Thyroid hormones in the cerebrospinal fluid of the third ventricle of adult female sheep during different periods of reproductive activity

Thyroid hormones (THs) are obligatory for transition from breeding season to anestrus in sheep. In this process, THs act during a very limited time of the year and primarily within the brain. In ewes chronically equipped for sampling cerebrospinal fluid (CSF) from the third ventricle, we have characterized the concentrations of total and free thyroxine (T4), triiodothyronine (T3), and total reverse T3 (rT3) in the CSF during breeding season, anestrus and during a critical period required for transition to anestrus (December-March). The total T4, T3, rT3 and free T3 average concentrations (+/- SEM) in CSF were 1.5 +/- 0.07 ng/ml, 14.5 +/- 1.2 pg/ml, 43 +/- 7.4 pg/ml, and 0.6 +/- 0.05 pg/ml, respectively, and all were significantly lower (p < 0.001) than in blood plasma except free T4 (12.6 +/- 1.1 pg/ml), which was similar to that in plasma. There was a seasonal trend (p < 0.05) in the concentration of total T3 (highest in December) and free T4 (highest in November) in the CSF that does not follow that in blood plasma. During the period of transition to anestrus the CSF total T3/TT4 molar ratio and free T3/T4 ratio were significantly lower (p < 0.05 and p < 0.01, respectively) than in blood plasma, while the total rT3/T4 ratio was significantly higher (p < 0.01) at the end of this period (March). Additionally, the CSF total rT3 concentrations were also significantly correlated with the CSF total T4 levels (r = 0.57; p < 0.05). In conclusion, the CSF in sheep may serve as a considerable source of thyroid hormones for neuroendocrine events. The lack of significant changes in THs concentrations in the CSF during the period of transition to anestrus indicate that neither seasonal changes of THs circulating in the blood plasma nor THs circulating in the CSF actively drive the transition to anestrus.     

Inbreeding in populations with incomplete pedigrees

Inbreeding has detrimental effects on a number of economically important traits. W iggans et al. (1995) estimated inbreeding depression of ?29 kg, ?1.08 kg and ?0.97 kg for each 1% increase of inbreeding for the traits milk, fat and protein yield, respectively, across several dairy cattle breeds. For post-weaning gain in Hereford cattle, the depression was ?0.24 kg (G engler et al. 1998). For the number of piglets born alive, 21-day litter weight, and days to 104.5 kg, it was ?0.023, ?0.052 and 0.21, respectively (C ulbertson et al. 1998). Inbreeding also adversely impacts reproductive traits, such as delayed puberty, reduced conception rates, higher likelihood of losing established pregnancies, increased mortality of calves and lowered bull fertility (Y oung et al. 1969). National genetic evaluations involve animals with incomplete pedigrees. Regular inbreeding algorithms (RA) based on the definition of W right (1922), such as those by Q uaas (1976), calculate the inbreeding of animals with at least one parent missing as zero. Even if an animal has both parents known, its inbreeding will be underestimated if some of its ancestors are unidentified. If the proportion of missing parents is large, the inbreeding trend in a population could be seriously underestimated. Subsequently, losses from inbreeding would be underestimated, and steps to slow the increase of inbreeding, such as using sires that are less related to the general population or mating less-related animals (T oro and P erez -E nciso , 1990; G rundy et al. 1994; M euwissen and S onneson 1998; V an R aden and S mith 1999), may be delayed. In particular, use of a mating system can result in matings adjusted for both inbreeding and dominance (M isztal et al. 1999). In populations that use AI substantially, unidentified parents may not differ genetically from identified parents, on average. Therefore the real average inbreeding in animals with unidentified parent(s) may be similar to their contemporaries with both parents known. V an R aden (1992) proposed an algorithm (VRA), where the inbreeding of animals whose parent(s) are unknown is equal to the mean inbreeding of their contemporaries with known parents. Contemporaries are stratified along unknown parent groups (UPG). VRA has been applied to a few US dairy breeds (V an R aden 1992; W iggans et al. 1995). The calculated inbreeding for the youngest Holstein animals was 3.7% with RA and increased to 4.2% with VRA (V an R aden 1992). The increase was small because the number of unidentified animals was small. However, the performance of VRA in recovering inbreeding lost for a range of incomplete pedigrees has not been evaluated. The objectives of this study were (i) to determine average inbreeding coefficients when pedigrees are increasingly more incomplete; (ii) to assess the efficacy of VRA in recovering these inbreeding coefficients; and (iii) to determine the mean inbreeding using the two inbreeding algorithms in a large beef population.     

