Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding

There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.     

A test of quantitative genetic theory using Drosophila- effects of inbreeding and rate of inbreeding on heritabilities and variance components

Inbreeding is expected to decrease the heritability within populations. However, results from empirical studies are inconclusive. In this study, we investigated the effects of three breeding treatments (fast and slow rate of inbreeding - inbred to the same absolute level - and a control) on heritability, phenotypic, genetic and environmental variances of sternopleural bristle number in Drosophila melanogaster. Heritability, and phenotypic, genetic and environmental variances were estimated in 10 replicate lines within each of the three treatments. Standard least squares regression models and Bayesian methods were used to analyse the data. Heritability and additive genetic variance within lines were higher in the control compared with both inbreeding treatments. Heritabilities and additive genetic variances within lines were higher in slow compared with fast inbred lines, indicating that slow inbred lines retain more evolutionary potential despite the same expected absolute level of inbreeding. The between line variance was larger with inbreeding and more than twice as large in the fast than in the slow inbred lines. The different pattern of redistribution of genetic variance within and between lines in the two inbred treatments cannot be explained invoking the standard model based on selective neutrality and additive gene action. Environmental variances were higher with inbreeding, and more so with fast inbreeding, indicating that inbreeding and the rate of inbreeding affect environmental sensitivity. The phenotypic variance decreased with inbreeding, but was not affected by the rate of inbreeding. No inbreeding depression for mean sternopleural bristle number was observed in this study. Considerable variance between lines in additive genetic variance within lines was observed, illustrating between line variation in evolutionary potential.     

The analysis of disease biomarker data using a mixed hidden Markov model (Open Access publication)

A mixed hidden Markov model (HMM) was developed for predicting breeding values of a biomarker (here, somatic cell score) and the individual probabilities of health and disease (here, mastitis) based upon the measurements of the biomarker. At a first level, the unobserved disease process (Markov model) was introduced and at a second level, the measurement process was modeled, making the link between the unobserved disease states and the observed biomarker values. This hierarchical formulation allows joint estimation of the parameters of both processes. The flexibility of this approach is illustrated on the simulated data. Firstly, lactation curves for the biomarker were generated based upon published parameters (mean, variance, and probabilities of infection) for cows with known clinical conditions (health or mastitis due to Escherichia coli or Staphylococcus aureus). Next, estimation of the parameters was performed via Gibbs sampling, assuming the health status was unknown. Results from the simulations and mathematics show that the mixed HMM is appropriate to estimate the quantities of interest although the accuracy of the estimates is moderate when the prevalence of the disease is low. The paper ends with some indications for further developments of the methodology.     

An approximate multitrait model for genetic evaluation in dairy cattle with a robust estimation of genetic trends (Open Access publication)

In a stochastic simulation study of a dairy cattle population three multitrait models for estimation of genetic parameters and prediction of breeding values were compared. The first model was an approximate multitrait model using a two-step procedure. The first step was a single trait model for all traits. The solutions for fixed effects from these analyses were subtracted from the phenotypes. A multitrait model only containing an overall mean, an additive genetic and a residual term was applied on these preadjusted data. The second model was similar to the first model, but the multitrait model also contained a year effect. The third model was a full multitrait model. Genetic trends for total merit and for the individual traits in the breeding goal were compared for the three scenarios to rank the models. The full multitrait model gave the highest genetic response, but was not significantly better than the approximate multitrait model including a year effect. The inclusion of a year effect into the second step of the approximate multitrait model significantly improved the genetic trend for total merit. In this study, estimation of genetic parameters for breeding value estimation using models corresponding to the ones used for prediction of breeding values increased the accuracy on the breeding values and thereby the genetic progress.     

Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)

Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme.     

Relatedness and inbreeding in a French population of the unicolonial antIndomyrmex humilis (Mayr)

Summary Worker and queen samples of the Argentine antIridomyrmex humilis were analysed using allozyme electrophoresis. Two loci,peptidase andglucosephosphate isomerase, were found to be stainable and polymorphic. Both revealed an estimated relatedness in nestmate females that was close to zero, which is a consequence of the strong polygyny in this species. The inbreeding coefficient was found to be close to zero, which can be explained, in spite of intra-nest mating taking place inI. humilis, by the high mobility of mated queens.     

