Bayesian optimisation for breeding schemes

INTRODUCTION

Advances in genotyping technologies have provided breeders with access to the genotypic values of several thousand genetic markers in their breeding materials. Combined with phenotypic data, this information facilitates genomic selection. Although genomic selection can benefit breeders, it does not guarantee efficient genetic improvement. Indeed, multiple components of breeding schemes may affect the efficiency of genetic improvement and controlling all components may not be possible. In this study, we propose a new application of Bayesian optimisation for optimizing breeding schemes under specific constraints using computer simulation.

METHODS

Breeding schemes are simulated according to nine different parameters. Five of those parameters are considered constraints, and 4 can be optimised. Two optimisation methods are used to optimise those parameters, Bayesian optimisation and random optimisation.

RESULTS

The results show that Bayesian optimisation indeed finds breeding scheme parametrisations that provide good breeding improvement with regard to the entire parameter space and outperforms random optimisation. Moreover, the results also show that the optimised parameter distributions differ according to breeder constraints.

DISCUSSION

This study is one of the first to apply Bayesian optimisation to the design of breeding schemes while considering constraints. The presented approach has some limitations and should be considered as a first proof of concept that demonstrates the potential of Bayesian optimisation when applied to breeding schemes. Determining a general "rule of thumb" for breeding optimisation may be difficult and considering the specific constraints of each breeding campaign is important for finding an optimal breeding scheme.

Emphasis on resilience in dairy cattle breeding: Possibilities and consequences

This study aimed to investigate dairy cattle breeding goals with more emphasis on resilience. We simulated the consequences of increasing weight on resilience indicators and an assumed true resilience trait (TR). Two environments with different breeding goals were simulated to represent the variability of production systems across Europe. Ten different scenarios were stochastically simulated in a so-called pseudogenomic simulation approach. We showed that many modern dairy cattle breeding goals most likely have negative genetic gain for TR and promising resilience indicators such as the log-transformed, daily deviation from the lactation curve (LnVAR). In addition, there were many ways of improving TR by increasing the breeding goal weight of different resilience indicators. The results showed that adding breeding goal weight to resilience indicators, such as body condition score and LnVAR, could reverse the negative trend observed for resilience indicators. Loss in the aggregate genotype calculated with only current breeding goal traits was 12 to 76%. This loss was mainly due to a reduction in genetic gain in milk production. We observed higher genetic gain in beef production, fertility, and udder health when breeding for more resilience, but from an economical point of view, this was not high enough to compensate for the reduction in genetic gain in milk production. The highest genetic gain in TR was obtained when adding the highest breeding goal weight to LnVAR or TR, both with 0.29 genetic standard deviation units. The indicators we used, body condition score and LnVAR, can be measured on a large scale today with relatively cheap methods, which is crucial if we want to improve these traits through breeding. Economic values for resilience have to be estimated to find the most optimal breeding goal for a more resilient dairy cow in the future.

Optimizing the Construction and Update Strategies for the Genomic Selection of Pig Reference and Candidate Populations in China

Optimizing the construction and update strategies for reference and candidate populations is the basis of the application of genomic selection (GS). In this study, we first simulated1200-purebred-pigs population that have been popular in China for 20 generations to study the effects of different population sizes and the relationship between individuals of the reference and candidate populations. The results showed that the accuracy was positively correlated with the size of the reference population within the same generation (r = 0.9366, p < 0.05), while was negatively correlated with the number of generation intervals between the reference and candidate populations (r = −0.9267, p < 0.01). When the reference population accumulated more than seven generations, the accuracy began to decline. We then simulated the population structure of 1200 purebred pigs for five generations and studied the effects of different heritabilities (0.1, 0.3, and 0.5), genotyping proportions (20, 30, and 50%), and sex ratios on the accuracy of the genomic estimate breeding value (GEBV) and genetic progress. The results showed that if the proportion of genotyping individuals accounts for 20% of the candidate population, the traits with different heritabilities can be genotyped according to the sex ratio of 1:1male to female. If the proportion is 30% and the traits are of low heritability (0.1), the sex ratio of 1:1 male to female is the best. If the traits are of medium or high heritability, the male-to-female ratio is 1:1, 1:2, or 2:1, which may achieve higher genetic progress. If the genotyping proportion is up to 50%, for low heritability traits (0.1), the proportion of sows from all genotyping individuals should not be less than 25%, and for the medium and high heritability traits, the optimal choice for the male-to-female ratio is 1:1, which may obtain the greatest genetic progress. This study provides a reference for determining a construction and update plan for the reference population of breeding pigs.

