Comparison of prediction models and cross-validation methods
This study is the first to investigate the use of genomic prediction to improve genetic gain for yield and yield stability in macadamia breeding. Our results suggest that yield-based traits are complex and highly polygenic, as indicated by low heritability, and that GS offers a suitable method to select genotypes to improve yield. Prediction accuracy is strongly influenced by the relatedness between training and validation populations , and unrelated population predictions are expected to perform poorly compared to related family prediction . This pattern was observed across the models in the current study; model prediction accuracy for randomly-grouped individuals was higher than family-grouped individuals (predictions in unrelated populations). This is because with random groupings for CV, the training set includes full-sibs from the validation set (e.g. progeny from the same cross will be split across the training and validation sets), and so large blocks of chromosomes will be shared between the training and validation sets. The low to moderate prediction accuracies observed by Muranty, Troggio  in apple were attributed to predictions across unrelated populations. By comparison, Kumar, Chagne  achieved high prediction accuracies (0.70 to 0.90) for apple fruit quality traits, with individuals randomly allocated to CV groups.
The CV method of family-grouped prediction represents an extreme version of the potential real-world application of GS in macadamia where predictions are performed across unrelated populations. It is likely that the training and target populations will actually be more closely related as there is often an overlap of cultivars used as parents between breeding populations, and elite individuals from one population are commonly used as parental germplasm in subsequent generations . It is expected that prediction of GEBVs in a breeding program will, therefore, have accuracies closer to that of the randomly-grouped predictions compared with unrelated population predictions presented in this study. Employing GS in a population closely related to that on which the model is based would provide more accurate predictions of yield. However, more research is needed using large training population sizes with validation sets of whole family groups to improve prediction accuracy before GS can be applied in macadamia breeding.
The implementation of GS in macadamia may include prediction and deployment across environments. The current study population had limited replication of genotypes across environments and did not include G x E interactions in prediction models as preliminary results found no evidence of G x E in this experimental material . Previous studies have found some evidence that G x E may affect macadamia yield [5, 12]. However, research has not yet identified any repeatable factors than can be used for targeted deployment.
Factors affecting accuracy of genomic prediction
The prediction accuracy for yield in the current study was moderate for randomly-grouped individuals (r = 0.57), and comparable to the prediction accuracy of yield as measured by phenotypes (h2 = 0.30, h = r = 0.55). These similar values for r demonstrate that the genomic prediction accuracy estimated in the current study will provide similar gain as phenotypic analysis, regardless of the time advantage in GS strategies. The prediction accuracy achieved in GS in this study was not as high as reported in some other horticulture crops, which may be attributed to several factors. Estimates of macadamia yield in the current and previous studies  involve a large non-genetic component, as indicated by the low heritability and/or high non-additive genetic variation for this trait, and suggest a quantitative nature of inheritance. Yield measurement inaccuracies can occur when overlapping canopies result in a mixture of dropped nuts from neighbouring trees. Additionally, the method used to obtain DNIS (dry nut-in-shell) weight per harvest assumes that the moisture content of the 1 kg sample is consistent through the entire harvest. For these reasons, measuring macadamia yield is very different to measuring yield in other fruit crops, which may inhibit accurate yield prediction.
This study is, to our knowledge, the first to estimate heritability of stability of yield over consecutive years for a nut tree, and use genomic prediction to predict genetic values of yield stability. Biennial bearing in apple has been researched by multiple authors. Guitton, Kelner  found three QTLs associated with biennial bearing that explain 50% of phenotypic variability. Additionally, Durand, Guitton  suggested that irregular bearing in apple may be more influenced by factors affecting floral induction rather than those affecting fruit set or drop. Predictions using randomly-grouped individuals were moderately high for yield stability, though this may be due to the low heritability of the trait inflating prediction accuracy. The low heritability of yield stability indicates that yield fluctuations between years is very weakly controlled by genetics, and may be more influenced by non-genetic factors. Thus, it would be up to breeders to determine the value of including yield stability in a selection index when identifying elite candidates for further testing.
