Segregation GWAS to linearize a non-additive locus with incomplete penetrance: an example of horn status in sheep.

BACKGROUND: The objective of this study was to introduce a genome-wide association study (GWAS) in conjunction with segregation analysis on monogenic categorical traits. Genotype probabilities calculated from phenotypes, mode of inheritance and pedigree information, are expressed as the expected allele count (EAC) (range 0 to 2), and are inherited additively, by definition, unlike the original phenotypes, which are non-additive and could be of incomplete penetrance. The EAC are regressed on the single nucleotide polymorphism (SNP) genotypes, similar to an additive GWAS. In this study, horn phenotypes in Merino sheep are used to illustrate the advantages of using the segregation GWAS, a trait believed to be monogenic, affected by dominance, sex-dependent expression and likely affected by incomplete penetrance. We also used simulation to investigate whether incomplete penetrance can cause prediction errors in Merino sheep for horn status. RESULTS: Estimated penetrance values differed between the sexes, where males showed almost complete penetrance, especially for horned and polled phenotypes, while females had low penetrance values for the horned status. This suggests that females homozygous for the 'horned allele' have a horned phenotype in only 22% of the cases while 78% will be knobbed or have scurs. The GWAS using EAC on 4001 animals and 510,174 SNP genotypes from the Illumina Ovine high-density (600k) chip gave a stronger association compared to using actual phenotypes. The correlation between the EAC and the allele count of the SNP with the highest -log10(p-value) was 0.73 in males and 0.67 in females. Simulations using penetrance values found by the segregation analyses resulted in higher correlations between the EAC and the causative mutation (0.95 for males and 0.89 for females, respectively), suggesting that the most predictive SNP is not in full LD with the causative mutation. CONCLUSIONS: Our results show clear differences in penetrance values between males and female Merino sheep for horn status. Segregation analysis for a trait with mutually exclusive phenotypes, non-additive inheritance, and/or incomplete penetrance can lead to considerably more power in a GWAS because the linearized genotype probabilities are additive and can accommodate incomplete penetrance. This method can be extended to any monogenic controlled categorical trait of which the phenotypes are mutually exclusive.

Management of diversity and inbreeding when importing new stock into an inbred population.

This article relates to breeding programs that seek to manage genetic diversity. The method maximizes a multicomponent objective function, applicable across breeding scenarios. However, this paper focuses on breeding decisions following immigration of 10 unrelated individuals into a highly inbred simulated population (F ≈ 0.34). We use Optimal Contribution Selection to maximize retention of genetic diversity. However, some treatments add Coancestry Assortative Mating (CAM). This helps to avoid early dilution of immigrant genetic material, maximizing its ability to contribute to genetic diversity in the longer term. After 20 generations, this resulted in considerably increased genetic diversity, with mean coancestries 59% of what random pairing gave. To manage progeny inbreeding, common practice is to reject matings above an upper limit. As a suboptimal rules-based approach, this resulted in 26% decreased genetic diversity and 8% increased inbreeding in the long term, compared with random pairing. In contrast, including mean progeny inbreeding as a continuous variable in the overall objective function decreased final inbreeding by 37% compared with random pairing. Adding some emphasis on selection for a single trait resulted in a similar pattern of effects on coancestry and inbreeding, with 12% higher trait response under CAM. Results indicate the properties of alternative methods, but we encourage users to do their own investigations of particular scenarios, such as including inbreeding depression. Practical implementation of these methods is discussed: they have been widely adopted in domestic animal breeding and are highly flexible to accommodate a wide range of technical and logistical objectives and constraints.

Management of lethal recessive alleles in beef cattle through the use of mate selection software.

