The PiGMaP consortium linkage map of the pig (Sus scrofa)

A linkage map of the porcine genome has been developed by segregation analysis of 239 genetic markers. Eighty-one of these markers correspond to known genes. Linkage groups have been assigned to all 18 autosomes plus the X Chromosome (Chr). As 69 of the markers on the linkage map have also been mapped physically (by others), there is significant integration of linkage and physical map data. Six informative markers failed to show linkage to these maps. As in other species, the genetic map of the heterogametic sex (male) was significantly shorter (16.5 Morgans) than the genetic map of the homogametic sex (female) (21.5 Morgans). The sex-averaged genetic map of the pig was estimated to be 18 Morgans in length. Mapping information for 61 Type I loci (genes) enhances the contribution of the pig gene map to comparative gene mapping. Because the linkage map incorporates both highly polymorphic Type II loci, predominantly microsatellites, and Type I loci, it will be useful both for large experiments to map quantitative trait loci and for the subsequent isolation of trait genes following a comparative and candidate gene approach.     

Evolutionary responses of foraging-related traits in unstable predator–prey systems

The evolutionary responses of predators to prey and of prey to predators are analysed using models for the dynamics of a quantitative trait that determines the capture rate of prey by an average searching predator. Unlike previous investigations, the analysis centres on models and/or parameter values for which the two-species equilibrium is locally unstable. The instability in some models is driven by the predators non-linear functional response to prey; in other models, the cycles are a direct consequence of evolutionary response to selection acting on the trait. When the values of predator and prey traits combine multiplicatively to determine the capture rate, the predators trait shows only a transient response to changes in the preys trait in stable systems. However, when the population densities exhibit sustained oscillations, predators often evolve an increased long-term mean capture rate in response to an increased prey escape ability. Under the multiplicative model, prey in stable systems always evolve increased escape ability in response to an increased predator capture a     

Selective genotyping for determination of linkage between a marker locus and a quantitative trait locus

Summary Selective genotyping is the term used when the determination of linkage between marker loci and quantitative trait loci (QTL) affecting some particular trait is carried out by genotyping only individuals from the high and low phenotypic tails of the entire sample population. Selective genotyping can markedly decrease the number of individuals genotyped for a given power at the expense of an increase in the number of individuals phenotyped. The optimum proportion of individuals genotyped from the point of view of minimizing costs for a given experimental power depends strongly on the cost of completely genotyping an individual for all of the markers included in the experiment (including the costs of obtaining a DNA sample) relative to the cost of rearing and trait evaluation of an individual. However, in single trait studies, it will almost never be useful to genotype more than the upper and lower 25% of a population. It is shown that the observed difference in quantitative trait values associated with alternative marker genotypes in the selected population can be much greater than the actual gene effect at the quantitative trait locus when the entire population is considered. An expression and a figure is provided for converting observed differences under selective genotyping to actual gene effects.     

Quantitative analysis of outward rectifying K+ channel currents in guard cell protoplasts fromVicia faba

Summary A quantitative analysis of the time and voltage dependence of outward-rectifying K⁺ currents ( ) in guard cells fromVicia faba is described using the whole-cell patch-clamp technique. After step depolarizations from –75 mV to potentials positive to –40 mV, time-dependent outward currents were produced, which have recently been identified as K⁺ channel currents. This K⁺ current was characterized according to its time dependence and its steady-state activation. could be described in terms of a Hodgkin-Huxley type conductance. Activation of the current in time was sigmoid and was well fitted by raising the activation variable to the second power. Deactivating tail currents were single exponentials, which suggests that only one conductance underlies this slow outward K⁺ current. Rates of channel closing were strongly dependent on the membrane potential, while rates of channel opening showed only limited voltage dependence leading to a highly asymmetric voltage dependence for channel closing and opening. The presented analysis provides a quantitative basis for the understanding of channel gating and channel functions in plant cells.     

