total genetic map lengths of the arms corresponded closely to those expected on the basis of their metaphase-I chiasma frequencies. As a consequence of this uneven distribution of recombination there can be a 153-fold difference (or more) in the number of DNA base pairs per unit (centiMorgan) of genetic length.     

A mathematically tractable family of genetic mapping functions with different amounts of interference

By extension of the argument of Kosambi (1944), a family of mapping functions can be derived, which has a parameter regulating the intensity of interference. Different values of this parameter yield the Haldane (1919) and Kosambi mapping functions as special cases. The parameter is the coincidence coefficient for nearby small intervals. The family includes mapping functions for negative interference. A simple rule for combining recombination fractions in adjacent intervals is also obtained.     

A high-density cytogenetic map of the Aegilops tauschii genome incorporating retrotransposons and defense-related genes: insights into cereal chromosome structure and function

Aegilops tauschii (Coss.) Schmal. (2n = 2x = 14, DD) (syn. A. squarrosa L.; Triticum tauschii) is well known as the D-genome donor of bread wheat (T. aestivum, 2n = 6x = 42, AABBDD). Because of conserved synteny, a high-density map of the A. tauschii genome will be useful for breeding and genetics within the tribe Triticeae which besides bread wheat also includes barley and rye. We have placed 249 new loci onto a high-density integrated cytological and genetic map of A. tauschii for a total of 732 loci making it one of the most extensive maps produced to date for the Triticeae species. Of the mapped loci, 160 are defense-related genes. The retrotransposon marker system recently developed for cultivated barley (Hordeum vulgare L.) was successfully applied to A. tauschii with the placement of 80 retrotransposon loci onto the map. A total of 50 microsatellite and ISSR loci were also added. Most of the retrotransposon loci, resistance (R), and defense-response (DR) genes are organized into clusters: retrotransposon clusters in the pericentromeric regions, R and DR gene clusters in distal/telomeric regions. Markers are non-randomly distributed with low density in the pericentromeric regions and marker clusters in the distal regions. A significant correlation between the physical density of markers (number of markers mapped to the chromosome segment/physical length of the same segment in microm) and recombination rate (genetic length of a chromosome segment/physical length of the same segment in microm) was demonstrated. Discrete regions of negative or positive interference (an excess or deficiency of crossovers in adjacent intervals relative to the expected rates on the assumption of no interference) was observed in most of the chromosomes. Surprisingly, pericentromeric regions showed negative interference. Islands with negative, positive and/or no interference were present in interstitial and distal regions. Most of the positive interference was restricted to the long arms. The model of chromosome structure and function in cereals with large genomes that emerges from these studies is discussed.     

Physical distribution of translocation breakpoints in homoeologous recombinants induced by the absence of the Ph1 gene in wheat and triticale

The physical distribution of translocation breakpoints was analyzed in homoeologous recombinants involving chromosomes 1A, 1B, 1D of wheat and 1R of rye, and the long arms of chromosome 7S of Aegilops speltoides and 7A of wheat. Recombination between homoeologues was induced by removal of the Ph1 gene. In all instances, translocation breakpoints were concentrated in the distal ends of the chromosome arms and were absent in the proximal halves of the arms. The relationship between the relative distance from the centromere and the relative homoeologous recombination frequency was best explained by the function f(x)=0.0091e^0.0592x. The pattern of recombination in homoeologous chromosomes was essentially the same as in homologues except that there were practically no double exchanges. Among 313 recombinant chromosomes, only one resulted from a double crossing-over. The distribution of translocation breakpoints in translocated arms indicated that positive chiasma interference operated in homoeologous recombination. This implies that the reduction of the length of alien chromosome segments present in translocations with wheat chromosomes may be more difficult than the production of the original recombinants.     

Recombination map of the common shrew, Sorex araneus (Eulipotyphla, Mammalia)

