Genomic mate-allocation strategies exploiting additive and non-additive 1 genetic effects to maximise total clonal performance in sugarcane 2

24 Mate-allocation in breeding programs can improve progeny performance by exploiting non- 25 additive effects. Breeding decisions in the mate-allocation approach are based on predicted 26 progeny merit rather than parental breeding value. This is particularly attractive when non-additive 27 effects are significant, and the best-predicted progeny can be clonally propagated, for example 28 sugarcane. We compared mate-allocation strategies that leverage non-additive and heterozygosity 29 effects to maximise sugarcane clonal performance to schemes that use only additive effects to 30 maximise breeding value. We used phenotypes and genotypes from a population of 2,909 clones 31 phenotyped in Australia’s sugarcane breeding program’s final assessment trials for three traits: 32 tonnes of cane per hectare (TCH), commercial cane sugar (CCS), and fibre. The clones from the 33 last generation of this data set were used as parents to simulate families from all possible crosses 34 (1,225), each with 50 progenies. The breeding and clonal values of progeny were predicted using 35 GBLUP (considering only additive effects) and the e-GBLUP model (incorporating additive, non- 36 additive and heterozygosity effects). Integer linear programming was used to identify the optimal 37 mate-allocation among the selected parents. Compared to the breeding value, the predicted 38 progeny value of allocated crossing pairs based on clonal performance (e-GBLUP) increased by 39 57%, 12%, and 16% for TCH, CCS, and fibre, respectively. In our study, the mate-allocation 40 strategy exploiting non-additive and heterozygosity effects resulted in better clonal performance. 41 However, there was a noticeable decline in additive gain, particularly for TCH, which might have


INTRODUCTION
Crop breeding strategies for producing enough food for a growing population have evolved 49 dramatically in different species over the last two decades. Sugarcane breeding programs were 50 initiated from crosses between sugar-rich cultivated species, primarily Saccharum Officinarum L., 51 and a wild relative, Saccharum Spontaneum L., which provided disease/pest resistance and abiotic 52 tolerance in a range of varieties (Wei and Jackson 2016;Yadav et al. 2020). In modern commercial 53 programs, the emphasis on sugarcane breeding has shifted to crossing highly heterozygous inter-54 specific hybrids ). The primary objective of this shift is to create genetic variation 55 that can be exploited via selection in the subsequent cycles before reverting to clonal selection. 56 However, the first and most challenging breeding decision is to select the appropriate genotypes 57 as parents for crosses to maximise the performance of progeny for variety development while  while considering dominance effects. 94 We hypothesised that mate-allocation based on predicted progeny performance 95 incorporating non-additive effects would improve the expected performance of the best clones 96 from a sugarcane breeding program. This study aimed to investigate improvements in the 97 prediction of clonal performance in an elite sugarcane population using mate-allocation strategies, 98 where parental clones were selected based on the genomic prediction of cross-performance; program) were reported to be low due to the high number of replications and large plot size within-134 region. BLUPs also accommodated small amounts of missing data.

135
A diploid parameterisation was utilised for genotype calling, with homozygous genotypes 136 for reference and alternative alleles classified as 0 and 2, respectively, and heterozygous genotypes calling. As quality controls, SNPs with a minor allele frequency of less than 0.01 were excluded, 140 as were SNPs with an Affymetrix QC score of less than 0.6 and at less than 90% of genotypes 141 called across genotyped clones. After quality control, the population included 2,909 clones with 142 26,086 highly polymorphic SNP genotypes.  156 As a first step in predicting the performance of parental crosses , the genotypes of the phantom 157 progeny had to be simulated. To model marker segregation in the progeny population, 70 parents 158 from the overall population were chosen for crossing based on their genomic predicted breeding 159 values (GEBVs). (Fig 1). To account for dioecy, 35 clones were randomly assigned as male and   (Haldane 1919). In a recent sugarcane study, the same 171 software was used to highlight the different approaches for implementing GS in a simulated 172 breeding environment, taking additive and non-additive effects into account for improving 173 complex sugarcane traits. We conducted ten repetitions in order to eliminate the sampling bias 174 between male and female parents. The parental clones were kept the same in each iteration in order 175 to compare the two strategies for mate allocation.  The additive genetic variance of offspring from a cross can be predicted deterministically using   188 Single-trait linear mixed models were fitted to estimate genetic variance components for TCH, progeny per family (Fig 2). The performance of these progeny in terms of breeding and clonal 196 value was predicted using a genomic prediction framework based solely on marker profiles (Fig   197   2).

198
In matrix notation, the GBLUP and the extended GBLUP model can be represented as follows: information" algorithm using REML for variance component estimates.
In a mixed model framework, Eq. 4 was used to predict breeding values, dominance where n is the total number of SNPs, being the allele frequency at SNP i, and is an indicator 282 variable for additive genetic effects and coded as 0, 1, and 2 for qq, Qq, and QQ genotypes.

