Genetic Architecture Underlying Nascent Speciation-The Evolution of Eurasian Pigs under Domestication.

Speciation is a process whereby the evolution of reproductive barriers leads to isolated species. Although many studies have addressed large-effect genetic footprints in the advanced stages of speciation, the genetics of reproductive isolation in nascent stage of speciation remains unclear. Here, we show that pig domestication offers an interesting model for studying the early stages of speciation in great details. Pig breeds have not evolved the large X-effect of hybrid incompatibility commonly observed between "good species." Instead, deleterious epistatic interactions among multiple autosomal loci are common. These weak Dobzhansky-Muller incompatibilities confer partial hybrid inviability with sex biases in crosses between European and East Asian domestic pigs. The genomic incompatibility is enriched in pathways for angiogenesis, androgen receptor signaling and immunity, with an observation of many highly differentiated cis-regulatory variants. Our study suggests that partial hybrid inviability caused by pervasive but weak interactions among autosomal loci may be a hallmark of nascent speciation in mammals.

Discovery of a major QTL for root-knot nematode (Meloidogyne incognita) resistance in cultivated sweetpotato (Ipomoea batatas).

KEY MESSAGE: Utilizing a high-density integrated genetic linkage map of hexaploid sweetpotato, we discovered a major dominant QTL for root-knot nematode (RKN) resistance and modeled its effects. This discovery is useful for development of a modern sweetpotato breeding program that utilizes marker-assisted selection and genomic selection approaches for faster genetic gain of RKN resistance. The root-knot nematode [Meloidogyne incognita (Kofoid & White) Chitwood] (RKN) causes significant storage root quality reduction and yields losses in cultivated sweetpotato [Ipomoea batatas (L.) Lam.]. In this study, resistance to RKN was examined in a mapping population consisting of 244 progenies derived from a cross (TB) between 'Tanzania,' a predominant African landrace cultivar with resistance to RKN, and 'Beauregard,' an RKN susceptible major cultivar in the USA. We performed quantitative trait loci (QTL) analysis using a random-effect QTL mapping model on the TB genetic map. An RKN bioassay incorporating potted cuttings of each genotype was conducted in the greenhouse and replicated five times over a period of 10 weeks. For each replication, each genotype was inoculated with ca. 20,000 RKN eggs, and root-knot galls were counted ~62 days after inoculation. Resistance to RKN in the progeny was highly skewed toward the resistant parent, exhibiting medium to high levels of resistance. We identified one major QTL on linkage group 7, dominant in nature, which explained 58.3% of the phenotypic variation in RKN counts. This work represents a significant step forward in our understanding of the genetic architecture of RKN resistance and sets the stage for future utilization of genomics-assisted breeding in sweetpotato breeding programs.

The recombination landscape and multiple QTL mapping in a Solanum tuberosum cv. 'Atlantic'-derived F1 population.

There are many challenges involved with the genetic analyses of autopolyploid species, such as the tetraploid potato, Solanum tuberosum (2n = 4x = 48). The development of new analytical methods has made it valuable to re-analyze an F1 population (n = 156) derived from a cross involving 'Atlantic', a widely grown chipping variety in the USA. A fully integrated genetic map with 4285 single nucleotide polymorphisms, spanning 1630 cM, was constructed with MAPpoly software. We observed that bivalent configurations were the most abundant ones (51.0~72.4% depending on parent and linkage group), though multivalent configurations were also observed (2.2~39.2%). Seven traits were evaluated over four years (2006-8 and 2014) and quantitative trait loci (QTL) mapping was carried out using QTLpoly software. Based on a multiple-QTL model approach, we detected 21 QTL for 15 out of 27 trait-year combination phenotypes. A hotspot on linkage group 5 was identified with co-located QTL for maturity, plant yield, specific gravity, and internal heat necrosis resistance evaluated over different years. Additional QTL for specific gravity and dry matter were detected with maturity-corrected phenotypes. Among the genes around QTL peaks, we found those on chromosome 5 that have been previously implicated in maturity (StCDF1) and tuber formation (POTH1). These analyses have the potential to provide insights into the biology and breeding of tetraploid potato and other autopolyploid species.

