A note on mate allocation for dominance handling in genomic selection
© Toro and Varona; licensee BioMed Central Ltd. 2010
Received: 30 April 2010
Accepted: 11 August 2010
Published: 11 August 2010
Estimation of non-additive genetic effects in animal breeding is important because it increases the accuracy of breeding value prediction and the value of mate allocation procedures. With the advent of genomic selection these ideas should be revisited. The objective of this study was to quantify the efficiency of including dominance effects and practising mating allocation under a whole-genome evaluation scenario. Four strategies of selection, carried out during five generations, were compared by simulation techniques. In the first scenario (MS), individuals were selected based on their own phenotypic information. In the second (GSA), they were selected based on the prediction generated by the Bayes A method of whole-genome evaluation under an additive model. In the third (GSD), the model was expanded to include dominance effects. These three scenarios used random mating to construct future generations, whereas in the fourth one (GSD + MA), matings were optimized by simulated annealing. The advantage of GSD over GSA ranges from 9 to 14% of the expected response and, in addition, using mate allocation (GSD + MA) provides an additional response ranging from 6% to 22%. However, mate selection can improve the expected genetic response over random mating only in the first generation of selection. Furthermore, the efficiency of genomic selection is eroded after a few generations of selection, thus, a continued collection of phenotypic data and re-evaluation will be required.
Estimation of non-additive genetic effects in animal breeding is important because ignoring these effects will produce less accurate estimates of breeding values and will have an effect on ranking breeding values. As a consequence, including these effects will produce a more accurate prediction and, therefore, more genetic response. This potential increase of genetic response is about 10% for traits with a low heritability, high proportion of dominance variance, low selection intensity and high percentage (>20%) of full-sibs .
However, dominance effects have rarely been included in genetic evaluations. The reasons, that can be argued, are the greater computational complexity and the inaccuracy in the estimation of variance components (it is commonly believed that 20 to 100 times more data are required including a high proportion of full-sibs ). It has also been claimed that there is little evidence of non-additive genetic variance in the literature (see for example ). However, although estimates are scarce, dominance variance usually amounts to about 10% of the phenotypic variance . Furthermore, in an extensive review , estimates of the ratio of additive to dominance variance have been reported in wild species i.e. about 1.17 for life-history traits, 1.06 for physiological traits and 0.19 for morphological traits. In the same study, the estimate of this ratio for domestic species was 0.80.
Moreover, mating plans (or mating allocations) have been used in animal breeding for several reasons: a) to control inbreeding; b) in situations where economic merit is not linear; c) when there is an intermediate optimum (or restricted traits); d) to increase connection among herds and, finally, e) to profit from dominance genetic effects. With respect to the last point, it is well known that every methodology pretending to use non-additive effects [6–8] must contemplate two types of mating: a) matings from which the population will be propagated; b) matings to obtain commercial animals. Among all the methodologies aimed at profiting from dominance, mating allocation could be the easiest option. Optimal mating allocation relies on the idea that although selection should be carried out on estimated additive breeding values, animals used for commercial production should be the product of planned mating which maximizes the overall (additive plus dominance effects) genetic merit of the offspring. Mating allocation profits from dominance when the commercial population is constructed, but for the next generation only additive effects are transmitted.
Although not considered here, other ideas could be used to exploit dominance in later generations. The key idea is that selection should be applied not only to individuals and should be extended to mating. Although it is usually thought that application of the above ideas requires two separate lines as in the classical crossbreeding programmes or in the so-called reciprocal recurrent selection, it can be carried out in a single population [6, 7]. Furthermore, a 'super-breed' model can be implemented to exploit both across- and within-breed dominance variances .
With the recent availability of very dense SNP panels and the advent of genomic selection  it seems natural that methods using dominance variation should be revisited. The aim of this study was to quantify the efficiency of mating allocation under a whole-genome evaluation scenario in terms of genetic response to selection in the first and subsequent generations.
A population was simulated for 1000 generations at an effective size of 100. After 1000 generations, the actual size of the population increased up to 1000 (500 per sex) and remained at 1000 for three discrete and consecutive generations. During the whole process, all individuals were generated with one gamete from a random father and one from a random mother. Therefore the data set for the estimation of the marker effects consisted of the 3000 individuals from the last three generations. These 3000 (generation 1001, 1002 and 1003) individuals were genotyped and phenotyped and then used as training population to estimate additive and dominance effects of SNP.
The genome was assumed to consist of 10 chromosomes each 100 cM long and 1000 loci/chromosome (i.e. a total of 9000 SNP plus 1000 QTL) were located at random map positions. Both SNP and QTL were biallelic. Mutations were generated at a rate of 2.5 × 10-3 per locus per generation at the marker loci and at a rate of 2.5 × 10-5 at the QTL loci. These mutation rates, taken from  are unrealistic but they seem to provide a reasonable level of segregation after only 1000 generations. Both the additive and the dominance effects were sampled from a standard normal distribution and scaled to obtain the desired values of h2 (VA/VP) and d2 (VD/VP) where VA, VD and VP the additive, dominance and phenotypic variances as defined in, for example . The simulation of additive and dominance effects was a bit simplistic because it is known that the distribution of additive effects is leptokurtic and the distribution of dominance effects is dependent on additive effects . In generation 1, about half of the loci were fixed for allele 1 and the other half were fixed for allele 2.
Model of analysis
- a)The first model assumed that the phenotypic value of individual j (j = 1, ... N) is
- b)The second model also assumed, in addition, that dominance effects were included for each SNP:
where S is a scale parameter and v is the number of degrees of freedom. As before, the values of v = 4.012 and S = 0.0020 were assumed.
