Legendre Polynomials Of Order Research Articles

Estimates of Genetic Parameters, Growth Curve, and Environmental Effects for Nellore Cattle in the Pantanal.

The objective was to estimate the growth curves and genetic parameters using random regression methodology for Nellore cattle raised in Pantanal, MS, Brazil (6974 calves; n = 53,233 weights), with at least four weighings per individual. The model considered direct and maternal genetic additives and maternal permanent environmental effects at random. Orthogonal Legendre polynomials of cubic order were used to fit the growth curve. Analyses of variance were performed using the GLM procedure. The model used contained the fixed effects of sex, year of birth, farm, and the covariates calf birth month (linear and quadratic) and cow age at calving (linear and quadratic). The adjusted mean weight at 120 days of age was 93.43 ± 19.78 kg, and for 205 days of age, it was 180.42 ± 26.58 kg. Animals born in the dry season had a higher average weight [kg] (219.57 vs. 211.78, 3.7% higher) and, consequently, had higher weights at 646 days of age. Estimates of direct heritabilities (h2a) ranged from 0.35 to 0.75 (high magnitudes), and maternal heritabilities (h2m) along the trajectory of low magnitudes ranged from 0.03 to 0.08, respectively. The use of random regression to evaluate beef animals allows for adjusting the growth curve and selecting the best animals to be the parents of future generations.

Imprints of a gravitational wave through the weak field deflection of photons* *A. Ö. and R. P. acknowledge the networking support of the COST Action CA18108 - COST Action CA21106 - COSMIC WISPers in the Dark Universe: Theory, astrophysics and experiments (CosmicWISPers), Quantum gravity phenomenology in the multi-messenger approach (QG-MM), the COST Action CA21136 - Addressing observational tensions in cosmology

In this study, we investigate the novel phenomenon of gravitational lensing experienced by gravitational waves traveling past a Schwarzschild black hole perturbed by a specific, first-order, polar gravitational wave. We apply the Gauss-Bonnet theorem, finding a topological contribution to the deflection of light rays passing near the black hole. We demonstrate that the deflection angle can be determined by analyzing a region entirely outside the path of the light ray, leading to a calculation based solely on the parameters of the perturbing wave (Legendre polynomial order, l; frequency, σ). This approach offers a unique perspective on gravitational lensing and expands our understanding of black hole interactions with gravitational waves.

Genetic parameters for novel mastitis traits defined by combining test-day somatic cell score and differential somatic cell count in the first lactation of Japanese Holsteins

