Assessment of a Poisson animal model for embryo yield in a simulated multiple ovulation-embryo transfer scheme

Assessment of a Poisson animal model for embryo yield in a simulated multiple ovulation-embryo transfer scheme RJ T 1 empelman D G 0 ianola 0 University of Wisconsin-Madison, Department of Meat and Animal Science , 1675, Observatory Drive, Madison, WI 53706 , USA 1 University of Wisconsin-Madison, Department of Dairy Science Summary - Estimation and prediction techniques for Poisson and linear animal models were compared in a simulation study where observations were modelled as embryo yields having a Poisson residual distribution. In a one-way model (fixed mean plus random animal marginal maximum likelihood (MML) gave estimates of '0;with smaller empirical bias and mean squared error (MSE) than restricted maximum likelihood (REML) analyses of raw and log-transformed data. Likewise, estimates of residual variance (the average Poisson parameter) were poorer when the estimation was by REML. These results were anticipated as there is no appropriate variance decomposition independent of location parameters in hCe linear model. Predictions of random effects obtained from the mode of the joint posterior distribution of fixed and random effects under the Poisson mixedmodel tended to have smaller empirical bias and MSE than best linear unbiased prediction (BLUP). Although the latter method does not take into account nonlinearity and does not make use of the assumption that the residual distribution was Poisson, predictions were essentially unbiased. After log transformation of the records, however, BLUP led to unsatisfactory predictions. When embryo yields of zero were ignored in the analysis, Poisson animal models accounting for truncation outperformed REML and BLUP. A mixed-model simulation involving one fixed factor (15 levels) and 2 random factors for 4 sets of variance components was also carried out; in this study, REML was not included in view of highly heterogeneous nature of variances generated on the observed scale. Poisson MML estimates of variance components were seemingly unbiased, suggesting that statistical information in the sample about the variances was adequate. Best linear unbiased estimation (BLUE) of fixed effects had greater empirical bias and MSE than the Poisson estimates from the joint posterior distribution, with differences between the effect) with genetic variance (0'; ) equal to 0; 056 or 0; 125 on a log linear scale; Poisson - 2 analyses increasing with the genetic variance and with the true values of the fixed effects. Although differences in prediction of random effects between BLUP and Poisson joint modes were small, they were often significant and in favor of those obtained with the Poisson mixed model. In conclusion, if the residual distribution is Poisson, and if the relationship between the Poisson parameter and the fixed and random effects is log linear, REML and BLUE may lead to poor inferences, whereas the BLUP of breeding values is remarkably robust to the departure from linearity in terms of average bias and MSE. Rsum - valuation dun modle individuel poissonnien pour le nombre dembryons dans un schma dovulation multiple et de transfert dembryons. Des techniques destimation et de prdiction pour des modles poissonniens et linaires ont t compares par simulation de nombres dembryons supposs suivre une distribution rsiduelle de Poisson. Dans un modle un facteur (moyenne fixe et effet individuel alatoire) avec des variances gntiques (Q! ) gales 0, 056 ou 0,125 sur une chelle loglinaire, la mthode de maximisation de la vraisemblance marginale (MML) de Poisson donne des estimes de ou2 ayant un biais empirique et une erreur quadratique moyenne (MSE) infrieurs lanalyse des donnes brutes, ou transformes en logarithmes, par le maximum de vraisemblance restreinte (REML). De mme, la variance rsiduelle (le paramtre de Poisson moyen) tait moins bien estime par le REML. Ce rsultat tait prvisible, car il nexiste pas de dcomposition approprie de la variance indpendante des paramtres de position dans le modle linaire. Les prdictions des effets alatoires obtenues partir du mode de la distribution conjointe a posteriori des effets fixs et alatoires sous un modle mixte poissonien tendent avoir un biais empirique et une MSE infrieurs la meilleure prdiction linaire sans biais (BLUP). Bien que cette dernire mthode ne prenne en compte ni la non-linarit ni lhypothse dune distribution rsiduelle de Poisson, les prdictions sont sans biais notable. Le BL UP appliqu aprs transformation logarithmique des donnes conduit cependant des prdictions non satisfaisantes. Quand les valeurs nulles du nombre dembryons sont ignores dans lanalyse, les modles individuels poissonniens prenant en compte la troncature donnent de meilleurs rsultats que le REML et le BL UP. Une simulation de modle mixte un facteur fix (15 niveaux) et 2 facteurs alatoires pour4 ensembles de composantes de variance a galement t ralise; dans cette tude, le REML ntait pas inclus cause de la nature hautement htrogne des variances gnres sur lchelle dobservation. Les estimes MML poissonniennes sont apparemment non biaises, ce qui suggre que linformation statistique sur les variances contenue dans lchantillon est adquate. La meilleure estimation linaire sans biais (BLUE) des effets fixs a un biais empirique et une MSE suprieurs aux estimes de Poisson drives de la distribution conjointe a posteriori, avec des diffrences entre les2 analyses qui augmentent avec la variance gntique et les vraies valeurs des effets fixs. Bien que les diffrences soient faibles entre les effets alatoires prdits par le BL UP et par les modes conjoints poissonniens, elles sont souvent significatives et en faveur de ces dernires. En conclusion, si la distribution rsiduelle est poissonnienne, et si la relation entre le paramtre de Poisson et les effets fixs et alatoires est loglinaire, REML et BLUE peuvent conduire des infrences de mauvaise qualit, alors que le BL UP des valeurs gntiques se comporte dune manire remarquablement robuste face aux carts la linarit, en termes de biais moyen et de MSE. distribution de Poisson / nombre dembryons / modle linaire mixte gnralis / composante de variance / comptage Reproductive technology is important in the genetic improvement of dairy cattle. For example, multiple ovulation and embryo transfer (MOET) schemes may aid in accelerating the rate of genetic progress attained with artificial insemination and progeny testing of bulls in the past 30 years (Nicholas and Smith, 1983). An important bottleneck of MOET technology, however, is the high variability in quantity and quality of embryos collected from superovulated donor dams (Lohuis et al, 1990 ; Liboriussen and Christensen, 1990; Hahn, 1992; Hasler, 1992). Keller and Teepker (1990) simulated the effect of variability in number of embryos following superovulation on the effectiveness of nucleus breeding schemes and concluded that increases of up to 40% in embryo recovery rate (percentage of cows producing no transferable embryos) co (...truncated)