Quantitative Trait Locus Mapping for Common Scab Resistance in a Tetraploid Potato Full-Sib Population.

Despite the negative impact of common scab (Streptomyces spp.) on the potato industry, little is known about the genetic architecture of resistance to this bacterial disease in the crop. We evaluated a mapping population (∼150 full sibs) derived from a cross between two tetraploid potatoes ('Atlantic' × B1829-5) in three environments (MN11, PA11, ME12) under natural common scab pressure. Three measures to common scab reaction, namely percentage of scabby tubers and disease area and lesion indices, were found to be highly correlated (>0.76). Because of the large environmental effect, heritability values were zero for all three traits in MN11, but moderate to high in PA11 and ME12 (∼0.44 to 0.79). We identified a single quantitative trait locus (QTL) for lesion index in PA11, ME12, and joint analyses on linkage group 3, explaining ∼22 to 30% of the total variation. The identification of QTL haplotypes and candidate genes contributing to disease resistance can support genomics-assisted breeding approaches in the crop.[Formula: see text] Copyright © 2021 The Author(s). This is an open access article distributed under the CC BY 4.0 International license.

Sequencing depth and genotype quality: accuracy and breeding operation considerations for genomic selection applications in autopolyploid crops.

KEY MESSAGE: Polypoid crop breeders can balance resources between density and sequencing depth, dosage information and fewer highly informative SNPs recommended, non-additive models and QTL advantages on prediction dependent on trait architecture. The autopolyploid nature of potato and sweetpotato ensures a wide range of meiotic configurations and linkage phases leading to complex gene-action and pose problems in genotype data quality and genomic selection analyses. We used a 315-progeny biparental F1 population of hexaploid sweetpotato and a diversity panel of 380 tetraploid potato, genotyped using different platforms to answer the following questions: (i) do polyploid crop breeders need to invest more for additional sequencing depth? (ii) how many markers are required to make selection decisions? (iii) does considering non-additive genetic effects improve predictive ability (PA)? (iv) does considering dosage or quantitative trait loci (QTL) offer significant improvement to PA? Our results show that only a small number of highly informative single nucleotide polymorphisms (SNPs; ≤ 1000) are adequate for prediction in the type of populations we analyzed. We also show that considering dosage information and models considering only additive effects had the best PA for most traits, while the comparative advantage of considering non-additive genetic effects and including known QTL in the predictive model depended on trait architecture. We conclude that genomic selection can help accelerate the rate of genetic gains in potato and sweetpotato. However, application of genomic selection should be considered as part of optimizing the entire breeding program. Additionally, since the predictions in the current study are based on single populations, further studies on the effects of haplotype structure and inheritance on PA should be studied in actual multi-generation breeding populations.

Quantitative trait loci and differential gene expression analyses reveal the genetic basis for negatively associated ß-carotene and starch content in hexaploid sweetpotato [Ipomoea batatas (L.) Lam.].

KEY MESSAGE: ß-Carotene content in sweetpotato is associated with the Orange and phytoene synthase genes; due to physical linkage of phytoene synthase with sucrose synthase, ß-carotene and starch content are negatively correlated. In populations depending on sweetpotato for food security, starch is an important source of calories, while ß-carotene is an important source of provitamin A. The negative association between the two traits contributes to the low nutritional quality of sweetpotato consumed, especially in sub-Saharan Africa. Using a biparental mapping population of 315 F1 progeny generated from a cross between an orange-fleshed and a non-orange-fleshed sweetpotato variety, we identified two major quantitative trait loci (QTL) on linkage group (LG) three (LG3) and twelve (LG12) affecting starch, ß-carotene, and their correlated traits, dry matter and flesh color. Analysis of parental haplotypes indicated that these two regions acted pleiotropically to reduce starch content and increase ß-carotene in genotypes carrying the orange-fleshed parental haplotype at the LG3 locus. Phytoene synthase and sucrose synthase, the rate-limiting and linked genes located within the QTL on LG3 involved in the carotenoid and starch biosynthesis, respectively, were differentially expressed in Beauregard versus Tanzania storage roots. The Orange gene, the molecular switch for chromoplast biogenesis, located within the QTL on LG12 while not differentially expressed was expressed in developing roots of the parental genotypes. We conclude that these two QTL regions act together in a cis and trans manner to inhibit starch biosynthesis in amyloplasts and enhance chromoplast biogenesis, carotenoid biosynthesis, and accumulation in orange-fleshed sweetpotato. Understanding the genetic basis of this negative association between starch and ß-carotene will inform future sweetpotato breeding strategies targeting sweetpotato for food and nutritional security.

