In previous analyses, the variation in actual, or realized, relationship has been derived as a function of map length of chromosomes and type of relationship, the variation being greater the shorter the total chromosome length and the coefficient of variation being greater the more distant the relationship. Here, the results are extended to allow for the relatives’ ancestor being inbred. Inbreeding of a parent reduces variation in actual relationship among its offspring, by an amount that depends on the inbreeding level and the type of mating that led to that level. For descendants of full-sibs, the variation is reduced in later generations, but for descendants of half-sibs, it is increased.

Epistasis plays important roles in evolution, for example in the evolution of recombination, but each of the current methods to study epistasis has limitations. Here, we propose a new strategy. If a quantitative trait locus (QTL) affecting a quantitative character has been identified, individuals who have the same genotype at that QTL can be regarded as comprising a subpopulation whose response to selection depends in part on interactions with other loci affecting the character. We define the marginal differences to be the differences in the average phenotypes of individuals with different genotypes of that QTL. We show that the response of the marginal differences to directional selection on the quantitative character depends on epistatic gene interactions. For a model with no interactions, the marginal differences do not differ on average from their starting values once linkage equilibrium has been re-established. If there is directional epistasis, meaning that interactions between the QTL and other loci tend to increase or decrease the character more than under an additive model, then the marginal differences will tend to increase or decrease accordingly when larger values of the character are selected for. We develop a likelihood ratio test for significant changes in the marginal differences and show that it has some power to detect directional epistasis for realistic sample sizes. We also show that epistatic interactions which affect the evolution of the marginal differences do not necessarily result in a substantial epistatic component of the genetic variance.

Recently, a Haley–Knott-type regression method using combined linkage disequilibrium and linkage analyses (LDLA) was proposed to map quantitative trait loci (QTLs). Chromosome of 5 and 25 cM with 0·25 and 0·05 cM, respectively, between markers were simulated. The differences between the LDLA approaches with regard to QTL position accuracy were very limited, with a significantly better mean square error (MSE) with the LDLA regression (LDLA_reg) in sparse map cases; the contrary was observed, but not significantly, in dense map situations. The computing time required for the LDLA variance components (LDLA_vc) model was much higher than the LDLA_reg model. The precision of QTL position estimation was compared for four numbers of half-sib families, four different family sizes and two experimental designs (half-sibs, and full- and half-sibs). Regarding the number of families, MSE values were lowest for 15 or 50 half-sib families, differences not being significant. We observed that the greater the number of progenies per sire, the more accurate the QTL position. However, for a fixed population size, reducing the number of families (e.g. using a small number of large full-sib families) could lead to less accuracy of estimated QTL position.

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

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.

FST, a measurement of the genetic differentiation among subpopulations, is a fundamental parameter in population genetics, with many valuable applications in molecular biology, evolutionary biology, conservation and forensics. One of its close relatives, GST, has been widely used to measure differentiation from highly polymorphic markers such as microsatellites. However, because of the high mutation rate of such markers, GST may underestimate the genomic differentiation due to demographic causes such as migration rate and subpopulation size. A new statistic proposed recently, Jost's D, was claimed to have better properties than GST and was advocated to replace GST as a measure of differentiation. This paper shows that D is not a proper measure of differentiation because it fails to meet some fundamental requirements as a differentiation statistic, and is hardly estimable without bias in practice. D is highly dependent on the gene diversity of a marker and on the unknown parameter of the number of subpopulations, is highly sensitive to how alleles and loci are defined and how data are analysed, does not increase monotonically with either divergence time or drift, and does not always have a maximal value of 1. The maximal D value can be zero or close to zero, depending on the number of alleles at a locus relative to the number of subpopulations. I suggest continuing the use of GST, with caution in its interpretation when highly polymorphic markers are used, before a better estimator of FST that explicitly accounts for mutations is developed.

The X-linked telomeric P elements (TPs) TP5 and TP6 regulate the activity of the entire P element family because they are inserted in a major locus for the production of Piwi-interacting RNAs (piRNAs). The potential for this cytotype regulation is significantly strengthened when either TP5 or TP6 is combined with a non-telomeric X-linked or autosomal transgene that contains a P element. By themselves, none of the transgenic P elements have any regulatory ability. Synergism between the telomeric and transgenic P elements is much greater when the TP is derived from a female. Once an enhanced regulatory state is established in a female, it is transmitted to her offspring independently of either the telomeric or transgenic P elements – that is, it works through a strictly maternal effect. Synergistic regulation collapses when either the telomeric or the transgenic P element is removed from the maternal genotype, and it is significantly impaired when the TPs come from stocks heterozygous for mutations in the genes aubergine, piwi or Su(var)205. The synergism between telomeric and transgenic P elements is consistent with a model in which P piRNAs are amplified by alternating, or ping-pong, targeting of primary piRNAs to sense and antisense P transcripts, with the sense transcripts being derived from the transgenic P element and the antisense transcripts being derived from the TP.

Using a dataset of karyotypic changes reported for bovids and the house mouse (Mus musculus domesticus) together with information from the cattle (Bos taurus) and mouse genomes, we examined two principal variables that have been proposed to predict chromosomal positioning in the nucleus, chromosome size and GC content. These were expected to influence the distribution of Robertsonian (Rb) fusions, the predominant mode of chromosomal change in both taxa. We found the largest chromosomes to be most frequently involved in fusions in bovids, and confirm earlier reports that chromosomes of intermediate size were the most frequent fusers in mice. We then tested whether chromosomal positioning can explain Rb fusion frequencies. We classified chromosomes into groups by size and considered the frequency of interactions between specific groups. Among the interactions, mouse chromosomes showed a slight tendency to fuse with neighbouring chromosomes, in line with expectations of chromosomal positioning, but also resembling predictions from meiotic spindle-induced bias. Bovids, on the other hand, showed no trend in interactions, with small chromosomes being the least frequent partner for all size classes. We discuss the results in terms of nuclear organization at various cell cycle stages and the proposed mechanisms of Rb fusion formation, and note that the difference can be explained by (i) considering bovid species generally to be characterized by a greater intermingling of chromosomal size classes than the house mouse, or (ii) by the vastly different timescales underpinning their evolutionary histories.