322
The estimates of variance components, heritabilities, and the maximum log-likelihood ratio 323 values obtained from the two described models (Eq.'s 1 and 2) are shown in Table 1 (Table 1, Fig 3). This indicates that a fraction of the non-additive genetic   368 The average heterozygosity across markers was used to determine genome-wide 369 heterozygosity per clone (Table 1). The regression coefficient on heterozygosity for TCH (92.84 370 ± 11.08) was significant, suggesting an increase in genome-wide heterozygosity is associated with 371 an increase in average cane yield. For CCS and fibre, however, the standard error of the regression 372 coefficient was substantially larger than the heterozygosity estimates and did not differ 373 significantly (Table 1). 375 The total variation of predicted breeding ̂ (and clonal ̂) value for all potential crossing 376 pairs (n=1,225), 50 best crosses selected from ILP, and the top decile of best crosses are depicted 377 in Fig. S1 for TCH, CCS and fibre content for one simulation iteration. The mean ̂ (or ̂) for all 378 potential crossing pairs (the baseline for our comparisons, n=1,225) was 2.02 ± 0.006 (4.80 ± 0.02) 379 tonnes/ha, 0.24 ± 0.0008 (0.31 ± 0.0009) measured in %, and 0.46 ± 0.002 (0.61 ± 0.002) % for 380 TCH, CCS and fibre, respectively across ten iterations ( Table 2). The average expected progeny 381 value of selected matings based on a model that exploited non-additive genetic effects (e-GBLUP) 382 was improved by 57%, 12%, and 16% for TCH, CCS, and fibre, respectively, compared to an 383 additive model (GBLUP) ( Table 2). The expected total genetic superiority of the progeny was higher for all traits when matings 409 were chosen based on clonal performance rather than breeding value, giving the offspring an 410 advantage for TCH, CCS, and fibre, respectively. However, a significant decrease in additive 411 genetic gain was found using the same selection strategy, notably for TCH. No major difference 412 was found between the two strategies in additive (∆u) and expected genetic (∆g) gain for CCS and 413 fibre. The rankings of crossing pairs differed significantly in terms of mate allocation techniques where selection is made on GEBVs or GPCPs. For example, only approximately six crossing pairs 415 out of 50 overlapped between the mate-allocation strategies, for TCH as expected, given its higher 416 epistatic effects. This indicates that different parents were selected to optimise the total additive 417 (or clonal) value.

419
Our study demonstrates mate-allocation strategies that account for non-additive genetic 420 effects in a sugarcane breeding scheme can improve progeny performance in the next generation.

421
Considering non-additive genetic effects in mating decisions is likely to lead to breeding of higher-  To balance long and short-term gain, the sugarcane breeding scheme could be considered 501 to have two (competing) aims: population improvement via recurrent GS focuses on allele 502 substitution effects, which control and increase the frequency of favourable alleles in the 503 population over time, and can be primarily driven for larger genetic gain in the long term; and a variety development pipeline for short-term development makes use of non-additive and 505 heterozygosity effects to improve the phenotypic performance of market-ready clones.

506
Preselection on GEBVs might restrict the opportunity to select alternative clones that might 507 potentially generate progeny with a greater overall genetic value when used in specific matings. It 508 is important to consider that mating, which benefits from non-additive effects, can only increase 509 progeny performance during its implementation and that the benefits resulting from specific 510 combining abilities cannot be accumulated over generations. It is essential to continually update 511 genomic prediction and mate-allocation programs to benefit from non-additive genetic effects in 512 the long run.

513
Our results are limited to a single population and a single-trait approach; therefore, the 514 proposed approach could select different parental lines for different target traits. In practice, 515 however, expanding the approach to multiple-trait selection is preferable. A simple extension 516 would be to use a selection index that includes multiple traits and then consider the selection index 517 as a new target trait for the existing single trait approach. Another possible modification is directly 518 implementing multi-trait genomic prediction models and evaluating selection lines using an 519 appropriate selection index. 520 Furthermore, in order to approximate a high-complexity genome, we used simplified 521 assumptions in our simulation schemes. However, genetics in auto-polyploid species is more 522 complicated than in diploid species since more than two alleles may occur at the same locus. As a 523 result, there are additional phases, and recombination and preferential pairing can vary. In addition, 524 there is limited theoretical and experimental information on recombination and segregation in 525 high-ploidy species. And determining which alleles co-occur on each homologous copy gets increasingly challenging as ploidy increases. Furthermore, a reference genome is essential for 527 phasing genotypes in heterozygous polyploids like sugarcane. Unfortunately, the sugarcane 528 community does not have access to the complete reference sequence, which did not allow for 529 leverage of genome-wide phased haplotypes. Nevertheless, the pseudo-diploid markers is a rough 530 approximation of what we used in our study because the majority of the markers in the SNP array 531 are single/low-dose markers. Based on genotype allele count (0, 1 and 2), the software we used to 532 simulate the progenies assumes that the input (marker) data is in the correct gametic phase. 533 We are aware of our research's limitations, as well as the fact that the most basic diploid  Therefore, conducting field trials to validate our findings would be worthwhile. Further research 543 is required to fully understand the benefits of mate-allocation methods in a larger context.

545
Genomic mate-allocation accounting for non-additive genetic effects is a feasible and 546 potentially effective method for improving the clonal performance of future offspring. For our 547 study, mate-allocation strategies that account for non-additive effects were favourable for all traits; progeny performance for cane yield improved by 57% when compared to strategies that solely 549 account for additive effects. Furthermore, when crossing pairs leverage non-additive and 550 heterozygosity effects, the average inbreeding coefficient of progeny was substantially lower, 551 particularly when TCH was the target trait, thus preserving long-term genetic gains. Mate-552 allocation accounting for non-additive genetic effects and heterozygosity (or inbreeding  569 The authors declare that they have no conflict of interest.