Impact of strong selection for the PrP major gene on genetic variability of four French sheep breeds (Open Access publication)

Effective selection on the PrP gene has been implemented since October 2001 in all French sheep breeds. After four years, the ARR "resistant" allele frequency increased by about 35% in young males. The aim of this study was to evaluate the impact of this strong selection on genetic variability. It is focussed on four French sheep breeds and based on the comparison of two groups of 94 animals within each breed: the first group of animals was born before the selection began, and the second, 3–4 years later. Genetic variability was assessed using genealogical and molecular data (29 microsatellite markers). The expected loss of genetic variability on the PrP gene was confirmed. Moreover, among the five markers located in the PrP region, only the three closest ones were affected. The evolution of the number of alleles, heterozygote deficiency within population, expected heterozygosity and the Reynolds distances agreed with the criteria from pedigree and pointed out that neutral genetic variability was not much affected. This trend depended on breed, i.e. on their initial states (population size, PrP frequencies) and on the selection strategies for improving scrapie resistance while carrying out selection for production traits.     

Effect of inbreeding and salinity on quantitative characters and asymmetry of Tisbe holothuriae (Humes)

Effects of differing salinities on morphological characters have been found in marine and brackish populations of Tisbe holothuriae. The results suggested an active role of salinity as a factor promoting divergence. In order to test if the observed differentiation could be due to the level of heterozygosity, a study was performed in strains with low and high homozygosity. Six quantitative traits, and their respective fluctuating asymmetry, have been measured in outbred (coefficient of consanguineity, F = 0) and inbred (F = 0.5) strains, raised at three salinities; 20, 25 and 35. The analysis of variance was applied to test if the morphological measures were the same, and if the variations induced by decreased salinity had the same trend, in the two strains. Wilcoxon test was applied to the asymmetry, when it was not possible to render the variances homogeneous. The results showed that the measures and the effects of salinity on morphometry differed in the strains with low and high homozygosity. No effect of salinity on asymmetry was found. Length measures showed higher asymmetry in the most homozygous strain.     

Analysis of the real EADGENE data set: Multivariate approaches and post analysis (Open Access publication)

The aim of this paper was to describe, and when possible compare, the multivariate methods used by the participants in the EADGENE WP1.4 workshop. The first approach was for class discovery and class prediction using evidence from the data at hand. Several teams used hierarchical clustering (HC) or principal component analysis (PCA) to identify groups of differentially expressed genes with a similar expression pattern over time points and infective agent (E. coli or S. aureus). The main result from these analyses was that HC and PCA were able to separate tissue samples taken at 24 h following E. coli infection from the other samples. The second approach identified groups of differentially co-expressed genes, by identifying clusters of genes highly correlated when animals were infected with E. coli but not correlated more than expected by chance when the infective pathogen was S. aureus. The third approach looked at differential expression of predefined gene sets. Gene sets were defined based on information retrieved from biological databases such as Gene Ontology. Based on these annotation sources the teams used either the GlobalTest or the Fisher exact test to identify differentially expressed gene sets. The main result from these analyses was that gene sets involved in immune defence responses were differentially expressed.     

Effects of inbreeding on traits that influence dispersal and progeny density in Cakile edentula var. lacustris (Brassicaceae)

