A quantitative genetics model for viability selection

Overt and concealed genetic loads revealed by QTL mapping of genotype-dependent viability in the Pacific oyster Crassostrea gigas

Understanding the genetic bases of inbreeding depression, heterosis, and genetic load is integral to understanding how genetic diversity is maintained in natural populations. The Pacific oyster Crassostrea gigas, like many long-lived plants, has high fecundity and high early mortality (type-III survivorship), manifesting a large, overt, genetic load; the oyster harbors an even greater concealed genetic load revealed by inbreeding. Here, we map viability QTL (vQTL) in six interrelated F2 oyster families, using high-density linkage maps of single nucleotide polymorphisms generated by genotyping-by-sequencing (GBS) methods. Altogether, we detect 70 vQTL and provisionally infer 89 causal mutations, 11 to 20 per family. Genetic mortality caused by independent (unlinked) vQTL ranges from 94.2% to 97.8% across families, consistent with previous reports. High-density maps provide better resolution of genetic mechanisms, however. Models of one causal mutation present in both identical-by-descent (IBD) homozygotes and heterozygotes fit genotype frequencies at 37 vQTL; consistent with the mutation-selection balance theory of genetic load, 20 are highly deleterious, completely recessive mutations and 17 are less deleterious, partially dominant mutations. Another 22 vQTL require pairs of recessive or partially dominant causal mutations, half showing selection against recessive mutations linked in repulsion, producing pseudo-overdominance. Only eight vQTL appear to support the overdominance theory of genetic load, with deficiencies of both IBD homozygotes, but at least four of these are likely caused by pseudo-overdominance. Evidence for epistasis is absent. A high mutation rate, random genetic drift, and pseudo-overdominance may explain both the oyster's extremely high genetic diversity and a high genetic load maintained primarily by mutation-selection balance.

Seed protein content and its relationships with agronomic traits in pigeonpea is controlled by both main and epistatic effects QTLs

The genetic architecture of seed protein content (SPC) and its relationships to agronomic traits in pigeonpea is poorly understood. Accordingly, five F₂ populations segregating for SPC and four agronomic traits (seed weight (SW), seed yield (SY), growth habit (GH) and days to first flowering (DFF)) were phenotyped and genotyped using genotyping-by-sequencing approach. Five high-density population-specific genetic maps were constructed with an average inter-marker distance of 1.6 to 3.5 cM, and subsequently, integrated into a consensus map with average marker spacing of 1.6 cM. Based on analysis of phenotyping data and genotyping data, 192 main effect QTLs (M-QTLs) with phenotypic variation explained (PVE) of 0.7 to 91.3% were detected for the five traits across the five populations. Major effect (PVE ≥ 10%) M-QTLs included 14 M-QTLs for SPC, 16 M-QTLs for SW, 17 M-QTLs for SY, 19 M-QTLs for GH and 24 M-QTLs for DFF. Also, 573 epistatic QTLs (E-QTLs) were detected with PVE ranging from 6.3 to 99.4% across traits and populations. Colocalization of M-QTLs and E-QTLs explained the genetic basis of the significant (P < 0.05) correlations of SPC with SW, SY, DFF and GH. The nature of genetic architecture of SPC and its relationship with agronomic traits suggest that genomics-assisted breeding targeting genome-wide variations would be effective for the simultaneous improvement of SPC and other important traits.

Construction of the First High-Density Genetic Linkage Map and Analysis of Quantitative Trait Loci for Growth-Related Traits in Sinonovacula constricta

The razor clam (Sinonovacula constricta) is an important aquaculture species, for which a high-density genetic linkage map would play an important role in marker-assisted selection (MAS). In this study, we constructed a high-density genetic map and detected quantitative trait loci (QTLs) for Sinonovacula constricta with an F₁ cross population by using the specific locus amplified fragment sequencing (SLAF-seq) method. A total of 315,553 SLAF markers out of 467.71 Mreads were developed. The final linkage map was composed of 7516 SLAFs (156.60-fold in the parents and 20.80-fold in each F₁ population on average). The total distance of the linkage map was 2383.85 cM, covering 19 linkage groups with an average inter-marker distance of 0.32 cM. The proportion of gaps less than 5.0 cM was on average 96.90%. A total of 16 suggestive QTLs for five growth-related traits (five QTLs for shell height, six QTLs for shell length, three QTLs for shell width, one QTL for total body weight, and one QTL for soft body weight) were identified. These QTLs were distributed on five linkage groups, and the regions showed overlapping on LG9 and LG13. In conclusion, the high-density genetic map and QTLs for S. constricta provide a valuable genetic resource and a basis for MAS.