Threshold-linear analysis of measures of fertility in artificial insemination data and days to calving in beef cattle

Mating and calving records for 47,533 first-calf heifers in Australian Angus herds were used to examine the relationship between days to calving (DC) and two measures of fertility in AI data: 1) calving to first insemination (CFI) and 2) calving success (CS). Calving to first insemination and calving success were defined as binary traits. A threshold-linear Bayesian model was employed for both analyses: 1) DC and CFI and 2) DC and CS. Posterior means (SD) of additive covariance and corresponding genetic correlation between the DC and CFI were -0.62 d (0.19 d) and -0.66 (0.12), respectively. The corresponding point estimates between the DC and CS were -0.70 d (0.14 d) and -0.73 (0.06), respectively. These genetic correlations indicate a strong, negative relationship between DC and both measures of fertility in AI data. Selecting for animals with shorter DC intervals genetically will lead to correlated increases in both CS and CFI. Posterior means (SD) for additive and residual variance and heritability for DC for the DC-CFI analysis were 23.5 d2 (4.1 d2), 363.2 d2 (4.8 d2), and 0.06 (0.01), respectively. The corresponding parameter estimates for the DC-CS analysis were very similar. Posterior means (SD) for additive, herd-year and service sire variance and heritability for CFI were 0.04 (0.01), 0.06 (0.06), 0.14 (0.16), and 0.03 (0.01), respectively. Posterior means (SD) for additive, herd-year, and service sire variance and heritability for CS were 0.04 (0.01), 0.07 (0.07), 0.14 (0.16), and 0.03 (0.01), respectively. The similarity of the parameter estimates for CFI and CS suggest that either trait could be used as a measure of fertility in AI data. However, the definition of CFI allows the identification of animals that not only record a calving event, but calve to their first insemination, and the value of this trait would be even greater in a more complete dataset than that used in this study. The magnitude of the correlations between DC and CS-CFI suggest that it may be possible to use a multitrait approach in the evaluation of AI and natural service data, and to report one genetic value that could be used for selection purposes.     

Joint longitudinal modeling of age of dam and age of animal for growth traits in beef cattle

Two methods to jointly model age of dam (AOD) and age of animal in random regression analyses of growth in Gelbvieh cattle were examined. The first method (M1) was analogous to the multiple-trait analysis and consisted of AOD as a nested class variable and a cubic polynomial regression on age nested within birth, weaning, and yearly weights. The second method (M2) used two-dimensional splines, with age knots at 150, 205, 270, 340, and 390 d. The AOD knots were placed at 725, 1,464, and 2,189 d. These selected knots were used to form a two-dimensional grid containing 15 knots, each representing a specific age and AOD combination. A data set containing Gelbvieh growth records was split along contemporary groups into two data sets. Data set 1 contained 316,078 records and was used for prediction by mixed-model equations. Data set 2 contained 164,167 records and was used for cross validation. In the complete data set, only 90 and 30% of animals with birth weight had records on weaning and yearling weights, respectively. Models were evaluated based on R2, average squared error (ASE), percent bias, and plots of solutions. The ASE for weights associated with birth weight, weaning weight, and yearling weight for M1 were 15, 505, and 703 kg2. With M2, large jumps in fixed-effect estimates were observed outside the two-dimensional grid. To eliminate this problem, weighted one-dimensional splines were used for extrapolation beyond the two-dimensional grid. For M2 with weighted spline extrapolation, the ASE were 15, 542, and 777 kg2 for birth weight, weaning weight, and yearling weight, respectively. Creation of optimal two-dimensional splines is difficult when data are clustered. Despite such difficulties, the two-dimensional spline was capable of jointly and continuously modeling AOD and age of animal.     