BACKGROUND: Recessive loss-of-function (LOF) alleles at genes which are essential for life, can result in early embryonic mortality. Cattle producers can use the LOF carrier status of individual animals to make selection and mate allocation decisions. METHODS: Two beef cattle breeding strategies i.e. (1) selection against LOF carriers as parents and (2) simultaneous selection and mate allocation to avoid the occurrence of homozygous offspring in three scenarios, which differed in number and frequency of LOF alleles were evaluated using the mate selection program, MateSel. Scenarios included (a) seven loci with high-frequency LOF alleles, (b) 76 loci with low-frequency LOF alleles, and (c) 50 loci with random high- and low-frequency LOF alleles. In addition, any savings resulting from the information obtained by varying the percentage (0-100%) of the herd genotyped, together with segregation analysis to cover ungenotyped animals, were calculated to determine (1) which percentage optimized net profit for a fixed cost of genotyping ($30/test), and (2) the breakeven cost for genotyping. RESULTS: With full knowledge of the LOF alleles carried by selection candidates, the most profitable breeding strategy was always simultaneous selection and mate allocation to avoid homozygous affected offspring (aa) as compared to indiscriminate selection against carrier parents (Aa). The breakeven value of genotyping depended on the number of loci modeled, the LOF allele frequencies, and the mating/selection strategies used. Genotyping was most valuable when it was used to avoid otherwise high levels of embryonic mortalities. As the number of essential loci with LOF alleles increased, especially when some were present at relatively high minor allele frequencies, embryonic losses increased, and profit was maximized by genotyping 10 to 20% of a herd and using that information to reduce these losses. CONCLUSIONS: Genotyping 100% of the herd was never the most profitable outcome in any scenario; however, genotyping some proportion of the herd, together with segregation analysis to cover ungenotyped animals, maximized overall profit in scenarios with large numbers of loci with LOF alleles. As more LOF alleles are identified, such a mate selection software will likely be required to optimally select and allocate matings to balance the rate of genetic gain, embryonic losses, and inbreeding.

Optimizing female allocation to reproductive technologies considering merit, inbreeding and cost in nucleus breeding programmes with genomic selection.

Female reproductive technologies such as multiple ovulation and embryo transfer (MOET) and juvenile in vitro fertilization and embryo transfer (JIVET) have been shown to accelerate genetic gain by increasing selection intensity and decreasing generation interval. Genomic selection (GS) increases the accuracy of selection of young candidates which can further accelerate genetic gain. Optimal contribution selection (OCS) is an effective method of keeping the rate of inbreeding at a sustainable level while increasing genetic merit. OCS could also be used to selectively and optimally allocate reproductive technologies in mate selection while accounting for their cost. This study uses stochastic simulation to simulate breeding programmes that use a combination of artificial insemination (AI) or natural mating (N), MOET and JIVET with GS. OCS was used to restrict inbreeding to 1.0% increase per generation and also to optimize use of reproductive technologies, considering their effect on genetic gain as well as their cost. Two Australian sheep breeding objectives were used as an example to illustrate the methodology-a terminal sire breeding objective (A) and a dual-purpose self-replacing breeding objective (B). The objective function used for optimization considered genetic merit, constrained inbreeding and cost of technologies where costs were offset by a premium paid to the seedstock breeder investing in female reproductive technologies. The premium was based on the cumulative discounted expression of genetic merit in the progeny of a commercial tier in the breeding programme multiplied by the proportion of that benefit received by the breeder. With breeding objective B, the highest premium of 64% paid to the breeder resulted in the highest allocation of reproductive technologies (4%-10% for MOET and 19%-54% for JIVET) and hence the highest annual genetic gain. Conversely, breeding objective A, which had a lower dollar value of the breeding objective and a maximum of 5% mating types for JIVET and zero for MOET were optimal, even when highest premiums were paid. This study highlights that the level of investment in breeding technologies to accelerate genetic gain depends on the investment of genetic improvement returned to the breeder per index point gain achieved. It also demonstrates that breeding programmes can be optimized including allocation of reproductive technologies at the individual animal level. Accounting for revenue to the breeder and cost of the technologies can facilitate more practical decision support for beef and sheep breeders.

hsphase: an R package for pedigree reconstruction, detection of recombination events, phasing and imputation of half-sib family groups.