The First Genetic Map in Sweet Osmanthus (Osmanthus fragrans Lour.) Using Specific Locus Amplified Fragment Sequencing

Osmanthus fragrans is an ornamental plant of substantial commercial value, and no genetic linkage maps of this species have previously been reported. Specific-locus amplified fragment sequencing (SLAF-seq) is a recently developed technology that allows massive single nucleotide polymorphisms (SNPs) to be identified and high-resolution genotyping. In our current research, we generated the first genetic map of O. fragrans using SLAF-seq, which is composed with 206.92 M paired-end reads and 173,537 SLAF markers. Among total 90,715 polymorphic SLAF markers, 15,317 polymorphic SLAFs could be used for genetic map construction. The integrated map contained 14,189 high quality SLAFs that were grouped in 23 genetic linkage groups, with a total length of 2962.46 cM and an average distance of 0.21 cM between two adjacent markers. In addition, 23,664 SNPs were identified from the mapped markers. As far as we know, this is the first of the genetic map of O. fragrans. Our results are further demonstrate that SLAF-seq is a very effective method for developing markers and constructing high-density linkage maps. The SNP markers and the genetic map reported in this study should be valuable resource in future research.

Influence of epistatic segregation distortion loci on genetic marker linkages in Japanese flounder

For genetic linkage analysis of Japanese flounder, 160 doubled haploids (DH) were artificially produced using mitotic gynogenesis and were genotyped for 458 simple sequence repeat (SSR) markers, 101 of which show distortional segregation. The genetic linkage map was constructed by modifying recombination fractions between the distorted markers. Between the corrected and uncorrected genetic maps, there were considerable differences in genetic distance, but not in relative locations among markers. Using a liability model, a segregation distortion locus (SDL), with an additive genetic effect of 1.772, was mapped between markers BDHYP387 and Poli56TUF of chromosome 24 in the corrected genetic map. Additionally, six pairs of epistatic SDLs were identified on chromosomes 1, 5, 8, 9, 23, and 24. Changes in genetic distances between markers did not occur on chromosome regions with main effect SDLs. However, most chromosome regions where genetic distances changed covered the detected epistatic SDLs. This study concluded that epistatic SDLs decrease linkages between markers and lengthen genetic distances in Japanese flounder. This finding has been partially validated in other DH populations derived from three female Japanese flounders.

A Mixed Model Approach to Genome-Wide Association Studies for Selection Signatures, with Application to Mice Bred for Voluntary Exercise Behavior

Selection experiments and experimental evolution provide unique opportunities to study the genetics of adaptation because the target and intensity of selection are known relatively precisely. In contrast to natural selection, where populations are never strictly "replicated," experimental evolution routinely includes replicate lines so that selection signatures-genomic regions showing excessive differentiation between treatments-can be separated from possible founder effects, genetic drift, and multiple adaptive solutions. We developed a mouse model with four lines within a high running (HR) selection treatment and four nonselected controls (C). At generation 61, we sampled 10 mice of each line and used the Mega Mouse Universal Genotyping Array to obtain single nucleotide polymorphism (SNP) data for 25,318 SNPs for each individual. Using an advanced mixed model procedure developed in this study, we identified 152 markers that were significantly different in frequency between the two selection treatments. They occurred on all chromosomes except 1, 2, 8, 13, and 19, and showed a variety of patterns in terms of fixation (or the lack thereof) in the four HR and four C lines. Importantly, none were fixed for alternative alleles between the two selection treatments. The current state-of-the-art regularized F test applied after pooling DNA samples for each line failed to detect any markers. We conclude that when SNP or sequence data are available from individuals, the mixed model methodology is recommended for selection signature detection. As sequencing at the individual level becomes increasingly feasible, the new methodology may be routinely applied for detection of selection.

Genetic linkage map construction and QTL mapping of seedling height, basal diameter and crown width of Taxodium 'Zhongshanshan 302' × T. mucronatum

Taxodium is a genus renowned for its fast growth, good form and tolerance of flooding, salt, alkalinity, disease and strong winds. In this study, a genetic linkage map was constructed using sequence-related amplified polymorphism (SRAP) and simple sequence repeat (SSR) markers based on an F₁ population containing 148 individuals generated from a cross between T. ‘Zhongshanshan 302’ and T. mucronatum. The map has a total length of 976.5 cM, with a mean distance of 7.0 cM between markers, and contains 34 linkage groups with 179 markers (171 SRAPs and 8 SSRs). Quantitative trait loci (QTLs) affecting growth traits, such as seedling height, basal diameter and crown width, were detected based on the constructed linkage map. Four significant QTLs were identified, three of which, namely qtSH-1 for seedling height, qtBD-1 for basal diameter and qtCW-1 for crown width, were located at 2.659 cM of LG7 with logarithm odds values of 3.72, 3.49 and 3.93, respectively, and explained 24.9, 27.0 and 21.7 % of the total variation of the three grown traits, respectively. Another QTL for crown width (qtCW-2) was detected at 1.0 cM on LG13, with a logarithm of odds value of 3.15, and explained 31.7 % of the total variation of crown width. This is the first report on the construction of a genetic linkage map and QTL analysis in Taxodium, laying the groundwork for the construction of a high-density genetic map and QTL mapping in the genus Taxodium.