Inbreeding may influence the intensity of sibling competition by altering the number of offspring produced or by changing plant morphology in ways that influence seed dispersion patterns. To test this possibility, effects of inbreeding on seed production and on traits that influence progeny density were measured using experimental pollinations of flowers of Cakile edentula var. lacustris. Different flowers on a plant were either hand pollinated with self pollen (with and without emasculation) or foreign pollen, or they were allowed to be pollinated naturally. Selfed flowers matured significantly fewer viable seeds than outcrossed flowers (10.3% less seed maturation with inbreeding depression of 19.2%), due in large part to a greater percentage of proximal seed abortions and lower germination success. Plants grown from selfed seeds tended to have lower seed production (37 fewer seeds on average, with inbreeding depression of 16.2%), caused in part by an increase in the percentage of fruits with proximal seed abortions, although this effect was not significant. Inbreeding depression in total fitness was 29.0%, which corresponds to a difference of 46 seeds per pollinated ovule. Selfing rate estimates were usually intermediate to high, indicating that inbreeding effects observed in this study would be present in naturally pollinated progeny. Although the influence of inbreeding directly on dispersal was negligible, the predicted reduction in sibling competition caused by reduced seed production resulted in an estimate of inbreeding depression of 17.5%, which is 11.5% lower than that measured under uniform conditions. Consequently, inbreeding depression estimated under natural dispersion patterns may be lower than that estimated under uniform conditions since seeds from self- and cross-pollination may not experience the same competitive environment in the field. Inbreeding in the maternal generation, therefore, could influence progeny fitness not only by determining the genetic composition of progeny, but also by influencing the competitive environment in which progeny grow.     

The risk of inbreeding due to habitat loss in the lion (Panthera leo)

A major concern in conservation biology is toavoid inbreeding depression in smallpopulations. Inbreeding has been shown to causeloss of fecundity and reduced survival innatural populations. To predict futureinbreeding levels, given changes in ecologicalconditions, data from large outbred populationsare needed. I use recent population geneticmodels to show how genetic data from such apopulation, combined with ecological data canbe used to predict future changes in levels ofinbreeding. In particular, data from the lion(Panthera leo) is used to simulate theeffect of habitat loss on the future levels ofinbreeding. To do this I used a deterministicpopulation genetics models and anindividual-based stochastic model. Two factorsstand out as particularly important: totalnumber of prides and male dispersal rates. Ifprides are very few (= 10) inbreeding (F)will increase from 0.0 in the initial state to0.26–0.45 after 30 generations, while if thenumber of prides is 100 this level is onlyaround 0.05 assuming no migration into thepopulation. Habitat heterogeneity had onlyminor effects. A reduction in male dispersalfrom their natal territory from 100% to 95%increased the level of inbreedingsubstantially, and never reached below F 0.25 regardless of the number ofprides. Therefore, to sustain a large outbredpopulation of lions, a continuous population ofat least 50 prides, but preferably 100 prides,with no limits to dispersal is required.     

High genetic diversity and no inbreeding in the endangered copper redhorse, Moxostoma hubbsi (Catostomidae, Pisces): the positive sides of a long generation time

The evolutionary potential of a species is determined by its genetic diversity. Thus, management plans should integrate genetic concerns into active conservation efforts. The copper redhorse (Moxostoma hubbsi) is an endangered species, with an endemic distribution limited to the Richelieu River and a short section of the St Lawrence River in Quebec, Canada. The population, gradually fragmented since 1849, is characterized by a decline in population size and a lack of recruitment. A total of 269 samples were collected between 1984 and 2004 and genotyped using 22 microsatellite loci, which indicated that these fish comprise a single population, with a global F(ST) value of only 0.0038. Despite a small census size ( approximately 500), a high degree of genetic diversity was observed compared to common values for freshwater fishes (average number of 12.5 alleles/locus and average HO of 0.77 +/- 0.08). No difference was observed between expected and observed pairwise values of relatedness (r(xy): -0.00013 +/- 0.11737), suggesting an outbred population. Long-term Ne was estimated at 4476 whereas contemporary Ne values ranged from 107 to 568, suggesting a pronounced yet gradual demographic decline of the population, as no bottleneck could be detected for the recent past. By means of simulations, we estimated Ne would need to remain at more than approximately 400 to retain 90% of the genetic diversity over 100 years. Overall, these observations corroborate other recent empirical studies confirming that long generation times may act as a buffering effect contributing to a reduction in the pace of genetic diversity erosion in threatened species.     