Linkage map construction and QTL analysis for internal heat necrosis in autotetraploid potato.

KEY MESSAGE: A tetraploid potato population was mapped for internal heat necrosis (IHN) using the Infinium ® 8303 potato SNP array, and QTL for IHN were identified on chromosomes 1, 5, 9 and 12 that explained 28.21% of the variation for incidence and 25.3% of the variation for severity. This research represents a significant step forward in our understanding of IHN, and sets the stage for future research focused on testing the utility of these markers in additional breeding populations. Internal heat necrosis (IHN) is a significant non-pathogenic disorder of potato tubers and previous studies have identified AFLP markers linked to IHN susceptibility in the tetraploid, B2721 potato mapping population. B2721 consists of an IHN susceptible×resistant cross: Atlantic×B1829-5. We developed a next-generation SNP-based linkage map of this cross using the Infinium® 8303 SNP array and conducted additional QTL analyses of IHN susceptibility in the B2721 population. Using SNP dosage sensitive markers, linkage maps for both parents were simultaneously analyzed. The linkage map contained 3427 SNPs and totaled 1397.68 cM. QTL were detected for IHN on chromosomes 1, 5, 9, and 12 using LOD permutation thresholds and colocation of high LOD scores across multiple years. Genetic effects were modeled for each putative QTL. Markers associated with a QTL were regressed in models of effects for IHN incidence and severity for all years. In the full model, the SNP markers were shown to have significant effects for IHN (p < 0.0001), and explained 28.21% of the variation for incidence and 25.3% of the variation for severity. We were able to utilize SNP dosage information to identify and model the effects of putative QTL, and identify SNP loci associated with IHN resistance that need to be confirmed. This research represents a significant step forward in our understanding of IHN, and sets the stage for future research focused on testing the utility of these markers in additional breeding populations.

Quantitative trait loci influencing forking defects in an outbred pedigree of loblolly pine.

BACKGROUND: The use of wood as an industrial raw material has led to development of plantation forestry, in which trees are planted, managed, and harvested as crops. The productivity of such plantations often exceeds that of less-intensively-managed forests, and land managers have the option of choosing specific planting stock to produce specific types of wood for industrial use. Stem forking, or division of the stem into two or more stems of roughly equal size, is a character trait important in determining the quality of the stem for production of solid wood products. This trait typically has very low individual-tree heritability, but can be more accurately assessed in clonally-replicated plantings where each genotype is represented by several individual trees. We report results from a quantitative trait mapping experiment in a clonally-replicated full-sibling family of loblolly pine (Pinus taeda L.). RESULTS: Quantitative trait loci influencing forking defects were identified in an outbred full-sibling family of loblolly pine, using single-nucleotide polymorphism markers. Genetic markers in this family segregated either in 1:2:1 (F2 intercross-like segregation) or 1:1 ratio (backcross-like segregation). An integrated linkage map combining markers with different segregation ratios was assembled for this full-sib family, and a total of 409 SNP markers were mapped on 12 linkage groups, covering 1622 cM. Two and three trait loci were identified for forking and ramicorn branch traits, respectively, using the interval mapping method. Three trait loci were detected for both traits using multiple-trait analysis. CONCLUSIONS: The detection of three loci for forking and ramicorn branching in a multiple-trait analysis could mean that there are genes with pleiotropic effects on both traits, or that separate genes affecting different traits are clustered together. The detection of genetic loci associated with variation in stem quality traits in this study supports the hypothesis that marker-assisted selection can be used to decrease the rate of stem defects in breeding populations of loblolly pine.

Mapping epistatic quantitative trait loci.