A High-Density SNP Genetic Linkage Map and QTL Analysis of Growth-Related Traits in a Hybrid Family of Oysters (Crassostrea gigas × Crassostrea angulata) Using Genotyping-by-Sequencing

Oysters are among the most important species in global aquaculture. Crassostrea gigas, and its subspecies C. angulata, are the major cultured species. To determine the genetic basis of growth-related traits in oysters, we constructed a second-generation linkage map from 3367 single-nucleotide polymorphisms (SNPs) based on genotyping-by-sequencing, genotyped from a C. gigas × C. angulata hybrid family. These 3367 SNPs were distributed on 1695 markers, which were assigned to 10 linkage groups. The genetic linkage map had a total length of 1084.3 cM, with an average of 0.8 cM between markers; it thus represents the densest genetic map constructed for oysters to date. Twenty-seven quantitative trait loci (QTL) for five growth-related traits were detected. These QTL could explain 4.2-7.7% (mean = 5.4%) of the phenotypic variation. In total, 50.8% of phenotypic variance for shell width, 7.7% for mass weight, and 34.1% for soft tissue weight were explained. The detected QTL were distributed among eight linkage groups, and more than half (16) were concentrated within narrow regions in their respective linkage groups. Thirty-eight annotated genes were identified within the QTL regions, two of which are key genes for carbohydrate metabolism. Other genes were found to participate in assembly and regulation of the actin cytoskeleton, signal transduction, and regulation of cell differentiation and development. The newly developed high-density genetic map, and the QTL and candidate genes identified provide a valuable genetic resource and a basis for marker-assisted selection for C. gigas and C. angulata.

Identification and Characterization of Segregation Distortion Loci on Cotton Chromosome 18

Segregation distortion is commonly detected via genetic mapping and this phenomenon has been reported in many species. However, the genetic causes of the segregation distortion regions in a majority of species are still unclear. To genetically dissect the SD on chromosome 18 in cotton, eight reciprocal backcross populations and two F₂ populations were developed. Eleven segregation distortion loci (SDL) were detected in these ten populations. Comparative analyses among populations revealed that SDL18.1 and SDL18.9 were consistent with male gametic competition; whereas SDL18.4 and SDL18.11 reflected female gametic selection. Similarly, other SDL could reflect zygotic selection. The surprising finding was that SDL18.8 was detected in all populations, and the direction was skewed towards heterozygotes. Consequently, zygotic selection or heterosis could represent the underlying genetic mechanism for SDL18.8. Among developed introgression lines, SDL18.8 was introgressed as a heterozygote, further substantiating that a heterozygote state was preferred under competition. Six out of 11 SDL on chromosome 18 were dependent on the cytoplasmic environment. These results indicated that different SDL showed varying responses to the cytoplasmic environment. Overall, the results provided a novel strategy to analyze the molecular mechanisms, which could be further exploited in cotton interspecific breeding programs.

SNP-Based QTL Mapping of 15 Complex Traits in Barley under Rain-Fed and Well-Watered Conditions by a Mixed Modeling Approach

This study identified single nucleotide polymorphism (SNP) markers associated with 15 complex traits in a breeding population of barley (Hordeum vulgare L.) consisting of 137 recombinant chromosome substitution lines (RCSL), evaluated under contrasting water availability conditions in the Mediterranean climatic region of central Chile. Given that markers showed a very strong segregation distortion, a quantitative trait locus/loci (QTL) mapping mixed model was used to account for the heterogeneity in genetic relatedness between genotypes. Fifty-seven QTL were detected under rain-fed conditions, which accounted for 5-22% of the phenotypic variation. In full irrigation conditions, 84 SNPs were significantly associated with the traits studied, explaining 5-35% of phenotypic variation. Most of the QTL were co-localized on chromosomes 2H and 3H. Environment-specific genomic regions were detected for 12 of the 15 traits scored. Although most QTL-trait associations were environment and trait specific, some important and stable associations were also detected. In full irrigation conditions, a relatively major genomic region was found underlying hectoliter weight (HW), on chromosome 1H, which explained between 27% (SNP 2711-234) and 35% (SNP 1923-265) of the phenotypic variation. Interestingly, the locus 1923-265 was also detected for grain yield at both environmental conditions, accounting for 9 and 18%, in the rain-fed and irrigation conditions, respectively. Analysis of QTL in this breeding population identified significant genomic regions that can be used for marker-assisted selection (MAS) of barley in areas where drought is a significant constraint.

