Orthogonal Polynomial Regression Research Articles

PSVI-17 Inclusion of glutathione precursor to diet of sows from d 114of lactation through to weaning d 21 improves serum hormone concentrations and piglet performance

Abstract Glutathione (GSH) is a critical endogenous antioxidant found in all eukaryotic cells and has a critical role in maintaining redox homeostasis. Greater GSH concentrations protect cellular damage, tissue degeneration, and disease progression in various models but very limited study exists in swine model. Thus, we aimed to examine the effect of GSH supplementation on lactating sows and their suckling performance. From d 114 of lactation to 21 d of weaning, a total of 40 multiparous sows (Landrace x Yorkshire, parity 2.4) were assigned to one of four dietary treatments. The test treatments were: CON, a basal diet and a basal diet supplemented with 0.1%, 0.2%, and 0.3% GSH precursors. Experimental data (reproductive performance, growth performance, and blood profile) was analyzed by the general linear model (GLM) procedure with individual sow and their progenies as an experimental unit. Orthogonal polynomial regression was conducted to determine the linear and quadratic effects of 0.1%, 0.2%, and 0.3% GSH precursors in pigs. Piglets born to sows fed GSH precursors showed linearly increased body weight and total average daily gain (P < 0.05) at the end of weaning d 21. Moreover, dietary GSH showed linearly increased (P < 0.05) GSH and GSH/GSSG (oxidized glutathione) ratio in sow blood at the end of lactation d 14 and d 21. Whereas, at the end of weaning serum cortisol concentration of sows was significantly reduced by GSH precursor supplementation. In conclusion, adding 0.3% of GSH supplement to lactating sow diet would be beneficial to enhance the immune status and performance of both sows and their progenies respectively.

Combined first trimester screening for trisomy 21: Assessment of excess risk in case of free ß-human chorionic gonadotrophin between 5 and 10 multiples of the median.

The first trimester combined risk of trisomy 21 is obtained by multiplying the risk related to maternal age by the likelihood ratios of nuchal translucency, free beta-human chorionic gonadotrophin (β-hCG) and placenta associated plasma protein-A. Beyond five multiples of the median (MoM) of β-hCG, the risk of trisomy 21 is truncated. The objective of the present study was to evaluate the evolution of the first trimester combined risk of trisomy 21 in individuals with first-trimester free-β-hCG levels between 5 and 10 MoM. We conducted a non-interventional cohort study from a 6-year database of combined first-trimester trisomy 21 screening of all individuals who underwent the screening in a French specialized medical analysis center. We included all pregnant individuals who had a serum-free β-hCG between 5 and 10 MoM. Patients for whom the status of the fetus, with or without trisomy 21, was not identified by the outcome of the pregnancy or by a karyotype result were excluded from the study. The discriminatory capacity of free-β-hCG above 5 MoM was studied by a receiver operating characteristic curve. We used an orthogonal polynomial regression to represent the evolution of likelihood ratios according to free-β-hCG in MoM. Among 413 216 combined first-trimester screens of trisomy 21, 2239 (0.5%) screens met the inclusion criteria. In the selected population, 801 (35.8%) were excluded from the study because of missing fetal or neonatal status, and 46 (3.2%) fetuses out of 1438 included were diagnosed with trisomy 21. For free β-hCG values between 5 and 10 MoM, the area under the curve is 0.56 (0.46-0.65). The scatterplot of the likelihood ratio of β-hCG showed an increasing parabolic pattern: the likelihood of trisomy 21 increases with the free-β-hCG threshold. To override the truncated risk of trisomy 21 in case of free β-hCG values between 5 and 10 MoM, the study has allowed us to estimate the adjusted risk of trisomy 21, enabling health professionals to offer appropriate prenatal counseling.