BACKGROUND: Identification of recombination events and which chromosomal segments contributed to an individual is useful for a number of applications in genomic analyses including haplotyping, imputation, signatures of selection, and improved estimates of relationship and probability of identity by descent. Genotypic data on half-sib family groups are widely available in livestock genomics. This structure makes it possible to identify recombination events accurately even with only a few individuals and it lends itself well to a range of applications such as parentage assignment and pedigree verification. RESULTS: Here we present hsphase, an R package that exploits the genetic structure found in half-sib livestock data to identify and count recombination events, impute and phase un-genotyped sires and phase its offspring. The package also allows reconstruction of family groups (pedigree inference), identification of pedigree errors and parentage assignment. Additional functions in the package allow identification of genomic mapping errors, imputation of paternal high density genotypes from low density genotypes, evaluation of phasing results either from hsphase or from other phasing programs. Various diagnostic plotting functions permit rapid visual inspection of results and evaluation of datasets. CONCLUSION: The hsphase package provides a suite of functions for analysis and visualization of genomic structures in half-sib family groups implemented in the widely used R programming environment. Low level functions were implemented in C++ and parallelized to improve performance. hsphase was primarily designed for use with high density SNP array data but it is fast enough to run directly on sequence data once they become more widely available. The package is available (GPL 3) from the Comprehensive R Archive Network (CRAN) or from http://www-personal.une.edu.au/~cgondro2/hsphase.htm.

Detection of recombination events, haplotype reconstruction and imputation of sires using half-sib SNP genotypes.

BACKGROUND: Identifying recombination events and the chromosomal segments that constitute a gamete is useful for a number of applications in genomic analyses. In livestock, genotypic data are commonly available for half-sib families. We propose a straightforward but computationally efficient method to use single nucleotide polymorphism marker genotypes on half-sibs to reconstruct the recombination and segregation events that occurred during meiosis in a sire to form the haplotypes observed in its offspring. These meiosis events determine a block structure in paternal haplotypes of the progeny and this can be used to phase the genotypes of individuals in single half-sib families, to impute haplotypes of the sire if they are not genotyped or to impute the paternal strand of the offspring's sequence based on sequence data of the sire. METHODS: The hsphase algorithm exploits information from opposing homozygotes among half-sibs to identify recombination events, and the chromosomal regions from the paternal and maternal strands of the sire (blocks) that were inherited by its progeny. This information is then used to impute the sire's genotype, which, in turn, is used to phase the half-sib family. Accuracy (defined as R2) and performance of this approach were evaluated by using simulated and real datasets. Phasing results for the half-sibs were benchmarked to other commonly used phasing programs - AlphaPhase, BEAGLE and PedPhase 3. RESULTS: Using a simulated dataset with 20 markers per cM, and for a half-sib family size of 4 and 40, the accuracy of block detection, was 0.58 and 0.96, respectively. The accuracy of inferring sire genotypes was 0.75 and 1.00 and the accuracy of phasing was around 0.97, respectively. hsphase was more robust to genotyping errors than PedPhase 3, AlphaPhase and BEAGLE. Computationally, hsphase was much faster than AlphaPhase and BEAGLE. CONCLUSIONS: In half-sib families of size 8 and above, hsphase can accurately detect block structure of paternal haplotypes, impute genotypes of ungenotyped sires and reconstruct haplotypes in progeny. The method is much faster and more accurate than other widely used population-based phasing programs. A program implementing the method is freely available as an R package (hsphase).

The effect of genomic information on optimal contribution selection in livestock breeding programs.