BACKGROUND: How to map quantitative trait loci (QTL) with epistasis efficiently and reliably has been a persistent problem for QTL mapping analysis. There are a number of difficulties for studying epistatic QTL. Linkage can impose a significant challenge for finding epistatic QTL reliably. If multiple QTL are in linkage and have interactions, searching for QTL can become a very delicate issue. A commonly used strategy that performs a two-dimensional genome scan to search for a pair of QTL with epistasis can suffer from low statistical power and also may lead to false identification due to complex linkage disequilibrium and interaction patterns. RESULTS: To tackle the problem of complex interaction of multiple QTL with linkage, we developed a three-stage search strategy. In the first stage, main effect QTL are searched and mapped. In the second stage, epistatic QTL that interact significantly with other identified QTL are searched. In the third stage, new epistatic QTL are searched in pairs. This strategy is based on the consideration that most genetic variance is due to the main effects of QTL. Thus by first mapping those main-effect QTL, the statistical power for the second and third stages of analysis for mapping epistatic QTL can be maximized. The search for main effect QTL is robust and does not bias the search for epistatic QTL due to a genetic property associated with the orthogonal genetic model that the additive and additive by additive variances are independent despite of linkage. The model search criterion is empirically and dynamically evaluated by using a score-statistic based resampling procedure. We demonstrate through simulations that the method has good power and low false positive in the identification of QTL and epistasis. CONCLUSION: This method provides an effective and powerful solution to map multiple QTL with complex epistatic pattern. The method has been implemented in the user-friendly computer software Windows QTL Cartographer. This will greatly facilitate the application of the method for QTL mapping data analysis.

Merging pharmacometabolomics with pharmacogenomics using '1000 Genomes' single-nucleotide polymorphism imputation: selective serotonin reuptake inhibitor response pharmacogenomics.

OBJECTIVE: We set out to test the hypothesis that pharmacometabolomic data could be efficiently merged with pharmacogenomic data by single-nucleotide polymorphism (SNP) imputation of metabolomic-derived pathway data on a 'scaffolding' of genome-wide association (GWAS) SNP data to broaden and accelerate 'pharmacometabolomics-informed pharmacogenomic' studies by eliminating the need for initial genotyping and by making broader SNP association testing possible. METHODS: We previously genotyped 131 tag SNPs for six genes encoding enzymes in the glycine synthesis and degradation pathway using DNA from 529 depressed patients treated with citalopram/escitalopram to pursue a glycine metabolomics 'signal' associated with selective serotonine reuptake inhibitor response. We identified a significant SNP in the glycine dehydrogenase gene. Subsequently, GWAS SNP data were generated for the same patients. In this study, we compared SNP imputation within 200 kb of these same six genes with the results of the previous tag SNP strategy as a rapid strategy for merging pharmacometabolomic and pharmacogenomic data. RESULTS: Imputed genotype data provided greater coverage and higher resolution than did tag SNP genotyping, with a higher average genotype concordance between genotyped and imputed SNP data for '1000 Genomes' (96.4%) than HapMap 2 (93.2%) imputation. Many low P-value SNPs with novel locations within genes were observed for imputed compared with tag SNPs, thus altering the focus for subsequent functional genomic studies. CONCLUSION: These results indicate that the use of GWAS data to impute SNPs for genes in pathways identified by other 'omics' approaches makes it possible to rapidly and cost efficiently identify SNP markers to 'broaden' and accelerate pharmacogenomic studies.

Multiple trait multiple interval mapping of quantitative trait loci from inbred line crosses.