Measuring case severity: a novel tool for benchmarking and clinical documentation improvement

BackgroundSeverity of illness (SOI) is an All Patients Refined Diagnosis Related Groups (APR DRG) modifier based on comorbidity capture. Tracking SOI helps hospitals improve performance and resource distribution. Furthermore, benchmarking SOI plays a key role in Quality Improvement (QI) efforts such as Clinical Documentation Improvement (CDI) programs. The current SOI system highly relies on the 3 M APR DRG grouper that is updated annually, making it difficult to track severity longitudinally and benchmark against hospitals with different patient populations. Here, we describe an alternative SOI scoring system that is grouper-independent and that can be tracked longitudinally.MethodsAdmission data for 2019–2020 U.S. News and World Report Honor Roll facilities were downloaded from the Vizient Clinical Database and split into training and testing datasets. Elixhauser comorbidities, body systems developed from the Healthcare Cost and Utilization Project (HCUP), and ICD-10-CM complication and comorbidity (CC/MCC) indicators were selected as the predictors for orthogonal polynomial regression models to predict patients’ admission and discharge SOI. Receiver operating characteristic (ROC) and Precision-Recall (PR) analysis, and prediction accuracy were used to evaluate model performance.ResultsIn the training dataset, the full model including both Elixhauser comorbidities and body system CC/MCC indicators had the highest ROC AUC, PR AUC and predication accuracy for both admission (ROC AUC: 92.9%; PR AUC: 91.0%; prediction accuracy: 85.4%) and discharge SOI (ROC AUC: 93.6%; PR AUC: 92.8%; prediction accuracy: 86.2%). The model including only body system CC/MCC indicators had similar performance for admission (ROC AUC: 92.4%; PR AUC: 90.4%; prediction accuracy: 84.8%) and discharge SOI (ROC AUC: 93.1%; PR AUC: 92.2%; prediction accuracy: 85.6%) as the full model. The model including only Elixhauser comorbidities exhibited the lowest performance. Similarly, in the validation dataset, the prediction accuracy was 86.2% for the full model, 85.6% for the body system model, and 79.3% for the comorbidity model. With fewer variables and less model complexity, the body system model was more efficient and was determined to be the optimal model. The probabilities generated from this model, named J_Score and J_Score_POA, successfully measured SOI and had practical applications in assessment of CDI performance.ConclusionsThe J_Scores generated from the body system model have significant value in evaluating admission and discharge severity of illness. We believe that this new scoring system will provide a useful tool for healthcare institutions to benchmark patients’ illness severity and augment Quality Improvement (QI) efforts.

Finite-sample properties of estimators for first and second order autoregressive processes

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying R-package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

Effect of a novel consensus bacterial 6-phytase variant in grower pigs fed corn-soybean meal-based diets formulated with a full nutrient matrix and no added inorganic phosphorus.

The capacity of a novel consensus bacterial 6-phytase variant (PhyG) to entirely replace dietary inorganic phosphorus (Pi) source in grower pigs fed diets with reduction of calcium (Ca), net energy (NE), and digestible amino acids (AA) was evaluated, using growth performance and apparent total tract digestibility (ATTD) of nutrients as outcome measures. A total of 352 mixed-sex pigs (initial BW 23.4 kg) were randomized to 4 treatments, 8 pigs/pen, and 11 pens/treatment. Diets were corn-soybean meal-based and formulated by phase (grower 1, 25 to 50 and grower 2, 50 to 75 kg BW). The positive control diet (PC) provided adequate nutrients and a negative control diet (NC) was formulated without Pi (1.2 g/kg ATTD P) and reduced in Ca (-0.12 to -0.13 percentage points), NE (-32 kcal/kg), and digestible essential AA (-0.004 to -0.026 percentage points) vs. PC. Two further treatments comprised the NC plus 500 or 1,000 FTU/kg of PhyG. Data were analyzed by ANOVA, mean contrasts and orthogonal polynomial regression. Nutrient reductions in the NC reduced (P < 0.05) average daily gain (ADG) during grower 1 and overall (73 to 136 d of age), increased (P < 0.05) feed conversion ratio (FCR) during grower 1 and overall and tended to reduce (P < 0.1) average daily feed intake (ADFI) during grower 2 and overall, vs. PC. Phytase supplementation improved (P < 0.05) FCR during grower 1, ADG during grower 2 and overall, ATTD of DM and P, and tended to improve DE (P = 0.053) in a linear dose-dependent manner. PhyG at 1,000 FTU/kg resulted in growth performance (all measures, all phases) equivalent to PC. The findings demonstrate that PhyG at 1,000 FTU/kg totally replaced Pi in complex grower pig diets containing industrial co-products, compensated a full nutrient matrix reduction and maintained performance.