BACKGROUND: Long-term benefits in animal breeding programs require that increases in genetic merit be balanced with the need to maintain diversity (lost due to inbreeding). This can be achieved by using optimal contribution selection. The availability of high-density DNA marker information enables the incorporation of genomic data into optimal contribution selection but this raises the question about how this information affects the balance between genetic merit and diversity. METHODS: The effect of using genomic information in optimal contribution selection was examined based on simulated and real data on dairy bulls. We compared the genetic merit of selected animals at various levels of co-ancestry restrictions when using estimated breeding values based on parent average, genomic or progeny test information. Furthermore, we estimated the proportion of variation in estimated breeding values that is due to within-family differences. RESULTS: Optimal selection on genomic estimated breeding values increased genetic gain. Genetic merit was further increased using genomic rather than pedigree-based measures of co-ancestry under an inbreeding restriction policy. Using genomic instead of pedigree relationships to restrict inbreeding had a significant effect only when the population consisted of many large full-sib families; with a half-sib family structure, no difference was observed. In real data from dairy bulls, optimal contribution selection based on genomic estimated breeding values allowed for additional improvements in genetic merit at low to moderate inbreeding levels. Genomic estimated breeding values were more accurate and showed more within-family variation than parent average breeding values; for genomic estimated breeding values, 30 to 40% of the variation was due to within-family differences. Finally, there was no difference between constraining inbreeding via pedigree or genomic relationships in the real data. CONCLUSIONS: The use of genomic estimated breeding values increased genetic gain in optimal contribution selection. Genomic estimated breeding values were more accurate and showed more within-family variation, which led to higher genetic gains for the same restriction on inbreeding. Using genomic relationships to restrict inbreeding provided no additional gain, except in the case of very large full-sib families.

Optimal Contribution Selection Improves the Rate of Genetic Gain in Grain Yield and Yield Stability in Spring Canola in Australia and Canada.

Crop breeding must achieve higher rates of genetic gain in grain yield (GY) and yield stability to meet future food demands in a changing climate. Optimal contributions selection (OCS) based on an index of key economic traits should increase the rate of genetic gain while minimising population inbreeding. Here we apply OCS in a global spring oilseed rape (canola) breeding program during three cycles of S0,1 family selection in 2016, 2018, and 2020, with several field trials per cycle in Australia and Canada. Economic weights in the index promoted high GY, seed oil, protein in meal, and Phoma stem canker (blackleg) disease resistance while maintaining plant height, flowering time, oleic acid, and seed size and decreasing glucosinolate content. After factor analytic modelling of the genotype-by-environment interaction for the additive effects, the linear rate of genetic gain in GY across cycles was 0.059 or 0.087 t ha-1 y-1 (2.9% or 4.3% y-1) based on genotype scores for the first factor (f1) expressed in trait units or average predicted breeding values across environments, respectively. Both GY and yield stability, defined as the root-mean-square deviation from the regression line associated with f1, were predicted to improve in the next cycle with a low achieved mean parental coancestry (0.087). These methods achieved rapid genetic gain in GY and other traits and are predicted to improve yield stability across global spring canola environments.

A phasing and imputation method for pedigreed populations that results in a single-stage genomic evaluation.

BACKGROUND: Efficient, robust, and accurate genotype imputation algorithms make large-scale application of genomic selection cost effective. An algorithm that imputes alleles or allele probabilities for all animals in the pedigree and for all genotyped single nucleotide polymorphisms (SNP) provides a framework to combine all pedigree, genomic, and phenotypic information into a single-stage genomic evaluation. METHODS: An algorithm was developed for imputation of genotypes in pedigreed populations that allows imputation for completely ungenotyped animals and for low-density genotyped animals, accommodates a wide variety of pedigree structures for genotyped animals, imputes unmapped SNP, and works for large datasets. The method involves simple phasing rules, long-range phasing and haplotype library imputation and segregation analysis. RESULTS: Imputation accuracy was high and computational cost was feasible for datasets with pedigrees of up to 25 000 animals. The resulting single-stage genomic evaluation increased the accuracy of estimated genomic breeding values compared to a scenario in which phenotypes on relatives that were not genotyped were ignored. CONCLUSIONS: The developed imputation algorithm and software and the resulting single-stage genomic evaluation method provide powerful new ways to exploit imputation and to obtain more accurate genetic evaluations.