Evolution of the polymorphism at molecular markers in QTL and non-QTL regions in selected chicken lines (Open Access publication)

We investigated the joint evolution of neutral and selected genomic regions in three chicken lines selected for immune response and in one control line. We compared the evolution of polymorphism of 21 supposedly neutral microsatellite markers versus 30 microsatellite markers located in seven quantitative trait loci (QTL) regions. Divergence of lines was observed by factor analysis. Five supposedly neutral markers and 12 markers in theQTL regions showed F_st values greater than 0.15. However, the non-significant difference (P > 0.05) between matrices of genetic distances based on genotypes at supposedly neutral markers on the one hand, and at markers in QTL regions, on the other hand, showed that none of the markers in the QTL regions were influenced by selection. A supposedly neutral marker and a marker located in the QTL region on chromosome 14 showed temporal variations in allele frequencies that could not be explained by drift only. Finally, to confirm thatmarkers located inQTL regions on chromosomes 1, 7 and 14were under the influence of selection, simulations were performed using haplotype dropping along the existing pedigree. In the zone located on chromosome 14, the simulation results confirmed that selection had an effect on the evolution of polymorphism of markers within the zone.     

Genetic variability in residual feed intake in rainbow trout clones and testing of indirect selection criteria (Open Access publication)

Little is known about the genetic basis of residual feed intake (RFI) variation in fish, since this trait is highly sensitive to environmental influences, and feed intake of individuals is difficult to measure accurately. The purpose of this work was (i) to assess the genetic variability of RFI estimated by an X-ray technique and (ii) to develop predictive criteria for RFI. Two predictive criteria were tested: loss of body weight during feed deprivation and compensatory growth during re-feeding. Ten heterozygous rainbow trout clones were used. Individual intake and body weight were measured three times at threeweek intervals. Then, individual body weight was recorded after two cycles of a three-week feed deprivation followed by a three-week re-feeding. The ratio of the genetic variance to the phenotypic variance was found high to moderate for growth, feed intake, and RFI (VG/VP = 0.63 ± 0.11, 0.29 ± 0.11, 0.29 ± 0.09, respectively). The index that integrates performances achieved during deprivation and re-feeding periods explained 59% of RFI variations. These results provide a basis for further studies on the origin of RFI differences and show that indirect criteria are good candidates for future selective breeding programs.     

Sexual reproduction in Daphnia pulex (Crustacea: Cladocera): observations on male mating behaviour and avoidance of inbreeding

1.  Mating behaviour in Daphnia appears to rely on random contact between males and sexual females rather than diffusible pheromones. Males may be able to discriminate sexually receptive females from females in other developmental stages and increase their mating efficiency. Males may also use chemical signals to avoid mating with females from the same clone and avoid the severe inbreeding depression that has been documented for intraclonal mating. The present study used experiments to test for the avoidance of intraclonal mating and assess male mating efficiency in D. pulex .
2.  Three clones were examined for the avoidance of intraclonal mating by providing males with an opportunity to mate with females of the same or two different clones. The proportion of intraclonal matings did not differ from the proportion of interclonal matings, suggesting that D. pulex males do not use kin discrimination to avoid mating with females from the same clone.
3.  The proportion of mated females decreased with increasing numbers and density of sexual females when exposed to a single male. This observation suggests that a male spends more time pursuing and copulating with sexually receptive females than non-receptive females and there is insufficient time to mate with all sexual females. The decrease in proportion of females mated could also be the result of sperm depletion in the male. Sperm depletion is unlikely to occur in nature because sexually receptive females are much rarer than in the experimental conditions.     

Consequence of emergence pattern on inbreeding risk in the aphid parasitoid Aphidius matricariae (Hymenoptera: Braconidae)

In insect parasitoids, mating strategy depends on mate availability and is influenced by the spatial and temporal emergence patterns of adults. For quasi-gregarious species, simultaneous emergence favors local mating and reduces search costs for partners while increasing the risk of inbreeding, particularly when only one female parasitizes the initial host patch. Consequently, in inbreeding sensitive species, mating on the place of adult emergence (patch mating) between siblings should be counter selected. In practice, the timing of male and female emergence and of their dispersal influences mate availability and can limit on patch mating. To test the role of these two factors, we analyzed the daily distribution of emergence and patch residence time of a cohort in the aphid parasitoid Aphidius matricariae (Hymenoptera: Braconidae). We observed that adult emergence is concentrated on the morning with males emerging on average before females with some overlaps. A more precise evaluation of emergence pattern within a brood suggests that brothers and sisters rarely emerge at the same time and rapid dispersal of males and females favors off-patch mating. The relationships between timing of emergence including differences between sex and consequences on inbreeding probability in these species are thus discussed.     