Geometry Analysis and Microhardness Prediction of Nickel-Based Laser Cladding Layer on the Surface of H13 Steel

In order to improve the resistance to thermal fatigue and wear resistance of H13 hot-working tool steel, a nickel-based composite coating was prepared on its surface by laser cladding technology. The relationship was studied between the main processing parameters and the size of the cladding layer such as height and width. Based on the orthogonal polynomial regression method, the relationships were modeled mathematically between laser power, scanning speed, powder feeding voltage and microhardness. This model was proved to be able to predict the laser power and powder feeding voltage under 1100 Hv microhardness.

Data-Driven Constitutive Model for the Inelastic Response of Metals: Application to 316H Steel

Predictions of the mechanical response of structural elements are conditioned by the accuracy of constitutive models used at the engineering length-scale. In this regard, a prospect of mechanistic crystal-plasticity-based constitutive models is that they could be used for extrapolation beyond regimes in which they are calibrated. However, their use for assessing the performance of a component is computationally onerous. To address this limitation, a new approach is proposed whereby a surrogate constitutive model (SM) of the inelastic response of 316H steel is derived from a mechanistic crystal plasticity-based polycrystal model tracking the evolution of dislocation densities on all slip systems. The latter is used to generate a database of the expected plastic response and dislocation content evolution associated with several instances of creep loading. From the database, a SM is developed. It relies on the use of orthogonal polynomial regression to describe the evolution of the dislocation content. The SM is then validated against predictions of the dead load creep response given by the polycrystal model across a range of temperatures and stresses. When the SM is used to predict the response of 316H during complex non monotonic loading, extrapolating to new loading conditions, it is found that predictions compare particularly well against those from the physics-based polycrystal model.

Quantitative study on SLIP model parameters based on multi-rigid-body dynamics

The spring-loaded inverted pendulum (SLIP) model is often used to describe the interaction between hindlimbs and the ground during the locomotion of animals or humans. This model is frequently adopted to qualitatively explain the flexible deformation of legs and feet and the trajectory change of center of mass (COM), caused by the impact between hindlimbs and the ground. However, such research cannot provide precise reference on the structural parameters, spring and damper selections and their collocations for the design of robotic legs and feet. In this study, an SLIP model was established on the multi-rigid-body dynamics software Adams. The main influence factors on the SLIP model were determined by targeting at the touchdown-phase duration of animal or human locomotion. Then the main factors were quantitatively studied by combining a multivariate orthogonal polynomial regression design. Simulation showed that spring stiffness coefficient (Z1), damping coefficient (Z2), swing angular velocity (Z3) and initial swing position (Z4) were the main factors affecting the trajectory of COM. Multivariate orthogonal polynomial regression analyses showed the relationship between the COM fluctuation (y) and the main factors satisfied the following equation: y = 217.33 - 16.25 Z1 + 0.3975 Z12 - 194.6 Z2 - 0.953 Z3 + 0.755 Z4 + 8.1 Z1 Z2 + 0.043 Z1 Z3 + 0.6 Z2 Z3 - 0.0055 Z3 Z4.

Multivariate orthogonal polynomial-based positioning error modeling and active compensation of dual-driven feed system

The nonsynchronous error of the dual-driven feed system seriously affects the positioning and machining accuracy of CNC machine tools. Improving the positioning error is an extremely important task as it determines the geometric accuracy of the manufactured parts. In this paper, a Multivariate Orthogonal Polynomial Regression model has been developed to predict the positioning error in terms of motion parameters such as position and speed of the X1 and X2 axes of the dual-driven worktable. Orthogonal Experimental Design has been engaged in conducting experiments. The positioning errors are measured by a dual-frequency laser interferometer. In addition, a real-time error compensation system is developed based on the proposed active compensation control strategy in the dual-driven feed system controlled by Beckhoff motion control card. Experimental results show that the proposed positioning error model and error compensation strategy can be utilized as an effective manner to improve the accuracy of dual-driven CNC machine tools.

Numerical simulation and analysis of influencing factors of vehicle–pedestrian accidents in untypical contact state

ABSTRACTCurrent numerical analysis of car–pedestrian accidents pays more attention to typical contact state, which means pedestrians collide with the front of vehicle, but less to untypical contact state, which means pedestrians collide with the edge of vehicle. The keystone of this study is to discover appropriate initial parameters of accidents in untypical contact state fast and accurately because numerical simulation usually takes long time. Meanwhile, functions between optimised parameters and initial input parameters in an untypical-contact-state accident are fitted by polynomial regression analysis and has achieved a high degree of accuracy. Simulation of typical case indicates that the combination of orthogonal test and polynomial regression analysis can determine appropriate initial parameters more accurately compared with orthogonal test. Furthermore, the results of numerical simulation and medical identification have achieved a high degree of consistency, which indicates that the reliability and rationality of simulation have been verified.

