RESUMEN
Local breeds are rarely subject to modern selection techniques; however, selection programs will be required if local breeds are to remain a viable livelihood option for farmers. Selection in small populations needs to take into account accurate inbreeding control. Optimum contribution selection (OCS) is efficient in controlling inbreeding and maximizes genetic gain. The current paper investigates genetic progress in simulated dairy cattle populations from 500 to 6,000 cows undergoing young bull selection schemes with OCS compared with truncation selection (TS) at an annual inbreeding rate of 0.003. Selection is carried out for a dairy trait with a base heritability of 0.3. A young bull selection scheme was used because of its simplicity in implementation. With TS, annual genetic gain from 0.111 standard deviation units with 500 cows increases rapidly to 0.145 standard deviation units with 4,000 cows. Then, genetic gain increases more slowly up to 6,000 cows. At the same inbreeding rate, OCS produces higher genetic progress than TS. Differences in genetic gain between OCS and TS vary from to 2 to 6.3%. Genetic gain is also improved by increasing the number of years that males can be used as sires of sires. When comparing OCS versus TS at different heritabilities, we observe an advantage of OCS only at high heritability, up to 8% with heritability of 0.9. By increasing the constraint on inbreeding, the difference of genetic gain between the 2 selection methods increases in favor of OCS, and the advantage at the inbreeding rate of 0.001 per generation is 6 times more than at the inbreeding rate of 0.003. Opportunities exist for selection even in dairy cattle populations of a few hundred females. In any case, selection in local breeds will most often require specific investments in infrastructure and manpower, including systems for accurate data recording and selection skills and the presence of artificial insemination and breeders organizations. A cost-benefit analysis is therefore advisable before considering the implementation of selection schemes in local dairy cattle breeds.
Asunto(s)
Bovinos/genética , Industria Lechera/métodos , Endogamia , Selección Genética , Animales , Masculino , Modelos GenéticosRESUMEN
The success of fine-scale mapping and genomic selection depends mainly on the strength of linkage disequilibrium (LD) between markers and causal mutations. With Lewontin's measure of LD (known as D'), high levels of LD that extend over several million base pairs have been reported in livestock. However, this measure of LD can be strongly biased upward by small samples and by low allele frequencies. The aim of this study was to characterize the level and extent of LD in Holstein cattle in North America (Canada and the United States for purposes of this study) by using the squared correlation of the alleles at 2 loci (r(2)). The Affymetrix MegAllele GeneChip Bovine Mapping 10K single nucleotide polymorphism (SNP) array was used to genotype 821 bulls, from which 497 were used in the analysis of the extent of LD. A total of 5,564 SNP were used after filtering out SNP with more than 5% of Mendelian inconsistencies, with more than 20% missing genotypes, or with a minor allele frequency of less than 10%. Analysis of syntenic pairs revealed that useful LD (measured as r(2) > 0.3) occurred at distances shorter than 100 kb. Linkage disequilibrium decayed very rapidly, within a few hundred kilobase pairs. In addition, no substantial LD between unlinked loci was found. Using a sliding window analysis, we observed an irregular pattern of LD across the genome. These findings suggest that to capture useful LD, which is required for whole-genome fine mapping and genomic selection, a denser SNP map would be needed.