Construction of a high-density genetic map using specific length amplified fragment markers and identification of a quantitative trait locus for anthracnose resistance in walnut (Juglans regia L.)

BACKGROUND

Walnut (Juglans regia, 2n = 32, approximately 606 Mb per 1C genome) is an economically important tree crop. Resistance to anthracnose, caused by Colletotrichum gloeosporioides, is a major objective of walnut genetic improvement in China. The recently developed specific length amplified fragment sequencing (SLAF-seq) is an efficient strategy that can obtain large numbers of markers with sufficient sequence information to construct high-density genetic maps and permits detection of quantitative trait loci (QTLs) for molecular breeding.

RESULTS

SLAF-seq generated 161.64 M paired-end reads. 153,820 SLAF markers were obtained, of which 49,174 were polymorphic. 13,635 polymorphic markers were sorted into five segregation types and 2,577 markers of them were used to construct genetic linkage maps: 2,395 of these fell into 16 linkage groups (LGs) for the female map, 448 markers for the male map, and 2,577 markers for the integrated map. Taking into account the size of all LGs, the marker coverage was 2,664.36 cM for the female map, 1,305.58 cM for the male map, and 2,457.82 cM for the integrated map. The average intervals between two adjacent mapped markers were 1.11 cM, 2.91 cM and 0.95 cM for three maps, respectively. 'SNP_only' markers accounted for 89.25% of the markers on the integrated map. Mapping markers contained 5,043 single nucleotide polymorphisms (SNPs) loci, which corresponded to two SNP loci per SLAF marker. According to the integrated map, we used interval mapping (Logarithm of odds, LOD > 3.0) to detect our quantitative trait. One QTL was detected for anthracnose resistance. The interval of this QTL ranged from 165.51 cM to 176.33 cM on LG14, and ten markers in this interval that were above the threshold value were considered to be linked markers to the anthracnose resistance trait. The phenotypic variance explained by each marker ranged from 16.2 to 19.9%, and their LOD scores varied from 3.22 to 4.04.

CONCLUSIONS

High-density genetic maps for walnut containing 16 LGs were constructed using the SLAF-seq method with an F1 population. One QTL for walnut anthracnose resistance was identified based on the map. The results will aid molecular marker-assisted breeding and walnut resistance genes identification.

Mapping quantitative trait loci in selected breeding populations: A segregation distortion approach

Quantitative trait locus (QTL) mapping is often conducted in line-crossing experiments where a sample of individuals is randomly selected from a pool of all potential progeny. QTLs detected from such an experiment are important for us to understand the genetic mechanisms governing a complex trait, but may not be directly relevant to plant breeding if they are not detected from the breeding population where selection is targeting for. QTLs segregating in one population may not necessarily segregate in another population. To facilitate marker-assisted selection, QTLs must be detected from the very population which the selection is targeting. However, selected breeding populations often have depleted genetic variation with small population sizes, resulting in low power in detecting useful QTLs. On the other hand, if selection is effective, loci controlling the selected trait will deviate from the expected Mendelian segregation ratio. In this study, we proposed to detect QTLs in selected breeding populations via the detection of marker segregation distortion in either a single population or multiple populations using the same selection scheme. Simulation studies showed that QTL can be detected in strong selected populations with selected population sizes as small as 25 plants. We applied the new method to detect QTLs in two breeding populations of rice selected for high grain yield. Seven QTLs were identified, four of which have been validated in advanced generations in a follow-up study. Cloned genes in the vicinity of the four QTLs were also reported in the literatures. This mapping-by-selection approach provides a new avenue for breeders to improve breeding progress. The new method can be applied to breeding programs not only in rice but also in other agricultural species including crops, trees and animals.