In this study, we aimed to improve current udder health genetic evaluations by addressing the limitations of monthly sampled somatic cell score (SCS) for distinguishing cows with robust innate immunity from those susceptible to chronic infections. The objectives were to (1) establish novel somatic cell traits by integrating SCS and the differential somatic cell count (DSCC), which represents the combined proportion of polymorphonuclear leukocytes and lymphocytes in somatic cells and (2) estimate genetic parameters for the new traits, including their daily heritability and genetic correlations with milk production traits and SCS, using a random regression test-day model (RRTDM). We derived 3 traits, namely ML_SCS_DSCC, SCS_4_DSCC_65_binary, and ML_SCS_DSCC_binary, by using milk loss estimates at corresponding SCS and DSCC levels, thresholds established in previous studies, and a threshold established from milk loss estimates, respectively. Data consisted of test-day records collected during January 2021 through March 2022 from 265 herds in Hokkaido, Japan. From these records, we extracted records between 7 to 305 d in milk (DIM) in the first lactation to fit the RRTDM. The model included the random effect of herd-test-day, the fixed effect of year-month, fixed lactation curves nested with calving age groups, and random regressions with Legendre polynomials of order 3 for additive genetic and permanent environmental effects. The analysis was performed using Gibbs sampling with Gibbsf90+ software. The averages (ranges) of daily heritability estimates over lactation were 0.086 (0.075 to 0.095) for SCS, 0.104 (0.073 to 0.127) for ML_SCS_DSCC, 0.137 (0.014 to 0.297) for SCS_4_DSCC_65_binary, and 0.138 (0.115 to 0.185) for ML_SCS_DSCC_binary; the heritability curve for SCS_4_DSCC_65_binary was erratic. Genetic correlations within the trait decreased as the DIM interval widened, especially for those integrating DSCC, indicating that these traits should be analyzed using RRTDM rather than repeatability models. The averages (ranges) of genetic correlations with milk yield over lactation were 0.01 (-0.22 to 0.28) for SCS, -0.05 (-0.40 to 0.13) for ML_SCS_DSCC, -0.08 (-0.17 to 0.09) for SCS_4_DSCC_65_binary, and -0.08 (-0.22 to 0.27) for ML_SCS_DSCC_binary. Compared with SCS, the newly defined traits exhibited slightly stronger negative genetic correlations with milk yield. Especially in late lactation stages, the genetic correlation between ML_SCS_DSCC and milk yield was significantly below zero, with a posterior median of -0.40. Furthermore, the new traits showed positive correlations with SCS, having estimates varying from 0.68 to 0.85 for ML_SCS_DSCC, 0.14 to 0.47 for SCS_4_DSCC_65_binary, and 0.61 to 0.66 for ML_SCS_DSCC_binary, depending on DIM. Considering that ML_SCS_DSCC and ML_SCS_DSCC_binary have relatively high heritability (compared with SCS) and favorable genetic correlations with milk production traits and SCS, their incorporation into breeding programs appears promising. Nevertheless, their genetic relationships with (sub)clinical mastitis require further investigation.

Impact of heat stress on genetic evaluation of oocyte and embryo production in Gir dairy cattle.

Identifying and selecting genotypes tolerant to heat stress might improve reproductive traits in dairy cattle, including oocyte and embryo production. The temperature-humidity index (THI) was used, via random regression models, to investigate the impact of heat stress on genetic parameters and breeding values of oocyte and embryo production in Gir dairy cattle. We evaluated records of total oocytes (TO), viable oocytes (VO), cleaved embryos (CE), and viable embryos (VE) from dairy Gir donors. Twenty-four models were tested, considering age at ovum pick-up (AOPU) and THI means as a regressor in the genetic evaluation. We computed THI in eight periods, from 0 to 112days before ovum pick-up, which were adjusted by different orders of Legendre polynomials (second, third, and fourth). The best-fit model according to Akaike's information criterion (AIC) and Model Posterior Probabilities (MPP) considered Legendre polynomials of third order and THI means of 112days for TO, fourth order and 56days for VO, second order and 28days for CE, and second order and 42days for VE, respectively. The heritability (h2) estimates across AOPU and THI scales ranged from 0.34 to 0.62 for TO, 0.31 to 0.58 for VO, 0.26 to 0.39 for CE, and 0.15 to 0.26 for VE, respectively. The fraction of the phenotypic variance explained by the permanent environment in different AOPU and THI scales ranged from 0.03 to 0.25 for TO, 0.05 to 0.26 for VO, 0.09 to 0.36 for CE, and 0.15 to 0.27 for VE, respectively. Spearman's rank correlation between the estimated breeding values in different AOPU and THI scale from the top 5% sires and females ranged from 0.18 to 0.90 for TO, 0.31 to 0.95 for VO, 0.14 to 0.85 for CE, and 0.47 to 0.94 for VE, respectively. The h2estimates for all evaluated traits varied from moderate to high magnitude across AOPU and THI scales, indicating that genetic selection can result in rapid genetic progress for the evaluated traits. There was a reranking among the best animals in different AOPU and THI. It is possible to select dairy Gir cattle tolerant to heat stress to improve oocyte and embryo production.