Comparative mapping in F2∶3 and F6∶7 generations of quantitative trait loci for grain yield and yield components in maize

This study was conducted to compare maize quantitative trait loci (QTL) detection for grain yield and yield components in F₂₃ and F₆₇ recombinant inbred (RI) lines from the same population. One hundred and eighty-six F₆₇ RIs from a Mo17×H99 population were grown in a replicated field experiment and analyzed at 101 loci detected by restriction fragment length polymorphisms (RFLPs). Single-factor analysis of variance was conducted for each locus-trait combination to identify QTL. For grain yield, 6 QTL were detected accounting for 22% of the phenotypic variation. A total of 63 QTL were identified for the seven grain yield components with alleles from both parents contributing to increased trait values. Several genetic regions were associated with more than one trait, indicating possible linked and/or pleiotropic effects. In a comparison with 150 F₂₃ lines from the same population, the same genetic regions and parental effects were detected across generations despite being evaluated under diverse environmental conditions. Some of the QTL detected in the F₂₃ seem to be dissected into multiple, linked QTL in the F₆₇ generation, indicating better genetic resolution for QTL detection with RIs. Also, genetic effects at QTL are smaller in the F₆₇ generation for all traits.Abbreviations RFLPs Restriction fragment length polymorphisms - QTL quantitative trait loci - RIs recombinant inbreds Journal Paper no. J-16261 of the Iowa Agric and Home Economics Exp Stn Project no. 3134     

Identification and mapping of cleistogamy genes in barley

Cleistogamy is a closed type of flowering with ensured self-pollination and an important trait to study evolutionary development in flower organs, reproduction systems, gene flow, and disease control. Still, very limited information is available about the genetic control and regulatory mechanism of this trait in barley. In this work, from the eight crosses between cleistogamous and chasmogamous accessions, five crosses generated chasmogamous F₁ plants and their F₂ plants segregated as 3 chasmogamous:1 cleistogamous, whereas three crosses generated cleistogamous F₁ plants, and their F₂ plants segregated as 1 chasmogamous:3 cleistogamous. Although a single gene was responsible for the control of cleistogamy in these two groups of crosses, the direction of dominance was opposite, suggesting two genes, cly1 and Cly2, for the genetic control of cleistogamy in barley. Epistatic type of gene interaction between the two loci was detected. In the analysis of 99 recombinant inbred lines of Azumamugi × Kanto Nakate Gold and doubled haploid lines of Harrington × Mikamo Golden, where in both crosses F₁ was chasmogamous, the cly1 locus has been mapped on chromosome 2HL. Using the analysis of the F₂ population of Misato Golden and Satsuki Nijo where F₁ was cleistogamous, the Cly2 locus was mapped in the same region of chromosome 2HL. Because the cly1 and Cly2 loci were mapped in the same region in these three different mapping populations, it was concluded that the expression of cleistogamy is under the control of two tightly linked genes or different alleles of the same gene.     

Effects of root temperature on uptake of nitrate and ammonium ions by barley grown in flowing-solution culture

Summary Barley plants (Hordeum vulgare L.) grown from seed for 28 days in flowing solution culture were subjected to different root temperatures (3, 5, 7, 9, 11, 13, 17, 25°C) for 14 days with a common air temperature of 25/15°C (day/night). Uptake of NH₄ and NO₃ ions was monitored separately and continuously from solutions maintained at 10 M NH₄NO₃ and pH 6.0. Effects of root temperature on unit absorption rate , flux and inflow were compared. After 5 days , and increased with temperature over the range 3–11°C for NH₄ ions and over the range 3–13°C for NO₃ ions, with little change for either ion above these temperatures. Q₁₀ temperature coefficients for NH₄ ions (3–13°C) were 1.9, 1.7 and 1.6 for , and respectively, the corresponding values for NO₃ ions being 5.0, 4.5 and 4.6. For both ions, , and changed with time as did their temperature dependence over the range 3–25°C, suggesting that rates of ontogenetic development and the extent of adaptation to temperature may have varied among treatments.     

Quantitative resistance to barley leaf stripe (Pyrenophora graminea) is dominated by one major locus

A major gene underlying quantitative resistance of barley against Pyrenophora graminea, a seedborne pathogen causing leaf stripe, was mapped with molecular markers in a barley doubled haploid (DH) population derived from the cross Proctor x Nudinka. This quantitative trait locus (QTL) accounts for r ²= 58.5% and was mapped on barley chromosome 1, tightly linked to the naked gene. A second resistance QTL accounting for 29.3% of the variation in the trait was identified on the P arm of barley chromosome 2. Another two minor QTLs were detected by further analysis. None of the QTLs was found in the barley chromosome 2 Vada region studied by Giese et al. (1993).     