The population size of this study was limited compared to other studies in fruit crops, though it did consist of a large number of full-sib families. In the first study of GS in cross-pollinated fruit crop species, Kumar, Chagne  obtained high model accuracy for fruit quality traits in apple. They used a much larger population (1120 seedlings) than the current study, albeit from a smaller parent population (seven full-sib families from four female and two male parents), and prediction accuracy ranged from r = 0.70 to 0.90 using RR-BLUP and Bayesian LASSO methods. GS in citrus achieved high (r > 0.7) prediction accuracy for some fruit quality traits using around 800 individuals, with the GBLUP model consistently out-performing other models . Similarly, using a Japanese pear population of 86 parents and 765 progeny, prediction accuracy varied between models and CV methods, and was commonly greater than 0.5 . However, the correlations found for citrus and Japanese pear may be inflated, since negative correlation coefficients were set to zero when calculating prediction accuracy for these studies. Increasing the size of a phenotyped and genotyped training population would increase the accuracy of yield prediction in macadamia.
LD between markers and genes controlling target traits is essential for GS . Previous studies have suggested increasing the number of markers used in GS may not necessarily achieve better accuracies. Studies investigating the prediction accuracy of GS in citrus, Japanese pear and apple all used fewer SNP markers than the current study (1841, 1502 and 2500, respectively) [30, 32, 33]. Using the same 4113 SNP markers used in the current study, O’Connor, Kilian  found that SNPs within 1 kb distance of each other on a scaffold (M. integrifolia v2 genome assembly, 4098 scaffolds) had an average LD of r2 = 0.124, with LD decaying rapidly over short distances and more moderately over long distances . These results are important for the current study to determine that genetic markers capture genetic variance of the target trait [15, 38]. Increasing the density of markers across the genome could lead to increased prediction accuracies, as suggested by Calus, Meuwissen , where models with r2 = 0.2 between markers were more accurate than models with fewer markers and lower densities. Future analysis of LD in macadamia could employ the use of an updated macadamia reference genome (45) to determine the distribution of markers across chromosomes, and include corrections for population structure and cryptic relatedness.
Genetic recombination occurs with successive generations of breeding, which may affect the linkage between markers and genes controlling target traits . Furthermore, selection for improved individuals will also alter the frequency of alleles in the population . These changes over generations will have consequences for genomic prediction accuracy. Meuwissen, Hayes  estimated that the prediction accuracy of GS models will decrease at around 5% per generation, due to recombination. Thus, it is necessary to recalibrate the model after every few generations as genetic variance explained by the markers will change, along with the allelic frequencies in the population [40, 53]. To aid in model recalibration, Grattapaglia  suggested that selection candidates should remain in the field and be grown for 5 to 6 years to provide phenotypes for updating the model. This strategy could be employed in macadamia to ensure accuracy of predictions through subsequent generations of GS.
Genetic gain from genomic selection
The results of this study indicated that genetic gain in macadamia breeding was particularly influenced by the length of the breeding cycle. Genotyping seedlings at a very early age, for example using their first leaf after germination, to identify high-yielding individuals through GS could halve the length of the SPT. Subsequently, elite trees could be cross-pollinated to produce the next generation as soon as they begin to flower, which is usually around the age of four. From there, clonally replicated trees could be phenotyped for other economically important traits, and candidate cultivars identified using a selection index. Similarly in apples, Muranty, Troggio  suggested that GS could increase genetic gain per year compared with conventional breeding, by shortening the breeding cycle from 7 to 4 years. In contrast, prediction accuracy was not sufficient for all target traits in oil palm to reduce the generation interval, meaning that breeding would still require the testing of progeny . The authors suggested that if given the resources to increase the size of the training set, and a greater ability to model G x E interactions, GS could be a valid option to increase genetic gain in oil palm.
In their review of GS in apple by Kumar et al. [32, 55], van Nocker and Gardiner  proposed using MAS and GS to identify elite apple accessions and then, to decrease time to reproductive maturity, to implement a regime to promote early flowering. Fruit would be phenotyped over two early seasons, and then BVs compared with the predicted GEBVs to analyse genetic gain. Using these methods, candidate cultivars could be clonally propagated 7 years earlier than traditional breeding. However, the predicted beneficial outcomes of using GS in apple may not be as achievable if predictions were to occur across families rather than in randomly-grouped individuals, as has been shown here in macadamia.
