Mating strategies with genomic information reduce rates of inbreeding in animal breeding schemes without compromising genetic gain

We tested the hypothesis that mating strategies with genomic information realise lower rates of inbreeding (∆F) than with pedigree information without compromising rates of genetic gain (∆G). We used stochastic simulation to compare ∆F and ∆G realised by two mating strategies with pedigree and genomic information in five breeding schemes. The two mating strategies were minimum-coancestry mating (MC) and minimising the covariance between ancestral genetic contributions (MCAC). We also simulated random mating (RAND) as a reference point. Generations were discrete. Animals were truncation-selected for a single trait that was controlled by 2000 quantitative trait loci, and the trait was observed for all selection candidates before selection. The criterion for selection was genomic-breeding values predicted by a ridge-regression model. Our results showed that MC and MCAC with genomic information realised 6% to 22% less ∆F than MC and MCAC with pedigree information without compromising ∆G across breeding schemes. MC and MCAC realised similar ∆F and ∆G. In turn, MC and MCAC with genomic information realised 28% to 44% less ∆F and up to 14% higher ∆G than RAND. These results indicated that MC and MCAC with genomic information are more effective than with pedigree information in controlling rates of inbreeding. This implies that genomic information should be applied to more than just prediction of breeding values in breeding schemes with truncation selection.     

Mating schemes for optimum contribution selection with constrained rates of inbreeding

The effect of non-random mating on genetic response was compared for populations with discrete generations. Mating followed a selection step where the average coancestry of selected animals was constrained, while genetic response was maximised. Minimum coancestry (MC), Minimum coancestry with a maximum of one offspring per mating pair (MC1) and Minimum variance of the relationships of offspring (MVRO) mating schemes resulted in a delay in inbreeding of about two generations compared with Random, Random factorial and Compensatory mating. In these breeding schemes where selection constrains the rate of inbreeding, ΔF, the improved family structure due to non-random mating increased genetic response. For schemes with ΔF constrained to 1.0% and 100 selection candidates, genetic response was 22% higher for the MC1 and MVRO schemes compared with Random mating schemes. For schemes with a less stringent constraint on ΔF or more selection candidates, the superiority of the MC1 and MVRO schemes was smaller (5–6%). In general, MC1 seemed to be the preferred mating method, since it almost always yielded the highest genetic response. MC1 mainly achieved these high genetic responses by avoiding extreme relationships among the offspring, i.e. fullsib offspring are avoided, and by making the contributions of ancestors to offspring more equal by mating least related animals.     

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 practical approach for minimising inbreeding and maximising genetic gain in dairy cattle

A method that predicts the genetic composition and inbreeding (F) of the future dairy cow population using information on the current cow population, semen use and progeny test bulls is described. This is combined with information on genetic merit of bulls to compare bull selection methods that minimise F and maximise breeding value for profit (called APR in Australia). The genetic composition of the future cow population of Australian Holstein-Friesian (HF) and Jersey up to 6 years into the future was predicted. F in Australian HF and Jersey breeds is likely to increase by about 0.002 and 0.003 per year between 2002 and 2008, respectively. A comparison of bull selection methods showed that a method that selects the best bull from all available bulls for each current or future cow, based on its calf''s APR minus F depression, is better than bull selection methods based on APR alone, APR adjusted for mean F of prospective progeny after random mating and mean APR adjusted for the relationship between the selected bulls. This method reduced F of prospective progeny by about a third to a half compared to the other methods when bulls are mated to current and future cows that will be available 5 to 6 years from now. The method also reduced the relationship between the bulls selected to nearly the same extent as the method that is aimed at maximising genetic gain adjusted for the relationship between bulls. The method achieves this because cows with different pedigree exist in the population and the method selects relatively unrelated bulls to mate to these different cows. Selecting the best bull for each current or future cow so that the calf''s genetic merit minus F depression is maximised can slow the rate of increase in F in the population.     

Optimal mass selection policies for schemes with overlapping generations and restricted inbreeding

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress (ΔG) are combined with expected rates of inbreeding (ΔF) in a linear objective function (Φ = ΔG - λΔF) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.     

Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.     

