It has been reported that genomic selection in aquaculture breeding schemes can increase selection accuracy for candidates and increase genetic gain compared to traditional aquaculture sib testing schemes
[8, 9, 19]. Our study shows that, when using genomic selection, creating double haploids as part of the process of sib testing can increase the selection accuracy of candidates and the genetic gain even more. These additional increases in accuracy and genetic gain were most dramatic with a low heritability (~22%) but were still substantial when heritability was 0.4 (~7%). However, this result was only obtained when both sexes were used to create double haploids for testing. When only one sex is double haploid, selection accuracy was reduced because only chromosome sets from the dam (sire) entered the test population and this was not offset by increasing the number of observations per chromosome set.
In this study, attempting to increase homozygosity above that obtained from random mating through maximum coancestry mating when breeding the test population had no detectable impact on genetic gain or inbreeding. This is because assortative mating was only done for one generation, which is unlikely to produce extreme genotypes. If breeding of the test population with the MaxC scheme had been continued for 10 generations or more, similar results to those obtained with the double haploids scheme would have been observed because it takes approximately 10 generations of continuous full sib mating to produce fully inbred lines
. Clearly one generation of either MaxC or MinC is insufficient to deliver any benefit.
The increase in selection accuracy of the candidate population is due to the increase in accuracy of the estimates of SNP effects in the test population because the double haploids have more extreme genotypic values. It is important to note that the study design used here permits this inference because the non-random mating structure in the test population was not replicated in the candidate breeding population, which was always bred at random. Therefore, the increased predictive accuracy was due to the test design and not the results of differences in family structure amongst the candidates. For example, if MinC mating had been implemented in the candidate population, say for five generations, to improve the family structure, genetic effects would eventually have been better estimated and a substantial increase in selection accuracy might have occurred
The benefit of the improved accuracy from generating extreme genotypes in the test population does come at a cost in robustness to the underlying genetic architecture. The design provides an estimate of a, i.e. half the difference between the genetic value of homozygotes. In this study, the allelic effects were simulated to be additive, so the estimates of an allelic substitution were not biased by the absence of heterozygotes. However, if the dominance deviation (d) is not equal to zero, the average effects obtained from homozygotes are biased by d(1-2p) where p is the minor allele frequency. This bias increases as p reduces. Most QTL are expected to have a low minor allele frequency, potentiating the bias. Presence of epistatic gene actions are expected to result in similar biases from estimations based on homozygotes only.
The advantage obtained with the MatPat scheme was achieved at a cost of reduced genetic variation in G2 compared to other schemes. However, the results show that this reduction in genetic variation was mainly generated by additional linkage disequilibrium
 created by the higher accuracy obtained with the MatPat scheme. First, inbreeding accounted for only a loss of 2% of the genetic variance and any difference in inbreeding between MatPat with the other schemes was not substantial. Under the infinitesimal model, the loss of genetic variance due to linkage disequilibrium would be ½ρ
2 where ρ is the accuracy of selection
. Thus with ρ = 0.6, predicted loss would be 18%. Using (1-½ρ
2)(1-F) predicted losses in genetic variance observed in Table
4 from the accuracies of selection presented in Table
1 gives a very close approximation. Experience with the infinitesimal model has demonstrated that increasing selection intensity results in greater short and medium term genetic gain even though this also increases the linkage disequilibrium. However, this is not the case when selection is on a known or marked QTL along with estimates of unlinked polygenic effects, for which slowing fixation of the QTL has been shown to result in increased long-term gain
. The existence of a trade-off between accuracy and long-term gain that is independent of inbreeding (genomic or pedigree) has not been reported to date.
There are two methodological approaches to produce double haploids, either mitotic or meiotic. In this study, mitotic gynogenesis and mitotic androgenesis were used. There are good reasons to expect that the extra genetic gains would have been somewhat less with meiotic gynogenesis and meiotic androgenesis because these technologies result in fish that are less homozygous than their mitotic counterparts, i.e. only a subset of their genotypes are homozygous
The increased accuracy of selection with use of a double haploid sib test population results from the explanatory variables in the regression equation (Equation 2) taking more extreme values due to inbreeding, which, based on regression theory
] , is known to increase the accuracy of the estimation of SNP effects. As derived in the Appendix, the increase selection accuracy from the perspective of genomic relationships and selection index theory can be explained using the formula:
21 is the relationship between sib test individuals and one of the selection candidates, and P is a phenotypic covariance matrix for the sib test individuals, and V is the variance of relationships between the test sibs.
This shows the expected reliability (= squared accuracy) of genomic selection is approximately equal to the reliability of traditional EBV plus a term that increases with the variances of the deviations of genomic relationships from their expectations in the test population. The implications of this formula go further in defining conditions that maximize the expected reliability of genomic selection: (1) the training animals should be as little related as possible, which makes P
-1 large; (2) the training animals should be as much related to the selection candidates as possible, which makes A
21 large; and (3) deviations of the genomic relationships from the traditional relationships should be as large as possible, resulting in large V. Points (1) and (2) were also observed by
. Double haploids have the same expected relationship with the candidates as diploid training animals (½), but the variance of their genomic relationship with the candidates is increased due to inbreeding. Thus, the increase in accuracy of genomic selection when using double haploids can be explained in two ways: (1) the more extreme regression factors in (Equation 2) allow SNP effects to be more accurately estimated, or (2) their more variable relationships with the candidates can be used by selection indices and BLUP to increase the accuracy of the EBV of the candidates.
 was used for genetic evaluation. Similar outcomes in terms of increases in accuracy and genetic gain from double haploids and non-random mating are expected with other genomic evaluation methods that are currently used. For example, the BayesB method
 concentrates on certain important regions of the genome. Double haploid individuals are also double haploids for these regions of the genome. Therefore, the variance of genomic relationships between individuals in the test and candidate individuals also increases at these regions of the genome and thus delivers a more accurate estimation of SNP effects than the test population produced by random mating.
It is expected that the use of double haploid sib test populations increases the accuracy of genomic selection for any candidate population because use of double haploids achieves a more accurate estimation of the SNP effects in the test population by increasing the variance of the genomic relationships between the test and candidate population. This is expected to hold for any candidate populations. However, the selection candidates should not be completely different from the test population
Relevance of the study
This study shows the benefits of using double haploids as test sibs in aquaculture genomic selection breeding schemes. An increase of 7 to 19% in selection accuracy, leading to a 6 to 22% increase in genetic gain was obtained. This resulted from more accurate estimation of SNP effects and required a mixture of paternal and maternal double haploid test sibs in combination with genomic selection. Increases in accuracy and genetic gain from use of double haploids were greater with lower heritability levels. Therefore, the outputs of this study can be used to increase genetic gain for difficult traits such as disease resistance and meat quality, which cannot be recorded on selection candidates. In practical applications, eggs may be collected from the nucleus breeding parents and divided in two parts and 50% would be fertilized in a natural way, forming the candidate population, and the rest further divided into one half that is submitted to gynogenesis and the other half to androgenesis. This would result in a mixture of maternal and paternal double haploid genome fishes from each family in the test population.
However, there are practical problems to overcome for the implementation of double haploids in aquaculture breeding schemes, including biases from non-additive gene effects costs and other practical constraints. There may also be ethical and regulatory issues related to animal welfare associated with the use of chromosome manipulation techniques.