The estimated heritability values for FW and PW in the present study are within the range (0.27–0.43) of values reported in recent studies in the same species for female body weight between 13 and 25 months [30–32]. In an study that accounted for random full-sib family effects in an animal model, Su et al.  estimated lower heritabilities for PW with values ranging from 0.09 for a control line to 0.26 for a line selected for egg size while the estimate was 0.13 for the line selected for yearling body weight; the full-sib family effect was very significant accounting for 22, 13 and 10% of the phenotypic variance for the three lines, respectively. In our study, no significant full-sib family effect was detected whatever the trait under consideration. It is likely due to the mixing of eyed-eggs from all the different families and their rearing in common tanks.
Heritability estimated for SD in our study was moderate in comparison to the large values (0.49 to 0.87 with a pooled heritability of 0.65) estimated by Su et al.  for their three rainbow trout lines bred derived from the same experimental base population of University of California. However, Gall and Neira  estimated a moderate heritability (0.24) for SD in Coho salmon that may be partially explained by the fact all the genetic variation was not accounted for because the spawned females represented a selected group of earliest spawners. The same explanation may also be considered to understand our own moderate estimate of heritability for SD in rainbow trout.
All our heritability estimates for rainbow trout reproductive traits (SD but also PW, SW, EN and EW) were in general close to those of Gall and Neira  in Coho salmon, although their heritability for EN was higher (0.42 vs 0.24 in our study) and more consistent with their heritability of SW than in our study. Considering EW as a measure of egg size, Gall and Neira  found a similar estimate of heritability as ours. In Su et al. , egg size was measured as a volume (in pl), neither corresponding to EW or ED. They found high estimates of heritability for their egg size trait with a pooled heritability of 0.60 across their three rainbow trout lines. Rather than measuring SW, Su et al.  measured the egg volume (ml) by allowing the eggs to settle in a volumetric cylinder after water hardening ; egg size was determined by dividing 30 by the count of eggs in a 30 ml sample. Egg number was then obtained by dividing egg volume by egg size and its pooled heritability was very high (0.55) compared to ours and in a lesser extent to Gall and Neira ’s one.
Regarding correlations between reproduction traits, the high correlation we estimated between EN and SW was also observed in Coho salmon . However these authors estimated a large negative genetic correlation (-0.63) between EN and EW for Coho salmon while we did not observed any significant correlations between EN and egg size traits in our study. Our result was only consistent with Su et al. ’ one for this particular point. Therefore the question is still pending whether or not selection for egg size may cause or not a decrease in egg number in salmonids.
Considering genetic correlations between egg size traits and SD, our estimates were consistent with the estimate (0.51) in Su et al. ’ study while Gall and Neira  reported a weaker (0.16) genetic correlation in Coho salmon. The positive, but weak, genetic correlations we estimated between egg quantity traits (EN and SW) and SD were also reported by Su et al.  and Gall and Neira  between EN and SD. However in Coho salmon the genetic correlation estimated between SW and SD was null .
Regarding the correlations between SD and female body weights, our results were in contradiction with the significant positive genetic correlation (0.51) reported by Su et al.  but very consistent with those for Coho salmon . This may be due to the inclusion of only early spawning females in our stdudy as in Gall and Neira’ one.
Although female body weights did not significantly correlated neither to egg quantity traits (EN, SW) or egg size traits (EW, ED) in our study, significant positive genetic correlations were found for PW with EN (0.47), egg size (0.51) and egg volume (0.67) in US lines of rainbow trout . Gall and Neira  reported also in Coho salmon that PW correlated moderately with EN (0.32) or EW (0.37), and more strongly with SW (0.56). Therefore our results are not consistent with the two previous studies in salmonid species regarding genetic associations between female body weight and egg production traits.
Earlier studies indicated that selection for body weight at any age would result in a correlated response for body weight at other ages including age at slaughter and age at spawning for females  and that genetic correlations between yearling weight, post-spawning weight of females and egg size, egg number and egg volume were moderate but positive in rainbow trout . These findings led to the assumption that breeding programs designed to increase body size would result in improving egg production traits . However our results do not really validate this assumption since FW and PW do not appear to be genetically correlated - neither positively nor negatively - to any of the reproduction traits (SD, SW, EN, EW or ED). It is therefore important to consider direct selection for improving egg production traits in rainbow trout breeding programs.
The credibility/confidence intervals associated with the QTLs were large in most cases, which precluded the meaningful identification of potential underlying candidate genes. Nevertheless, based on the functional information given in the human gene database GeneCards® [34, 35] and described phenotypes in mutant mice or worms, we were able to propose five candidate genes for female reproduction traits (3 for SD, 1 for ED and 1 shared by EN and SW). No phenotypes were described for these candidate genes in the zebrafish database ZFIN . As far as we know, our study is the first report for QTLs and candidate genes playing for fecundity and egg size traits in rainbow trout.
