Joint modeling of additive and non-additive genetic line effects in single field trials

A statistical approach is presented for selection of best performing lines for commercial release and best parents for future breeding programs from standard agronomic trials. The method involves the partitioning of the genetic effect of a line into additive and non-additive effects using pedigree based inter-line relationships, in a similar manner to that used in animal breeding. A difference is the ability to estimate non-additive effects. Line performance can be assessed by an overall genetic line effect with greater accuracy than when ignoring pedigree information and the additive effects are predicted breeding values. A generalized definition of heritability is developed to account for the complex models presented.     

Something Old and Something New: Wedding Recombinant Inbred Lines with Traditional Line Cross Analysis Increases Power to Describe Gene Interactions

In this paper we present a novel approach to quantifying genetic architecture that combines recombinant inbred lines (RIL) with line cross analysis (LCA). LCA is a method of quantifying directional genetic effects (i.e. summed effects of all loci) that differentiate two parental lines. Directional genetic effects are thought to be critical components of genetic architecture for the long term response to selection and as a cause of inbreeding depression. LCA typically begins with two inbred parental lines that are crossed to produce several generations such as F1, F2, and backcrosses to each parent. When a RIL population (founded from the same P1 and P2 as was used to found the line cross population) is added to the LCA, the sampling variance of several nonadditive genetic effect estimates is greatly reduced. Specifically, estimates of directional dominance, additive x additive, and dominance x dominance epistatic effects are reduced by 92%, 94%, and 56% respectively. The RIL population can be simultaneously used for QTL identification, thus uncovering the effects of specific loci or genomic regions as elements of genetic architecture. LCA and QTL mapping with RIL provide two qualitatively different measures of genetic architecture with the potential to overcome weaknesses of each approach alone. This approach provides cross-validation of the estimates of additive and additive x additive effects, much smaller confidence intervals on dominance, additive x additive and dominance x dominance estimates, qualitatively different measures of genetic architecture, and the potential when used together to balance the weaknesses of LCA or RIL QTL analyses when used alone.     

Genetic dissection of chromosome substitution lines of cotton to discover novel Gossypium barbadense L. alleles for improvement of agronomic traits

We recently released a set of 17 chromosome substitution (CS-B) lines (2n = 52) that contain Gossypium barbadense L. doubled-haploid line ‘3-79’ germplasm systematically introgressed into the Upland inbred ‘TM-1’ of G. hirsutum (L.). TM-1 yields much more than 3-79, but cotton from the latter has superior fiber properties. To explore the use of these quasi-isogenic lines in studying gene interactions, we created a partial diallel among six CS-B lines and the inbred TM-1, and characterized their descendents for lint percentage, boll weight, seedcotton yield and lint yield across four environments. Phenotypic data on the traits were analyzed according to the ADAA genetic model to detect significant additive, dominance, and additive-by-additive epistasis effects at the chromosome and chromosome-by-chromosome levels of CS-B lines. For example, line 3-79 had the lowest boll weight, seedcotton yield and lint yield, but CS-B22Lo homozygous dominance genetic effects on seedcotton and lint yield were nearly four times those of TM-1, and its hybrids with TM-1 had the highest additive-by-additive epistatic effects on seedcotton and lint yield. CS-B14sh, 17, 22Lo and 25 produced positive homozygous dominance effects on lint yield, whereas doubly heterozygous combinations of CS-B14sh with CS-B17, 22Lo and 25 produced negative dominance effects, suggesting that epistatic effects between genes in these chromosomes strongly affect lint yield. The results underscore the opportunities to systematically identify genomic regions harboring genes that impart agronomically significant effects via epistatic interactions. The chromosome-by-chromosome approach significantly complements other strategies to detect and quantify epistatic interaction effects, and the quasi-isogenic nature of families and lines from CS-B intermatings will facilitate high-resolution localization, development of markers for selection and map-assisted identification of genes involved in strong epistatic effects.     