Asunto(s)
Bovinos/genética , Desequilibrio de Ligamiento/genética , Animales , Canadá , Mapeo Cromosómico , Frecuencia de los Genes/genética , Genotipo , Haplotipos , Modelos Lineales , Masculino , Mutación , Linaje , Polimorfismo de Nucleótido Simple , Selección Genética , Estados UnidosRESUMEN
The aim of this study was to identify the presence of SNPs in the chemokine genes CCL2 and IL8 and the chemokine receptor genes IL8RA and CCR2, and assess their potential contribution to variation in estimated breeding values (EBVs) for somatic cell score (SCS) and four other traits in Canadian Holstein bulls. Pools of DNA for bulls with high (H) and low (L) EBVs for SCS were used for identification of 11 SNPs. Two unreported SNPs were found in the CCL2 gene and one SNP was found in the CCR2 gene. Previously reported SNPs (three in the IL8 gene and five in the IL8RA chemokine receptor) were also identified. Two SNPs in CCL2, three in IL8, one in IL8RA and one in CCR2 were genotyped in Canadian Holstein bulls (n = 338) using tetra primer ARMS-PCR. We investigated associations of these seven polymorphisms with three production traits (milk yield, fat yield and protein yield) and one conformation trait related to mastitis (udder depth). The allele substitution effect for the CCL2 rs41255713:T>C SNP was significant at an experimental-wise level for milk yield (247.5 +/- 79.9 kg) and protein yield (7.4 +/- 2.3 kg) EBVs (P
Asunto(s)
Bovinos/genética , Quimiocina CCL2/genética , Interleucina-8/genética , Receptores CCR2/genética , Receptores de Interleucina-8/genética , Animales , Composición Corporal , Canadá , Frecuencia de los Genes , Leche , Polimorfismo de Nucleótido Simple/genética , Mapeo de Híbrido por RadiaciónRESUMEN
Mastitis is the most frequent, complex, and costly disease in dairy cattle. Genetic improvement of milk production traits has accompanied an increased susceptibility to mastitis. To determine genome-wide quantitative trait locus-linked markers for mastitis resistance, a total of 200 cows, comprising 100 top clinical mastitis- (CM) resistant and 100 top CM-susceptible cows, were screened by selective DNA pooling and amplified fragment length polymorphism (AFLP) technique. The AFLP analysis on resistant and susceptible pools using 89 selective primer combinations revealed 27 significant AFLP markers at a false discovery rate (FDR) of < 5%. The most promising AFLP marker was then selected for further characterization. Individual AFLP genotyping of the marker on all selected animals confirmed a significant difference. Sequence analysis detected a single nucleotide polymorphism (A<-->G) responsible for the AFLP polymorphism, which was named CGIL4. The PCR-RFLP analysis indicated that the frequency of allele A was significantly higher in the resistant group. The logistic regression analysis demonstrated that the marker was significantly associated with somatic cell score, CM residual values, and production traits. Radiation hybrid mapping assigned the marker to Bos taurus autosome 22. The present study provides promising markers for marker-assisted selection for CM resistance. Our results also demonstrated the capability of AFLP on selective DNA pools as a method for detection of genome regions containing quantitative trait loci.
Asunto(s)
Análisis del Polimorfismo de Longitud de Fragmentos Amplificados/veterinaria , Bovinos/genética , Marcadores Genéticos , Mastitis Bovina/genética , Sitios de Carácter Cuantitativo , Animales , Canadá , Cartilla de ADN/química , Femenino , Frecuencia de los Genes , Inmunidad Innata/genética , Modelos Logísticos , Mastitis Bovina/inmunología , Modelos Genéticos , Polimorfismo Genético , Polimorfismo de Longitud del Fragmento de Restricción , Mapeo de Híbrido por Radiación/veterinariaRESUMEN
The performance of several transmission disequilibrium tests (TDT) for detection of quantitative trait loci (QTL) in data structures typical of outbred livestock populations were investigated. Factorial mating designs were simulated with 10 sires mated to either 50 or 200 dams, each family having five or eight full sibs. A single marker and QTL, both bi-allelic, were simulated using a disequilibrium coefficient based on complete initial disequilibrium and 50 generations of recombination [i.e. D = D(0)(1 - theta)50], where theta is the recombination fraction between marker and QTL. The QTL explained either 10% (small QTL) or 30% (large QTL) of the genetic variance for a trait with heritability of 0.3. Methods were: TDT for QTL (Q-TDT; both parents known), 1-TDT (only one parent known) and sibling-based TDT (S-TDT; neither parent known, but sibs available). All were found to be effective tests for association and linkage between the QTL and a tightly linked marker (theta < 0.02) in these designs. For a large QTL, theta = 0.01, and five full sibs per family, the empirical power for Q-TDT, 1-TDT and S-TDT was 0.966, 0.602 and 0.974, respectively, in a large population, versus 0.700, 0.414 and 0.654, respectively, in a small population. For a small QTL effect, theta = 0.01, large population the empirical power of these tests were 0.709, 0.287 and 0.634. The power of Q-TDT, 1-TDT and S-TDT was satisfactory for large populations, for QTL with large effects and for five full sibs per family. The 1-TDT based on a linear model was more powerful than the normal 1-TDT. The empirical power for Q-TDT and 1-TDT with a linear model was 0.978 and 0.995 respectively. TDT based on analogous linear models, incorporating the polygenic covariance structure, provided only small increases in power compared with the usual TDT for QTL.