Analysis of allozymic and quantitative variation produced by artificial selection in Drosophila melanogaster

In order to study a possible connection between allozymic and quantitative variation in D. melanogaster, three selection experiments were carried out, using founder strains of known genetic and chromosomal composition.The Adh and Gpdh-1 enzyme loci have been used as genetic markers and the maximum wing length has been the quantitative trait chosen. Two selected lines (high and low) were maintained and also one without selection (drift), to estimate the effect of random fluctuation on gene frequency variation. The allozymic variation was analysed by means of a polynomial regression, and a normal linear model allowed to make pairwise comparisons.The allelic combination ((F), A(-)) was favoured in the low lines of the selection experiments; the selection acted in favour of homozygotes, with a correlated loss of genetic homoeostasis. The similar behaviour of the drift and the control lines shows that random fluctuations in the gene frequencies in selected lines are negligible.     

QTL analysis of horticultural traits differentiating the cultivated tomato from the closely related species Lycopersicon pimpinellifolium

Molecular markers were used to map and characterize quantitative trait loci (QTLs) for several characters of agronomic and biological importance in an interspecific backcross of tomato. The parents of the cross were an elite processing inbred Lycopersicon esculentum cv M82-1-7 and the closely related red-fruited wild species L. pimpinellifolium (LA1589). A total of 257 BC₁ plants were grown under field conditions in Ithaca, New York and scored for 19 quantitative traits. A genetic linkage map was constructed for the same population using 115 RFLP, 3 RAPD and 2 morphological markers that spanned 1,279 cM of the tomato genome with an average interval length of 10.7 cM. A minimum of 54 putatively significant QTLs (P<0.001; LOD> 2.4) were detected for all characters with a range of 1–7 QTLs detected per character. Of the total 54 QTLs 11% had alleles with effects opposite to those predicted by the parental phenotypes. The percentage of phenotypic variation associated with single QTLs ranged from 4% to 47%. Multilocus analysis showed that the cumulative action of all QTLs detected for each trait accounted for 12–59% of the phenotypic variation. The difference in fruit weight was controlled largely by a single major QTL (fw2.2). Digenic epistasis was not evident. Several regions of the genome (including the region near sp on chromosome 6) showed effects on more than one trait. Implications for variety improvement and inferences about the domestication of the cultivated tomato are discussed.     

Determining the linkage of quantitative trait loci to RFLP markers using extreme phenotypes of recombinant inbreds of soybean (Glycine max L. Merr.)

An experimental test is described for linkages between RFLP markers and quantitative trait loci (QTL). Two hundred and eighty-four F₇-derived recombinant inbred lines (RIL) obtained from crossing the soybean cultivars (Glycine max L. Merr.) Minsoy and Noir 1 were evaluated for maturity, plant height, lodging, and seed yield. RIL exhibiting an extreme phenotype for each trait (earliest and latest plants for maturity, etc.) were selected, and two bulked DNA samples were prepared for each trait. A Southern transfer of the digested bulked DNA was hybridized with restriction fragement length polymorphism (RFLP) probes, and linkages with QTL were established by quantitating the amount of radioactive probe that bound to fragments defining alternative parental RFLP alleles. When an RFLP marker was linked to a QTL, one parental allele predominated in the bulked DNA from a particular phenotype; the other allele was associated with the opposite phenotype. When linkage was absent, radioactivity was associated equally with both alleles for a given phenotype (or with both phenotypes for a given allele). These results confirmed RFLP-QTL associations previously discovered by interval mapping on a smaller segregating population from the same cross. New linkages to QTL were also verified.     

Origin of genetic variation: regulation of genetic recombination in the higher organisms — a theory