Quantitative Genetics of Doubled Haploid Populations and Application to the Theory of Line Development

The line value of a genotype is defined as the expected value of all lines that can be derived from this genotype. Specific genetic effects are defined for this value: only additive and additive by additive epistatic effects are necessary. There is no dominance effect for such a value. A general expression for the covariances between related lines is given. From a design with several lines per haplodiploidized plant taken at random from a population it is possible to estimate the additive variance for line value and the variance of additive by additive epistasis for line value. Variances of higher order epistasis can be estimated with a two-factor mating design in which a cross is replaced by the population of lines that can be derived from it. With a diallel or a factorial design a direct test for the presence of homozygous by homozygous epistasis is possible. The application of the concept of line value to the theory of line development leads to simple expressions of genetic advance in one cycle of recurrent selection according to the testing system. A brief consideration of these expressions leads to the conclusion that single doubled haploid descent recurrent selection will be one of the most efficient methods for low heritabilities and with a rapid development of doubled haploid lines.     

Analysis of genealogical structure of populations. I. A method of collecting genealogical data in numerical form

A method for collecting genealogical data with respect to an individual, a family, and members of the whole population is suggested. The essence of vertical pedigree construction consists of the same type of steps for filling in data (in the fixed order which excludes skips in the enumeration of lines of descent) about the father and the mother of the next ancestor. Each number in the received ordered list of ancestors uniquely determines a path (line of descent) to the given pedigree member. The path is explicitly described by a sequence of digits 0 and 1 (that corresponds to the sequence of fathers and mothers in the line of descent) at binary notation of this number. As a result, a pedigree is presented as a set of numbered rows that contain information, which uniquely identifies direct ancestors as individual persons. Results of joining separate pedigrees are recorded as a family list that contains lists of children for each parental pair. A pair of parents (more exactly, pointers of their families in the previous generation and numbers of pair members in their families) plays the role of the family "heading." Such a family list permits one to trace lines of descent and relationships for any population members presented in the list. It contains all genealogical information within the bounds of the study in a compact form. Here the process of collection requires considerably less time than traditional graphic representation of pedigrees. In addition, due to repeated checks of data during accumulation of material, error is minimized. Using pedigrees that have been collected, it is possible to calculate the coefficient of inbreeding manually. In connection with the wide prevalence of personal computers at present, it is also important that the data received are in fact ready to direct input to a computer for further automated data processing.     

An additive-dominance model to determine chromosomal effects in chromosome substitution lines and other gemplasms

When using chromosome substitution (CS) lines in a crop breeding improvement program, one needs to separate the effects of the substituted chromosome from the remaining chromosomes. This cannot be done with the traditional additive-dominance (AD) model where CS lines, recurrent parent, and their hybrids are used. In this study, we develop a new genetic model and software, called a modified AD model with genotype × environment interactions, which can predict additive and dominance genetic effects attributed to a substituted alien chromosome in a CS line as well as the overall genetic effects of the non-substituted chromosomes. In addition, this model will predict the additive and dominance effects of the same chromosome of interest (i.e. chromosome 25 of cotton in this study) in an inbred line, as well as the effects of the remaining chromosomes in the inbred line. The model requires a CS line, its recurrent parent and their F₁ and/or F₂ hybrids between the substitution lines and several inbred lines. Monte Carlo simulation results showed that genetic variance components were estimated with no or slight bias when we considered this modified AD model as random. The correlation coefficient between predicted effects and true effects due to the chromosomes of interest varied from zero to greater than 0.90 and it was positively relative to the difference between the CS line and the recurrent line. To illustrate the use of this new genetic model, an upland cotton, Gossypium hirsusum L, CS line (CS-B25), TM-1 (the recurrent parent), five elite cultivars, and the F₂ hybrids from test-crossing these two lines with the five elite cultivars were grown in two environments in Mississippi. Agronomic and fiber data were collected and analyzed. The results showed that the CS line, CS-B25, which has chromosome 25 from line 3 to 79, Gossypium barbadense substituted into TM-1, had positive genetic associations with several fiber traits. We also determined that Chromosome 25 from FiberMax 966 had significantly positive associations with fiber length and strength; whereas, chromosome 25 from TM-1 and SureGrow 747 had detectable negative genetic effects on fiber strength. The new model will be useful to determine effects of the chromosomes of interest in various inbred lines in any diploid or amphidiploid crop for which CS lines are available.     