Genetic Map Construction and Quantitative Trait Locus (QTL) Detection of Six Economic Traits Using an F2 Population of the Hybrid from Saccharina longissima and Saccharina japonica

Saccharina (Laminaria) is one of the most important economic seaweeds. Previously, four genetic linkage maps of Saccharina have been constructed and five QTLs have been identified. However, they were not enough for its breeding. In this work, Saccharina longissima (♀) and Saccharina japonica (♂), which showed obvious differences in morphology and genetics, were applied in hybridization to yield the F₂ mapping population with 102 individuals. Using these 102 F₂ hybrids, the genetic linkage map of Saccharina was constructed by MapMaker software based on 37 amplified fragment length polymorphisms (AFLPs), 22 sequence-related amplified polymorphisms (SRAPs) and 139 simple sequence repeats (SSRs) markers. Meanwhile, QTL analysis was performed for six economic traits. The linkage map constructed in this research consisted of 422 marker loci (137 AFLPs, 57 SRAPs and 228 SSRs), which formed 45 linkage groups (LGs) with an average marker space of 7.92 cM; they spanned a total length of 2233.1 cM, covering the whole estimated genome size. A total of 29 QTLs were identified for six economic traits, which explained 1.06 to 64.00% of phenotypic variation, including three QTLs for frond length (FL) and raw weight (RW), five QTLs for frond width (FW), two QTLs for frond fascia width (FFW) and frond thickness (FT), and fourteen QTLs for base shape (BS). The results of this research will improve the breeding efficiency and be beneficial for marker-assisted selection (MAS) schemes in Saccharina breeding.

Genetic Map Construction and Detection of Genetic Loci Underlying Segregation Distortion in an Intraspecific Cross of Populus deltoides

Based on a two-way pseudo-testcross strategy, high density and complete coverage linkage maps were constructed for the maternal and paternal parents of an intraspecific F2 pedigree of Populus deltoides. A total of 1,107 testcross markers were obtained, and the mapping population consisted of 376 progeny. Among these markers, 597 were from the mother, and were assigned into 19 linkage groups, spanning a total genetic distance of 1,940.3 cM. The remaining 519 markers were from the father, and were also were mapped into 19 linkage groups, covering 2,496.3 cM. The genome coverage of both maps was estimated as greater than 99.9% at 20 cM per marker, and the numbers of linkage groups of both maps were in accordance with the 19 haploid chromosomes in Populus. Marker segregation distortion was observed in large contiguous blocks on some of the linkage groups. Subsequently, we mapped the segregation distortion loci in this mapping pedigree. Altogether, eight segregation distortion loci with significant logarithm of odds supports were detected. Segregation distortion indicated the uneven transmission of the alternate alleles from the mapping parents. The corresponding genome regions might contain deleterious genes or be associated with hybridization incompatibility. In addition to the detection of segregation distortion loci, the established genetic maps will serve as a basic resource for mapping genetic loci controlling traits of interest in future studies.

Linkage group correction using epistatic distorted markers in F2 and backcross populations

Epistasis has been frequently observed in all types of mapping populations. However, relatively little is known about the effect of epistatic distorted markers on linkage group construction. In this study, a new approach was proposed to correct the recombination fraction between epistatic distorted markers in backcross and F2 populations under the framework of fitness and liability models. The information for three or four markers flanking with an epistatic segregation distortion locus was used to estimate the recombination fraction by the maximum likelihood method, implemented via an expectation-maximisation algorithm. A set of Monte Carlo simulation experiments along with a real data analysis in rice was performed to validate the new method. The results showed that the estimates from the new method are unbiased. In addition, five statistical properties for the new method in a backcross were summarised and confirmed by theoretical, simulated and real data analyses.

Genetic mapping of sterile genes with epistasis in backcross designs

The mapping of sterile genes is an essential issue, which should be solved for the investigation of sterility mechanism in wide hybridization of plants. However, the methods formerly developed cannot address the problem of mapping sterile loci with epistasis. In this study, we developed a new method to map sterile genes with epistasis in wide hybridizations of plants using a backcross design. The maximum likelihood method was used to estimate the parameters of recombination fractions and effects of sterile genes, and the convergent results of these parameters were obtained using the expectation maximization (EM) algorithm. The application and efficiency of this method were tested and demonstrated by a set of simulated data and real data analysis. Results from the simulation experiments showed that the method works well for simultaneously estimating the positions and effects of sterile genes, as well as the epistasis between sterile genes. A real data set of a backcross (BC) population from an interspecific hybrid between cultivated rice, Oryza sativa, and its wild African relative, Oryza longistaminata, was analyzed using the new method. Five sterile genes were detected on the chromosomes of 1, 3, 6, 8 and 10, and significant epistatic effects were found among the four pairs of sterile genes.