The Eurasian common shrew (Sorex araneus L.) is characterized by spectacular chromosomal variation, both autosomal variation of the Robertsonian type and an XX/XY(1)Y(2) system of sex determination. It is an important mammalian model of chromosomal and genome evolution as it is one of the few species with a complete genome sequence. Here we generate a high-precision cytological recombination map for the species, the third such map produced in mammals, following those for humans and house mice. We prepared synaptonemal complex (SC) spreads of meiotic chromosomes from 638 spermatocytes of 22 males of nine different Robertsonian karyotypes, identifying each autosome arm by differential DAPI staining. Altogether we mapped 13,983 recombination sites along 7095 individual autosomes, using immunolocalization of MLH1, a mismatch repair protein marking recombination sites. We estimated the total recombination length of the shrew genome as 1145 cM. The majority of bivalents showed a high recombination frequency near the telomeres and a low frequency near the centromeres. The distances between MLH1 foci were consistent with crossover interference both within chromosome arms and across the centromere in metacentric bivalents. The pattern of recombination along a chromosome arm was a function of its length, interference, and centromere and telomere effects. The specific DNA sequence must also be important because chromosome arms of the same length differed substantially in their recombination pattern. These features of recombination show great similarity with humans and mice and suggest generality among mammals. However, contrary to a widespread perception, the metacentric bivalent tu usually lacked an MLH1 focus on one of its chromosome arms, arguing against a minimum requirement of one chiasma per chromosome arm for correct segregation. With regard to autosomal chromosomal variation, the chromosomes showing Robertsonian polymorphism display MLH1 foci that become increasingly distal when comparing acrocentric homozygotes, heterozygotes, and metacentric homozygotes. Within the sex trivalent XY(1)Y(2), the autosomal part of the complex behaves similarly to other autosomes.     

Occurrence of Double Strand DNA Breaks and Pairing of Homologous Chromosomes are Preconditions of Crossing Over in Drosophila Melanogaster, and Its Timing

Brood pattern analysis of the effect of a heat shock (35°C 24 h) given to the parental females in presence and absence of In (2L + 2R) Cy in heterozygous condition in the second chromosome on recombination and interference in the cv − v − f region of the X chromosome showed the following: (i) In the absence of the inversion recombination frequencies in both gene intervals increased in the daily broods, which represent oocytes in which premeiotic DNA synthesis was occurring during the heat shock treatment. (ii) In the presence of the inversion recombination frequencies did not increase in any of the daily broods. (iii) The frequencies of double crossovers did not increase in any broods either in the presence or in the absence of inversion. (iv) The coefficient of coincidence changed in virtually all broods both in the presence and absence of the inversion, indicating that the heat shock affects the distribution of single crossovers. (v) The results showed that the effect of the heat shock on the coefficient of coincidence was similar during premeiotic DNA synthesis both in the absence and presence of the inversion, but different in the broods representing oocytes which were undergoing the first meiotic division, suggesting that crossing over occurs during this division, probably during pachytene. This revised version was published online in July 2006 with corrections to the Cover Date.     

A recombinational portrait of the Drosophila pseudoobscura genome

Drosophila pseudoobscura has been intensively studied by evolutionary biologists for over 70 years. The recent publication of the genome sequence not only permits studies of comparative genomics with other dipterans but also opens the door to identifying genes associated with adaptive traits or speciation or testing for the signature of natural selection across the genome. Information on regional rates of recombination, localization of inversion breakpoints distinguishing it from its sibling species D. persimilis, and known polymorphic markers may be useful in such studies. Here, we present a molecular linkage map of four of the five major chromosome arms of D. pseudoobscura. In doing so, we order and orient several sequence contig groups, localize the inversion breakpoints on chromosome 2 to intervals of 200 kilobases, and identify one error in the published sequence assembly. Our results show that regional recombination rates in D. pseudoobscura are much higher than in D. melanogaster and significantly higher even than in D. persimilis. Furthermore, we detect a non-significant positive correlation between recombination rate and published DNA sequence variation. Finally, the online Appendix presents 200 primer sequence pairs for molecular markers that can be used for mapping of quantitative trait loci, of which 125 are known to be polymorphic within or between species.     

Linkage Group Xix of Chlamydomonas Reinhardtii Has a Linear Map

Linkage group XIX (or the UNI linkage group) of Chlamydomonas reinhardtii has been reported to show a circular meiotic recombination map. A circular map predicts the existence of strong chiasma and chromatid interference, which would lead to an excess number of two-strand double crossovers during meiosis. We have tested this prediction in multipoint crosses. Our results are consistent with a linear linkage group that shows positive chiasma interference and no chromatid interference. Chiasma interference occurs both within arms and across the centromere. Of the original loci that contributed to the circular map, we find that two map to other linkage groups and a third cannot be retested because the mutant strain that defined it has been lost. A second reported unusual property for linkage group XIX was the increase in meiotic recombination with increases in temperature during a period that precedes the onset of meiosis. Although we observed changes in recombination frequencies in some intervals on linkage group XIX in crosses to CC-1952, and in strains heterozygous for the mutation ger1 at 16°, we also show that our strains do not exhibit the previously observed patterns of temperature-sensitive recombination for two different pairs of loci on linkage group XIX. We conclude that linkage group XIX has a linear genetic map that is not significantly different from other Chlamydomonas linkage groups.     