转cry1 Ab基因粳稻对稻田节肢动物群落的影响

在将稻田节肢动物群落按营养关系分为植食类、寄生类、捕食类、腐食类和其他类等5个功能团的基础上,从功能团优势度、群落结构参数及群落相异性等方面,经2年3点的调查就2个转cry1Ab基因粳稻（Bt粳稻）品系KMD1和KMD2对稻田节肢动物群落结构的影响做了评价。结果表明：在大多数情况下,Bt粳稻与对照间各功能团优势度、群落结构参数[物种丰富度（S）、Shannon-Wiener多样性指数（H′）、均匀性指数（J）、优势集中性指数（C）]及其时间动态无明显差异;Bt粳稻与对照间植食类、寄生类、捕食类亚群落,及整个节肢动物群落的相似性也较高。综合分析认为,Bt粳稻对稻田节肢动物群落结构无明显的负面影响。     

Delineation of interspecific epistasis on fiber quality traits in Gossypium hirsutum by ADAA analysis of intermated G. barbadense chromosome substitution lines

Genetic diversity is the foundation of any crop improvement program, but the most cultivated Upland cotton [Gossypium hirsutum L., 2n?=?52, genomic formula?2(AD)₁] has a very narrow gene pool resulting from its evolutionary origin and domestication history. Cultivars of this cotton species (G. hirsutum L.) are prized for their combination of exceptional yield, other agronomic traits, and good fiber properties, whereas the other cultivated 52-chromosome species, G. barbadense L. [2n?=?52, genomic formula?2(AD)₂], is widely regarded as having the opposite attributes. It has exceptionally good fiber qualities, but generally lower yield and less desirable agronomic traits. Breeders have long aspired to combine the best attributes of G. hirsutum and G. barbadense, but have had limited success. F₁ hybrids are readily created and largely fertile, so the limited success may be due to cryptic biological and technical challenges associated with the conventional methods of interspecific introgression. We have developed a complementary alternative approach for introgression based on chromosome substitution line, followed by increasingly sophisticated genetic analyses of chromosome-derived families to describe the inheritance and breeding values of the chromosome substitution lines. Here, we analyze fiber quality traits of progeny families from a partial diallel crossing scheme among selected chromosome substitution lines (CS-B lines). The results provide a more detailed and precise QTL dissection of fiber traits, and an opportunity to examine allelic interaction effects between two substituted chromosomes versus one substituted chromosome. This approach creates new germplasm based on pair wise combinations of quasi-isogenic chromosome substitutions. The relative genetic simplicity of two-chromosome interactions departs significantly from complex or RIL-based populations, in which huge numbers of loci are segregating in all 26 chromosome pairs. Data were analyzed according to the ADAA genetic model, which revealed significant additive, dominance, and additive-by-additive epistasis effects on all of the fiber quality traits associated with the substituted chromosome or chromosome arm of CS-B lines. Fiber of line 3-79, the donor parent for the substituted chromosomes, had the highest Upper Half Mean length (UHM), uniformity ratio, strength, elongation, and lowest micronaire among all parents and hybrids. CS-B16 and CS-B25 had significant additive effects for all fiber traits. Assuming a uniform genetic background of the CS-B lines, the comparative analysis of the double-heterozygous hybrid combinations (CS-B?×?CS-B) versus their respective single heterozygous combinations (CS-B?×?TM-1) demonstrated that interspecific epistatic effects between the genes in the chromosomes played a major role in most of the fiber quality traits. Results showed that fiber of several hybrids including CS-B16?×?CS-B22Lo, CS-B16?×?CS-B25 and CS-B16?×?TM-1 had significantly greater dominance effects for elongation and hybrid CS-B16?×?CS-B17 had higher fiber strength than their parental lines. Multiple antagonistic genetic effects were also present for fiber quality traits associated with most of the substituted chromosomes and chromosome arms. Results from this study highlight the vital importance of epistasis in fiber quality traits and detected novel effects of some cryptic beneficial alleles affecting fiber quality on the 3-79 chromosomes, whose effects were not detected in the 3-79 parental lines.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Combining ability and heterosis for earliness characters in line x tester population of Gossypium hirsutum L