Taxonomic, functional, and phylogenetic dimensions of rodent biodiversity along an extensive tropical elevational gradient

Relationships among taxonomic, functional, and phylogenetic dimensions of biodiversity provide insight about the relative contributions of ecological and evolutionary processes in structuring local assemblages. We used data for rodent species distributions from an extensive tropical elevational gradient to 1) describe elevational gradients for each of three dimensions of biodiversity, 2) evaluate the sufficiency of species richness as a surrogate for other dimensions, and 3) quantify the relative support for mechanisms that increase or decrease phylogenetic or functional dispersion. Taxonomic biodiversity was quantified by species richness, as well as by richness, evenness, diversity, dominance, and rarity at generic and familial levels. Morphological and categorical traits were used to estimate functional biodiversity, and an ultrametric mammalian supertree was used as the basis for estimating phylogenetic biodiversity. Elevational gradients of each dimension of biodiversity were strong, with significant linear and non‐linear components based on orthogonal polynomial regression. Empirical linear and non‐linear regression components were consistently different than those expected based on species richness for generic, familial, and phylogenetic biodiversity, but not for functional biodiversity. Nevertheless, the congruence of dimensions of biodiversity based on correlation analyses indicated that any one dimension is a useful surrogate for the other dimensions for rodents at Manu. Given variation in species richness, assemblages from lowland rainforests comprised more biodiversity than expected, whereas assemblages from cloud and elfin forests represented less biodiversity than expected. Warm temperatures, vertical complexity of the vegetation, and high productivity likely facilitate niche differentiation in rainforests, whereas cricetid rodents are competitively superior to other clades in the less structurally complex, less productive, and colder, high elevation habitats.

FRICTIONAL CONTACT PERFORMANCE TEST AND ANALYSIS OF CIRCULAR-ARC BIONIC NON-SMOOTH CONCAVE SURFACE

Circular arc bionic non-smooth concave surface is used in friction driving. The frictional contact performance between circular arc bionic non-smooth concave surface and contact area is critical role for the mechanical drive of equipment whole. In this paper through orthogonal polynomial regression experiments, the influence of diameter, distribution density and height of the coating layer unit of circular arc non-smooth bionic concave on the friction coefficient is studied. The regression equation between the non-smooth geometric parameters of the circular arc bionic non-smooth concave surface and the frictional coefficient is obtained by experiment, and get the optimal solution by optimization analysis of regression equation. The experiment result shows that circular arc bionic non-smooth concave surface can increase the driving force and improve the transmission efficiency

The use of improved TOPSIS method based on experimental design and Chebyshev regression in solving MCDM problems

Decision makers today are faced with a wide range of alternative options and a large set of conflicting criteria. How to make trade-off between these conflicting attributes and make a scientific decision is always a difficult task. Although a lot of multiple criteria decision making (MCDM) methods are available to deal with selection applications, it's observed that in most of these methods the ranking results are very sensitive to the changes in the attribute weights. The calculation process is also ineffective when a new alternative is added or removed from the MCDM problem. This paper presents an improved TOPSIS method based on experimental design and Chebyshev orthogonal polynomial regression. A feature of this method is that it employs the experimental design technique to assign the attribute weights and uses Chebyshev regression to build a regression model. This model can help and guide a decision maker to make a reasonable judgment easily. The proposed methodology is particularized through an equipment selection problem in manufacturing environment. Two more illustrative examples are conducted to demonstrate the applicability of the proposed method. In all the cases, the results obtained using the proposed method almost corroborate with those derived by the earlier researchers which proves the validity, capability and potentiality of this method in solving real-life MCDM problems.