Estimation of variance components including competitive effects of Large White growing gilts

Records of on-test ADG of Large White gilts were analyzed to estimate variance components of direct and associative genetic effects. Models included the effects of contemporary group (farm-barn-batch), birth litter, pen group, and direct and associative additive genetic effects. The area of each pen was 14 m2. The additive genetic variance was a function of the number of competitors in a group, the additive relationships between the animal performing the record and its pen mates, and the additive relationships between pen mates. To partially account for differences in the number of pen mates, a covariable (qi = 1, 1/n, or 1/n(1/2)) was added to the associative genetic effect. There were 4,946 records from 2,409 litters and 362 pen groups. Pen group size ranged from 12 to 16 gilts. Analyses by REML converged very slowly. A grid search showed that the likelihood function was almost flat when the additive genetic associative effect was fitted. Estimates of direct and associative heritability were 0.15 and 0.03, respectively. Within the BLUPF90 family of programs, the mixed-model equations can be set up directly. For variance component estimation, simple programs (REMLF90 and GIBBSF90) worked without modifications, but more optimized programs did not. Estimates obtained using the three values of qi were similar. With the data structure available for this study and under an environment with relative low competition among animals, accurate estimation of associative genetic effects was not possible. Estimation of competitive effects with large pen size is difficult. The magnitude of competition effects may be larger in commercial populations, where housing is denser and food is limited.     

Comparison of computing properties of derivative and derivative-free algorithms in variance-component estimation by REML

SUMMARY: Computing properties of better derivative and derivative-free algorithms were compared both theoretically and practically. Assuming that the log-likelihood function is approximately quadratic, in a t-trait analysis the number of steps to achieve convergence increases as t(2) in 'better' derivative-free algorithms and is independent of that number in 'better' derivative algorithms. The cost of one step increases as t(3) . Consequently, both classes of algorithms have a similar computational cost for single-trait models. In multiple traits, the computing costs increase as t(3) and t(5) , respectively. The derivative-free algorithms have worse numerical properties. Four programs were used to obtain one-, two-, and three-trait REML estimates from field data. Compared to single-trait analyses, the cost of one run for derivative-free algorithms increased by 27-40 times for two traits and 152-686 times for three traits. A similar increase in rounds of iteration for a derivative algorithm reached 5 and 21, and 1.8 and 2.2 in canonical transformation. Convergence and estimates of derivative algorithms were more predictable and, unlike derivative-free algorithms, were much less dependent on the choice of priors. Well-implemented derivative REML algorithms are less expensive and more reliable in multiple traits than derivative-free ones. ZUSAMMENFASSUNG: Vergleich von Rechen (Computing) merkmalen von abgeleiteten und ableitungsfreien Algorithmen zur Varianzkomponentensch?tzung mittels REML Rechenmerkmale von verbesserten ableitungsfreien und Algorithmen, die Ableitung benutzen, werden theoretisch und praktisch verglichen. Unter der Annahme einer ungef?hr quadratischen log-likelihood Funktion, nimmt in der Analyse von t Merkmalen die Zahl der Rechenschritte bis zu Konvergenz mit t(2) in 'besseren' ableitungsfreien Algorithmen zu und ist davon unabh?ngig von dieser Zahl in der 'besseren' Ableitung. Die Kosten je Schritt steigen mit t(3) . Daher haben beide Berechnungsarten für Einzelmerkmale ?hnliche Rechenkosten. Bei mehreren Merkmalen steigen die Kosten mit t(3) bzw. t(5) und ableitungsfreie Algorithmen haben schlechtere numerische Eigenschagten. Vier Programme haben für ein-, zwei- und drei-Merkmale REML Sch?tzungen von Felddaten erzeugt. Im Vergleich zu Ein-Merkmal Analysen stiegen Kosten für einen Lauf bei ableitungsfreien Algorithmen um das 27-40 fache bei zwei- und um das 152-686 fache bei drei-Merkmalen. Die Steigerungen je Lauf bei auf Ableitung beruhenden Algorithmen waren 5-21 fach und 1.8 und 2.2 fach bei kanonischer Transformation. Konvergenz und Sch?tzwerte von Algorithmen mit Ableitung waren besser vorhersagbar und weniger von der Wahl der priors beeinflu?t. Gut ausgestattete REML Methoden, die Ableitungen benutzen, sind ?konomischer und verl??licher bei Mehrmerkmalsproblemen als ableitungsfreie.     

