Evaluation of body condition score measured throughout lactation as an indicator of fertility in dairy cattle

Body condition score (BCS) records of primiparous Holstein cows were analyzed both as a single measure per animal and as repeated measures per sire of cow. The former resulted in a single, average, genetic evaluation for each sire, and the latter resulted in separate genetic evaluations per day of lactation. Repeated measure analysis yielded genetic correlations of less than unity between days of lactation, suggesting that BCS may not be the same trait across lactation. Differences between daily genetic evaluations on d 10 or 30 and subsequent daily evaluations were used to assess BCS change at different stages of lactation. Genetic evaluations for BCS level or change were used to estimate genetic correlations between BCS measures and fertility traits in order to assess the capacity of BCS to predict fertility. Genetic correlation estimates with calving interval and non-return rate were consistently higher for daily BCS than single measure BCS evaluations, but results were not always statistically different. Genetic correlations between BCS change and fertility traits were not significantly different from zero. The product of the accuracy of BCS evaluations with their genetic correlation with the UK fertility index, comprising calving interval and non-return rate, was consistently higher for daily than for single BCS evaluations, by 28 to 53%. This product is associated with the conceptual correlated response in fertility from BCS selection and was highest for early (d 10 to 75) evaluations.</p

Genetic profile of total body energy content of Holstein cows in the first three lactations

Weekly total body energy content (TBEC) was calculated for 444 Holstein cows in their first 3 lactations. These calculations were based on body lipid and protein changes predicted from weekly changes in body condition score and live weight of each cow. In first lactation, cows lost TBEC during the initial 8 wk, regained it by wk 22, and continued to build up their reserves until wk 37. Cows started lactations 2 and 3 with considerable reserves from the dry period that they used during the first 13 wk of lactation. Variance components for TBEC were estimated using random regression analysis allowing for heterogeneous residual variance. The genetic variance increased within each lactation, suggesting that the genetic component becomes more important as lactation progresses. The genetic correlations between very early ( wk 1 to 4) and later stages of first lactation were near zero but they increased considerably between later lactation stages. Genetic correlations between TBEC on wk 5 of first lactation and the remainder of this lactation ranged from 0.64 for the more distant weeks to 0.99 for the immediately subsequent weeks. Genetic correlations with TBEC in second lactation were moderately high (0.68 to 0.70) for the early weeks ( 1 to 8) and decreased gradually to 0.56 for weeks at the end of lactation. For third lactation, these estimates ranged from 0.53 to 0.63. Genetic correlation estimates of TBEC in wk 12 of first lactation with subsequent first-lactation weeks varied from 0.79 to 0.99, whereas they ranged from 0.65 to 0.77 and from 0.57 to 0.68 in second and third lactations, respectively. The genetic correlation between TBEC in later weeks of first lactation and the rest of productive life increased as first lactation progressed, but the improvement diminished. Weekly genetic evaluations for first-lactation TBEC were used to predict second- and third-lactation energy content. The accuracy of these predictions increased with progressing weeks in first lactation, but about three-fourths of the improvement occurred by wk 5. Our results suggest that TBEC calculated after a month from the first calving may give useful information about the future energy content of a cow.</p