커먼레일 디젤인젝터의 분사성능 개선을 위한 내부유로형상 최적화에 관한 수치적 연구

The common-rail injectors are the most critical component of the CRDI diesel engines that dominantly affect engine performances through high pressure injection with exact control. Thus, from now on the advanced combustion technologies for common-rail diesel injection engine require high performance fuel injectors. Accordingly, the previous studies on the numerical and experimental analysis of the diesel injector have focused on a optimum geometry to induce proper injection rate. In this study, computational predictions of performance of the diesel injector have been performed to evaluate internal flow characteristics for various needle lift and the spray pattern at the nozzle exit. To our knowledge, three-dimensional computational fluid dynamics (CFD) model of the internal flow passage of an entire injector duct including injection and return routes has never been studied. In this study, major design parameters concerning internal routes in the injector are optimized by using a CFD analysis and Response Surface Method (RSM). The computational prediction of the internal flow characteristics of the common-rail diesel injector was carried out by using STAR-CCM+7.06 code. In this work, computations were carried out under the assumption that the internal flow passage is a steady-state condition at the maximum needle lift. The design parameters are optimized by using the L16 orthogonal array and polynomial regression, local-approximation characteristics of RSM. Meanwhile, the optimum values are confirmed to be valid in 95% confidence and 5% significance level through analysis of variance (ANOVA). In addition, optimal design and prototype design were confirmed by calculating the injection quantities, resulting in the improvement of the injection performance by more than 54%.

Multiple dimensions of bat biodiversity along an extensive tropical elevational gradient

Research concerning spatial dynamics of biodiversity generally has been limited to considerations of the taxonomic dimension, which is insensitive to interspecific variation in ecological or evolutionary characteristics that play important roles in species assembly and provide linkages to ecosystem services. Consequently, the assumption that the taxonomic dimension is a good surrogate for other dimensions remains unconfirmed. We assessed variation in taxonomic (species richness) as well as phylogenetic and functional (Rao's quadratic entropy, a measurement of dispersion) dimensions of bat biodiversity along an elevational gradient in the Manu Biosphere Reserve of Peru. Phylogenetic dispersion was based on relatedness of species derived from a mammalian supertree. Functional dispersion was estimated separately for each of six functional components that reflect particular niche axes (e.g. diet, foraging strategy, body size) and for all functional components combined. Species richness declined nonlinearly with elevation, whereas phylogenetic dispersion and functional dispersion based on all functional components were not significantly associated with elevation (orthogonal polynomial regression). Moreover, considerable heterogeneity in the form of elevational relationships existed among functional components. After accounting for variation in species richness, dispersion of phylogenetic, diet and foraging strategy attributes were significantly greater than expected at high elevations, whereas dispersion of body size was significantly less than expected at high elevations. Species richness was a poor surrogate for phylogenetic or functional dispersion. Functional dispersion based on multiple components obscured patterns detected by particular components and hindered identification of mechanistic explanations for elevational variation in biodiversity. Variation in phylogenetic dispersion effectively captured the composite variation represented by all functional components, suggesting a phylogenetic signal in functional attributes. Mechanisms that give rise to variation in richness do not fully account for variation in phylogenetic or functional characteristics of assemblages. Greater than expected phylogenetic, diet and foraging strategy dispersion at high elevations were associated with the loss of phylogenetically or functionally redundant species, suggesting that increasing interspecific competition with decreasing productivity resulted in competitive exclusion. In contrast, low dispersion of size attributes at high elevations suggests the importance of abiotic filtering that favours small-sized species that can more easily enter torpor.

Experimental Study on Abrasion Resistance of Grinding Rolls with Stripes Surface

In order to study the impact on the roller abrasion resistance of the surface structure parameters such as stripes depth and number, roller abrasion model experiments were carried out with quartz sand as granular material and optimal design method was used to arrange testing program. Based on structural features of roller press, a model test bed was build and stripes roller were design and manufactured according to similar principles. Roller surface structure parameters were determined by orthogonal polynomial regression design method. By processing the test data, a regression equation was obtained with stripes depth, number and the amount of wear as parameters. The results showed that: Stripes structure grinding rollers have better abrasion resistance than the light roller; The depth and the number of stripes have a greater impact on the abrasion resistance and there was an interaction between them; In the same conditions, when the stripe depth is fixed, the wear amount increases with the number of stripes increasing; when a fixed number of stripes, the wear amount decreases with stripes depth increasing.