Gibbs sampling based on posterior distributions conditional on other effects was implemented for estimation by averaging the samples from 10,000 cycles, after discarding the first 1,000.
Prediction of breeding values
where wij is an indicator function of the genotype of the jth marker of the ith individual that takes the values 1, 0, -1 when the genotypes are AA, Aa or aa, respectively. Moreover, pj and qj are the allelic frequencies (A or a) for the jth marker in the training population and α is the average effect of substitution for the jth marker calculated as α j = α j under model a) and α j = α j + d j (q j - p j ) under model b).
Prediction of genotype effects of future matings
where pr ijk (AA), pr ijk (Aα) and pr ijk (aa) are the probabilities of the genotypes AA, Aa and aa for the combination of the ith and jth individual and the kth marker.
Generation 1004 was formed from 25 sires and 250 dams selected from generation 1003. Two strategies of selection, carried out during five generations, were compared. In the first strategy, 25 males and 250 females were selected from 500 males and 500 females based on the prediction of breeding values from the estimation of markers effect under model a) and b), denoted and GSA and GSD, respectively. Afterwards they were mated randomly (10 dams per sire) and four sibs were obtained from each mating; the true genotypic values of the offspring were calculated.
In the second (GSD + MA), from the 6250 (25 × 250) possible matings, we chose the best 250 based on the prediction of the mating (Gij), and we generated four new individuals for each mating mate. The true genotypic values of the offspring were also calculated. The algorithm of searching used was the simulated annealing.
Finally, phenotypic selection was also carried out as a control, and we replicated the selection strategies by considering the true QTL as markers and the simulated effects of the additive and dominance effects of the QTL as known.
Fifty replicates of each method and strategy were performed.
Results and discussion
Number of SNP with different degrees of linkage disequilibrium with the QTL
First generation response
Comparison of selection response in the first generation with different methods
GSD + MA
Furthermore, it must be mentioned that the use of a model including dominance does not give worse results even when the true simulated model is purely additive. For just one generation, the selection responses with and without dominance in the evaluation model were 0.4724 vs. 0.4670 (h2 = 0.20) and 0.7832 vs. 0.7728 (h2 = 0.40), respectively.
Subsequent generation response
The loss of efficiency of GS after the first generation can be attributed to the reduction of genetic variance caused by the reduced population size of the selected population and by the increase of linkage disequilibrium among the QTL as a consequence of selection, the so-called Bulmer effect . In fact, the LD among QTL increases from an r2 value of 0.0014 in generation 1003 to a value of 0.0032 in generation 1004.
Furthermore, additional reduction of the expected response is explained by the loss of linkage disequilibrium between the SNP and the QTL due to recombination.
Response after random mating
Selection response after several generations without selection (GS)
h2= 0.20 d2= 0.05
h2= 0.20 d2= 0.10
h2= 0.40 d2= 0.05
h2= 0.40 d2= 0.10
GSD + MA
GSD + MA
GSD + MA
GSD + MA
Known QTL genotypes and effects
Selection response after several generations of genomic selection
h2= 0.20 d2= 0.05
h2= 0.20 d2= 0.10
GSD + MA
GSD + MA
h 2 = 0.40 d 2 = 0.05
h 2 = 0.40 d 2 = 0.10
GSD + MA
GSD + MA
If we examine the increase of response due to MA in the first generation, in Scenario A (QTL genotypes known) it ranges from 19% (h2 = 0.40 and d2 = 0.05) to 45% (h2 = 0.20 and d2 = 0.10) and in Scenario B (QTL genotypes and effects known) from 17% (h2 = 0.40 and d2 = 0.05) to 38% (h2 = 0.20 and d2 = 0.10). Although the percentage of increase over GSD is greater in Scenario A, the absolute value of extra response due to MA is bigger in Scenario B, as expected when maximum information is available. Success of MA is due to the possibility of predicting the genotype of future offspring and of estimating the additive and dominance effects. The first challenge is accomplished even in Scenario A, which shows a higher relative superiority than Scenario B. In addition, these extra genetic responses are greater than the ones shown in Table 2, when SNP genotypes are used to predict additive and dominance effects.
Furthermore, a strong reduction in the genetic response is observed between the first and the second generations for every scenario. However, the response is maintained at a higher degree when QTL effects are known than when SNP or QTL effects are estimated. As expected, the scenario in which QTL genotypes are known but their effects need to be estimated, provides an intermediate response.
Introduction of dominance effects in genetic evaluation is easier to achieve in the whole-genome evaluation scenario than in the classical polygenic model, where potential parental combinations have to be defined and evaluated. Introduction of dominance effects in models of whole-genome evaluation provides two main results. First, it increases the accuracy of prediction of breeding values and second, it makes it possible to obtain an extra response by the appropriate design of future matings using mate allocation techniques.
Thus, mate allocation is recommended in the genetic management of populations under selection by whole-genome evaluation procedures, although the potential extra response is achieved only in the first generation and then maintained afterwards.
Our results also show that in most scenarios of genomic selection a continued collection of phenotypic data and re-evaluation of the additive and dominance effects of markers will be required, because the ability of predicting breeding values is greatly reduced when selection is carried out.
The research was supported by Project CGL2009-13278-C02-02/BOS (Ministerio de Educación y Ciencia, Spain). It was prepared for the 2009 Chapman Lectures in Animal Breeding and Genetics at the University of Wisconsin-Madison
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