BACKGROUND: Although many experiments have measurements on multiple traits, most studies performed the analysis of mapping of quantitative trait loci (QTL) for each trait separately using single trait analysis. Single trait analysis does not take advantage of possible genetic and environmental correlations between traits. In this paper, we propose a novel statistical method for multiple trait multiple interval mapping (MTMIM) of QTL for inbred line crosses. We also develop a novel score-based method for estimating genome-wide significance level of putative QTL effects suitable for the MTMIM model. The MTMIM method is implemented in the freely available and widely used Windows QTL Cartographer software. RESULTS: Throughout the paper, we provide compelling empirical evidences that: (1) the score-based threshold maintains proper type I error rate and tends to keep false discovery rate within an acceptable level; (2) the MTMIM method can deliver better parameter estimates and power than single trait multiple interval mapping method; (3) an analysis of Drosophila dataset illustrates how the MTMIM method can better extract information from datasets with measurements in multiple traits. CONCLUSIONS: The MTMIM method represents a convenient statistical framework to test hypotheses of pleiotropic QTL versus closely linked nonpleiotropic QTL, QTL by environment interaction, and to estimate the total genotypic variance-covariance matrix between traits and to decompose it in terms of QTL-specific variance-covariance matrices, therefore, providing more details on the genetic architecture of complex traits.

From classical genetics to quantitative genetics to systems biology: modeling epistasis.

Gene expression data has been used in lieu of phenotype in both classical and quantitative genetic settings. These two disciplines have separate approaches to measuring and interpreting epistasis, which is the interaction between alleles at different loci. We propose a framework for estimating and interpreting epistasis from a classical experiment that combines the strengths of each approach. A regression analysis step accommodates the quantitative nature of expression measurements by estimating the effect of gene deletions plus any interaction. Effects are selected by significance such that a reduced model describes each expression trait. We show how the resulting models correspond to specific hierarchical relationships between two regulator genes and a target gene. These relationships are the basic units of genetic pathways and genomic system diagrams. Our approach can be extended to analyze data from a variety of experiments, multiple loci, and multiple environments.

A joint association test for multiple SNPs in genetic case-control studies.

For a dense set of genetic markers such as single nucleotide polymorphisms (SNPs) on high linkage disequilibrium within a small candidate region, a haplotype-based approach for testing association between a disease phenotype and the set of markers is attractive in reducing the data complexity and increasing the statistical power. However, due to unknown status of the underlying disease variant, a comprehensive association test may require consideration of various combinations of the SNPs, which often leads to severe multiple testing problems. In this paper, we propose a latent variable approach to test for association of multiple tightly linked SNPs in case-control studies. First, we introduce a latent variable into the penetrance model to characterize a putative disease susceptible locus (DSL) that may consist of a marker allele, a haplotype from a subset of the markers, or an allele at a putative locus between the markers. Next, through using of a retrospective likelihood to adjust for the case-control sampling ascertainment and appropriately handle the Hardy-Weinberg equilibrium constraint, we develop an expectation-maximization (EM)-based algorithm to fit the penetrance model and estimate the joint haplotype frequencies of the DSL and markers simultaneously. With the latent variable to describe a flexible role of the DSL, the likelihood ratio statistic can then provide a joint association test for the set of markers without requiring an adjustment for testing of multiple haplotypes. Our simulation results also reveal that the latent variable approach may have improved power under certain scenarios comparing with classical haplotype association methods.

Current progress on statistical methods for mapping quantitative trait loci from inbred line crosses.

Tremendous progress has been made in recent years on developing statistical methods for mapping quantitative trait loci (QTL) from crosses of inbred lines. Most of the recent research is focused on strategies for mapping multiple-QTL and associated model selection procedures and criterion. We review the progress of research in this area on one trait and multiple traits by maximum likelihood and Bayesian methods.

Unraveling the Hexaploid Sweetpotato Inheritance Using Ultra-Dense Multilocus Mapping.

The hexaploid sweetpotato (Ipomoea batatas (L.) Lam., 2n = 6x = 90) is an important staple food crop worldwide and plays a vital role in alleviating famine in developing countries. Due to its high ploidy level, genetic studies in sweetpotato lag behind major diploid crops significantly. We built an ultra-dense multilocus integrated genetic map and characterized the inheritance system in a sweetpotato full-sib family using our newly developed software, MAPpoly. The resulting genetic map revealed 96.5% collinearity between I. batatas and its diploid relative I. trifida We computed the genotypic probabilities across the whole genome for all individuals in the mapping population and inferred their complete hexaploid haplotypes. We provide evidence that most of the meiotic configurations (73.3%) were resolved in bivalents, although a small portion of multivalent signatures (15.7%), among other inconclusive configurations (11.0%), were also observed. Except for low levels of preferential pairing in linkage group 2, we observed a hexasomic inheritance mechanism in all linkage groups. We propose that the hexasomic-bivalent inheritance promotes stability to the allelic transmission in sweetpotato.