Fitness traits such as spawning date and body weight are major factors in the life history of salmonid fishes. Despite the fact that some recent QTLs studies have focused on growth traits in rainbow trout [30, 32] the only significant SNP we detected for female body weight was not in the vicinity of any QTL regions reported for trout body weight. This SNP was not presented in Table 4 because the detected association was considered as a spurious one. There was indeed no evidence for a QTL under GBLUP analysis and only a single SNP was detected on Omy1 with a logBF> 6 in an intergenic region between crocc2 and slco1f1 genes that are not annotated as playing a role in growth function.
In our study, the highest significant (p-value < 10-6 at the genome level) SNP was found for SD on Omy6. It corresponds to the only significant QTL for SD under GBLUP analysis and this single SNP explained over 7% of the genetic variance under BayesC approach. The SNP Affx-88920061 is located within the importin-11 gene (alias Ran-Binding Protein 11) that plays a receptor role in nuclear protein import. The phenotypes observed in a MGI mouse strain (ID MGI:5617259) with a mutation in this gene may help to understand the effects of a variant allele may have on spawning date in rainbow trout. The double mutant homozygote is a pre-weaning lethal phenotype in mouse and the heterozygote exhibits decreasing levels of iron and glucose levels in the blood. In addition, the heterozygote male had an abnormal eye (lens) morphology. However we may wonder whether the association is a spurious one due to a very high rate of mendelian errors at this SNP position when comparing genotypes from progeny and their parents. Indeed, 104 mendelian errors were observed at this SNP while the medium number of mendelian errors was only 3 for the 4,067 SNPs (out of 27,799 SNPs) with at least one mendelian error detected.
While the genetic architecture underlying SD is still largely unknown, a lot of QTLs affecting SD or age at sexual maturation have been detected in salmonid species during the last twenty years [37–43]. Due to the low density of markers and the non standardisation of linkage group names in early studies, it is difficult to report whether our QTLs may have been detected in other studies. Nevertheless, as far as we know, no QTL for SD in salmonid species has been reported in the neighborhood of the highly significant SNP we observed on Omy6. Under Bayesian GWAS, three others QTLs for SD were detected on Omy11, Omy15 and Omy27. Each of them explained between 1.2 and 1.9% of the genetic variance of SD. There is no obvious candidate gene for the large QTL region on Omy11. On the contrary, it is worth mentioning that the peak SNP on Omy15 is positioned within the ARHGEF4 (Rho Guanine Nucleotide Exchange Factor 4) gene that acts as guanine nucleotide exchange factor (GEF) for RHOA, RAC1 and CDC42 GTPases. MGI mutant phenotypes for ARHGEF4 concern in particular immune system and metabolism with decreased hemoglobin content, decreased IgE level, decreased IgG1 level, decreased T cell number, increased mature B cell number, increased circulating alkaline phosphatase level, increased circulating total protein level and decreased circulating triglyceride level. Despite the large credibility interval for the last QTL on Omy27, we may also propose NR2E1 as a convincing candidate gene because the peak SNP is located just behind this estrogen-related receptor gamma-like gene. This gene is an orphan receptor that binds DNA as a monomer to hormone response elements and is in particular involved in the regulation of retinal development and essential for vision. It may be involved in retinoic acid receptor regulation in retinal cells. MGI mutant phenotypes for NR2E1 have abnormal optic nerve and retina morphology, abnormal brain morphology, decreased body size and total body fat amount and decreased female fertility. Interestingly, we can hypothesize that two of the four QTLs detected for SD may be associated to abnormal eye morphology and defects in vision that may render trout less sensitive to the photoperiod stimuli.
Concerning the fecundity traits EN and SW, two QTLs sharing the same SNP peaks on Omy2 (Affx-88951720) and Omy12 (Affx-88950456) were detected, confirming that the two traits are biologically very close. The QTL on Omy2 explained 3.2% and 3.0% of the genetic variance for EN and SW, respectively. The QTL on Omy12 explained about 2.5-2.7% of the genetic variance for each trait. For EN, a third QTL was detected on Omy8 that explained 1.4% of the genetic variance. No obvious gene candidate could be proposed for this QTL. For SW, a third QTL was detected on Omy2 that explained 1.9% of the genetic variance and a last QTL was detected on Omy1 that explained 1.3% of the genetic variance. These last two QTLs for SW had large credibility intervals (> 1 Mb) and no obvious candidate gene could be proposed. Concerning the common peak SNP for the QTL on Omy2 shared by EN and SW, its location is in-between the MPRD gene (cation-dependent mannose-6-phosphate receptor-like) and the PHC1 gene (polyhomeotic-like protein 1). This PHC1 gene is a homolog of the Drosophila polyhomeotic gene, which is a member of the Polycomb group of genes. It is a component of a Polycomb group (PcG) multiprotein PRC1-like complex, a complex class required to maintain the transcriptionally repressive state of many genes, including Hox genes, throughout development . MGI homozygous mutant phenotypes for the PHC1 gene exhibit perinatal lethality, posterior skeletal transformations and defects in neural crest derived tissues, including ocular abnormalities, cleft palate, parathyroid and thymic hypoplasia and cardiac anomalies. We hypothesize that this gene may have a role in rainbow trout fecundity.