Asunto(s)
Animales Domésticos/genética , Simulación por Computador , Variación Genética , Modelos Genéticos , Sitios de Carácter Cuantitativo/genética , Algoritmos , Alelos , Animales , Cruzamiento , Femenino , Marcadores Genéticos/genética , Genotipo , Modelos Lineales , Masculino , Densidad de PoblaciónRESUMEN
Several reports have demonstrated that bovine chromosome 26 (BTA26) harbours significant or suggestive quantitative trait loci (QTL) for milk production and composition traits in dairy cattle. Our previous study showed that a C/T substitution in the bovine TCF7L2 gene on BTA26 was significantly linked to QTL for protein yield (PY) in a Canadian dairy cattle population. Actually, this polymorphism was one of the markers derived from a genome-wide screening of QTL for milk PY using an amplified fragment length polymorphism technique combined with a DNA pooling strategy. In the present study, 990 Holstein bulls with complete genotype and phenotype data from 14 sire families were analysed to confirm, if the QTL effects exist in other populations. Statistical analysis revealed that this marker was significantly associated with PY, protein percentage, milk yield and fat yield (FY) (p < 0.001) in the US Holstein population. These results indicate that this QTL region has a pleiotrophic effecton different milk traits and is portable in different populations.
Asunto(s)
Bovinos/genética , Lactancia/genética , Leche/química , Leche/metabolismo , Sitios de Carácter Cuantitativo , Factores de Transcripción TCF/genética , Análisis de Varianza , Animales , Bovinos/fisiología , ADN/química , Frecuencia de los Genes , Genotipo , Reacción en Cadena de la Polimerasa/veterinaria , Factores de Transcripción TCF/fisiología , Proteína 2 Similar al Factor de Transcripción 7RESUMEN
Neospora caninum has been reported to be an important cause of endemic fetal loss and occasional abortion epidemics in cattle around the world. This study examined 12,016 sera collected from 9723 Holstein cows on 125 herds across Ontario in 1998, 1999, and 2000. An enzyme-linked immunosorbent assay was used to examine the sera for antibodies to N. caninum. The overall prevalence of N. caninum antibodies in the cattle was 11.2% and the prevalence in individual herds varied from 0 to 70.4%. Among 3109 daughter-dam pairs, 619 positive dams had 252 positive daughters, giving a detected vertical transmission rate of 40.7%. In contrast, there were only 6.7% positive daughters from negative dams (167 of 2490). Pedigree edits left 8031 cows with 1463 sires for estimation of heritability. Five genetic models (sire model, animal model, sire-dam model, a sire-maternal grandsire model, and a maternal effects model) with fixed effects of bleeding year-month, age of the animals, and herd were fitted to the data. The estimated heritability of susceptibility to N. caninum ranged between 0.084 and 0.124. The sire-maternal grandsire model and the maternal effects model provided better fit than the other models because the maternal genetic variance was much greater than the direct genetic variance. To reduce the incidence of N. caninum infection, more emphasis should be placed on management practices than on genetic selection.
Asunto(s)
Enfermedades de los Bovinos/genética , Coccidiosis/veterinaria , Predisposición Genética a la Enfermedad , Neospora/inmunología , Selección Genética , Animales , Anticuerpos Antiprotozoarios/sangre , Bovinos , Enfermedades de los Bovinos/inmunología , Enfermedades de los Bovinos/transmisión , Coccidiosis/genética , Coccidiosis/inmunología , Coccidiosis/transmisión , Ensayo de Inmunoadsorción Enzimática/veterinaria , Femenino , Variación Genética , Transmisión Vertical de Enfermedad Infecciosa/veterinaria , Masculino , Modelos Genéticos , Ontario , Estudios SeroepidemiológicosRESUMEN
The objectives of this study were to estimate heritability of acetone concentration in milk, based on monthly samples of milk obtained as part of a routine milk testing program, and to evaluate the feasibility of using such data in a genetic evaluation program for selection against ketosis incidence. Milk samples were collected from January to December of 1999 in herds enrolled in the Ontario Dairy Herd Improvement Association, and acetone concentration was measured using an inline chemical procedure. The original data included more than 50,000 records. Because ketosis is generally a problem during early lactation, only the single test with the fewest days in milk was retained. In addition, data were retained only for cows with pedigree information. The final data set included 10,375 records. Among these data, only 6.56% had detectable levels of acetone. Acetone data were log-transformed prior to statistical analysis. Simple ANOVA indicated that herd, parity number, days in milk, and month of test had significant effects on acetone concentration. Acetone levels increased with lactation number and were higher in early lactation. Three approaches were applied for genetic analysis. First, REML was used with a simple linear animal model. Then, a separate procedure used data augmentation and Gibbs Sampling to obtain continuously distributed underlying values for records with zero acetone concentration, and these data were analyzed with both an animal and sire model. Heritability of acetone concentration was less than 1% for all 3 analyses. Herd effects accounted for about 5% of the phenotypic variance. Low estimates of heritability were due either to low actual levels of genetic variance or inability to detect all of the genetic variance present, due to infrequent recording during the early part of the lactation. Genetic evaluation based on recording of acetone concentration on a monthly basis seems of little use as a selection tool to decrease incidence of ketosis.