Modeling daily yields of milk, fat, protein, and lactose of New Zealand dairy goats undergoing standard and extended lactations

This study aimed to assess the milk production data for New Zealand dairy goats in either a standard lactation (SL; ≤305 d in milk [DIM]) or extended lactation (EL; >305 and ≤670 DIM) using a random regression (RR) with third- and fifth-order Legendre polynomials, respectively. Persistency of EL was defined as (B/A) × 100, where A was the accumulated yield from d 1 to 305, and B was the accumulated yield from d 366 to 670. On average, goats in SL produced 1,183 kg of milk, 37 kg of fat, 37 kg of protein, and 54 kg of lactose. The average production of milk, fat, protein, and lactose in EL were 2,473 kg, 78 kg, 79 kg, and 112 kg, respectively. The average persistences for milk, fat, protein, and lactose yields during EL were 98%, 98%, 102%, and 96%, respectively. The relative prediction errors were close to 10% and the concordance correlation coefficients >0.92, indicating that the RR model with Legendre polynomials is adequate for modeling lactation curves for both SL and EL. Total yields and persistency were analyzed with a mixed model that included the fixed effects (year, month of kidding, parity, and proportion of Saanen) as covariates and the random effects of animal and residual errors. Effects of year, month of kidding, and parity were significant on the total yields of milk, fat, protein, and lactose for both SL and EL. The total milk yield of first-parity goats with SL was 946 kg and the total milk yield of second-parity goats with SL was 1,284 kg, making a total of 2,230 kg over 2 years. The total milk yield of a first-parity goat with EL was 2,140 kg. Thus, on average, a goat with SL for the first and second parity produced 90 kg more milk than a first-parity goat subjected to EL. However, a second-parity goat subjected to EL produced 43 kg more milk (2,639 kg) than a goat with SL following the second and third parity (1,284 kg + 1,312 kg). These data, along with the various other benefits of EL (e.g., fewer offspring born and reduced risk of mastitis, lameness, and metabolic problems in early lactation), indicate that EL as a management strategy holds the potential to improve dairy goat longevity and lifetime efficiency without compromising milk production.

Effect of transgenerational environmental condition on genetics parameters of Italian Brown Swiss

The aim of this study was to infer the effects of heat stress (HS) of dams during late gestation on direct and maternal genetic parameters for traits related to milk production and milk quality parameters (90,558 records) in Italian browns Swiss cattle (12,072 cows in 617 herds). Daily Average Temperature-humidity indices (THI) during the last 56 d of pregnancy were calculated, using the climate data from the nearest public weather station for each herd. Heat load effects were considered as the average across the entire periods considering a thermoneutrality condition for data below the THI 60. For parameter estimation a random regression model using the second order Legendre polynomial regression coefficient for THI considering both animal and maternal effect for heat load. Direct heritability increased sharply from THI 60 to 65, then decreased gradually up to THI ∼72, and sharply thereafter. Maternal heritability showed a different trend, with values close to 0 up until to THI 65 and slightly increasing toward extreme THI values. The study suggests a lower threshold of THI 60 for the onset of heat stress. Higher heritability values indicate greater selective efficiency in the THI range of 65-70, even if an higher standard deviation value have been detected. The effects of high THI during intrauterine life varied among traits with different heritability levels. Genetic correlations for milk, fat and protein content at 60 THI with increasing value of environmental variable, remained constant (∼0.90) until THI >75, where they slightly decreased (∼0.85). Fat and protein yields, as well as milk and ECM, showed correlations dropping to 0.80 around THI 67-68 and stabilizing between 0.75 and 0.85 at extreme THI values. Maternal component correlations dropped close to zero, with negative values for protein content at THI 65-70. Antagonism between direct and maternal components was stronger for intermediate THI values but less divergent for extremes. G x E interaction was observed, indicating the selection of resilient animals would be theoretically possible. The application of climate variables in selection schemes should in the future take into account above all the dimensions of the genetic correlations to be able to decide between the simple inclusion of the environmental effect in the statistical models rather than a real parallel genetic evaluation.