Summary Recent studies in the fungi, particularly Neurospora and Schizophyllum, have revealed a number of genetic features which, viewed in conjunction with earlier observations on other organisms, form a pattern, or model, which appears to be basic to the control of recombination in all eukaryotes, including higher organisms. It is assumed that the control is exercised on mechanisms that produce new alleles through recombination, as understood in broad terms and including such a likely phenomenon as gene conversion, which may or may not involve crossing-over, as well as equal and unequal crossing-over. The recombination may thus occur between alleles in either the homozygous or heterozygous condition. In the model, regulatory genes and breeding behaviour are integrated into one self-regulatory system controlling the production of new genetic variation.The model is based on the following five general features, largely substantiated by the results in Neurospora and Schizophyllum: 1) The frequency of recombination in a particular chromosomal region is controlled by specific regulatory genes (rec). 2) There may be a number of such specific, regulatory genes responsible for recombination in a given region. 3) A rec. locus may influence recombination in more than one region. 4) The regulatory genes have no specific physical relationship with the region(s) they control, and are usually located at random in the genome. 5) Of the allelic forms of the regulatory genes it is always the dominant gene which suppresses recombination and the recessive gene which increases recombination. The rec system is epistatic to other genetic elements jointly involved in the overall control of recombination in a specific region. It is suggested that usually the control of recombination in a given region is exercised, cumulatively, by the balance of the dominant and recessive genes of the specific rec loci in the organism. Outbreeding, with the associated high heterozygosity of the regulatory rec loci, virtually switches off recombination, producing few new variations. Inbreeding produces homozygosity of these loci, resulting in certain individuals which will have a considerable number of their regulatory loci in the homozygous recessive condition and in which recombination will be switched on, producing new variation at a high frequency. Inbreeding is thus an integrated, evolutionary system of considerable importance, and is not a degenerate dead end, as many investigators have previously thought.The model has another compensatory function in evolution. In major loci, or in an operon, where there are structural genes and closely linked operator genes, as exemplified by the S locus, there are indications that the present model is concerned with the regulation of both structural and operator genes. The consequences of the model in the two classes of genes, however, are in direct contrast to each other: High heterozygosity which is instrumental in switching off recombination, and which is therefore helpful in maintaining stability in the structural gene, is conducive to functional variation of the operator gene; and high homozygosity, which is instrumental in switching on recombination, and which is therefore helpful in producing variation in the structural gene, is conducive to the stability of the operator gene.This model of the control of genetic variation in a specific chromosomal region is significant in development as well as in evolution, and throws light on a number of hitherto intractable problems peculiar to the higher organisms. For example, the model is helpful in explaining: 1) the origin of new self-incompatibility alleles in the flowering plants; 2) the impressive speciation in the waif flora (and fauna) of the oceanic islands; 3) the presence of high genetic variability in inbreeding species of plants; 4) environmentally-induced heritable variation in certain plants; and 5) the genetic mechanism of antibody diversity in animals.     

Contribution of a plasma membrane redox system to the superoxide production by wheat root cells

Summary Wound stress activated wheat root cells to produce oxygen radicals. The production was accompanied by an increased permeability for potassium ions and a depolarization of the plasma membrane. Various electron donors, such as the nonpenetrating donor potassium ferrocyanide as well as NADH and NADPH, caused the amplification of superoxide production by root cells. The -generating system in wheat root cells was found to be considerably sensitive to diphenylene iodonium, which is generally considered as a suicide inhibitor of neutrophil NADPH oxidase, and to other inhibitors of flavoprotein activity, chlorpromazine and quinine. The xenobiotic compound amidopyrine caused activation of the -generating system, which was depressed by DPI. The -generating system in root cells was shown to be significantly dependent on calcium content. Calcium loading of the root cells induced a powerful increase of the superoxide release. Data obtained indicate that superoxide generation is one of the early events of the wound stress response. Redox systems of the plasma membrane may be involved in the superoxide production in response to wound stress and detoxification of xenobiotic compounds in root cells.Abbreviations DPI diphenylene iodonium - MP membrane potential - superoxide anion radical - ROS reactive-oxygen species - SOD superoxide dismutase     

Functional association between malting quality trait components and cDNA array based expression patterns in barley (Hordeum vulgare L.)

We developed an approach for relating differences in gene expression to the phenotypic variation of a trait of interest. This allows the identification of candidate genes for traits that display quantitative variation. To validate the principle, gene expression was monitored on a cDNA array with 1400 ESTs to identify genes involved in the variation of the complex trait malting quality in barley. RNA profiles were monitored during grain germination in a set of 10 barley genotypes that had been characterized for 6 quality-associated trait components. The selection of the candidate genes was achieved via a correlation of dissimilarity matrices that were based on (i) trait variation and (ii) gene expression data. As expected, a comparison based on the complete set of differentially-expressed genes did not reveal any correlation between the matrices, because not all genes that show differential expression between the 10 cultivars are responsible for the observed differences in malting quality. However, by iteratively taking out one gene (with replacement) and re-computing the correlation, those genes that are positively contributing to the correlation could be identified. Using this procedure between 17 and 30 candidate genes were identified for each of the six malting parameters analysed. In addition to genes of unknown function, the list of candidates contains well-known malting-related genes. Five out of eight mapped candidate genes display linkage to known QTLs for malting quality traits. The described functional association strategy may provide an efficient link between functional genomics and plant breeding.     