The spatial regulation of meiotic recombination hotspots: Are all DSB hotspots crossover hotspots?

A key step for the success of meiosis is programmed homologous recombination, during which crossovers, or exchange of chromosome arms, take place. Crossovers increase genetic diversity but their main function is to ensure accurate chromosome segregation. Defects in crossover number and position produce aneuploidies that represent the main cause of miscarriages and chromosomal abnormalities such as Down's syndrome. Recombination is initiated by the formation of programmed double strand breaks (DSBs), which occur preferentially at places called DSB hotspots. Among all DSBs generated, only a small fraction is repaired by crossover, the other being repaired by other homologous recombination pathways. Crossover maps have been generated in a number of organisms, defining crossover hotspots. With the availability of genome-wide maps of DSBs as well as the ability to measure genetically the repair outcome at several hotspots, it is becoming more and more clear that not all DSB hotspots behave the same for crossover formation, suggesting that chromosomal features distinguish different types of hotspots.     

C-L processes involving higher order positive (negative) interference for any two collections of disjoint chromosomal regions

Interference is said to take place whenever crossover events fail to occur at random along the chromosome. The nature of higher order interference (positive or negative) is introduced. It is shown how interference is determined by the chiasma formation process operating along the chromosome and especially by the count-location (C-L) chiasma formation process. We discuss a simple mechanism among C-L processes that can generate prescribed higher order positive interference or prescribed higher order negative interference between any two collections of disjoint genomic regions.Supported in part by NIH grant GM 28016     

Chromosome size-dependent control of meiotic reciprocal recombination in Saccharomyces cerevisiae: the role of crossover interference.

In the yeast Saccharomyces cerevisiae, small chromosomes undergo meiotic reciprocal recombination (crossing over) at rates (centimorgans per kilobases) greater than those of large chromosomes, and recombination rates respond directly to changes in the total size of a chromosomal DNA molecule. This phenomenon, termed chromosome size-dependent control of meiotic reciprocal recombination, has been suggested to be important for ensuring that homologous chromosomes cross over during meiosis. The mechanism of this regulation was investigated by analyzing recombination in identical genetic intervals present on different size chromosomes. The results indicate that chromosome size-dependent control is due to different amounts of crossover interference. Large chromosomes have high levels of interference while small chromosomes have much lower levels of interference. A model for how crossover interference directly responds to chromosome size is presented. In addition, chromosome size-dependent control was shown to lower the frequency of homologous chromosomes that failed to undergo crossovers, suggesting that this control is an integral part of the mechanism for ensuring meiotic crossing over between homologous chromosomes.     

The effect of a deficiency and a deletion on recombination in chromosome 1BL in wheat

To test two models of chiasma allocation and the distribution of crossing-over in chromosomes, genetic mapping was performed in normal, deletion and deficiency chromosome arms 1BL of wheat, Triticum aestivum L. Shortening of the chromosome arm, either by a deletion of the proximal half of the arm or by a deficiency of the terminal quarter of the arm's length, significantly reduced the frequency of multiple crossovers but did not affect the distribution of the distal, presumably the first, crossover in the arm. In the deficiency chromosome, the recombination rate in the terminal segment was much higher than that in the same segment of the complete arm. This suggests that recombination frequency is not an inherent characteristic of a segment but depends on the segment's position on the centromere-telomere axis. These observations support the classical model of chiasma distribution along the chromosome based on the point of pairing initiation, chromosome length and the positive chiasma interference. The study also demonstrates that the distribution and frequency of recombination in a chromosome segment can be manipulated. Therefore, even the segments with very low recombination frequencies could be saturated with large numbers of crossover events to produce high-density genetic maps.     

A high-density rice genetic linkage map with 2275 markers using a single F2 population.

