Principal component approach in variance component estimation for international sire evaluation

<p>Abstract</p> <p>Background</p> <p>The dairy cattle breeding industry is a highly globalized business, which needs internationally comparable and reliable breeding values of sires. The international Bull Evaluation Service, Interbull, was established in 1983 to respond to this need. Currently, Interbull performs multiple-trait across country evaluations (MACE) for several traits and breeds in dairy cattle and provides international breeding values to its member countries. Estimating parameters for MACE is challenging since the structure of datasets and conventional use of multiple-trait models easily result in over-parameterized genetic covariance matrices. The number of parameters to be estimated can be reduced by taking into account only the leading principal components of the traits considered. For MACE, this is readily implemented in a random regression model.</p> <p>Methods</p> <p>This article compares two principal component approaches to estimate variance components for MACE using real datasets. The methods tested were a REML approach that directly estimates the genetic principal components (direct PC) and the so-called bottom-up REML approach (bottom-up PC), in which traits are sequentially added to the analysis and the statistically significant genetic principal components are retained. Furthermore, this article evaluates the utility of the bottom-up PC approach to determine the appropriate rank of the (co)variance matrix.</p> <p>Results</p> <p>Our study demonstrates the usefulness of both approaches and shows that they can be applied to large multi-country models considering all concerned countries simultaneously. These strategies can thus replace the current practice of estimating the covariance components required through a series of analyses involving selected subsets of traits. Our results support the importance of using the appropriate rank in the genetic (co)variance matrix. Using too low a rank resulted in biased parameter estimates, whereas too high a rank did not result in bias, but increased standard errors of the estimates and notably the computing time.</p> <p>Conclusions</p> <p>In terms of estimation's accuracy, both principal component approaches performed equally well and permitted the use of more parsimonious models through random regression MACE. The advantage of the bottom-up PC approach is that it does not need any previous knowledge on the rank. However, with a predetermined rank, the direct PC approach needs less computing time than the bottom-up PC.</p

Principal component and factor analytic models in international sire evaluation

<p>Abstract</p> <p>Background</p> <p>Interbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured.</p> <p>Methods</p> <p>Principal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries.</p> <p>Results</p> <p>In total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared.</p> <p>Conclusions</p> <p>Genetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.</p

Genotype by environment interaction for 450-day weight of Nelore cattle analyzed by reaction norm models

Genotype by environment interactions (GEI) have attracted increasing attention in tropical breeding programs because of the variety of production systems involved. In this work, we assessed GEI in 450-day adjusted weight (W450) Nelore cattle from 366 Brazilian herds by comparing traditional univariate single-environment model analysis (UM) and random regression first order reaction norm models for six environmental variables: standard deviations of herd-year (RRMw) and herd-year-season-management (RRMw-m) groups for mean W450, standard deviations of herd-year (RRMg) and herd-year-season-management (RRMg-m) groups adjusted for 365-450 days weight gain (G450) averages, and two iterative algorithms using herd-year-season-management group solution estimates from a first RRMw-m and RRMg-m analysis (RRMITw-m and RRMITg-m, respectively). The RRM results showed similar tendencies in the variance components and heritability estimates along environmental gradient. Some of the variation among RRM estimates may have been related to the precision of the predictor and to correlations between environmental variables and the likely components of the weight trait. GEI, which was assessed by estimating the genetic correlation surfaces, had values < 0.5 between extreme environments in all models. Regression analyses showed that the correlation between the expected progeny differences for UM and the corresponding differences estimated by RRM was higher in intermediate and favorable environments than in unfavorable environments (p < 0.0001)

Precision of genetic parameters and breeding values estimated in marker assisted BLUP genetic evaluation

In practical implementations of marker-assisted selection economic and logistic restrictions frequently lead to incomplete genotypic data for the animals of interest. This may result in bias and larger standard errors of the estimated parameters and, as a consequence, reduce the benefits of applying marker-assisted selection. Our study examines the impact of the following factors: phenotypic information, depth of pedigree, and missing genotypes in the application of marker-assisted selection. Stochastic simulations were conducted to generate a typical dairy cattle population. Genetic parameters and breeding values were estimated using a two-step approach. First, pre-corrected phenotypes (daughter yield deviations (DYD) for bulls, yield deviations (YD) for cows) were calculated in polygenic animal models for the entire population. These estimated phenotypes were then used in marker assisted BLUP (MA-BLUP) evaluations where only the genotyped animals and their close relatives were included

Improving the performance of sorter systems by scheduling inbound containers

This paper addresses the inbound containers scheduling problem for automated sorter systems in two different industrial sectors: parcel & postal sorting and baggage handling. We build on existing literature, particularly on the dynamic load balancing algorithm designed for the parcel hub scheduling problem, and adapt the existing algorithm to include travel times on sorters. Then, we show how to apply the scheduling algorithms in baggage handling and propose two extensions for scheduling containers in baggage handling. Finally, we conduct computational experiments to analyze the best scheduling approaches for each industrial sector, operational scenario, and system layout. One of the extensions that we propose for the baggage handling sector is the delayability extension, which significantly improves the performance of scheduling approaches

New insight into social relationships in dairy cows and how time of birth, parity, and relatedness affect spatial interactions later in life

Social interactions between cows play a fundamental role in the daily activities of dairy cattle. Real-time location systems provide on a continuous and automated basis information about the position of individual cows inside barns, offering a valuable opportunity to monitor dyadic social contacts. Understanding dyadic social interactions could be applied to enhance the stability of the social structure promoting animal welfare and to model disease transmission in dairy cattle. This study aimed to identify the effect of different cow characteristics on the likelihood of the formation and persistence of social contacts in dairy cattle. The individual position of the lactating cows was automatically collected once per second for 2 wk, using an ultra-wideband system on a Swedish commercial farm consisting of almost 200 dairy cows inside a freestall barn. Social networks were constructed using the position data of 149 cows with available information on all characteristics during the study period. Social contacts were considered as a binary variable indicating whether a cow pair was within 2.5 m of each other for at least 10 min per day. The role of cow characteristics in social networks was studied by applying separable temporal exponential random graph models. Our results revealed that cows of the same parity interacted more consistently, as well as those born within 7 d of each other or closely related by pedigree. The repeatability of the topological parameters indicated a consistent short-term stability of the individual animal roles within the social network structure. Additional research is required to elucidate the underlying mechanisms governing the long-term evolution of social contacts among dairy cattle and to investigate the relationship between these networks and the transmission of diseases in the dairy cattle population. .his project was funded by Formas, a Swedish Research Council for Sustainable Development, Stockholm, Sweden (ID: 2019–02276 and 2019–02111) and by the Kjell and Märta Beijer Foundation (Stockholm, Sweden).</p