The genomic measure of inbreeding is closer to the actual inbreeding than the pedigree-based measure. However, it cannot be computed for ungenotyped animals. An estimate of genomic inbreeding comes ...from the diagonal of matrix H used in single-step methods. This matrix projects genomic relationships to all ungenotyped members of the pedigree. The diagonal element of H−1 gives an estimate of the genomic inbreeding coefficient. However, so far no computational methods are available to compute the diagonal of H. Here we propose 3 exact methods to compute this diagonal. The first uses an already-existing algorithm to compute, for each ungenotyped individual, products of the form Hx to obtain the corresponding diagonal element of H. The second method computes, for each ungenotyped individual, a term that can be written as a quadratic form involving pedigree and genomic relationships. For both methods, the computational burden is linear in the number of ungenotyped animals. The last method reorders the computations of the second method so that they become linear in the number of genotyped animals, which is usually much smaller. We tested the methods in 3 small data sets (with ~2,000 genotyped animals and 30,000–500,000 animals in pedigree) and in a large simulated population (with 1,220,000 animals in pedigree and 36,000 genotyped animals). Tests resulted in satisfactory computing times (<10 min in the largest example using 10 parallel threads). Computing times were much shorter for the third method, as expected. Using these methods, estimates of genomic inbreeding in ungenotyped animals can be obtained on a regular basis.
Summary
Inbreeding coefficients of animals are required in many genetic analyses of livestock records. A modification of Colleau's indirect algorithm to compute inbreeding coefficients in large ...populations is presented. With overlapping generations, the modified algorithm evaluated all progeny of each sire simultaneously in one back and forth exploration of a reduced pedigree. Simulation for a relatively large number of generations, different number of sires, family sizes and mating designs showed that Colleau's algorithm was faster (from 1.2 to 143 times) than two other algorithms under comparison (Tier, modified Meuwissen and Luo), in all situations investigated. Modifying Colleau's algorithm considerably decreased computation time (from 50 to 89%), resulting in a very fast algorithm. The number of sires mostly affected computational efficiency of the modified algorithm, whereas family size and mating design had virtually no effect. In the updating situation, when only animals born in the last year were evaluated, given known inbreeding coefficients for the other, the modified algorithm was also fast compared with the other three algorithms. Memory requirements for the algorithms were also discussed.
An indirect approach to the extensive calculation of relationship coefficients Colleau, J.J. ((Institut National de la Recherche Agronomique, Jouy-en-Josas (France). Centre de Jouy-en-Josas, Station de Génétique Quantitative et Appliquée))
Genetics selection evolution (Paris),
07/2002, Letnik:
34, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A method was described for calculating population statistics on relationship coefficients without using corresponding individual data. It relied on the structure of the inverse of the numerator ...relationship matrix between individuals under investigation and ancestors. Computation times were observed on simulated populations and were compared to those incurred with a conventional direct approach. The indirect approach turned out to be very efficient for multiplying the relationship matrix corresponding to planned matings (full design) by any vector. Efficiency was generally still good or very good for calculating statistics on these simulated populations. An extreme implementation of the method is the calculation of inbreeding coefficients themselves. Relative performances of the indirect method were good except when many full-sibs during many generations existed in the population
A marker-assisted selection program (MAS) has been implemented in dairy cattle in France. The efficiency of such a selection program depends on the use of correct genetic parameters for the marked ...quantitative trait loci (QTL). Therefore, the objective of this study was to estimate the proportion of genetic variance explained by 4 QTL described in previous studies (these QTL are segregating on chromosomes 6, 14, 20, and 26). Genotypes for 11 markers were available for 3,974 bulls grouped within 54 sire families of the French Holstein population undergoing MAS. The parameters were estimated for 4 QTL and 5 dairy traits: milk, fat and protein yields, and fat and protein percentages. The proportion of genetic variance explained by the QTL ranged from as low as 0.03 to 0.36%. Both lack of marker informativity and poor monitoring of QTL transmission might limit the accuracy of estimation. The QTL explained a larger proportion of genetic variance for milk composition traits. The QTL on chromosome 14 and chromosomes 6 and 20 have their largest influence on fat and protein percentages, respectively. The overall proportions of genetic variance explained by the QTL were 27.0, 30.7, 24.1, 48.2, and 33.6% for milk, fat and protein yields, and fat and protein percentages, respectively. These results clearly indicated that a large part of the genetic variance is explained by a small number of QTL and that their use in MAS might be beneficial for dairy cattle breeding programs.
Selection in dairy cattle populations usually takes into account both the breed profiles for many traits and their overall estimated breeding values (EBV). This can result in effective contributions ...of breeding animals departing substantially from contributions optimised for saving future genetic variability. In this work, we propose a mating method that considers not only inbreeding but also the detailed EBV of progeny or the EBV of sires in reference to acceptance thresholds. Penalties were defined for inbreeding and for inadequate EBV profiles. Relative reductions of penalties yielded by any mating design were expressed on a scale ranging from 0 to 1. A value of 0 represented the average performance of random matings and a value of 1 represented the maximal reduction allowed by a specialized, single-penalty, mating design. The core of the method was an adaptative simulated annealing, where the maximized function was the average of both ratios, under the constraints that both relative penalty reductions should be equal and that the within-herd concentration criterion should be equal to a predefined reasonable value. The method was tested on two French dairy cattle populations originating from the same AI organization. The optimised mating design allowed substantial reductions of penalty: 70% and 64% for the Holstein and the Normandy populations, respectively. Thus, this mating method decreased inbreeding and met various demands from breeders.