Estimation of genetic parameters for feed efficiency traits using random regression models in dairy cattle

Feed efficiency has become an increasingly important research topic in recent years. As feed costs rise and the environmental impacts of agriculture become more apparent, improving the efficiency with which dairy cows convert feed to milk is increasingly important. However, feed intake is expensive to measure accurately on large populations, making the inclusion of this trait in breeding programs difficult. Understanding how the genetic parameters of feed efficiency and traits related to feed efficiency vary throughout the lactation period is valuable to gain understanding into the genetic nature of feed efficiency. This study used 121,226 dry matter intake (DMI) records, 120,500 energy-corrected milk (ECM) records, and 98,975 metabolic body weight (MBW) records, collected on 7,440 first-lactation Holstein cows from 6 countries (Canada, Denmark, Germany, Spain, Switzerland, and the United States), from January 2003 to February 2022. Genetic parameters were estimated using a multiple-trait random regression model with a fourth-order Legendre polynomial for all traits. Weekly phenotypes for DMI were re-parameterized using linear regressions of DMI on ECM and MBW, creating a measure of feed efficiency that was genetically corrected for ECM and MBW, referred to as genomic residual feed intake (gRFI). Heritability (SE) estimates varied from 0.15 (0.03) to 0.29 (0.02) for DMI, 0.24 (0.01) to 0.29 (0.03) for ECM, 0.55 (0.03) to 0.83 (0.05) for MBW, and 0.12 (0.03) to 0.22 (0.06) for gRFI. In general, heritability estimates were lower in the first stage of lactation compared with the later stages of lactation. Additive genetic correlations between weeks of lactation varied, with stronger correlations between weeks of lactation that were close together. The results of this study contribute to a better understanding of the change in genetic parameters across the first lactation, providing insight into potential selection strategies to include feed efficiency in breeding programs.

An efficient null-broadening adaptive beamformer based on magnitude response constraints

To reduce computational complexity of the minimum power distortionless response (MPDR) beamformer, a novel efficient null-broadening method based on magnitude response constraints is proposed in this paper. We convert the original quadratic power constraint to multiple first-order magnitude response constraints using Gauss-Legendre quadrature (GLQ) rather than eigenvalue decomposition (EVD). In addition, the number of first-order constraints only depends on the order of Legendre polynomials. Furthermore, based on the conjugate symmetry of the beamforming weight vector on centro-symmetric array, the nonlinear modular operation in magnitude response constraints is transformed into equivalent linear real operation. Finally, we relax the inequality constraints in the model into equality constraints, which can be solved by Lagrange multiplier method. Simulation shows that the proposed magnitude response constrained MPDR (MRC-MPDR) beamformer can achieve the same dynamic interference suppression capability as other beamformers with shorter calculation time.

Free energy landscape of wrapping of lipid nanocluster by polysaccharides

Wrapping of a 20-mer cholesterol nano-cluster (CHL-nanoC) by two widely different types of β-glucan polysaccharides (23–25 mers) having significantly varying glycosidic linkage patterns and side chains is studied by Well-Tempered MetaDynamics (WT-MetaD) simulations. The problem has its relevance in the faecal sterol and bile acid excretion in humans and the role of dietary fibres in aiding the process and combating dyslipidemia. Additionally, the distinctive collective variables studied here can be extended for modeling of polymer wrapped soft clusters/nano-particles in general. The wrapping ability is observed to be significantly correlated to the bending of the polysaccharide chain, an attribute of the glycosidic linkage type. By biasing two unique collective variables, the radius of gyration of the polysaccharide (Rg, poly) and the second order Legendre polynomial of the segment orientation parameter, θ, we could successfully observe the wrapping process. This work compares in detail the physical properties of the polysaccharide encapsulated CHL-nanoC by probing the radius of curvature (Rcurv, poly) of the polysaccharides, their coordination number with respect to the CHL-nanoC (CN), fractional CHL-nanoC surface coverage and the electrostatic surface potentials of the complex assembly. Results indicate that the β-glucan having 1–4 glycosidic linked monomers with intermittent 1–3 linkage is able to wrap the CHL-nanoC more effectively. The 1–3 glycosidic linked β-glucan with 1–6 glycosidic bonds in side chains is significantly curled up and appears to be less efficient in wrapping the nanoC. This work provides a comparative molecular level picture of mutual interaction between two major dietary polysaccharide variants and lipid globules as indicated by numerous clinical level studies involving mice and human models.