Breeding schemes with optimum-contribution selection or truncation selection for beef cattle destined for use on dairy females

We tested the hypothesis that the size of a beef cattle population destined for use on dairy females is smaller under optimum-contribution selection (OCS) than under truncation selection (TRS) at the same genetic gain (ΔG) and the same rate of inbreeding (ΔF). We used stochastic simulation to estimate true ΔG realized at a 0.005 ΔF in breeding schemes with OCS or TRS. The schemes for the beef cattle population also differed in the number of purebred offspring per dam and the total number of purebred offspring per generation. Dams of the next generation were exclusively selected among the one-year-old heifers. All dams were donors for embryo transfer and produced a maximum of 5 or 10 offspring. The total number of purebred offspring per generation was: 400, 800, 1,600 or 4,000 calves, and it was used as a measure of population size. Rate of inbreeding was predicted and controlled using pedigree relationships. Each OCS (TRS) scheme was simulated for 10 discrete generations and replicated 100 (200) times. The OCS scheme and the TRS scheme with a maximum of 10 offspring per dam required approximately 783 and 1,257 purebred offspring per generation to realize a true ΔG of €14 and a ΔF of 0.005 per generation. Schemes with a maximum of 5 offspring per dam required more purebred offspring per generation to realize a similar true ΔG and a similar ΔF. Our results show that OCS and multiple ovulation and embryo transfer act on selection intensity through different mechanisms to achieve fewer selection candidates and fewer selected sires and dams than under TRS at the same ΔG and a fixed ΔF. Therefore, we advocate the use of a breeding scheme with OCS and multiple ovulation and embryo transfer for beef cattle destined for use on dairy females because it is favorable both from an economic perspective and a carbon footprint perspective.

Breeding Schemes: What Are They, How to Formalize Them, and How to Improve Them?

Formalized breeding schemes are a key component of breeding program design and a gateway to conducting plant breeding as a quantitative process. Unfortunately, breeding schemes are rarely defined, expressed in a quantifiable format, or stored in a database. Furthermore, the continuous review and improvement of breeding schemes is not routinely conducted in many breeding programs. Given the rapid development of novel breeding methodologies, it is important to adopt a philosophy of continuous improvement regarding breeding scheme design. Here, we discuss terms and definitions that are relevant to formalizing breeding pipelines, market segments and breeding schemes, and we present a software tool, Breeding Pipeline Manager, that can be used to formalize and continuously improve breeding schemes. In addition, we detail the use of continuous improvement methods and tools such as genetic simulation through a case study in the International Institute of Tropical Agriculture (IITA) Cassava east-Africa pipeline. We successfully deploy these tools and methods to optimize the program size as well as allocation of resources to the number of parents used, number of crosses made, and number of progeny produced. We propose a structured approach to improve breeding schemes which will help to sustain the rates of response to selection and help to deliver better products to farmers and consumers.

Competitive gene flow does not necessarily maximize the genetic gain of genomic breeding programs in the presence of genotype-by-environment interaction