A 2275-marker genetic map of rice (Oryza sativa L.) covering 1521.6 cM in the Kosambi function has been constructed using 186 F2 plants from a single cross between the japonica variety Nipponbare and the indica variety Kasalath. The map provides the most detailed and informative genetic map of any plant. Centromere locations on 12 linkage groups were determined by dosage analysis of secondary and telotrisomics using > 130 DNA markers located on respective chromosome arms. A limited influence on meiotic recombination inhibition by the centromere in the genetic map was discussed. The main sources of the markers in this map were expressed sequence tag (EST) clones from Nipponbare callus, root, and shoot libraries. We mapped 1455 loci using ESTs; 615 of these loci showed significant similarities to known genes, including single-copy genes, family genes, and isozyme genes. The high-resolution genetic map permitted us to characterize meiotic recombinations in the whole genome. Positive interference of meiotic recombination was detected both by the distribution of recombination number per each chromosome and by the distribution of double crossover interval lengths.     

A Polymerization Model of Chiasma Interference and Corresponding Computer Simulation

A model of chiasma interference is proposed and simulated on a computer. The model uses random events and a polymerization reaction to regulate meiotic recombination between and along chromosomes. A computer simulation of the model generates distributions of crossovers per chromosome arm, position of events along the chromosome arm, distance between crossovers in two-event tetrads, and coincidence as a function of distance. Outputs from the simulation are compared to data from Saccharomyces cerevisiae and the X chromosome of Drosophila melanogaster. The simulation demonstrates that the proposed model can produce the regulation of recombination observed in both genetic and cytological experiments. While the model was quantitatively compared to data from only Drosophila and Saccharomyces, the regulation observed in these species is qualitatively similar to the regulation of recombination observed in other organisms.     

A high-density cytogenetic map of the Aegilops tauschii genome incorporating retrotransposons and defense-related genes: insights into cereal chromosome structure and function

Aegilops tauschii (Coss.) Schmal. (2n=2x=14, DD) (syn. A. squarrosa L.; Triticum tauschii) is well known as the D-genome donor of bread wheat (T. aestivum, 2n=6x=42, AABBDD). Because of conserved synteny, a high-density map of the A. tauschii genome will be useful for breeding and genetics within the tribe Triticeae which besides bread wheat also includes barley and rye. We have placed 249 new loci onto a high-density integrated cytological and genetic map of A. tauschii for a total of 732 loci making it one of the most extensive maps produced to date for the Triticeae species. Of the mapped loci, 160 are defense-related genes. The retrotransposon marker system recently developed for cultivated barley (Hordeum vulgare L.) was successfully applied to A. tauschii with the placement of 80 retrotransposon loci onto the map. A total of 50 microsatellite and ISSR loci were also added. Most of the retrotransposon loci, resistance (R), and defense-response (DR) genes are organized into clusters: retrotransposon clusters in the pericentromeric regions, R and DR gene clusters in distal/telomeric regions. Markers are non-randomly distributed with low density in the pericentromeric regions and marker clusters in the distal regions. A significant correlation between the physical density of markers (number of markers mapped to the chromosome segment/physical length of the same segment in m) and recombination rate (genetic length of a chromosome segment/physical length of the same segment in m) was demonstrated. Discrete regions of negative or positive interference (an excess or deficiency of crossovers in adjacent intervals relative to the expected rates on the assumption of no interference) was observed in most of the chromosomes. Surprisingly, pericentromeric regions showed negative interference. Islands with negative, positive and/or no interference were present in interstitial and distal regions. Most of the positive interference was restricted to the long arms. The model of chromosome structure and function in cereals with large genomes that emerges from these studies is discussed.     

Mapping functions

Accurate estimation of map distance between markers is important for the construction of large-scale linkage maps because it provides reliable and useful linkage information of markers on chromosomes. How to improve accuracy of estimating map distances depends on an appropriate mapping function. We used the coefficient of coincidence to integrate the Haldane function, in which crossovers are assumed to be independent and the Morgan function, in which crossovers are assumed to be interfered, and produce a new mapping function. The mapping function based on positive interference is referred to as the positive function and that on negative interference as the negative function. In these two mapping functions, map distances between loci are determined by both recombination frequencies and the coefficient of coincidence. We applied our mapping functions to four examples and show that our map estimates have much higher goodness-of-fit to the observed mapping data than the Haldane and Kosambi functions. Therefore, they can provide much more precise estimates of map distances than the two conventional mapping functions. Furthermore, our mapping functions produced almost linear (additive) map distances.     