Assembly of whole-chromosome pseudomolecules for polyploid plant genomes using outbred mapping populations.

Despite advances in sequencing technologies, assembly of complex plant genomes remains elusive due to polyploidy and high repeat content. Here we report PolyGembler for grouping and ordering contigs into pseudomolecules by genetic linkage analysis. Our approach also provides an accurate method with which to detect and fix assembly errors. Using simulated data, we demonstrate that our approach is of high accuracy and outperforms three existing state-of-the-art genetic mapping tools. Particularly, our approach is more robust to the presence of missing genotype data and genotyping errors. We used our method to construct pseudomolecules for allotetraploid lawn grass utilizing PacBio long reads in combination with restriction site-associated DNA sequencing, and for diploid Ipomoea trifida and autotetraploid potato utilizing contigs assembled from Illumina reads in combination with genotype data generated by single-nucleotide polymorphism arrays and genotyping by sequencing, respectively. We resolved 13 assembly errors for a published I. trifida genome assembly and anchored eight unplaced scaffolds in the published potato genome.

Multiple QTL Mapping in Autopolyploids: A Random-Effect Model Approach with Application in a Hexaploid Sweetpotato Full-Sib Population.

In developing countries, the sweetpotato, Ipomoea batatas (L.) Lam. [Formula: see text], is an important autopolyploid species, both socially and economically. However, quantitative trait loci (QTL) mapping has remained limited due to its genetic complexity. Current fixed-effect models can fit only a single QTL and are generally hard to interpret. Here, we report the use of a random-effect model approach to map multiple QTL based on score statistics in a sweetpotato biparental population ('Beauregard' × 'Tanzania') with 315 full-sibs. Phenotypic data were collected for eight yield component traits in six environments in Peru, and jointly adjusted means were obtained using mixed-effect models. An integrated linkage map consisting of 30,684 markers distributed along 15 linkage groups (LGs) was used to obtain the genotype conditional probabilities of putative QTL at every centiMorgan position. Multiple interval mapping was performed using our R package QTLpoly and detected a total of 13 QTL, ranging from none to four QTL per trait, which explained up to 55% of the total variance. Some regions, such as those on LGs 3 and 15, were consistently detected among root number and yield traits, and provided a basis for candidate gene search. In addition, some QTL were found to affect commercial and noncommercial root traits distinctly. Further best linear unbiased predictions were decomposed into additive allele effects and were used to compute multiple QTL-based breeding values for selection. Together with quantitative genotyping and its appropriate usage in linkage analyses, this QTL mapping methodology will facilitate the use of genomic tools in sweetpotato breeding as well as in other autopolyploids.

Quantitative trait loci mapping and the genetic basis of heterosis in maize and rice.

Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive x additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software.

Multiple interval mapping for gene expression QTL analysis.

To find the correlations between genome-wide gene expression variations and sequence polymorphisms in inbred cross populations, we developed a statistical method to claim expression quantitative trait loci (eQTL) in a genome. The method is based on multiple interval mapping (MIM), a model selection procedure, and uses false discovery rate (FDR) to measure the statistical significance of the large number of eQTL. We compared our method with a similar procedure proposed by Storey et al. and found that our method can be more powerful. We identified the features in the two methods that resulted in different statistical powers for eQTL detection, and confirmed them by simulation. We organized our computational procedure in an R package which can estimate FDR for positive findings from similar model selection procedures. The R package, MIM-eQTL, can be found at http://www.statgen.ncsu.edu/~wzou/MIM.eQTL.html .

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium.

BACKGROUND: Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F(infinity) genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F(infinity) model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD). RESULTS: In this paper, we further explore the differences and links between the F(infinity) and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the Finfinity models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F(infinity) model. A new way of linking the Cockerham and F(infinity) model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F(infinity) models are applied. CONCLUSION: The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F(infinity) regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F(infinity) model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F(infinity) model can then be calculated by translating formulas derived for the Cockerham models.