The objective of this study was to estimate the general combining ability of the parents and specific combining ability of hybrids for earliness traits for line selection. Inheritance and interrelationships of earliness characters were evaluated in a line x tester design. Three intermediate-early-maturing female (lines) which are grown regionally and four early-maturing males (testers) cotton varieties were crossed in 2003. The twelve F(1) and seven parents were planted randomized block design with three replications in 2004. For each earliness trait, general combining ability (GCA) and specific combining ability and gene effects were estimated using the line x tester method of analysis and also were determined heterosis and narrow sense heritability. Parents and their hybrids (except the monopodial branch) were significant for all the earliness traits studied. Estimates of variance due to GCA and SCA and their ratio revealed predominantly non-additive gene effects for date of first square, date of first flowers and harvested rate of first picking. Among the lines, Ersan 92 and Maras 92 and among the testers Acala Royal was found to be the best general combiners for most of the earliness characters. Four out of twelve crosses namely Ersan 92 x Chirpan 603, Ersan 92 x Acala Maxa, Maras 92 x Acala Royal and Nazilli 87 x Acala Royal were found to be the best crosses for investigated earliness characters.     

云南香型软米水稻资源农艺性状遗传效应研究

选取5份云南地方香型软米水稻种质资源和6份自育香型软米保持系按5×6不完全双列杂交设计(NCⅡ)配制成30个组合,采用加性-显性-上位性遗传模型,分析云南香型软米11个农艺性状的遗传效应。结果表明,云南香型软米多数农艺性状的遗传主要受加×加上位性效应、加性×环境效应、显性×环境效应的影响,还存在不同程度的加性效应和显性效应,单株产量受基因加性效应、显性效应、加×加上位性效应、加性×环境效应、显性×环境效应的影响;株高、有效穗的遗传率以普通狭义遗传率为主,其他性状的普通狭义遗传率和互作狭义遗传率均达极显著水平;产量构成性状之间存在不同类型和不同程度的遗传相关,多数性状之间以加×加上位性、加性×环境和显性×环境互作效应显著。     

Inheritance of parthenocarpy in summer squash (Cucurbita pepo L.)

The inheritance of the tendency to set parthenocarpic fruit in the summer squash (Cucurbita pepo L.) line Whitaker was studied. Two parental lines, Whitaker (parthenocarpic) and Caserta (non-parthenocarpic), and the F1 and F2 generations and backcrosses to both parents were tested. The parthenocarpic tendency of individual plants was scored on a scale from 1 (non-parthenocarpic fruit) to 5 (parthenocarpic fruit). The Whitaker line produced parthenocarpic fruit and had a mean score of 4.2, whereas Caserta did not set parthenocarpic fruit and had a score of 1.55. The heritability estimates indicated that genetic gains from selection were feasible. The additive-dominant model showed a good fit, with epistasis being negligible or nonexistent. The hypothesis of monogenic inheritance with incomplete dominance was not rejected within the degree of dominance range from 0.2 to 0.5. These results indicate that parthenocarpy is controlled by a single locus, with incomplete dominance in the direction of parthenocarpic expression.     

Magnitude of hybrid vigor retained in double haploid lines of some heterotic rice hybrids

Sixty one double haploid (DH) lines were evaluated for yield components and yield and compared with the three corresponding hybrids from which they were derived through anther culture. Analysis of a 6×6 diallel experiment led to the selection of these hybrids based on their high heterosis and revealed the nature of gene action of the characters under evaluation. The DH lines along with the hybrids and parents were planted following a simple lattice design with two replications. The results show that in DH lines the values of the characters expressing predominantly additive genetic effects could reach the heterotic level of the hybrids. For characters including yield showing predominantly dominance effects, values in the DH lines were significantly lower than those of the corresponding hybrids. The promising DH lines, however, possess a higher yield potential than the better parents.     

Maximizing crossbred performance through purebred genomic selection

Background

In livestock production, many animals are crossbred, with two distinct advantages: heterosis and breed complementarity. Genomic selection (GS) can be used to select purebred parental lines for crossbred performance (CP). Dominance being the likely genetic basis of heterosis, explicitly including dominance in the GS model may be an advantage to select purebreds for CP. Estimated breeding values for CP can be calculated from additive and dominance effects of alleles that are estimated using pure line data. The objective of this simulation study was to investigate the benefits of applying GS to select purebred animals for CP, based on purebred phenotypic and genotypic information. A second objective was to compare the use of two separate pure line reference populations to that of a single reference population that combines both pure lines. These objectives were investigated under two conditions, i.e. either a low or a high correlation of linkage disequilibrium (LD) phase between the pure lines.