Asunto(s)
Acetona/análisis , Bovinos/genética , Leche/química , Fenotipo , Animales , Bovinos/metabolismo , Femenino , Lactancia , Modelos Genéticos , Linaje , Carácter Cuantitativo Heredable , Sensibilidad y Especificidad , Programas InformáticosRESUMEN
A maximum likelihood method was developed for QTL mapping in half-sib designs and compared to the regression method in analyses of both field and simulated data. The field data consisted of milk production evaluations of 433 progeny tested sons of 6 sires and 64 microsatellite markers distributed over 12 chromosomes. Based on permutation tests, 5 significant QTL were detected in the field data by the regression method compared with 10 by the maximum likelihood method (P < 0.05). In field data analysis, the maximum likelihood method detected more significant QTL and had a smaller residual variance than the regression method. The simulation included 9 scenarios differing in number of families, family size, QTL variance, and marker density, each replicated 100 times. The simulation results suggested that, as for the regression method, the precision of estimating QTL from the maximum likelihood method improves with increasing number of sons per sire, increasing the ratio of QTL to phenotypic variance, and decreasing marker interval. The maximum likelihood method had a smaller dispersion of estimated QTL positions than the regression method in 6 of 9 scenarios simulated. Overall, the maximum likelihood method shows potential advantage in QTL detection over the regression method, especially in the situations with less favorable conditions for QTL detection.
Asunto(s)
Bovinos/genética , Lactancia/genética , Funciones de Verosimilitud , Sitios de Carácter Cuantitativo/genética , Algoritmos , Animales , Cruzamiento , Femenino , Masculino , Modelos Estadísticos , Fenotipo , Análisis de Regresión , Sensibilidad y EspecificidadRESUMEN
The objective of this study was to use field data collected by dairy herd improvement programs to estimate genetic parameters for concentrations of milk urea nitrogen (MUN). Edited data were 36,074 test-day records of MUN and yields of milk, fat, and protein obtained from 6102 cows in Holstein herds in Ontario, Canada. Data were divided into three sets, for the first three lactations. Two analyses were performed on data from each lactation. The first procedure used ANOVA to estimate the significance of the effects of several environmental factors on MUN. Herd-test-day effects had the most significant impact on MUN. Effects of stage of lactation were also important, and MUN levels tended to increase from the time of peak yield until the end of lactation. The second analysis used a random regression model to estimate heritabilities and genetic correlations of MUN and the yield traits. Heritability estimates for MUN in lactations one, two, and three were 0.44, 0.59, and 0.48, respectively. Heritabilities for the yield traits were of a similar magnitude. Little relationship was observed between MUN and yield. Raw phenotypic correlations were all <0.10 (absolute value). Genetic correlations with production traits were close to zero in lactations one and three and only slightly positive in lactation two. The results indicate that selection on MUN is possible, but relationships between MUN and other economically important traits such as metabolic disease and fertility are needed.