Identification of RAPD markers linked to the loci controlling erucic acid level in rapeseed

The recent development of the industrial use of rapeseed oil rich in erucic acid has led to increased interest in the improvement of the high-erucic-acid (50–60%) varieties and to research towards genotypes containing a very high erucic acid content. This trait is controlled by two genes with additive effects. The low-erucic-acid trait was relatively easily introduced through backcrosses into various backgrounds because the zero-erucic-acid homozygotes were clearly identified in the segregating populations. To select for high erucic acid level is more difficult because of the partial overlap of the high-erucic-acid homozygous class and the intermediate one, containing heterozygotes. In order to help conventional breeding, RAPD markers were used to map the two genes involved in determining the erucic acid content in a doubled haploid progeny derived from a low x high erucic acid F1 hybrid. The two genes were successfully localized in two independent linkage group, through a QTL approach. A close association was found between individual plant genotypes and the erucic acid content of the doubled haploid progeny, and it was shown that the two genes do not contribute uniformly to the C22:1 level. The value of molecular gene mapping of such a trait in a conventional breeding programme is discussed.Abbreviations BSA bulked segregant analysis - DH doubled haploid - NIL near-isogenic lines - QTL quantitative trait locus - C22:1 erucic acid - TAG triacyl glycerol - SCAR sequence characterized amplified region     

Association analysis for udder health based on SNP-panel and sequence data in Danish Holsteins

Background

The sensitivity of genome-wide association studies for the detection of quantitative trait loci (QTL) depends on the density of markers examined and the statistical models used. This study compares the performance of three marker densities to refine six previously detected QTL regions for mastitis traits: 54 k markers of a medium-density SNP (single nucleotide polymorphism) chip (MD), imputed 777 k markers of a high-density SNP chip (HD), and imputed whole-genome sequencing data (SEQ). Each dataset contained data for 4496 Danish Holstein cattle. Comparisons were performed using a linear mixed model (LM) and a Bayesian variable selection model (BVS).

Results

After quality control, 587, 7825, and 78 856 SNPs in the six targeted regions remained for MD, HD, and SEQ data, respectively. In general, the association patterns between SNPs and traits were similar for the three marker densities when tested using the same statistical model. With the LM model, 120 (MD), 967 (HD), and 7209 (SEQ) SNPs were significantly associated with mastitis, whereas with the BVS model, 43 (MD), 131 (HD), and 1052 (SEQ) significant SNPs (Bayes factor > 3.2) were observed. A total of 26 (MD), 75 (HD), and 465 (SEQ) significant SNPs were identified by both models. In addition, one, 16, and 33 QTL peaks for MD, HD, and SEQ data were detected according to the QTL intensity profile of SNP bins by post-analysis of the BVS model.

Conclusions

The power to detect significant associations increased with increasing marker density. The BVS model resulted in clearer boundaries between linked QTL than the LM model. Using SEQ data, the six targeted regions were refined to 33 candidate QTL regions for udder health. The comparison between these candidate QTL regions and known genes suggested that NPFFR2, SLC4A4, DCK, LIFR, and EDN3 may be considered as candidate genes for mastitis susceptibility.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0129-1) contains supplementary material, which is available to authorized users.     

Body temperatures during rest and exercise in residents and sojourners in hot climate

Rectal (T_re), mean skin temperature ( _sk) and sweating rate ( ) were measured in 4 residents of temperate climate under acute moderate heat exposure (designated EE in such an experimental situation), after 3 weeks in India (designated as EI) and in 8 Indian residents (designated as II) both at rest and during submaximal exercises at 2 different intensities. At rest, T_re is higher in EI (37.6°C) than in EE (36.8°C, P<0.01) and reaches 37.8°C in II. At the end of exercise, the increment in T_re seems to depend on work load only and to be independent of thermal environment; S follows a similar pattern in the 3 groups of subjects: _sk is altered neither by exercise nor acclimatization. Under chronic heat exposure compared to acute conditions: (1) identical is achieved with higher T_re and similar _sk so that the linear relationships vs T_re is shifted to the right. (2) the T_re — _sk difference is greater at rest and during exercise: hence, skin blood flow, calculated from heat balance equation diminishes. In hot climate, a rise in T_re seems to be an adaptive response which allows the body to reduce skin blood flow.     