Modeling daily energy balance of dairy cows in the first three lactations

Daily energy balance was calculated for 111 Holstein cows in their first 3 lactations, based on combinations of smoothed preadjusted phenotypic records for milk yield, feed intake, live weight, and body condition score. Two energy balance traits were defined: one based on milk yield and feed intake (EB1) and the other on live weight and body condition score change (EB2). Bessel functions (BF), Legendre polynomials ( LP), sinusoidal functions ( SF), and cubic splines ( CS) were used to model energy balance within and across lactations. Models with BF or LP fitted fixed regressions of order 1 to 6 and random regressions of order 1 to 10. Cubic splines were fitted at 5 to 30 equally spaced knot points. In within-lactation analyses with BF and LP models, likelihood ratio tests revealed that the fit improved significantly up to random regression order of 5 for EB1 and 4 for EB2, independently of the fixed regression order. For EB1 analyses with LP, improvement was marginal albeit significant even for higher random regression order. For CS models, optimal number of knot points was 13 and 12 for EB1 and EB2, respectively. Residual variance and comparisons between actual and predicted energy balance showed that LP of minimum order 8 and 5 modeled, respectively, EB1 and EB2 better than the other 3 functions. In across-lactation analyses with BF and LP models, likelihood ratio tests were significant as the random regression order increased, for any order of the fixed regression. For CS models, optimal number of knot points was 14 and 16 for EB1 and EB2, respectively. Residual variance and comparisons between actual and predicted energy balance showed that models fitting CS and high (&gt;8) random order BF or LP provided the best fit to both traits. However, in an across-lactation analysis, even higher order of LP or BF will be required to provide as good a fit as within-lactation analyses.</p

Genetic parameters of growth in dairy cattle and associations between growth and health traits

Body weight (BW) observations on dairy cattle taken on average 35 times between birth and 1,000 d of life were used to estimate daily heritabilities and predict daily breeding values for both pregnancy-adjusted BW (PABW) and growth rate. Daily heritabilities for PABW were moderate to high, ranging from 0.41 (+/- 0.027) to 0.82 (+/- 0.041). Daily heritabilities for growth rate were high (&gt; 0.68 +/- 0.034). The genetic association between various health events, including mastitis and lameness, and weight and growth was investigated by regressing the incidence of health events on breeding values for weight at birth, weaning, calving, and growth rate at 56 d after calving, growth rate at 110 d after calving, and maximum growth rate. Growth at weaning was the only BW measure to significantly affect mastitis (r(g) = 0.24), indicating that cows growing faster at weaning are more prone to mastitis. Increased weight (r(g) = 0.65) and growth rate at weaning (r(g) = 0.38) and increased maximum growth rate (r(g) = 0.71) all contributed to increased feet disorders. The only significant negative genetic association was obtained between reproduction and weight at calving (r(g) = -0.61).</p

Magnetization dynamics of two interacting spins in an external magnetic field

The longitudinal relaxation time of the magnetization of a system of two exchange coupled spins subjected to a strong magnetic field is calculated exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the magnetization, i.e., the Langevin equation of the process, over its realizations so reducing the problem to a system of linear differential-recurrence relations for the statistical moments (averaged spherical harmonics). The system is solved in the frequency domain by matrix continued fractions yielding the complete solution of the two-spin problem in external fields for all values of the damping and barrier height parameters. The magnetization relaxation time extracted from the exact solution is compared with the inverse relaxation rate from Langer's theory of the decay of metastable states, which yields in the high barrier and intermediate-to-high damping limits the asymptotic behaviour of the greatest relaxation time.Comment: 32 pages, 5 figures. The paper has been revised and new results added (e.g., Fig. 5

Prenatal maternal effects on body condition score, female fertility, and milk yield of dairy cows

In this study, maternal effects were described as age of dam at first and second calving, first-lactation body condition score (BCS) of the dam during gestation, and milk yield of the dam. The impact of these effects on first-lactation daughter BCS, fertility, and test-day milk yield was assessed. The effect of milk yield of dam on daughter 305-d yield in the latter's first 3 lactations was also investigated. The proportion of total phenotypic variance in daughter traits accounted for by maternal effects was calculated. Dams calving early for the first time (18 to 23 mo of age) had daughters that produced 4.5% more first-lactation daily milk, had 7% higher BCS, and had their first service 3 d earlier than cows whose dams calved late (30 to 36 mo). However, daughters of dams that calved early had difficulties conceiving as they needed 7% more inseminations and had a 7.5% higher return rate. Cows from second calvings of relatively young (36 to 41 mo) dams produced 6% more first-lactation daily milk, had 2% higher BCS, and showed a significantly better fertility profile than cows whose dams calved at a late age (47 to 55 mo) High maternal BCS during gestation had a favorable effect on daughter BCS, nonreturn rate, and number of inseminations per conception. However, it was also associated with a small decrease in daughter daily milk yield. Changes in dam BCS during gestation did not affect daughter performance significantly. Maternal effects of milk yield of the dam, expressed as her permanent environment during lactation, adversely affected daughter 305-d milk, fat, and protein yield. However, although the effect was significant, it was practically negligible (&lt;0.3% of the mean). Finally, overall maternal effects accounted for a significant proportion of the total phenotypic variance of calving interval (1.4 +/- 0.6%) and nonreturn rate (1.1 +/- 0.5%).</p