An algorithm for efficient constrained mate selection.

BACKGROUND: Mate selection can be used as a framework to balance key technical, cost and logistical issues while implementing a breeding program at a tactical level. The resulting mating lists accommodate optimal contributions of parents to future generations, in conjunction with other factors such as progeny inbreeding, connection between herds, use of reproductive technologies, management of the genetic distribution of nominated traits, and management of allele/genotype frequencies for nominated QTL/markers. METHODS: This paper describes a mate selection algorithm that is widely used and presents an extension that makes it possible to apply constraints on certain matings, as dictated through a group mating permission matrix. RESULTS: This full algorithm leads to simpler applications, and to computing speed for the scenario tested, which is several hundred times faster than the previous strategy of penalising solutions that break constraints. CONCLUSIONS: The much higher speed of the method presented here extends the use of mate selection and enables implementation in relatively large programs across breeding units.

A combined long-range phasing and long haplotype imputation method to impute phase for SNP genotypes.

BACKGROUND: Knowing the phase of marker genotype data can be useful in genome-wide association studies, because it makes it possible to use analysis frameworks that account for identity by descent or parent of origin of alleles and it can lead to a large increase in data quantities via genotype or sequence imputation. Long-range phasing and haplotype library imputation constitute a fast and accurate method to impute phase for SNP data. METHODS: A long-range phasing and haplotype library imputation algorithm was developed. It combines information from surrogate parents and long haplotypes to resolve phase in a manner that is not dependent on the family structure of a dataset or on the presence of pedigree information. RESULTS: The algorithm performed well in both simulated and real livestock and human datasets in terms of both phasing accuracy and computation efficiency. The percentage of alleles that could be phased in both simulated and real datasets of varying size generally exceeded 98% while the percentage of alleles incorrectly phased in simulated data was generally less than 0.5%. The accuracy of phasing was affected by dataset size, with lower accuracy for dataset sizes less than 1000, but was not affected by effective population size, family data structure, presence or absence of pedigree information, and SNP density. The method was computationally fast. In comparison to a commonly used statistical method (fastPHASE), the current method made about 8% less phasing mistakes and ran about 26 times faster for a small dataset. For larger datasets, the differences in computational time are expected to be even greater. A computer program implementing these methods has been made available. CONCLUSIONS: The algorithm and software developed in this study make feasible the routine phasing of high-density SNP chips in large datasets.

Multivariate genomic analysis and optimal contributions selection predicts high genetic gains in cooking time, iron, zinc, and grain yield in common beans in East Africa.

Common bean (Phaseolus vulgaris L.) is important in African diets for protein, iron (Fe), and zinc (Zn), but traditional cultivars have long cooking time (CKT), which increases the time, energy, and health costs of cooking. Genomic selection was used to predict genomic estimated breeding values (GEBV) for grain yield (GY), CKT, Fe, and Zn in an African bean panel of 358 genotypes in a two-stage analysis. In Stage 1, best linear unbiased estimates (BLUE) for each trait were obtained from 898 genotypes across 33 field trials in East Africa. In Stage 2, BLUE in a training population of 141 genotypes were used in a multivariate genomic analysis with genome-wide single nucleotide polymorphism data from the African bean panel. Moderate to high genomic heritability was found for GY (0.45 ± 0.10), CKT (0.50 ± 0.15), Fe (0.57 ± 0.12), and Zn (0.61 ± 0.13). There were significant favorable genetic correlations between Fe and Zn (0.91 ± 0.06), GY and Fe (0.66 ± 0.17), GY and Zn (0.44 ± 0.19), CKT and Fe (-0.57 ± 0.21), and CKT and Zn (-0.67 ± 0.20). Optimal contributions selection (OCS), based on economic index of weighted GEBV for each trait, was used to design crossing within four market groups relevant to East Africa. Progeny were predicted by OCS to increase in mean GY by 12.4%, decrease in mean CKT by 9.3%, and increase in mean Fe and Zn content by 6.9 and 4.6%, respectively, with low achieved coancestry of 0.032. Genomic selection with OCS will accelerate breeding of high-yielding, biofortified, and rapid cooking African common bean cultivars.