Asunto(s)
Bovinos/genética , Lactancia/genética , Leche/química , Nitrógeno/análisis , Urea/química , Animales , Bovinos/metabolismo , Ambiente , Femenino , Lípidos/análisis , Proteínas de la Leche/análisis , Fenotipo , Análisis de Regresión , Selección GenéticaRESUMEN
The objectives of this study were to develop and simulate the implementation of several strategies for repeated application of quantitative trait loci (QTL) detection and marker-assisted selection (MAS) and to compare the short-term and continual genetic responses. A finite locus model was simulated with 20 QTL randomly distributed across 30 chromosome. Three hundred markers were evenly spaced across the genome. Allelic effects were sampled from a double exponential distribution. A daughter design was used every generation to determine the marker alleles favorably associated to QTL alleles. The MAS was applied within family to young bulls, before progeny testing, as part of an open nucleus. Young bulls were selected using strategies based on 1) the single marker with greatest contrast (BEST1), 2) the sum of n greatest contrasts (BESTn), 3) the best n contrasts, limited to one per chromosome (LIMn), 4) the sum of all contrasts exceeding a given threshold n (THRESn), and 5) the sum of contrasts exceeding a threshold, but limited to one per chromosome (LIMT). The maximum progress was achieved by strategies that selected upon several markers flanking multiple QTL in each generation. When THRES was applied, the mean true breeding value (TBV) of selected bulls was increased by 11.98% (over conventional selection) versus 6.73% for BEST1 in the first generation. Applying a full genome scan in each generation allowed selection for different QTL across time. By selecting for multiple QTL over time, MAS maintained superiority over conventional selection for many generations.
Asunto(s)
Cruzamiento , Bovinos/genética , Marcadores Genéticos , Sitios de Carácter Cuantitativo , Selección Genética , Alelos , Animales , Femenino , Masculino , Modelos GenéticosRESUMEN
Multi-primer target polymerase chain reaction (MPT-PCR) is a rapid method for the identification of specific BoLA-DRB3 alleles. In a single PCR reaction, the presence of two alleles associated with increased risk, DRB3.2*23 (DRB3*2701-2703, 2705-2707) and decreased risk, DRB3.2*16 (DRB3*1501, 1502), of mastitis in Canadian Holstein can be detected. Two outer primers amplify exon 2 of DRB3. Simultaneously, two inner, allele-specific primers amplify individual alleles. Initially, 40 cows previously typed by PCR-restriction fragment length polymorphism (PCR-RFLP) were genotyped using the multi-primer approach. An additional 30 cows were first genotyped by multi-primer target PCR, then by PCR-RFLP. All animals were correctly identified and there were no false positives. This technique can readily be modified to identify other BoLA alleles of interest.
Asunto(s)
Alelos , Bovinos/genética , Antígenos de Histocompatibilidad Clase II/genética , Antígenos de Histocompatibilidad Clase II/inmunología , Reacción en Cadena de la Polimerasa/veterinaria , Animales , Bovinos/inmunología , ADN/química , ADN/genética , ADN/aislamiento & purificación , Femenino , Genotipo , Antígenos de Histocompatibilidad Clase II/análisis , Reacción en Cadena de la Polimerasa/métodosRESUMEN
Sons (n = 71 to 75) of each of six Holstein sires were genotyped at 69 microsatellite loci covering a total of 676 cM on chromosomes 3, 5, 9, 10, 13, 15, 17, 20, 23, and 26. Estimates of quantitative trait loci (QTL) effect and location were made using a least squares interval mapping approach based on daughter yield deviations of sons for 305 d milk, fat, and protein yield and fat and protein percentage. Thresholds for statistical significance of QTL effects were determined from interval mapping of 10,000 random permutations of the data across the bull sire families and within each sire family separately. Analyses combining data across sires indicated the presence of QTL affecting milk, fat, and protein yield on chromosomes 20 and 26 and a QTL affecting fat and protein percentage on chromosome 3. Analyses within each sire family separately indicated the presence of segregating QTL in at least one family on 7 of the 10 chromosomes. Statistically significant estimates of QTL effects on breeding value ranged from 438 to 658 kg of milk, from 17.4 to 24.9 kg of fat, 13.0 to 17.0 kg of protein, 0.04 to 0.17% fat, and 0.07 to 0.10% protein.