Variation in the intensity of inbreeding depression among successive life-cycle stages and generations in gynodioecious Silene vulgaris (Caryophyllaceae)

Inbreeding depression is one of the hypotheses explaining the maintenance of females within gynodioecious plant populations. However, the measurement of fitness components in selfed and outcrossed progeny depends on life-cycle stage and the history of inbreeding. Comparative data indicate that strong inbreeding depression is more likely to occur at later life-cycle stages. We used hermaphrodite individuals of Silene vulgaris originating from three populations located in different valleys in the Swiss Alps to investigate the effect of two generations of self- and cross-fertilization on fitness components among successive stages of the life cycle in a glasshouse experiment. We detected significant inbreeding depression for most life-cycle stages including: the number of viable and aborted seeds per fruit, probability of germination, above ground biomass, probability of flowering, number of flowers per plant, flower size and pollen viability. Overall, the intensity of inbreeding depression increased among successive stages of the life cycle and cumulative inbreeding depression was significantly stronger in the first generation (delta approximately 0.5) compared with the second generation (delta approximately 0.35). We found no evidence for synergistic epistasis in our experiment. Our finding of more intense inbreeding depression during later stages of the life cycle may help to explain the maintenance of females in gynodioecious populations of S. vulgaris because purging of genetic load is less likely to occur.     

Detection of quantitative trait loci for reproduction and production traits in Large White and French Landrace pig populations (Open Access publication)

A genome-wide scan was performed in Large White and French Landrace pig populations in order to identify QTL affecting reproduction and production traits. The experiment was based on a granddaughter design, including five Large White and three French Landrace half-sib families identified in the French porcine national database. A total of 239 animals (166 sons and 73 daughters of the eight male founders) distributed in eight families were genotyped for 144 microsatellite markers. The design included 51 262 animals recorded for production traits, and 53 205 litter size records were considered. Three production and three reproduction traits were analysed: average backfat thickness (US_M) and live weight (LWGT) at the end of the on-farm test, age of candidates adjusted at 100 kg live weight, total number of piglets born per litter, and numbers of stillborn (STILLp) and born alive (LIVp) piglets per litter. Ten QTL with medium to large effects were detected at a chromosome-wide significance level of 5% affecting traits US_M (on SSC2, SSC3 and SSC17), LWGT (on SSC4), STILLp (on SSC6, SSC11 and SSC14) and LIVp (on SSC7, SSC16 and SSC18). The number of heterozygous male founders varied from 1 to 3 depending on the QTL.     

The relationship between homozygosity level and animal physiology: Iron content of plasma and whole blood as well as total iron binding capacity by transferrin (TIBC) in rats of various inbreeding coefficient

Male and female wild Norway rats (Rattus norvegicus Erxleben) and male and female albino outbred rats (Ipf:RIZ) were crossbred. These animals were the control, noninbred group (0% inbred). By systematic full-sib mating, two experimental groups (50 and 91% of inbred) were raised. Half of each group (both males and females) was exposed to physical stress (3 days of starvation and 3 hr of swimming). The other half of each group was ether anesthetized to collect blood. The iron content of plasma and whole blood, as well as the total iron binding capacity, was determined by the Atom-Spec method. A significant decrease in the iron content of plasma and whole blood as well as the TIBC was observed by an increase in the inbreeding coefficient. Stress significantly influenced the iron content of plasma and whole blood as well as the TIBC, whereas the sex of the rats affected the whole-blood iron concentration and TIBC. Moreover, some double interactions had an impact on the iron content and TIBC. The interactions were as follows: plasma—inbreeding level and stress; whole blood—sex and stress; and TIBC—inbreeding level and sex.