Using an evolutionary algorithm and parallel computing for haplotyping in a general complex pedigree with multiple marker loci.

BACKGROUND: Haplotype reconstruction is important in linkage mapping and association mapping of quantitative trait loci (QTL). One widely used statistical approach for haplotype reconstruction is simulated annealing (SA), implemented in SimWalk2. However, the algorithm needs a very large number of sequential iterations, and it does not clearly show if convergence of the likelihood is obtained. RESULTS: An evolutionary algorithm (EA) is a good alternative whose convergence can be easily assessed during the process. It is feasible to use a powerful parallel-computing strategy with the EA, increasing the computational efficiency. It is shown that the EA can be approximately 4 times faster and gives more reliable estimates than SimWalk2 when using 4 processors. In addition, jointly updating dependent variables can increase the computational efficiency up to approximately 2 times. Overall, the proposed method with 4 processors increases the computational efficiency up to approximately 8 times compared to SimWalk2. The efficiency will increase more with a larger number of processors. CONCLUSION: The use of the evolutionary algorithm and the joint updating method can be a promising tool for haplotype reconstruction in linkage and association mapping of QTL.

Inheritance of rupture of the cranial cruciate ligament in Newfoundlands.

OBJECTIVE: To determine prevalence, level of inbreeding, heritability, and mode of inheritance for rupture of the cranial cruciate ligament (RCCL) in Newfoundlands. DESIGN: Retrospective and recruitment study. ANIMALS: 574 client-owned Newfoundlands. PROCEDURE: Medical records from January 1, 1996, to December 31, 2002, were evaluated for prevalence of RCCL. A pedigree was constructed by use of recruited Newfoundlands with RCCL status based on results of veterinary examination; level of inbreeding, heritability, and mode of inheritance were calculated. RESULTS: Hospital prevalence for RCCL was 22%; dogs in the pedigree from the recruitment study had a mean level of inbreeding of 1.19 x 10(4), heritability of 0.27, and a possible recessive mode of inheritance with 51% penetrance for RCCL. CONCLUSIONS AND CLINICAL RELEVANCE: Identification of a genetic basis for RCCL in Newfoundlands provided evidence that investigators can now focus on developing methods to identify carriers to reduce the prevalence of RCCL.

Periodicity of DNA in exons.

BACKGROUND: The periodic pattern of DNA in exons is a known phenomenon. It was suggested that one of the initial causes of periodicity could be the universal (RNY)npattern (R = A or G, Y = C or U, N = any base) of ancient RNA. Two major questions were addressed in this paper. Firstly, the cause of DNA periodicity, which was investigated by comparisons between real and simulated coding sequences. Secondly, quantification of DNA periodicity was made using an evolutionary algorithm, which was not previously used for such purposes. RESULTS: We have shown that simulated coding sequences, which were composed using codon usage frequencies only, demonstrate DNA periodicity very similar to the observed in real exons. It was also found that DNA periodicity disappears in the simulated sequences, when the frequencies of codons become equal. Frequencies of the nucleotides (and the dinucleotide AG) at each location along phase 0 exons were calculated for C. elegans, D. melanogaster and H. sapiens. Two models were used to fit these data, with the key objective of describing periodicity. Both of the models showed that the best-fit curves closely matched the actual data points. The first dynamic period determination model consistently generated a value, which was very close to the period equal to 3 nucleotides. The second fixed period model, as expected, kept the period exactly equal to 3 and did not detract from its goodness of fit. CONCLUSIONS: Conclusion can be drawn that DNA periodicity in exons is determined by codon usage frequencies. It is essential to differentiate between DNA periodicity itself, and the length of the period equal to 3. Periodicity itself is a result of certain combinations of codons with different frequencies typical for a species. The length of period equal to 3, instead, is caused by the triplet nature of genetic code. The models and evolutionary algorithm used for characterising DNA periodicity are proven to be an effective tool for describing the periodicity pattern in a species, when a number of exons in the same phase are analysed.