Comparison of Random Regression Models with Different Order Legendre Polynomials for Genetic Parameter Estimation on Race Completion Speed of Arabian Horses.

Simple SummaryThis study aimed to compare different order Legendre polynomials for Arabian racing horses. The present work’s results indicated that the L(2,2) Legendre polynomial (that suggests generalizations and connections to the various mathematical structures and numerical applications) model could be reliably used to estimate heritability values for the racing speed of Arabian horses in the presence of repeated observations.This work aimed to compare the fitting performance of the random regression models applied to the different order orthogonal Legendre polynomials on the race completion speed (m/s) of Arabian racing horses. Legendre polynomial function for additive genetic, permanent environmental variances and heritability values with the L(2,2), L(2,3), L(3,2) and L(3,3) models (where L(i,j) means L(order of fit for additive genetic effects, order of fit for permanent environmental effects)) was estimated. A total of 233,491 race speed records (m/s) of Arabian horses were taken from the Jockey Club of Turkey between 2005 and 2016. The mean and standard deviation of heritability values were estimated as 0.294 ± 0.0746, 0.285 ± 0.0620, 0.302 ± 0.0767 and 0.290 ± 0.1018 for L(2,2), L(2,3), L(3,2), and L(3,3), respectively. The steady decreasing trend of permanent environmental variances for L(2,2) provided stationery for heritability values. According to Akaike information criterion (AIC) and Bayesian information criterion (BIC) values, the L(2,2) model could be reliably used to estimate heritability values for the racing speed of Arabian horses in the presence of repeated observations.

Genetic parameters of weekly egg production using random regression models in two strains of Japanese quails.

The main objective of the present study was to detect the most appropriate random regression model for estimating the genetic parameters of weekly egg production. Two strains of Japanese quails including wild and white quails and pure and cross mating methods were considered. The egg collection started at the seventh week of age and lasted for 7weeks. A random regression model using Legendre polynomial was used to analyze the weekly egg records. The model with Legendre polynomial of order 1 for the additive genetic and order 3 for permanent environmental effect was chosen as the appropriate model, based on Bayesian information criterion (BIC) and Akaike information criterion (AIC). The heritability estimates for weekly egg production were low (ranging from 0.06 to 0.09). Furthermore, the ratios of permanent environmental variance to the phenotypic variance were almost moderate, varying from 0.18 to 0.44. Genetic and phenotypic correlations between weekly egg records ranged from 0.65 to 0.93 and from 0.27 to 0.67, respectively. These results indicated that the selection based on the early egg numbers could effectively improve egg production in later periods. Furthermore, the efficiency of egg production can be enhanced with a combination of breeding programs and management strategies.

Integrals of Legendre polynomials over half range and their relation to the electrostatic potential in hemispherical geometry

Spherical symmetry is often encountered in many problems in mathematics and physical sciences. On the other hand, cases that involve hemispherical geometry lead to much less studied mathematical situations. In this work, we consider a case study that arises from potential theory where absence of a full spherical symmetry gives rise to expressions involving Legendre polynomials constrained in an interval that is different from the usual range in which they are orthogonal. We use exact mathematical results for the integrals of Legendre polynomials of arbitrary order over half range to obtain analytic expressions for the electrostatic potential created by a solid hemisphere with uniform volume charge density.