Effects of short term pollution on the level of fluctuating asymmetry – a case study using damselflies

Fluctuating asymmetry (FA), a measure of developmental stability, has been suggested as a monitoring tool for environmental pollution. However, there have been few investigations into the effects of short term pollution on the level of FA. This paper explores effects of exposing late instar larvae to short term pollution on the level of FA in the wings of adult damselflies. In these insects FA in wing length and in cell patterns have different windows of opportunity in relation to environmental stress. If increased environmental stress is applied after the window of opportunity of one trait had closed, while the window of the other trait was still open then the level of FA of the first trait should not be altered whereas that of the latter should increase. If short term pollution killed part of a population, symmetrical individuals (low FA) should survive better than highly asymmetrical ones, because FA reflects the overall ability of an individual to cope with stress. If the pollution event occurred at a time when the level of FA was already fixed, the level of FA of the remaining population should be lower than that in controls. An experiment was carried out, using 10 artificial ponds, each holding a population of larvae of the damselfly Xanthocnemis zealandica (McLachlan). Damselfly larvae were exposed to carbaryl at a nominal concentration of 100 g l^–1, which reduced emergence success after 10–20 days by ca. 50%. Based on laboratory experiments, it was assumed that despite the high mortality, the short exposure to carbaryl late in the last instar would ensure that the wing cell patterns of the damselflies were not altered by the increased stress. The level of FA in wing length increased in the damselflies surviving the exposure to carbaryl but the level of FA in cell patterns did not differ significantly between the treatment and the control. The effects of differential mortality, as well as the effects of pollution, on the level of FA in traits with different windows of opportunity need further investigation.     

Genetic Linkage Maps of the Guppy (Poecilia reticulata): Assignment of RAPD Markers to Multipoint Linkage Groups

Genetic linkage maps of the guppy (Poecilia reticulata) were constructed from independent crosses between the Tuxedo strain and a feral line (Wildtype). Segregation patterns of random amplified polymorphic DNA (RAPD) markers and phenotypic markers were investigated in F₂ offspring of Tuxedo × Wildtype and Wildtype × Tuxedo crosses. Among the 300 and 276 RAPD markers scored for the respective crosses, linkages were identified for 230 and 212, respectively. The Tuxedo × Wildtype and Wildtype × Tuxedo maps spanned 2100 Kosambi centiMorgans (cM_K) and 1900 cM_K, respectively, in 28 linkage groups. Average marker resolution was 10 cM_K. Genome length was estimated at 4410 cM_K and 4060 cM_K for the respective crosses, with an average physical distance of 166 kbp/cM_K. Several RAPD markers were closely linked to or mapped onto the loci for the sex-determining region (SdR), and the sex-linked black caudal-peduncle (Bcp) and red tail (Rdt) genes. These primary linkage maps are the initial step toward the construction of a composite high-density map to facilitate map-based cloning and marker-assisted selection of quantitative trait loci that are essential for the development of comprehensive breeding programs for the guppy.     

Statistical analysis of a linkage experiment in barley involving quantitative trait loci for height and ear-emergence time and two genetic markers on chromosome 4

Summary The quantitative traits height and ear-emergence date were analyzed in the F₂ progeny of a cross between a tall winter barley cultivar (Gerbel) and a short spring barley cultivar (Heriot). The trait distributions were found to be related to the genotypes at two biochemical loci, -amylase (Bmy1) and water-soluble protein (Wsp3), which are known to lie on the long arm of chromosome 4. Linkages between each trait and the markers were investigated using normal mixture models. The two parental phenotypes and the heterozygote phenotype of Bmy1 were distinguishable so the model could be used directly to estimate linkage between Bmy1 and a quantitative trait locus (QTL) for height (Height). The Gerbel homozygote and heterozygote phenotype of Wsp3 could not be distinguished and the model was adapted accordingly. The proportion of plants requiring vernalization was consistent with control by two independent genes acting epistatically, and a normal mixture model based on a two-gene hypothesis was fitted to the distribution of ear-emergence date to estimate linkage between the marker loci and a QTL for ear-emergence date (Vrn1). The parameters of each model were the recombination fraction between the marker locus and the QTL and the means and standard deviations associated with each QTL genotype; these were estimated by maximum likelihood. The fitted distributions correspond well to those observed and the order of the loci along the chromosome is inferred to be Height — Vrn1 — Bmy1 — Wsp3, with Wsp3 being the most distal.