Mating practices and the dissemination of genetic disorders in domestic animals,based on the example of dog breeding

On the basis of simulations and genealogical data of ten dog breeds, three popular mating practices (popular sire effect, line breeding, close breeding) were investigated along with their effects on the dissemination of genetic disorders. Our results showed that the use of sires in these ten breeds is clearly unbalanced. Depending on the breed, the effective number of sires represented between 33% and 70% of the total number of sires. Mating between close relatives was also found to be quite common, and the percentage of dogs inbred after two generations ranged from 1% to about 8%. A more or less long‐term genetic differentiation, linked to line breeding practices, was also emphasized in most breeds. F_IT index based on gene dropping proved to be efficient in differentiating the effects of the different mating practices, and it ranged from ?1.3% to 3.2% when real founders were used to begin a gene dropping process. Simulation results confirmed that the popular sire practice leads to a dissemination of genetic disorders. Under a realistic scenario, regarding the imbalance in the use of sires, the dissemination risk was indeed 4.4 times higher than under random mating conditions. In contrast, line breeding and close breeding practices tend to decrease the risk of the dissemination of genetic disorders.     

Positive assortative mating with selection restrictions on group coancestry enhances gain while conserving genetic diversity in long-term forest tree breeding

Selection and mating principles in a closed breeding population (BP) were studied by computer simulation. The BP was advanced, either by random assortment of mates (RAM), or by positive assortative mating (PAM). Selection was done with high precision using clonal testing. Selection considered both genetic gain and gene diversity by "group-merit selection", i.e. selection for breeding value weighted by group coancestry of the selected individuals. A range of weights on group coancestry was applied during selection to vary parent contributions and thereby adjust the balance between gain and diversity. This resulted in a series of scenarios with low to high effective population sizes measured by status effective number. Production populations (PP) were selected only for gain, as a subset of the BP. PAM improved gain in the PP substantially, by increasing the additive variance (i.e. the gain potential) of the BP. This effect was more pronounced under restricted selection when parent contributions to the next generation were more balanced with within-family selection as the extreme, i.e. when a higher status effective number was maintained in the BP. In that case, the additional gain over the BP mean for the clone PP and seed PPs was 32 and 84% higher, respectively, for PAM than for RAM in generation 5. PAM did not reduce gene diversity of the BP but increased inbreeding, and in that way caused a departure from Hardy-Weinberg equilibrium. The effect of inbreeding was eliminated by recombination during the production of seed orchard progeny. Also, for a given level of inbreeding in the seed orchard progeny or in a mixture of genotypes selected for clonal deployment, gain was higher for PAM than for RAM. After including inbreeding depression in the simulation, inbreeding was counteracted by selection, and the enhancement of PAM on production population gain was slightly reduced. In the presence of inbreeding depression the greatest PP gain was achieved at still higher levels of status effective number, i.e. when more gene diversity was conserved in the BP. Thus, the combination of precise selection and PAM resulted in close to maximal short-term PP gain, while conserving maximal gene diversity in the BP.Communicated by O. Savolainen     

A comparison of two methods for prediction of response and rates of inbreeding in selected populations with the results obtained in two selection experiments

Selection programmes are mainly concerned with increasing genetic gain. However, short-term progress should not be obtained at the expense of the within-population genetic variability. Different prediction models for the evolution within a small population of the genetic mean of a selected trait, its genetic variance and its inbreeding have been developed but have mainly been validated through Monte Carlo simulation studies. The purpose of this study was to compare theoretical predictions to experimental results. Two deterministic methods were considered, both grounded on a polygenic additive model. Differences between theoretical predictions and experimental results arise from differences between the true and the assumed genetic model, and from mathematical simplifications applied in the prediction methods. Two sets of experimental lines of chickens were used in this study: the Dutch lines undergoing true truncation mass selection, the other lines (French) undergoing mass selection with a restriction on the representation of the different families. This study confirmed, on an experimental basis, that modelling is an efficient approach to make useful predictions of the evolution of selected populations although the basic assumptions considered in the models (polygenic additive model, normality of the distribution, base population at the equilibrium, etc.) are not met in reality. The two deterministic methods compared yielded results that were close to those observed in real data, especially when the selection scheme followed the rules of strict mass selection: for instance, both predictions overestimated the genetic gain in the French experiment, whereas both predictions were close to the observed values in the Dutch experiment.