Time-varying spillovers of higher moments between Bitcoin and crude oil markets and the impact of the US–China trade war: a regime-switching perspective

As the popularity of Bitcoin among finance communities continues, research on the relationship between Bitcoin and conventional commodities is becoming increasingly important. However, to date the literature has not yet found clear evidence of the dynamics of informational linkages between Bitcoin and the crude oil markets. This paper considers both static and time-varying information transmission of volatility, skewness and kurtosis, between two popular Bitcoin markets, Bitstamp and ItBit, and two major crude oil markets, WTI and Brent crude oil. A two-state regime-switching model is employed to estimate higher order moments and Legendre polynomials are applied to specify the time variations of spillovers. In addition, the latent impacts of the recent US–China trade war on spillovers are also explored. We conclude that crude oil is an information transmitter while Bitcoin is an information receiver in terms of the static and time-varying between-market transmission of three types of risk. The effect is affected by the occurrence of the trade war such that the information content of Bitcoin is enhanced once it begins. Moreover, Bitcoin is a diversifier for oil risk and this effect becomes more pronounced in the post-trade war period.

Predicting breeding values in Murrah buffaloes using random regression models

Various random regression models with different order of Legendre polynomials for permanent environmental and genetic effects were constructed to evaluate Murrah buffaloes under field condition. A total of 24,160 test-day (TD) milk yield records of 2,336 buffaloes belonging to six districts of Haryana state from 2014 to 2019 under CHRS Rohtak were considered for estimating the random covariate coefficients using REML algorithm. The R2 and BIC improved up to seventh order of the polynomials but decreased at 8th order. The lowest value of AIC was for 8th order of polynomial. The models with LPs of order 5 and above gave an improved fit of the lactation curve having high R2 value (>98%). However, the number of parameters increased from 13 for LP of order 3 to 73 for LP of order 8 indicating over parameterization of models. Best order of fit was 7th order having highest R2 (99.23%), lowest AIC and lowest BIC value. The lactation curves plotted from the ETDMYs obtained under RRMs using LP5 and LP7 were smoother as compared to the lactation curve obtained from arithmetic mean. The 301 day lactation yield under RRMs using LP of order 7 and 5 averaged 3470.42±2.76 kg and 3460.72±3.10 kg, respectively. The milk yield ranged from 3,456.38 kg in Bhiwani district to 3,480.86 kg in Sonipat district under LP7 model while it ranged from 3,426.35 kg in Jhajjar district to 3,503.95 kg in Bhiwani district under LP5 model. It was observed that less than 50% were common in top 1% of total buffaloes under the two RRMs. The RRM using LP of order 7, which provided more accurate breeding values, must be considered for selection of top ranking/ superior animals for breeding purpose.

Pulsation, translation and P1 deformation of two aspherical bubbles in liquid.

In this work, the interactions between the axial translational motions and aspherical oscillations of two gas bubbles in an incompressible liquid are considered. Representing the surface function by the Legendre polynomial of first order, we derive a dynamic model to describe the motions of two aspherical bubbles in Lagrangian mechanics. An apple-shaped bubble from simulations based on the model can be well consistent with known experimental observation. The bubble appears as the shape of a sphere at maximum expansion. The maximum asymmetry of the bubbles occurs during collapse. The surface tension is a key factor to stable oscillatory deformation. It is also found that the aspherical amplitudes of two bubbles decrease with increasing distance or decreasing driving pressure.

Repeatability and random regression models to estimate genetic parameters for oocyte and embryo production in the Gir breed

Context Greater production of oocytes and embryos from Gir donors contributes to greater fertility and genetic progress. Aims This study aimed to obtain genetic parameters for oocyte and embryo production in the Gir breed. Methods Repeatability and random regression models were applied to data consisting of 17 526 Ovum Pick Up observations from 1641 Gir donors from five different herds. Single and multi-trait analyses were carried out with the application of both models for the traits: number of viable oocytes, number of total oocytes and number of embryos, using the BLUPF90 family programs. Legendre polynomials of second order were used in the random regression model. Key results Considering the repeatability model, additive genetic variance ranged from 0.06 to 0.13 and permanent environment variance ranged from 0.05 to 0.08 for all evaluated traits. Residual variance ranged from 0.30 to 0.45. Heritability estimates were 0.10 for number of embryos, 0.24 for total oocytes, and 0.25 for viable oocytes. Repeatability estimates were moderate, ranging from 0.20 to 0.40, and genetic correlation estimates were always above 0.80. Phenotypic correlation was high only between viable and total oocytes (0.95), and moderate in the other cases. Random regression model results were consistent with those from the repeatability model. The heritability values remained similar throughout the donors’ ages, with moderate values for viable and total oocytes, and low values for number of embryos. Genetic correlations among ages for each trait were moderate to high. Also, the genetic correlations between traits within each age were high, with values always above 0.7. Conclusions Selection of Gir donors for total oocyte production at any time, between 1 and 16 years of age, might lead to an increase in the number of viable oocytes and embryos obtained, but it’s preferable at younger ages to hasten genetic progress. Repeatability models could be the best method, as they require less computational effort when compared to the random regression models and the parameter estimates do not vary substantially throughout different ages of the donor. Implications The use of repeatability models to estimate genetic parameters of oocytes and embryos resulted in similar results compared to random regression models.