Results

The results demonstrate that the gain in CP was higher when parental lines were selected for CP, rather than purebred performance, both with a low and a high correlation of LD phase. For a low correlation of LD phase between the pure lines, the use of two separate reference populations yielded a higher gain in CP than use of a single reference population that combines both pure lines. However, for a high correlation of LD phase, marker effects that were estimated using a single combined reference population increased the gain in CP.

Conclusions

Under the hypothesis that performance of crossbred animals differs from that of purebred animals due to dominance, a dominance model can be used for GS of purebred individuals for CP, without using crossbred data. Furthermore, if the correlation of LD phase between pure lines is high, accuracy of selection can be increased by combining the two pure lines into a single reference population to estimate marker effects.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0099-3) contains supplementary material, which is available to authorized users.     

Interspecific chromosomal effects on agronomic traits in Gossypium hirsutum by AD analysis using intermated G. barbadense chromosome substitution lines

The untapped potential of the beneficial alleles from Gossypium barbadense L. has not been well utilized in G. hirsutum L. (often referred to as Upland cotton) breeding programs. This is primarily due to genomic incompatibility and technical challenges associated with conventional methods of interspecific introgression. In this study, we used a hypoaneuploid-based chromosome substitution line as a means for systematically introgressing G. barbadense doubled-haploid line ‘3-79’ germplasm into a common Upland genetic background, inbred ‘Texas marker-1’ (‘TM-1’). We reported on the chromosomal effects, lint percentage, boll weight, seedcotton yield and lint yield in chromosome substitution CS-B (G. barbadense L.) lines. Using an additive-dominance genetic model, we studied the interaction of alleles located on two alien substituted chromosomes versus one alien substituted chromosome using a partial diallel mating design of selected CS-B lines (CS-B05sh, CS-B06, CS-B09, CS-B10, CS-B12, CS-B17 and CS-B18). Among these parents, CS-B09 and CS-B10 were reported for the first time. The donor parent 3-79, had the lowest additive effect for all of the agronomic traits. All of the CS-B lines had significant additive effects with boll weight and lint percentage. CS-B10 had the highest additive effects for lint percentage, and seedcotton and lint yield among all of the lines showing a transgressive genetic mode of inheritance for these traits. CS-B09 had greater additive genetic effects on lint yield, while CS-B06, CS-B10 and CS-B17 had superior additive genetic effects on both lint and seedcotton yield compared to TM-1 parent. The 3-79 line had the highest dominance effects for boll weight (0.513 g) and CS-B10 had the lowest dominance effect for boll weight (?0.702). Some major antagonistic genetic effects for the agronomic traits were present with most of the substituted chromosomes and chromosome arms, a finding suggested their recalcitrance to conventional breeding efforts. The results revealed that the substituted chromosomes and arms of 3-79 carried some cryptic beneficial alleles with potential to improve agronomic traits including yield, whose effects were masked at the whole genome level in 3-79.     

Studies of heterosis,combining ability and inheritance of yield and yield components in a diallel cross of bengal gram (Cicer arietinum L.)

Summary A 5 X 5 diallel cross among well-adapted varieties of gram from different agroclimatic regions was studied for heterosis, combining ability and inheritance of days-to-flowering, primary branches, pods per plant, 100-seed weight and grain yield. A high degree of heterosis over mid-parent and better parent was observed for primary branches, no. of pods and grain yield, whereas very little heterosis was exhibited for days-to-flower and 100-seed weight. Crosses among lines of diverse origin generally gave higher heterosis and over-dominance than lines from the same region. Primary branch number, pod number, and grain yield exhibited positive over-dominance; days-to-flower showed negative over-dominance while 100-seed weight had no dominance. Both general and specific combining ability effects were significant for all the characters studied but g.c.a. effects appeared to be more important for days-to-flower, 100-seed weight and grain yield. Graphical analysis indicated additive effects for all the characters, with complete dominance for days-to-flower, no dominance for 100-seed weight and over-dominance for the other three characters. Dominant genes conditioned earliness, primary branch number and 100-seed weight. The role of various parents and crosses in planning a hybridization programme has been discussed.     