National and international across-population selection is often recommended and fairly common in the current breeding practice of dairy cattle, with the primary aims to increase genetic gain and genetic variability. The aim of this study was to test the hypothesis that the strategy of truncation selection of sires across populations [i.e., competitive gene flow strategy (CGF)] may not necessarily maximize genetic gain in the long term in the presence of genotype-by-environment interaction (G×E). Two alternative strategies used to be compared with CGF were forced gene flow (FGF) strategies, with 10 or 50% of domestic dams forced to be mated with foreign sires (FGF10%, FGF50%). Two equal-size populations (N_dams = 1,000) that were selected for the same breeding goal trait (h² = 0.3) under G×E correlation (r_g) of either 0.9 or 0.8 were simulated to test these 3 different strategies. Each population first experienced either 5 or 20 differentiation generations (G_d), then 15 migration generations. Discrete generations were simulated for simplicity. Each population performed a within-population conventional breeding program during differentiation generations and the 3 across-population sire selection strategies based on joint genomic prediction during migration generations. The 4 G_{d_}r_g combinations defined 4 different levels of differentiation degree between the 2 populations at the start of migration. The true rate of inbreeding over the last 10 migration generations in each scenario was constrained at 0.01 to provide a fair basis for comparison of genetic gain across scenarios. Results showed that CGF maximized the genetic gain after 15 migration generations in 5_0.9 combination only, the case of the lowest differentiation degree, with a superiority of 0.4% (0.04 genetic SD units) over the suboptimal strategy. While in 5_0.8, 20_0.9, and 20_0.8 combinations, 2 FGF strategies had a superiority in genetic gain of 2.3 to 12.5% (0.21-1.07 genetic SD units) over CGF after 15 migration generations, especially FGF50%. The superiority of FGF strategies over CGF was that they alleviated inbreeding, introduced new genetic variance in the early migration period, and improved accuracy in the entire migration period. Therefore, we concluded that CGF does not necessarily maximize the genetic gain of across-population genomic breeding programs given moderate G×E. The across-population selection strategy remains to be optimized to maximize genetic gain.

Favorable Conditions for Genomic Evaluation to Outperform Classical Pedigree Evaluation Highlighted by a Proof-of-Concept Study in Poplar

Forest trees like poplar are particular in many ways compared to other domesticated species. They have long juvenile phases, ongoing crop-wild gene flow, extensive outcrossing, and slow growth. All these particularities tend to make the conduction of breeding programs and evaluation stages costly both in time and resources. Perennials like trees are therefore good candidates for the implementation of genomic selection (GS) which is a good way to accelerate the breeding process, by unchaining selection from phenotypic evaluation without affecting precision. In this study, we tried to compare GS to pedigree-based traditional evaluation, and evaluated under which conditions genomic evaluation outperforms classical pedigree evaluation. Several conditions were evaluated as the constitution of the training population by cross-validation, the implementation of multi-trait, single trait, additive and non-additive models with different estimation methods (G-BLUP or weighted G-BLUP). Finally, the impact of the marker densification was tested through four marker density sets. The population under study corresponds to a pedigree of 24 parents and 1,011 offspring, structured into 35 full-sib families. Four evaluation batches were planted in the same location and seven traits were evaluated on 1 and 2 years old trees. The quality of prediction was reported by the accuracy, the Spearman rank correlation and prediction bias and tested with a cross-validation and an independent individual test set. Our results show that genomic evaluation performance could be comparable to the already well-optimized pedigree-based evaluation under certain conditions. Genomic evaluation appeared to be advantageous when using an independent test set and a set of less precise phenotypes. Genome-based methods showed advantages over pedigree counterparts when ranking candidates at the within-family levels, for most of the families. Our study also showed that looking at ranking criteria as Spearman rank correlation can reveal benefits to genomic selection hidden by biased predictions.

Strategies for implementing genomic selection for feed efficiency in dairy cattle breeding schemes

Alternative genomic selection and traditional BLUP breeding schemes were compared for the genetic improvement of feed efficiency in simulated Norwegian Red dairy cattle populations. The change in genetic gain over time and achievable selection accuracy were studied for milk yield and residual feed intake, as a measure of feed efficiency. When including feed efficiency in genomic BLUP schemes, it was possible to achieve high selection accuracies for genomic selection, and all genomic BLUP schemes gave better genetic gain for feed efficiency than BLUP using a pedigree relationship matrix. However, introducing a second trait in the breeding goal caused a reduction in the genetic gain for milk yield. When using contracted test herds with genotyped and feed efficiency recorded cows as a reference population, adding an additional 4,000 new heifers per year to the reference population gave accuracies that were comparable to a male reference population that used progeny testing with 250 daughters per sire. When the test herd consisted of 500 or 1,000 cows, lower genetic gain was found than using progeny test records to update the reference population. It was concluded that to improve difficult to record traits, the use of contracted test herds that had additional recording (e.g., measurements required to calculate feed efficiency) is a viable option, possibly through international collaborations.