Genetic analysis of milk urea concentration and its genetic relationship with selected traits of interest in dairy cows

The aim of this study was to estimate genetic parameters of milk urea concentration (MU) and its genetic correlations with milk production traits, longevity, and functional traits in the first 3 parities in dairy cows. The edited data set consisted in 9,107,349 MU test-day records from the first 3 parities of 560,739 cows in 2,356 herds collected during the years 1994 to 2020. To estimate the genetic parameters of MU, data of 109 randomly selected herds, with a total of 770,016 MU test-day records, were used. Genetic parameters and estimated breeding values were estimated using a multiple-trait (parity) random regression model. Herd-test-day, age-year-season of calving, and days in milk classes (every 5 d as a class) were used as fixed effects, whereas effects of herd-year of calving, permanent environment, and animal were modeled using random regressions and Legendre polynomials of order 2. The average daily heritability and repeatability of MU during days in milk 5 to 365 in the first 3 parities were 0.19, 0.22, 0.20, and 0.48, 0.48, 0.47, respectively. The mean genetic correlation estimated among MU in the first 3 parities ranged from 0.96 to 0.97. The average daily estimated breeding values for MU of the selected bulls (n = 1,900) ranged from -9.09 to 7.37 mg/dL. In the last 10 yr, the genetic trend of MU has gradually increased. The genetic correlation between MU and 11 traits of interest ranged from -0.28 (milk yield) to 0.28 (somatic cell score). The findings of this study can be used as the first step for development of a routine genetic evaluation for MU and its inclusion into the genetic selection program in the Walloon Region of Belgium.

Genotype by heat stress interactions for production and functional traits in dairy cows from an across-generation perspective

The aim of this study was to analyze time-lagged heat stress (HS) effects during late gestation on genetic co(variance) components in dairy cattle across generations for production, female fertility, and health traits. The data set for production and female fertility traits considered 162,492 Holstein Friesian cows from calving years 2003 to 2012, kept in medium-sized family farms. The health data set included 69,986 cows from calving years 2008 to 2016, kept in participating large-scale co-operator herds. Production traits were milk yield (MKG), fat percentage (fat%), and somatic cell score (SCS) from the first official test-day in first lactation. Female fertility traits were the nonreturn rate after 56 d (NRR56) in heifers and the interval from calving to first insemination (ICFI) in first-parity cows. Health traits included clinical mastitis (MAST), digital dermatitis (DD), and endometritis (EM) in the early lactation period in first-parity cows. Meteorological data included temperature and humidity from public weather stations in closest herd distance. The HS indicator was the temperature-humidity index (THI) during dams' late gestation, also defined as in utero HS. For the genetic analyses of production, female fertility, and health traits in the offspring generation, a sire-maternal grandsire random regression model with Legendre polynomials of order 3 for the production and of order 2 for the fertility and health traits on prenatal THI, was applied. All statistical models additionally considered a random maternal effect. THI from late gestation (i.e., prenatal climate conditions), influenced genetic parameter estimates in the offspring generation. For MKG, heritabilities and additive genetic variances decreased in a wave-like pattern with increasing THI. Especially for THI >58, the decrease was very obvious with a minimal heritability of 0.08. For fat% and SCS, heritabilities increased slightly subjected to prenatal HS conditions at THI >67. The ICFI heritabilities differed marginally across THI [heritability (h2) = 0.02-0.04]. For NRR56, MAST, and DD, curves for heritabilities and genetic variances were U-shaped, with largest estimates at the extreme ends of the THI scale. For EM, heritability increased from THI 25 (h2 = 0.13) to THI 71 (h2 = 0.39). The trait-specific alterations of genetic parameters along the THI gradient indicate pronounced genetic differentiation due to intrauterine HS for NRR56, MAST, DD, and EM, but decreasing genetic variation for MKG and ICFI. Genetic correlations smaller than 0.80 for NRR56, MAST, DD, and EM between THI 65 with corresponding traits at remaining THI indicated genotype by environment interactions. The lowest genetic correlations were identified when considering the most distant THI. For MKG, fat%, SCS, and ICFI, genetic correlations throughout were larger than 0.80, disproving concerns for any genotype by environment interactions. Variations in genetic (co)variance components across prenatal THI may be due to epigenetic modifications in the offspring genome, triggered by in utero HS. Epigenetic modifications have a persistent effect on phenotypic responses, even for traits recorded late in life. However, it is imperative to infer the underlying epigenetic mechanisms in ongoing molecular experiments.