Poultry breeding schemes permanently face the need to control the evolution of coancestry and some critical traits, while selecting for a main breeding objective. The main aims of this article are ...first to present an efficient selection algorithm adapted to this situation and then to measure how the severity of constraints impacted on the degree of loss for the main trait, compared to BLUP selection on the main trait, without any constraint. Broiler dam and sire line schemes were mimicked by simulation over 10 generations and selection was carried out on the main trait under constraints for coancestry and for another trait, antagonistic with the main trait. The selection algorithm was a special simulated annealing (adaptative simulated annealing (ASA)). It was found to be rapid and able to meet constraints very accurately. A constraint on the second trait was found to induce an impact similar to or even greater than the impact of the constraint on coancestry. The family structure of selected poultry populations made it easy to control the evolution of coancestry at a reasonable cost but was not as useful for reducing the cost of controlling evolution of the antagonistic traits. Multiple constraints impacted almost additively on the genetic gain for the main trait. Adding constraints for several traits would therefore be justified in real life breeding schemes, possibly after evaluating their impact through simulated annealing.
The development of inbreeding in rotation breeding schemes, sequentially using artificial insemination (AI) sires over generations, was investigated for a full AI scheme. Asymptotic prediction ...formulae of inbreeding coefficients were established when the first rotation list of AI sires (possibly related) was in use. Simulated annealing provided the optimal rotation order of sires within this list, when the sires were related. These methods were also used for subsequent rotation lists, needed by the exhaustion of semen stores for the first bulls. Simulation was carried out starting with groups of independent sires, with different sizes. To generate a yearly inbreeding rate substantially lower than 0.05% (considered to be within reach by conventional conservation schemes using frequent replacements), the results obtained showed that the number of sires should be at least 10-15 and that the same sires should be used during at least 50 years. The ultimate objective was to examine the relevance of implementing rotation in breeding schemes on the actual rare French cattle breeds under conservation. The best candidate for such a test was the Villard-de-Lans breed (27 bulls and 73 000 doses for only 340 females) and it turned out to be the best performer with an inbreeding coefficient of only 7.4% after 500 years and five different sire lists. Due to the strong requirements on semen stores and on the stability of population size, actual implementation of this kind of conservation scheme was recommended only in special ('niche') cattle populations.
Summary
In real data, inbreeding is usually underestimated because of missing pedigree information. A method adapted to the dairy cattle situation is presented to approximate inbreeding when the ...stored population pedigree is incomplete. Missing parents in incomplete pedigrees were given a dummy identification and assigned to groups (up to nine for a given birth date of progeny). These groups were linked to contemporary reference groups with known parents. An explicit model considered that polygenic breeding values in a censored group were centred on a function of the average breeding value in the corresponding reference group and deviated independently. Inbreeding coefficients were obtained progressively over birth dates starting from founders. For each date considered, the parameters pertaining to its groups were computed using the parameters already obtained from groups belonging to the previous dates. The updating algorithms were given in detail. An indirect method was implemented to expedite mass computations of the relationship coefficients involved (MIM). MIM was compared to Van Raden’s (VR) method using simulated populations with 20 overlapping generations and different rates of missing sires and dams. In the situation of random matings, the average inbreeding coefficients by date obtained by MIM were close to true values, whereas they were strongly underestimated by VR. In the situation of assortative matings, MIM gave average inbreeding coefficients moderately underestimated, whereas those of VR’s method were still strongly underestimated. The main conclusion of this study adapted to the situation of dairy cattle with incomplete pedigrees was that corrections for inbreeding and coancestry coefficients are more efficient with an explicit appropriate genetic model than without.
The benefits of marker-assisted selection were examined by simulation of an adult multiple ovulation and embryo transfer nucleus breeding scheme. Animals were either typed for two polymorphic marker ...loci, 20 centimorgans apart, flanking a single biallelic quantitative trait locus and were evaluated using a model accounting for marker information, or animals were not typed but were evaluated by a conventional BLUP animal model. Selection was for a single trait measured on females, and each dam had 4 sons and 4 daughters. Nucleus foundation animals were chosen from a base population in linkage equilibrium. With the favorable allele at an initial frequency of 0.5, marker-assisted selection substantially increased responses at the quantitative trait locus but reduced the polygenic responses. Cumulative genetic gain increased by up to 3, 9, 12, and 6% after one, two, three, and six generations of selection, respectively. If the favorable allele was initially rare (frequency of 0.1), the merits of marker-assisted selection were even more pronounced (genetic gains increased by up to 9, 19, 24 and 15%, respectively). The superiority of marker-assisted selection over conventional BLUP increased when a restriction was placed on selection of full brothers and decreased when variance of the quantitative trait locus used in the evaluation model was overestimated.
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