Evolution under relaxed sexual conflict in the bulb mite Rhizoglyphus robini

The experimental evolution under different levels of sexual conflict have been used to demonstrate antagonistic coevolution in muscids, but among other taxa a similar approach has not been employed. Here, we describe the results of 37 generations of evolution under either experimentally enforced monogamy or polygamy in the bulb mite Rhizoglyphus robini. Three replicates were maintained for each treatment. Monogamy makes male and female interests congruent; thus selection is expected to decrease harmfulness of males to their partners. Our results were consistent with this prediction in that females from monogamous lines achieved lower fecundity when housed with males from polygamous lines. Fecundity of polygamous females was not affected by mating system under which their partners evolved, which suggests that they were more resistant to male-induced harm. As predicted by the antagonistic coevolution hypothesis, the decrease in harmfulness of monogamous males was accompanied by a decline in reproductive competitiveness. In contrast, female fecundity and embryonic viability, which were not expected to be correlated with male harmfulness, did not differ between monogamous and polygamous lines. None of the fitness components assayed differed between individuals obtained from crosses between parents from the same line and those obtained from crosses between parents from different lines within the same mating system. This indicates that inbreeding depression did not confound our results. However, interpretation of our results is complicated by the fact that both males and females from monogamous lines evolved smaller body size compared to individuals from polygamous lines. Although a decrease in reproductive performance of males from monogamous lines was still significant when body size was taken into account, we were not able to separate the effects of male body size and mating system in their influence on fecundity of their female partners.     

Estimation of genetic parameters in barley (Hordeum vulgare L.)

Summary Four exotic and four indigenous strains of barley were used for making diallel crosses. The sets of parents and crosses making full, half and quarter diallel were analysed in a randomized block design for plant height, number of effective tillers, ear length, grain yield per plant, 100 grain weight and number of grains per ear.The three alternatives of diallel were similar with respect to the estimates of degree of dominance, general combining ability and specific combining ability, indicating that all these three methods of diallel were equally efficient. However, as the number of entries are minimum in quarter diallel, it would be economical in terms of cost, time and labour to estimate genetic parameters by this method. Average degree of dominance was found in the range of overdominance. The ranking of parents on the basis of their array mean was similar to the ranking based on gca effects. Similarly, the ranking of crosses on the basis of per se performance was similar to the ranking based on sca effects. This suggests that the selection of best general combiner or best cross combinations may be easier and more effective through array mean for per se performance rather than through high gca and sea effects, respectively. From among 56 crosses, IB-226 X X C-164 was the one which showed superiority for maximum number of characters followed by AB-12/59 X PTS-57. High sea effect for plant height, ear length, grain yield, 100 grain weight and number of grains per ear was the result of cross between parents having high X low general combining ability, indicating additive X dominance type of gene interaction. For number of effective tillers, high sca was produced by low x low general combiners, indicating dominance x dominance gene interaction.Part of a Ph. D. thesis submitted by senior author to Haryana Agricultural University, Hissar.     

Estimating allelic number and identity in state of QTLs in interconnected families

When multiple related families derived from inbred lines are jointly analysed to detect quantitative trait loci (QTLs), the analysis should estimate allelic effects as accurately as possible and estimate the probability that different parents carry alleles that are identical in state. Analyses exist that assume that all parents carry unique alleles or that all parents but one carry the same allele. In practice, many configurations are possible that group different parents according to their identity-in-state condition at a putative QTL allele. Here, we propose a variable model Bayesian analysis that selects among possible identity-in-state configurations and jointly estimates the allelic effects of identical-in-state parents. We contrast this analysis with a fixed model analysis that estimates unique allelic effects for all parents. We analyse two simulated mating designs: an experimental design in which three inbred parents were crossed to generate two families of 150 doubled haploid lines; and a breeding design in which 20 inbred parents were crossed to generate 60 families of 20 doubled haploid lines, with each parent contributing to six families. In all cases where some parents were simulated to carry alleles of identical effect (that is, they were identical in state), the variable analysis estimated allelic effects with lower mean-squared error than the fixed analysis. The variable analysis showed that, unless each family contains many individuals (more than 100), there is insufficient information in DNA-marker and phenotypic data to determine with high probability the QTL allelic number.