Dry matter grain yield per plot from three genetically homogeneous single-cross maize hybrids were analysed to investigate whether environmental variance depends on genotype. Three genotypes were tested at 20 locations in 3 years. The data were analysed using a non-parametric approach and fully parametric Bayesian models. Both analyses reveal effects of genotype on environmental variation. The Bayesian analyses indicate that genotype by location–year interactions are the most important effects acting at the level of the mean. The best-fitting Bayesian model is one postulating genotype by location–year interactions acting on the mean and main effects of genotype and of location–year on the variance. Despite the detection of genotypic effects acting on the variance, location–year effects constitute the biggest relative source of variance heterogeneity.

Fertility transmission (FT) is a phenomenon with a cultural and/or genetic basis, whereby a positive correlation exists between the number of offspring of an individual and that of his/her parents. Theoretical studies using a haploid individual-based model have shown that FT increases the variance and intergenerational correlation in reproductive success and results in an imbalance in the coalescent tree of sampled genes. This phenomenon has been documented in several demographic studies conducted on the correlation in fertility between generations, or through the reconstruction of the genealogical trees of mitochondrial DNA sequences. However, as mtDNA is a single locus, potentially subject to other forces (e.g. natural selection), it is of interest to extend the theory of FT to nuclear loci. We show that because random mating between individuals leads to a mixing of their fertility profiles, FT in these cases will have less influence on the variance and intergenerational correlation of reproductive success. This, in turn, results in less impact on the shape of the coalescent trees. Nevertheless, in the presence of FT, high heterogeneity in reproductive success and homogamy for family size will increase the imbalance in the coalescent tree. Thus, FT should be easier to detect when occurring in conjunction with these other factors. We also show the utility of analysing different kinds of loci (X-linked, Y-linked, mitochondrial and autosomal) to assess whether FT is matrilineal, patrilineal or biparental. Finally, we demonstrate that the shape of the coalescent tree depends upon population size, in contrast to the classical Kingman's model.

Imputation of moderate-density genotypes from low-density panels is of increasing interest in genomic selection, because it can dramatically reduce genotyping costs. Several imputation software packages have been developed, but they vary in imputation accuracy, and imputed genotypes may be inconsistent among methods. An AdaBoost-like approach is proposed to combine imputation results from several independent software packages, i.e. Beagle(v3.3), IMPUTE(v2.0), fastPHASE(v1.4), AlphaImpute, findhap(v2) and Fimpute(v2), with each package serving as a basic classifier in an ensemble-based system. The ensemble-based method computes weights sequentially for all classifiers, and combines results from component methods via weighted majority ‘voting’ to determine unknown genotypes. The data included 3078 registered Angus cattle, each genotyped with the Illumina BovineSNP50 BeadChip. SNP genotypes on three chromosomes (BTA1, BTA16 and BTA28) were used to compare imputation accuracy among methods, and the application involved the imputation of 50K genotypes covering 29 chromosomes based on a set of 5K genotypes. Beagle and Fimpute had the greatest accuracy among the six imputation packages, which ranged from 0·8677 to 0·9858. The proposed ensemble method was better than any of these packages, but the sequence of independent classifiers in the voting scheme affected imputation accuracy. The ensemble systems yielding the best imputation accuracies were those that had Beagle as first classifier, followed by one or two methods that utilized pedigree information. A salient feature of the proposed ensemble method is that it can solve imputation inconsistencies among different imputation methods, hence leading to a more reliable system for imputing genotypes relative to independent methods.

In this paper, we developed and compared several expectation–maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).

Linkage analysis plays an important role in genetic studies. In linkage analysis, accurate estimation of recombination frequency is essential. Many bi-parental populations have been used, and determining an appropriate population is of great importance in precise recombination frequency. In this study, we investigated the estimation efficiency of recombination frequency in 12 bi-parental populations. The criteria that we used for comparison were LOD score in testing linkage relationship, deviation between estimated and real recombination frequency, standard error (SE) of estimates and the least theoretical population size (PS) required to observe at least one recombinant and to declare the statistically significant linkage relationship. Theoretical and simulation results indicated that larger PS and smaller recombination frequency resulted in higher LOD score and smaller deviation. Lower LOD score, higher deviation and higher SE for estimating the recombination frequency in the advanced backcrossing and selfing populations are larger than those in backcross and F2 populations, respectively. For advanced backcrossing and selfing populations, larger populations were needed in order to observe at least one recombinant and to declare significant linkage. In comparison, in F2 and F3 populations higher LOD score, lower deviation and SE were observed for co-dominant markers. A much larger population was needed to observe at least one recombinant and to detect loose linkage for dominant and recessive markers. Therefore, advanced backcrossing and selfing populations had lower precision in estimating the recombination frequency. F2 and F3 populations together with co-dominant markers represent the ideal situation for linkage analysis and linkage map construction.