Genotype imputation for the prediction of genomic breeding values in non-genotyped and low-density genotyped individuals.

BACKGROUND: There is wide interest in calculating genomic breeding values (GEBVs) in livestock using dense, genome-wide SNP data. The general framework for genomic selection assumes all individuals are genotyped at high-density, which may not be true in practice. Methods to add additional genotypes for individuals not genotyped at high density have the potential to increase GEBV accuracy with little or no additional cost. In this study a long haplotype library was created using a long range phasing algorithm and used in combination with segregation analysis to impute dense genotypes for non-genotyped dams in the training dataset (S1) and for non-genotyped or low-density genotyped individuals in the prediction dataset (S2), using the 14th QTL-MAS Workshop dataset. Alternative low-density scenarios were evaluated for accuracy of imputed genotypes and prediction of GEBVs. RESULTS: In S1, females in the training population were not genotyped and prediction individuals were either not genotyped or genotyped at low-density (evenly spaced at 2, 5 or 10 Mb). The proportion of correctly imputed genotypes for training females did not change when genotypes were added for individuals in the prediction set whereas the number of correctly imputed genotypes in the prediction set increased slightly (S1). The S2 scenario assumed the complete training set was genotyped for all SNPs and the prediction set was not genotyped or genotyped at low-density. The number of correctly imputed genotypes increased with genotyping density in the prediction set. Accuracy of genomic breeding values for the prediction set in each scenario were the correlation of GEBVs with true breeding values and were used to evaluate the potential loss in accuracy with reduced genotyping. For both S1 and S2 the GEBV accuracies were similar when the prediction set was not genotyped and increased with the addition of low-density genotypes, with the increase larger for S2 than S1. CONCLUSIONS: Genotype imputation using a long haplotype library and segregation analysis is promising for application in sparsely-genotyped pedigrees. The results of this study suggest that dense genotypes can be imputed for selection candidates with some loss in genomic breeding value accuracy, but with levels of accuracy higher than traditional BLUP estimated breeding values. Accurate genotype imputation would allow for a single low-density SNP panel to be used across traits.

Optimization of cDNA microarray experimental designs using an evolutionary algorithm.

The cDNA microarray is an important tool for generating large datasets of gene expression measurements.An efficient design is critical to ensure that the experiment will be able to address relevant biological questions. Microarray experimental design can be treated as a multicriterion optimization problem. For this class of problems evolutionary algorithms (EAs) are well suited, as they can search the solution space and evolve a design that optimizes the parameters of interest based on their relative value to the researcher under a given set of constraints. This paper introduces the use of EAs for optimization of experimental designs of spotted microarrays using a weighted objective function. The EA and the various criteria relevant to design optimization are discussed. Evolved designs are compared with designs obtained through exhaustive search with results suggesting that the EA can find just as efficient optimal or near-optimal designs within atractable timeframe.

Optimization of a crossing system using mate selection.

A simple model based on one single identified quantitative trait locus (QTL) in a two-way crossing system was used to demonstrate the power of mate selection algorithms as a natural means of opportunistic line development for optimization of crossbreeding programs over multiple generations. Mate selection automatically invokes divergent selection in two parental lines for an over-dominant QTL and increased frequency of the favorable allele toward fixation in the sire-line for a fully-dominant QTL. It was concluded that an optimal strategy of line development could be found by mate selection algorithms for a given set of parameters such as genetic model of QTL, breeding objective and initial frequency of the favorable allele in the base populations, etc. The same framework could be used in other scenarios, such as programs involving crossing to exploit breed effects and heterosis. In contrast to classical index selection, this approach to mate selection can optimize long-term responses.