Multi-QTL mapping for quantitative traits using epistatic distorted markers

The interaction between segregation distortion loci (SDL) has been often observed in all kinds of mapping populations. However, little has been known about the effect of epistatic SDL on quantitative trait locus (QTL) mapping. Here we proposed a multi-QTL mapping approach using epistatic distorted markers. Using the corrected linkage groups, epistatic SDL was identified. Then, these SDL parameters were used to correct the conditional probabilities of QTL genotypes, and these corrections were further incorporated into the new QTL mapping approach. Finally, a set of simulated datasets and a real data in 304 mouse F2 individuals were used to validate the new method. As compared with the old method, the new one corrects genetic distance between distorted markers, and considers epistasis between two linked SDL. As a result, the power in the detection of QTL is higher for the new method than for the old one, and significant differences for estimates of QTL parameters between the two methods were observed, except for QTL position. Among two QTL for mouse weight, one significant difference for QTL additive effect between the above two methods was observed, because epistatic SDL between markers C66 and T93 exists (P = 2.94e-4).

The maternal cytoplasmic environment may be involved in the viability selection of gametes and zygotes

Segregation distortion is the phenomenon whereby the observed genotypic frequencies of a locus fall outside the expected Mendelian segregation ratio, and it is increasingly recognised as a potentially powerful evolutionary force. The main reason for segregation distortion is a difference in the viability of gametes and zygotes caused by viability loci in the segregating progeny. However, the maternal cytoplasm may also be involved in the viability selection of gametes and zygotes. The objectives of this study were to map the segregation distortion loci (SDL) in maize and to test the hypothesis that the viability of gametes and zygotes may also be associated with the maternal cytoplasmic environment. In the present study, a reciprocal mating design was conducted to generate an F2-segregating population. A linkage map was constructed with 126 microsatellite markers. A whole-genome scan was performed to detect the SDL in segregating populations with different maternal cytoplasm environments. Altogether, 14 SDL with strong LOD (logarithm (base 10) of odds) supports were identified in the specifically designed F2 populations. Interestingly, we found dramatic changes in the genotypic frequencies of the SDL in the two maternal cytoplasmic backgrounds, which indicated a change in the viability of gametes and zygotes in different cytoplasmic environments. Furthermore, in the JB cytoplasmic background, most of the detected SDL and complete distortion markers exhibited similar bias patterns favouring the Y53 alleles. These results suggested that selfish cytoplasmic elements may have an important role in shaping the patterns of segregation distortion in F2 populations through selective viability of gametes and zygotes.

Generalized linear mixed model for segregation distortion analysis

Background

Segregation distortion is a phenomenon that the observed genotypic frequencies of a locus fall outside the expected Mendelian segregation ratio. The main cause of segregation distortion is viability selection on linked marker loci. These viability selection loci can be mapped using genome-wide marker information.

Results

We developed a generalized linear mixed model (GLMM) under the liability model to jointly map all viability selection loci of the genome. Using a hierarchical generalized linear mixed model, we can handle the number of loci several times larger than the sample size. We used a dataset from an F₂ mouse family derived from the cross of two inbred lines to test the model and detected a major segregation distortion locus contributing 75% of the variance of the underlying liability. Replicated simulation experiments confirm that the power of viability locus detection is high and the false positive rate is low.

Conclusions

Not only can the method be used to detect segregation distortion loci, but also used for mapping quantitative trait loci of disease traits using case only data in humans and selected populations in plants and animals.

Prevalence of segregation distortion in diploid alfalfa and its implications for genetics and breeding applications

Segregation distortion (SD) is often observed in plant populations; its presence can affect mapping and breeding applications. To investigate the prevalence of SD in diploid alfalfa (Medicago sativa L.), we developed two unrelated segregating F(1) populations and one F(2) population. We genotyped all populations with SSR markers and assessed SD at each locus in each population. The three maps were syntenic and largely colinear with the Medicago truncatula genome sequence. We found genotypic SD for 24 and 34% of markers in the F(1) populations and 68% of markers in the F(2) population; distorted markers were identified on every linkage group. The smaller percentage of genotypic SD in the F(1) populations could be because they were non-inbred and/or due to non-fully informative markers. For the F(2) population, 60 of 90 mapped markers were distorted, and they clustered into eight segregation distortion regions (SDR). Most SDR identified in the F(1) populations were also identified in the F(2) population. Genotypic SD was primarily due to zygotic rather than allelic distortion, suggesting zygotic not gametic selection is the main cause of SD. On the F(2) linkage map, distorted markers in all SDR except two showed heterozygote excess. The severe SD in the F(2) population likely biased genetic distances among markers and possibly also marker ordering and could affect QTL mapping of agronomic traits. To reduce the effects of SD and non-fully informative markers, we suggest constructing linkage maps and conducting QTL mapping in advanced generation populations.