Genetic evaluation of growth in a multibreed beef cattle population using random regression-linear spline models

The objective of this study was to examine the feasibility of using random regression-spline (RR-spline) models for fitting growth traits in a multibreed beef cattle population. To meet the objective, the results from the RR-spline model were compared with the widely used multitrait (MT) model when both were fit to a data set (1.8 million records and 1.1 million animals) provided by the American Gelbvieh Association. The effect of prior information on the EBV of sires was also investigated. In both RR-spline and MT models, the following effects were considered: individual direct and maternal additive genetic effects, contemporary group, age of the animal at measurement, direct and maternal heterosis, and direct and maternal additive genetic mean effect of the breed. Additionally, the RR-spline model included an individual direct permanent environmental effect. When both MT and RR-spline models were applied to a data set containing records for weaning weight (WWT) and yearling weight (YWT) within specified age ranges, the rankings of bulls' direct EBV (as measured via Pearson correlations) provided by both models were comparable, with slightly greater differences in the reranking of bulls observed for YWT evaluations (>or=0.99 for BWT and WWT and >or=0.98 for YWT); also, some bulls dropped from the top 100 list when these lists were compared across methods. For maternal effects, the estimated correlations were slightly smaller, particularly for YWT; again, some drops from the top 100 animals were observed. As in regular MT multibreed genetic evaluations, the heterosis effects and the additive genetic effects of the breed could not be estimated from field data, because there were not enough contemporary groups with the proper composition of purebred and crossbred animals; thus, prior information based on literature values had to be included. The inclusion of prior information had a negligible effect in the overall ranking for bulls with greater than 20 birth weight progeny records; however, the effect of prior information for breeds or groups poorly represented in the data was important. The Pearson correlations for direct and maternal WWT and YWT ranged from 0.95 to 0.98 when comparing evaluations of data sets for which the out-of-range age records were removed or retained. Random regression allows for avoiding the discarding of records that are outside the usual age ranges of measurement; thus, greater accuracies are achieved, and greater genetic progress could be expected.     

Reliable computing in estimation of variance components

The purpose of this study is to present guidelines in selection of statistical and computing algorithms for variance components estimation when computing involves software packages. For this purpose two major methods are to be considered: residual maximal likelihood (REML) and Bayesian via Gibbs sampling. Expectation‐Maximization (EM) REML is regarded as a very stable algorithm that is able to converge when covariance matrices are close to singular, however it is slow. However, convergence problems can occur with random regression models, especially if the starting values are much lower than those at convergence. Average Information (AI) REML is much faster for common problems but it relies on heuristics for convergence, and it may be very slow or even diverge for complex models. REML algorithms for general models become unstable with larger number of traits. REML by canonical transformation is stable in such cases but can support only a limited class of models. In general, REML algorithms are difficult to program. Bayesian methods via Gibbs sampling are much easier to program than REML, especially for complex models, and they can support much larger datasets; however, the termination criterion can be hard to determine, and the quality of estimates depends on a number of details. Computing speed varies with computing optimizations, with which some large data sets and complex models can be supported in a reasonable time; however, optimizations increase complexity of programming and restrict the types of models applicable. Several examples from past research are discussed to illustrate the fact that different problems required different methods.     

Validation of single‐step GBLUP genomic predictions from threshold models using the linear regression method: An application in chicken mortality

The objective of this study was to determine whether the linear regression (LR) method could be used to validate genomic threshold models. Statistics for the LR method were computed from estimated breeding values (EBVs) using the whole and truncated data sets with variances from the reference and validation populations. The method was tested using simulated and real chicken data sets. The simulated data set included 10 generations of 4,500 birds each; genotypes were available for the last three generations. Each animal was assigned a continuous trait, which was converted to a binary score assuming an incidence of failure of 7%. The real data set included the survival status of 186,596 broilers (mortality rate equal to 7.2%) and genotypes of 18,047 birds. Both data sets were analysed using best linear unbiased predictor (BLUP) or single‐step GBLUP (ssGBLUP). The whole data set included all phenotypes available, whereas in the partial data set, phenotypes of the most recent generation were removed. In the simulated data set, the accuracies based on the LR formulas were 0.45 for BLUP and 0.76 for ssGBLUP, whereas the correlations between true breeding values and EBVs (i.e. true accuracies) were 0.37 and 0.65, respectively. The gain in accuracy by adding genomic information was overestimated by 0.09 when using the LR method compared to the true increase in accuracy. However, when the estimated ratio between the additive variance computed based on pedigree only and on pedigree and genomic information was considered, the difference between true and estimated gain was <0.02. Accuracies of BLUP and ssGBLUP with the real data set were 0.41 and 0.47, respectively. This small improvement in accuracy when using ssGBLUP with the real data set was due to population structure and lower heritability. The LR method is a useful tool for estimating improvements in accuracy of EBVs due to the inclusion of genomic information when traditional validation methods as k‐fold validation and predictive ability are not applicable.