For egg size traits measured by EW and ED respectively, we will focus on the three QTLs on Omy1 showing the highest consistency of results across GWAS (Table 4). Among those QTLs, the same QTL region on Omy1, spanning between 66.539 Mb and 68.881 Mb was detected for the two traits, although the peak SNPs were different across GWAS (67.15 Mb for GBLUP and 68.66 Mb for BayesCᴨ). No obvious candidate gene could be proposed in this large QTL region that explained 2% of the genetic variance for EW.
Regarding EW, there was a strong evidence for a distinct QTL explaining 1.2% of the genetic variance, in the region spanning from 60.498 Mb and 64.633 Mb on Omy1 with the peak SNP very close to 64.633 Mb in an uncharacterized protein (LOC110527930). No candidate gene could be proposed within this QTL region, but in the close vicinity of this QTL region, let us mention the presence of the prkg2 gene (located between 64.660 and 64.676 Mb on Omy1) whose role is important in oocyte maturation in mammals and zebrafish . This prkg2 gene may be therefore suggested as a functional candidate gene.
Regarding ED, there was evidence for another QTL on Omy1 that explained nearly 2% of the genetic variance in the region spanning between 70.848 Mb and 71.813 Mb. The peak SNP (at 71.813 Mb) is close to the position (71.675 – 71.699 Mb) of the WAPLA gene (wings apart-like protein homolog) which is a straightforward gene candidate for explaining this last QTL on Omy1. Indeed this gene is a regulator of meiotic chromosome structure and function, playing a role in sister chromatid cohesion, cohesin association with chromatin, DNA double strand break repair and polar body positioning following meiotic divisions during oogenesis [46, 47]. Worm C. elegans mutants have an egg-laying defect and reduced brood size with 21% displaying embryonic lethality whilst 28% arrest at the larval stage .
The implementation of genomic selection in a breeding program for female reproduction traits would allow a gain in accuracy of 16% to 32% (depending on the trait studied) compared to BLUP selection when considering a reference population of about 1100 individuals. For a smaller reference population of 670 individuals, genomic selection will also be more efficient than pedigree-based selection. In the literature, several studies in salmonids [30, 48–51] reported moderate to strong gains in accuracy (+11% to 110%) for genomic selection compared to BLUP selection of depending on the genetic architecture of the traits and the size of the reference populations. Increasing by 60% the size of the training population (starting from 670 individuals) in a fish line whose effective population size is estimated around 50 , increased the accuracy of GEBVs by 6% to 11% depending on the trait considered. Considering Goddard  prediction equation of GS accuracy, we could have expect an increase of accuracy of about 20% in our rainbow trout line when increase our training population from 670 to 1070 animals. Significantly higher gain in accuracy (about +80%) was described for gestation length (h²=0.4) in a pig line when increasing by 130% the training population size (starting from 550 sows) in a Large White line with effective population size estimated to be about 100 .
We showed a severe loss of accuracy when the degree of kinship between the training and the validation populations was less related and this was more important for BLUP than GBLUP. It is well known that close relationships between animals in the training and validation sets increase the accuracy of genomic predictions compared to the ones derived for an independent validation population . Under scenarios T1 and T2, our estimates of GS accuracy are close to the theoretical estimates derived from Goddard ’ formula, which makes sense since one of the basic assumption beyond his formula is that GS accuracy comes only from linkage disequilibrium across the whole population and not from any linkage association and family structure. The fact that the loss of accuracy was less severe for GBLUP than for BLUP had also be shown on poultry . This phenomenon has also been quantified in a salmon population dedicated to genomic selection for sea lice resistance . What is less known is that these strong decreases in accuracy are also associated with strong biased in the predictions (see Supplementary Table 2, Additional File 1). While the variance of GEBVs was not significantly overestimated when the training and validation sets were closely related (see Supplementary Table 1, Additional File 1), it became either strongly inflated or deflated when relationships became more distant. The same observation held for BLUP predictions, even in a larger extent. This may be a strong issue to correctly predict genetic trends or performing optimal multitrait index selection since the magnitude of the inflation varied a lot across traits. Nevertheless, when performing selection within cohort based on a training population including sibs of the candidates, it does not appear to be a problem.