Logistics of using genomic selection to increase genetic gain
The opportunity to employ GS in a wider range of crops is increasing with declining genotyping costs and advancements in technology [20, 51, 57]. Implementing genomics-assisted breeding may be expensive due to the cost of genotyping large numbers of candidates at each cycle. However, the cost of genotyping will be a trade-off with a decrease in the costs needed for phenotyping  due to the elimination of costs involved in measuring yield during the SPT. An evaluation of costs involved in MAS versus GS has been made for maize and wheat, and GS outperformed MAS even when prediction accuracies were low . Breeders should compare selection strategies to determine which combination of genotyping and phenotyping is most suitable for their crop and program to maximise accuracy of trait prediction in fruit crops .
Currently, costs involved in genotyping may restrict the implementation of GS in the Australian macadamia breeding program. To reduce genotyping costs, delaying GS to deploy on a smaller population size may be a viable option, similar to a strategy proposed by Gardiner, Volz ; to reduce the size of the seedling population to be genotyped, pre-screen the population for essential traits first. Seedlings could be grown out as per a traditional SPT, but only evaluated to age four, and precocious (early bearing) trees evaluated for KR (high KR attracts a higher commission per kilogram than low KR ). Breeders could pre-select precocious seedlings with high KR, genotype this reduced number of potentially elite individuals, and then the highest-yielding trees could be selected through GS for evaluation in RVTs. Longer generation intervals, due to phenotyping for precocity and KR for several years initially, would lead to a lower genetic gain using this strategy than GS of more seedlings at an earlier stage; however, it may be a more cost-effective option. Additionally, whilst implementing GS in macadamia may not decrease the time from seed to reproductive maturity, selecting for precocious individuals may aid in producing more individuals with a shortened juvenile stage. Reaching reproductive maturity at an earlier stage will further increase genetic gain by reducing the generation length of 4 years in the GS strategy. Extending quantitative modelling of different options for using GS in a breeding program may help to compare possible approaches and identify optimum strategies. Comparing costs of traditional breeding versus strategies using GS is not the focus of this study, though this should be evaluated to determine the prospect of implementing GS in the Australian macadamia breeding program.
Future research using GS in macadamia
Future work employing GS to increase genetic gain in macadamia could investigate other economically important traits, such as tree size. In the same population as the current study, O'Connor et al.  found 16 QTLs linked with trunk circumference. The large number of markers associated with this trait, compared with other traits in the study, means that GS may be more appropriate than GWAS and MAS to increase genetic gain, given the seemingly quantitative nature of trunk circumference. GS may also be a good candidate for other traits, such as resistance to diseases and pathogens, including husk spot and phytophthora . Furthermore, the significant associations identified between traits and markers could be incorporated into GS models. Genomic prediction methods including BayesR and BayesB allow the effect of some markers, such as those of significant effect, to be larger than others [15, 62]. Different model types could therefore be tested in the future to determine which are the most accurate in predictions.
Further work could also include multi-trait models to investigate whether the inclusion of additional traits, such as trunk circumference and nut weight, increases the accuracy of yield prediction. Jia and Jannink  found that prediction accuracy was increased for a trait with low heritability by including information for a correlated trait with high heritability. Estimates of heritability and genetic correlations between yield and various component traits have been made  and, thus, this information could be used to inform multi-trait GS. Distinctions can also be made between linked QTLs (linkage between multiple QTLs affecting different traits) and pleiotropic QTL (one gene affecting multiple traits), using multi-trait methods, like those employed by Bolormaa, Pryce .
Finally, future GS analyses could involve more genetic markers and/or more evenly-distributed markers across the genome. This approach may ensure that small-effect loci are captured, since LD in macadamia decays rapidly over short distances . With the aid of the recently published macadamia reference genome (45), future sequencing of individuals for GS analysis and the calling of SNPs may be more accurate and avoid potential issues associated with allelic dropouts .