Effect of gravitational wave on shadow of a Schwarzschild black hole

We have studied the shadows of a Schwarzschild black hole under a special polar gravitational perturbation, which is a particular solution of Einstein equations expanded up to first order. It is shown that the black hole shadow changes periodically with time and the change of shadow depends on the Legendre polynomial order parameter l and the frequency sigma of gravitational wave. For the odd order of Legendre polynomial, the center of shadow oscillates along the direction which is vertical to equatorial plane. For even l, the center of shadow does not move, but the shadow alternately stretches and squeezes with time along the vertical direction. Moreover, the presence of the gravitational wave leads to the self-similar fractal structures appearing in the boundary of the black hole shadow. We also find that this special gravitational wave has a greater influence on the vertical direction of black hole shadow.

Selection for Test-Day Milk Yield and Thermotolerance in Brazilian Holstein Cattle

Simple SummaryInterest in selection for milk yield and thermotolerance in cattle has grown, since heat stress has caused great losses in milk yield. However, few studies on how to carry out concurrent selection are available. Milk yield was analyzed by traditional methods, including heat stress indicators, in genetic evaluation. The results showed that the best sires for milk yield are not the best for heat tolerance, and only a small proportion of individuals have the aptitude for joint selection. Despite a small population fraction allowed for joint selection, sufficient genetic variability for selecting more resilient sires was found, which promoted concomitant genetic gains in milk yield and thermotolerance.Intense selection for milk yield has increased environmental sensitivity in animals, and currently, heat stress is an expensive problem in dairy farming. The objectives were to identify the best model for characterizing environmental sensitivity in Holstein cattle, using the test-day milk yield (TDMY) combined with the temperature–humidity index (THI), and identify sires genetically superior for heat-stress (HS) tolerance and milk yield, through random regression. The data comprised 94,549 TDMYs of 11,294 first-parity Holstein cows in Brazil, collected from 1997 to 2013. The yield data were fitted to Legendre orthogonal polynomials, linear splines and the Wilmink function. The THI (the average of two days before the dairy control) was used as an environmental gradient. An animal model that fitted production using a Legendre polynomials of quartic order for the days in milk and quadratic equations for the THI presented a better quality of fit (Akaike’s information criterion (AIC) and Bayesian information criterion (BIC)). The Spearman correlation coefficient of greatest impact was 0.54, between the top 1% for TDMY and top 1% for HS. Only 9% of the sires showed plasticity and an aptitude for joint selection. Thus, despite the small population fraction allowed for joint selection, sufficient genetic variability for selecting more resilient sires was found, which promoted concomitant genetic gains in milk yield and thermotolerance.