Mapping quantitative trait Loci using distorted markers

Quantitative trait locus (QTL) mapping is usually performed using markers that follow a Mendelian segregation ratio. We developed a new method of QTL mapping that can use markers with segregation distortion (non-Mendelian markers). An EM (expectation-maximization) algorithm is used to estimate QTL and SDL (segregation distortion loci) parameters. The joint analysis of QTL and SDL is particularly useful for selective genotyping. Application of the joint analysis is demonstrated using a real life data from a wheat QTL mapping experiment.

Method for the mapping of a female partial-sterile locus on a molecular marker linkage map

The female gametophyte is an absolutely essential structure for angiosperm reproduction, and female sterility has been reported in a number of crops. In this paper, a maximum-likelihood method is presented for estimating the position and effect of a female partial-sterile locus in a backcross population using the observed data of dominant or codominant markers. The ML solutions are obtained via Bailey's method. The process for the estimating of the recombination fractions and the viabilities of female gametes are described, and the variances of the estimates of the parameters are also presented. Application of the method is demonstrated using a set of simulated data. This method circumvents the problems of the traditional mapping methods for female sterile genes which were based on data from seed set or embryo-sac morphology and anatomy.

Mapping quantitative trait loci for binary trait in the F2:3 design

In the analysis of inheritance of quantitative traits with low heritability, an F(2:3) design that genotypes plants in F(2) and phenotypes plants in F(2:3) progeny is often used in plant genetics. Although statistical approaches for mapping quantitative trait loci (QTL) in the F(2:3) design have been well developed, those for binary traits of biological interest and economic importance are seldom addressed. In this study, an attempt was made to map binary trait loci (BTL) in the F(2:3) design. The fundamental idea was: the F(2) plants were genotyped, all phenotypic values of each F(2:3) progeny were measured for binary trait, and these binary trait values and the marker genotype informations were used to detect BTL under the penetrance and liability models. The proposed method was verified by a series of Monte-Carlo simulation experiments. These results showed that maximum likelihood approaches under the penetrance and liability models provide accurate estimates for the effects and the locations of BTL with high statistical power, even under of low heritability. Moreover, the penetrance model is as efficient as the liability model, and the F(2:3) design is more efficient than classical F(2) design, even though only a single progeny is collected from each F(2:3) family. With the maximum likelihood approaches under the penetrance and the liability models developed in this study, we can map binary traits as we can do for quantitative trait in the F(2:3) design.

Quantitative trait locus mapping can benefit from segregation distortion

Segregation distortion is a phenomenon that has been observed in many experimental systems. How segregation distortion among markers arises and its impact on mapping studies are the focus of this work. Segregation distortion of markers can be considered to arise from segregation distortion loci (SDL). I develop a theory of segregation distortion and show that the presence of only a few SDL can cause the entire chromosome to distort from Mendelian segregation. Segregation distortion is detrimental to the power of detecting quantitative trait loci (QTL) with dominance effects, but it is not always a detriment to QTL mapping for additive effects. When segregation distortion of a locus is a random event, the SDL is beneficial to QTL mapping approximately 44% of the time. If SDL are present and ignored, power loss can be substantial. A dense marker map can be used to ameliorate the situation, and if dense marker information is incorporated, power loss is minimal. However, other situations are less benign. A method that can simultaneously map QTL and SDL is discussed, maximizing both use of mapping resources and use by agricultural and evolutionary biologists.

Methodologies for segregation analysis and QTL mapping in plants

Most characters of biological interest and economic importance are quantitative traits. To uncover the genetic architecture of quantitative traits, two approaches have become popular in China. One is the establishment of an analytical model for mixed major-gene plus polygenes inheritance and the other the discovery of quantitative trait locus (QTL). Here we review our progress employing these two approaches. First, we proposed joint segregation analysis of multiple generations for mixed major-gene plus polygenes inheritance. Second, we extended the multilocus method of Lander and Green (1987), Jiang and Zeng (1997) to a more generalized approach. Our methodology handles distorted, dominant and missing markers, including the effect of linked segregation distortion loci on the estimation of map distance. Finally, we developed several QTL mapping methods. In the Bayesian shrinkage estimation (BSE) method, we suggested a method to test the significance of QTL effects and studied the effect of the prior distribution of the variance of QTL effect on QTL mapping. To reduce running time, a penalized maximum likelihood method was adopted. To mine novel genes in crop inbred lines generated in the course of normal crop breeding work, three methods were introduced. If a well-documented genealogical history of the lines is available, two-stage variance component analysis and multi-QTL Haseman-Elston regression were suggested; if unavailable, multiple loci in silico mapping was proposed.