Construction of a 10,000-marker ultradense genetic recombination map of potato: providing a framework for accelerated gene isolation and a genomewide physical map

An ultradense genetic linkage map with >10,000 AFLP loci was constructed from a heterozygous diploid potato population. To our knowledge, this is the densest meiotic recombination map ever constructed. A fast marker-ordering algorithm was used, based on the minimization of the total number of recombination events within a given marker order in combination with genotyping error-detection software. This resulted in "skeleton bin maps," which can be viewed as the most parsimonious marker order. The unit of distance is not expressed in centimorgans but in "bins." A bin is a position on the genetic map with a unique segregation pattern that is separated from adjacent bins by a single recombination event. Putative centromeres were identified by a strong clustering of markers, probably due to cold spots for recombination. Conversely, recombination hot spots resulted in large intervals of up to 15 cM without markers. The current level of marker saturation suggests that marker density is proportional to physical distance and independent of recombination frequency. Most chromatids (92%) recombined once or never, suggesting strong chiasma interference. Absolute chiasma interference within a chromosome arm could not be demonstrated. Two examples of contig construction and map-based cloning have demonstrated that the marker spacing was in accordance with the expected physical distance: approximately one marker per BAC length. Currently, the markers are used for genetic anchoring of a physical map of potato to deliver a sequence-ready minimal tiling path of BAC contigs of specific chromosomal regions for the potato genome sequencing consortium (http://www.potatogenome.net).     

Recombination patterns reveal information about centromere location on linkage maps

Linkage mapping is often used to identify genes associated with phenotypic traits and for aiding genome assemblies. Still, many emerging maps do not locate centromeres – an essential component of the genomic landscape. Here, we demonstrate that for genomes with strong chiasma interference, approximate centromere placement is possible by phasing the same data used to generate linkage maps. Assuming one obligate crossover per chromosome arm, information about centromere location can be revealed by tracking the accumulated recombination frequency along linkage groups, similar to half‐tetrad analyses. We validate the method on a linkage map for sockeye salmon (Oncorhynchus nerka) with known centromeric regions. Further tests suggest that the method will work well in other salmonids and other eukaryotes. However, the method performed weakly when applied to a male linkage map (rainbow trout; O. mykiss) characterized by low and unevenly distributed recombination – a general feature of male meiosis in many species. Further, a high frequency of double crossovers along chromosome arms in barley reduced resolution for locating centromeric regions on most linkage groups. Despite these limitations, our method should work well for high‐density maps in species with strong recombination interference and will enrich many existing and future mapping resources.     

Recombination, dominance and selection on amino acid polymorphism in the Drosophila genome: contrasting patterns on the X and fourth chromosomes

Surveys of nucleotide polymorphism and divergence indicate that the average selection coefficient on Drosophila proteins is weakly positive. Similar surveys in mitochondrial genomes and in the selfing plant Arabidopsis show that weak negative selection has operated. These differences have been attributed to the low recombination environment of mtDNA and Arabidopsis that has hindered adaptive evolution through the interference effects of linkage. We test this hypothesis with new sequence surveys of proteins lying in low recombination regions of the Drosophila genome. We surveyed >3800 bp across four proteins at the tip of the X chromosome and >3600 bp across four proteins on the fourth chromosome in 24 strains of D. melanogaster and 5 strains of D. simulans. This design seeks to study the interaction of selection and linkage by comparing silent and replacement variation in semihaploid (X chromosome) and diploid (fourth chromosome) environments lying in regions of low recombination. While the data do indicate very low rates of exchange, all four gametic phases were observed both at the tip of the X and across the fourth chromosome. Silent variation is very low at the tip of the X (thetaS = 0.0015) and on the fourth chromosome (thetaS = 0.0002), but the tip of the X shows a greater proportional loss of variation than the fourth shows relative to normal-recombination regions. In contrast, replacement polymorphism at the tip of the X is not reduced (thetaR = 0.00065, very close to the X chromosome average). MK and HKA tests both indicate a significant excess of amino acid polymorphism at the tip of the X relative to the fourth. Selection is significantly negative at the tip of the X (Nes = -1.53) and nonsignificantly positive on the fourth (Nes approximately 2.9), analogous to the difference between mtDNA (or Arabidopsis) and the Drosophila genome average. Our distal X data are distinct from regions of normal recombination where the X shows a deficiency of amino acid polymorphism relative to the autosomes, suggesting more efficient selection against recessive deleterious replacement mutations. We suggest that the excess amino acid polymorphism on the distal X relative to the fourth chromosome is due to (1) differences in the mutation rate for selected mutations on the distal X or (2) a greater relaxation of selection from stronger linkage-related interference effects on the distal X. This relaxation of selection is presumed to be greater in magnitude than the difference in efficiency of selection between X-linked vs. autosomal selection.