Morphometry of Middle Bronze Age palstaves. Part II – spatial distribution of shapes in two typological groups, implications for production and exportation

For archaeologists, metallic artifacts are key materials to assess Middle Bronze Age production areas and cultural exchanges. Here, a set of 629 bronze palstaves excavated in northern France, belonging to Breton and Norman typological groups, was treated by (open) outline-based morphometrics with orthogonal polynomial regression. Using robust statistics developed for outlier detection, these Norman and Breton palstave outlines can be divided into two groups: those for which the shape fluctuates close to the standard shape, called “congruent” axes, and those which are far enough from this standard to be considered as “non-congruent”, although they possess most of the features of the typological group. The highest density of discovery (whether congruent and non-congruent in shape) is in the extreme east of Brittany for the Breton axes, while the Norman axes are concentrated in northern Normandy, hence the choice of names. However, the distribution of congruent and non-congruent artifacts appears to be spatially dependent for the Norman group, and to a lesser extent for the Breton group, as there are proportionally more congruent specimens inside the supposed production areas than outside. This contradicts the generally accepted archaeological scheme which hypothesizes that all axes in a group originate from the same production center, and that some items were exported from there to supply neighboring regions. Other minor production centers probably existed, copying the original model with greater shape variation.

Analysing and modeling the relationship between yield and yield components in sunflower under different planting dates

The relationships between planting dates and yield and it's components in sunflower was evaluated through orthogonal polynomial regression analysis. Five field experiments were conducted during the summer season of 2011 to study the effect of five planting dates and three oilseed sunflower genotypes and their interactions on yield and yield components of sunflower. The highest seed yield, oil yield, plant height, head diameter, 1000-seed weight, seed yield plant-1 and oil content were obtained at the earliest planting date (1st May). The evaluated genotypes differed significantly for all the studied traits. Sakha 53 cultivar was the best cultivar in seed yield, oil yield, plant height, head diameter, thousand seed weight and seed yield plant plant-1 followed by Giza 102 and Pioneer hybrid 63M02, respectively. Orthogonal polynomial regression analysis revealed that, yield and yield components were significantly affected by planting date in linear responses. Multiple linear regression analysis indicated that seed yield plant-1, head diameter and thousand seed weight were the most important variables contributing toward higher seed yield (kg ha-1). Finally, it can be concluded that planting sunflower cultivar Sakha 53 on 1st May was recommended for maximizing seed and oil yields per unit area under the environmental conditions of this study. Key words: Sunflower, planting date, genotype, regression analysis, yield, yield components.

Reaction norms and genotype‐by‐environment interaction in the German Holstein dairy cattle

Reaction norm random regression sire models were used to study genotype-by-environment interactions (G × E) in the German Holstein dairy cattle population. Around 2300 sires with a minimum of 50 daughters per sire and seven first-lactation test day observations per daughter were analysed. Corrected test day records for milk yield, protein yield, fat yield and somatic cell score (SCS) were used. Herd test day solutions for milk traits, milk energy yield or SCS were used as environmental descriptors. Second-order orthogonal polynomial regressions were applied to the sire effects. The results revealed significant slope variances of the reaction norms, which caused a non-constant additive genetic variance across the environmental ranges considered. This pointed to the presence of minor G × E effects. The additive genetic variance increased when the environment improved, that is, higher (lower) herd test day solutions for milk traits (SCS). This was also influenced by pure scaling effects, because the non-genetic variance increased in an improved environment and the heritability was less influenced by the environment. The G × E effects caused very little reranking of the sires for the environmental range considered in this study.

Estimates of (co)variance function for growth to yearling in Horro sheep of Ethiopia using random regression model

Abstract. Random regression analyses of weight data from birth to 396 days were done using 22 141 weight records of 1 951 Horro lambs. Six different models formed from three different orthogonal polynomial regressions (legendre scale)orders (quadratic, cubic, quartic) of fit for both additive genetic and animals’ permanent environmental effects, with assumption of either homogeneous or heterogeneous residual variance, were compared. Fixed effects of year and type of birth, sex and age of dam were fitted along with a fourth order polynomial. Both likelihood ratio test (LRT) and Akaike's Information Criterion (AIC) were used for model comparison. Model fit improved with increased order of polynomial and assumption of heterogeneity of residual variance. Components for additive genetic and permanent environmental (co)variance increased from 0.03 and 0.09 at birth to 23.8 and 37.6 at 396 days of age, respectively. The first three eigenvalues of the coefficient matrix of the additive genetic covariance accounted for about 98 % of the sum of all the eigenvalues. Heritability estimates have shown a declining and increasing trend at different parts of the trajectory, the lowest estimate being 0.14 for weight at birth while the highest being 0.36 for weight at about 390 days of age. Higher heritability estimates in previous uni- and bi-variate models and in the current study and also strong correlation with weight at early age makes weight at one year of age the most important trait to consider in improving productivity in Horro sheep.