Asunto(s)
Bovinos/genética , Lactancia/genética , Leche/química , Animales , Cruzamiento , Bovinos/fisiología , Mapeo Cromosómico/veterinaria , Femenino , Genotipo , Lactancia/fisiología , Lípidos/genética , Masculino , Repeticiones de Microsatélite , Proteínas de la Leche/genética , Carácter Cuantitativo HeredableRESUMEN
Local administration of calcitonin gene-related peptide (CGRP) has been shown to improve tissue survival in surgical skin flaps. Moreover, topical CGRP has been demonstrated to exert anti-inflammatory effects in different animal models of skin inflammation. The aim of the present study was to establish whether systemic treatment with low doses of CGRP may improve survival and reduce neutrophil accumulation in surgical skin flaps. Using a well-established dorsal skin-flap model in the rat, we found that intraperitoneal (i.p.) pretreatment with low doses of CGRP dose-dependently increased flap survival. Thus, in untreated animals flap survival at day 7 after surgery was 42%, as compared to 44%, 60%, 69% and 73% survival after a single preoperative i.p. injection of 10(-15), 10(-12), 10(-9) and 10(-6) mol CGRP, respectively (P < 0.05 versus control for the three highest doses). The three effective doses had no detectable effects on either flap blood flow (laser Doppler) or mean arterial blood pressure. On the other hand, 5 x 10(-9) mol CGRP i.p. significantly reduced the marked surgery-induced accumulation of flap myeloperoxidase (a marker for neutrophil recruitment) without affecting the circulating neutrophil count. Taken together, our findings demonstrate that low systemic doses of CGRP can cause a major improvement in skin-flap survival in the rat, possibly via inhibition of surgically induced neutrophil recruitment.
Asunto(s)
Péptido Relacionado con Gen de Calcitonina/uso terapéutico , Supervivencia de Injerto/efectos de los fármacos , Infiltración Neutrófila/efectos de los fármacos , Colgajos Quirúrgicos/irrigación sanguínea , Vasodilatadores/uso terapéutico , Animales , Masculino , Distribución Aleatoria , Ratas , Ratas Sprague-Dawley , Estadísticas no Paramétricas , Colgajos Quirúrgicos/inmunología , Colgajos Quirúrgicos/patologíaRESUMEN
This study evaluated the adequacy of an alternate a.m.-p.m. testing scheme for milk yield in comparison with the official test method based on weighing two milkings within 24 h. A total of 88,558 single test day milking weights from 15,670 Italian Friesian cows in 610 herds in the province of Milano (Italy) were collected between September 1991 and October 1992. Ratios were computed for daily milk yield to a.m. and p.m. milking weights (direct yield ratios) and ratios of a.m and p.m. milking weights to daily milk yield (inverse yield ratios). Analysis of variance indicated that the milking interval is the most important source of variation for yield ratios. Factors for estimating daily milk yield from single milking weights adjusted for milking intervals were derived through regression analysis of direct and inverse yield ratios on the length of the milking interval. Daily milk yield was estimated more precisely and accurately when adjustment factors were used than when single milking weights were doubled. The doubling of a.m. and p.m. milking weights overestimated and underestimated (5% on average) daily milk yield, respectively. For 305-d lactation yield, accuracies of these methods were comparable. In conclusion, alternate recording of a.m. and p.m. milking weights led to reliable estimates of milk yield. Effects of the alternate a.m.-p.m. testing scheme on estimates of milk components and genetic evaluations of dams of sires should be investigated.
Asunto(s)
Bovinos , Industria Lechera/métodos , Lactancia , Animales , Sesgo , Femenino , Italia , Análisis de Regresión , Factores de TiempoRESUMEN
Mate selection can increase progency merit if overall merit is nonlinear for one or more component traits. An index of expected progeny merit could be calculated for all possible mating pairs, and the set of pairs with the highest progeny mean could be selected. There are serious computational problems for more than a few males and females. To select and mate f, females, and m, males, from n of each, with k0 females per male, would require (nf)(nm)f!/(k0!)m evaluations. Linear programming algorithms can determine the optimal strategy efficiently by considering only a subset of these possibilities. Let pi ij be the index of progency merit of the ith sire mated to the jth dam and Xij be the decision variable for that mating (restricted to 0 or 1). Then the problem of selecting mating pairs can be stated as: maximize sigma i sigma j pi ij Xij, subject to sigma i Xij less than or equal to 1, sigma j Xij less than or equal to k0, sigma i sigma j Xij = f, and Xij = 0 or 1. By including an artificial sire and an artificial dam and choosing appropriate merit values for the artificial matings, this problem can be solved by efficient "transportation" algorithms. These algorithms could be used to develop rational mating packages for dairy artificial insemination studs provided that an objective evaluation of progeny merit could be formulated, provided that merit is not simply additively inherited.