Patterns of quantitative genetic variation in multiple dimensions

A fundamental question for both evolutionary biologists and breeders is the extent to which genetic correlations limit the ability of populations to respond to selection. Here I view this topic from three perspectives. First, I propose several nondimensional statistics to quantify the genetic variation present in a suite of traits and to describe the extent to which correlations limit their selection response. A review of five data sets suggests that the total variation differs substantially between populations. In all cases analyzed, however, the "effective number of dimensions" is less than two: more than half of the total genetic variation is explained by a single combination of traits. Second, I consider how patterns of variation affect the average evolutionary response to selection in a random direction. When genetic variation lies in a small number of dimensions but there are a large number of traits under selection, then the average selection response will be reduced substantially from its potential maximum. Third, I discuss how a low genetic correlation between male fitness and female fitness limits the ability of populations to adapt. Data from two recent studies of natural populations suggest this correlation can diminish or even erase any genetic benefit to mate choice. Together these results suggest that adaptation (in natural populations) and genetic improvement (in domesticated populations) may often be as much constrained by patterns of genetic correlation as by the overall amount of genetic variation.

Mapping quantitative trait loci from a single-tail sample of the phenotype distribution including survival data

A new effective Bayesian quantitative trait locus (QTL) mapping approach for the analysis of single-tail selected samples of the phenotype distribution is presented. The approach extends the affected-only tests to single-tail sampling with quantitative traits such as the log-normal survival time or censored/selected traits. A great benefit of the approach is that it enables the utilization of multiple-QTL models, is easy to incorporate into different data designs (experimental and outbred populations), and can potentially be extended to epistatic models. In inbred lines, the method exploits the fact that the parental mating type and the linkage phases (haplotypes) are known by definition. In outbred populations, two-generation data are needed, for example, selected offspring and one of the parents (the sires) in breeding material. The idea is to statistically (computationally) generate a fully complementary, maximally dissimilar, observation for each offspring in the sample. Bayesian data augmentation is then used to sample the space of possible trait values for the pseudoobservations. The benefits of the approach are illustrated using simulated data sets and a real data set on the survival of F(2) mice following infection with Listeria monocytogenes.

An EM algorithm for mapping segregation distortion loci

BACKGROUND

Chromosomal region that causes distorted segregation ratios is referred to as segregation distortion locus (SDL). The distortion is caused either by differential representation of SDL genotypes in gametes before fertilization or by viability differences of SDL genotypes after fertilization but before genotype scoring. In both cases, observable phenotypes are distorted for marker loci in the chromosomal region close to the SDL. Under the quantitative genetics model for viability selection by proposing a continuous liability controlling the viability of individual, a simplex algorithm has been used to search for the solution in SDL mapping. However, they did not consider the effects of SDL on the construction of linkage maps.

RESULTS

We proposed a multipoint maximum-likelihood method to estimate the position and the effects of SDL under the liability model together with both selection coefficients of marker genotypes and recombination fractions. The method was implemented via an expectation and maximization (EM) algorithm. The superiority of the method proposed under the liability model over the previous methods was verified by a series of Monte Carlo simulation experiments, together with a working example derived from the MAPMAKER/QTL software.

CONCLUSION

Our results suggested that the new method can serve as a powerful alternative to existing methods for SDL mapping. Under the liability model, the new method can simultaneously estimate the position and the effects of SDL as well as the recombinant fractions between adjacent markers, and also be used to probe into the genetic mechanism for the bias of uncorrected map distance and to elucidate the relationship between the viability selection and genetic linkage.

Modeling segregation distortion for viability selection. I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F(2) population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.

Testing for segregation distortion in genetic scoring data from backcross or doubled haploid populations

It is important that breeders have the means to assess genetic scoring data for segregation distortion because of its probable effect on the design of efficient breeding strategies. Scoring data is usually assessed for segregation distortion by separate nonindependent chi2 tests at each locus in a set of marker loci. This analysis gives the loci most affected by selection if it exists, but it cannot give a statistically correct test for the presence or absence of selection in a linkage group as a whole. I have used a combined test based on the statistic, which is the most significant P-value from the above tests, called the single locus test. I have also derived mathematically a new combined statistical test, the overall test, for segregation distortion that requires genetic scoring data for a single linkage group. This test also takes genetic linkage into account. Using a range of marker densities and population sizes, simulations were carried out, to compare the power of these two statistical tests to detect the effect of selection at one or two loci. The single locus test was always found to be more powerful than the overall test, but the single locus test required a more complicated P-value correction. For the single locus test, approximate correction factors for the P-values are given for a range of marker densities and genetic lengths.