Indirect comparison of Debrecen and Greenwich daily sums of sunspot areas

Sunspot area data play an important role in the studies of solar activity and its long-term variations. In order to reveal real long-term solar variations precise homogeneous sunspot area databases should be used. However, the measured areas may be burdened with systematic deviations, which may vary in time. Thus, there is a need to investigate the long-term variation of sunspot area datasets and to determine the time-dependent cross-calibration factors. In this study, we investigate the time-dependent differences between the available long-term sunspot databases. Using the results, we estimate the correction factor to calibrate the corrected daily sunspot areas of Debrecen Photoheliographic Data (DPD) to the same data of Greenwich Photoheliographic Results (GPR) by using the overlapping Kislovodsk and Pulkovo data. We give the correction factor as GPR=1.08(\pm 0.11)*DPDComment: 9 pages, 7 figures, Accepted for publication in MNRA

GLUMIP 2.0: SAS/IML Software for Planning Internal Pilots

Internal pilot designs involve conducting interim power analysis (without interim data analysis) to modify the final sample size. Recently developed techniques have been described to avoid the type~I error rate inflation inherent to unadjusted hypothesis tests, while still providing the advantages of an internal pilot design. We present GLUMIP 2.0, the latest version of our free SAS/IML software for planning internal pilot studies in the general linear univariate model (GLUM) framework. The new analytic forms incorporated into the updated software solve many problems inherent to current internal pilot techniques for linear models with Gaussian errors. Hence, the GLUMIP 2.0 software makes it easy to perform exact power analysis for internal pilots under the GLUM framework with independent Gaussian errors and fixed predictors.

Calculation of multiple-trait sire reliability for traits included in a dairy cattle fertility index

The advent of genetic evaluations for fertility traits in the UK offers valuable information to farmers that can be used to control fertility problems and safeguard against involuntary culling. In addition to estimated genetic merit, proof reliabilities are required to make correct use of this genetic information. Exact reliabilities, based on the inverse of the coefficient matrix, cannot be estimated for large data sets because of computational restrictions. A method to calculate approximate reliabilities was implemented based on a six-trait sire model. Traits considered were interval between first and second calving, interval between first calving and first service, non-return rate 56 days post first service, number of inseminations per conception, daily milk yield at test nearest day 110 and body condition score. Sire reliabilities were calculated in four steps. Firstly, the number of effective daughters was calculated for each bull, separately for each trait, based on total number of daughters and daughter distribution across herd-year-seasons. Secondly, multiple-trait reliabilities were calculated, based on bull daughter contribution, applying selection index theory on independent daughter groups. Thirdly, (great-) grand-daughter contribution was added to the reliability of each bull, using daughter-based reliability of sons and maternal grandsons. An adjustment was made to account for the probability of bull and son or grandson having daughters in the same herd-year-season. Without the adjustment, reliabilities were inflated by proportionately 0·15 to 0·25. Finally, parent (sire and maternal grandsire) contribution was added to the reliability of each bull. The procedure was first tested on a data subset of 28 061 cow records from 285 bulls. Approximate reliabilities were compared with exact estimates based on the inverse of the coefficient matrix. Mean absolute differences ranged from 0·014 to 0·020 for the six traits and correlation between exact and approximate estimates neared unity. In a full-scale application, sire reliability for the fertility traits increased by proportionately 0·47 to 0·79 over single-trait estimates and the number of bulls with a reliability of 0·60 or more increased by 42 to 115%