BURAK KARACAÖREN, Luc L.G. JANSS, Haja N. KADARMIDEN

Predicting breeding values in animals by kalman filter: Application to body condition scores in dairy cattle

Bu çalışmanın ana amacı; rassal yürüyüş taslamını kalman süzgeci (RY-KS) ile kullanarak çiftlik hayvanlarında zamana dayalı damızlık değerlerinin tahmin edilebilmesinin uygunluğunun araştırılmasıdır. Veri seti Chamau enstitüsündeki süt ineklerinden, İsviçre Holştayn birliği tarafından elde edilmiştir (n=80). Yerel ağırlıklı uzanım tahmincisi (LOWESS) yöntemi ve RY-KS benzeşim yolu ile farklı deneme desenleri için karşılaştırıldı, sonuçlar benzer bulunsa da, bazı şartlar altında RY-KS daha uygun sonuçlar verdi. Birey ve gözlem sayılarının varyans unsurları ve üreteç tahminine olan etkileri incelendi ve her ikisinin arttırılmasının daha doğru tahminleri daha küçük standart hatalarla verdiği saptandı. Varyans unsurları gibbs örneklemesi ile tahmin edildi. Soncul ortalamalar genetik varyans için 0.03 (0.006), kalıcı çevre için 0.21 (0.02) ve hata varyansı için 0.21 (0.02) olarak hesaplandı. Kalman Süzgeci damızlık değerlerinin güncel tahminlerini vermesi ve matrislerin devrilmesine ihtiyaç göstermemesi nedeni ile büyük veri setlerinden zamana dayalı damızlık değerlerinin tahmin edilmesinde faydalı olabilir.

Anahtar Kelimeler:

metodoloji, benzetim, süt üretimi, vücut kondüsyonu, damızlık değeri, sığır, inek, süt sığırı, süt ineği

Damızlık değerlerinin kalman süzgeci ile tahmini: Süt sığırlarından toplanan vücut kondüsyon puanları için bir uygulama

The aim of this study was to investigate usefulness of Kalman Filter (KF) Random Walk methodology (KF-RW) for prediction of breeding values in animals. We used body condition score (BCS) from dairy cattle for illustrating use of KF-RW. BCS was measured by Swiss Holstein Breeding Association during May 2004-March 2005 for 7 times approximately at monthly intervals from dairy cows (n=80) stationed at the Chamau research farm of Eidgenössische Technische Hochschule (ETH), Switzerland. Benefits of KF were demonstrated using random walk models via simulations. Breeding values were predicted over days in milk for BCS by KF-RW. Variance components were predicted by Gibbs sampling. Locally weighted scatter plot smoothing (LOWESS) and KF-RW were compared under different longitudinal experimental designs, and results showed that KF-RW gave more reasonable estimates especially for lower smoother span of LOWESS. Estimates of variance components were found more accurate when the number of observations and number of subjects increased and increasing these quantities decreased standard errors. Fifty subjects with 10 observations each, started to give reasonable estimates. Posterior means for variance components were found (with standard errors) 0.03 (0.006) for animal genetic variance 0.04 (0.007) for permanent environmental variance and 0.21 (0.02) for error variance. Since KF gives online estimation of breeding values and does not need to store or invert matrices, this methodology could be useful in animal breeding industry for obtaining online estimation of breeding values over days in milk.

Keywords:

methodology, simulation, milk production, body condition, breeding value, cattle, cows, dairy cattle, dairy cows,

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1. Grewal MS, Andrews AP: Kalman Filtering: Theory and practice using MATLAB. JohnWiley&Sons, 2001.
2. Harrison PJ, Stevens C: A Bayesian approach to short term forecasting. Oper Res Quart, 22, 341-362, 1971.
3. Meinhold RJ, Singpurwalla ND: Understanding the Kalman Filter. Am. Stat, 37, 123-127, 1983.
4. West M, Harrison PJ: Bayesian forecasting and dynamic models. Springer. 1997.
5. Migon H, Gamerman D, Lopes H, Ferreira M: Dynamic models. In Dey D, Rao C (Eds): Handbook of Statistics. p. 25. Elsevier, 2005.
6. Karacaören B: Phenotypic and genetic analysis of functional traits in dairy cattle under experimental management system. PhD Thesis. Swiss Federal Institute of Technology Zurich, 2006.
7. Van Bebber J, Reinsch N, Junge W, Kalm E: Monitoring daily milk yields with a recursive test day repeatability model (Kalman Filter). J Dairy Sci, 82, 2421-2429, 1999.
8. Kadarmideen HN, Wegmann S: Genetic parameters for body condition score and its relationship with type and production traits in Swiss Holsteins. J Dairy Sci, 86, 3685-3693, 2003.
9. Kadarmideen HN: Genetic correlations among body condition score, somatic cell count, production, reproduction, and conformation traits in Swiss Holsteins. Anim Sci, 79, 191-201, 2004.
10. Veerkamp RF, Brotherstone S: Genetic correlations between linear type traits, food intake, live weight and condition score in Holstein Friesian dairy cattle. Anim Sci, 64, 385-392 1997.
11. Jones HE, White IMS, Brotherstone S: Genetic evaluation of holstein friesian sires for daughter condition-score changes using random regression model. Anim Sci, 68, 467-475, 1999.
12. Sallas WM, Harville DA: Best linear recursive estimation for mixed linear models. J Amer Statist Assoc, 76, 860-869, 1981.
13. Forni S, Gianola D, Rosa GJM, de los Campos G: A dynamic linear model for genetic analysis of longitudinal traits. J Anim Sci, 87, 3845-3853, 2009.
14. R Development Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2004
15. Venables WN, Ripley BD: Modern Applied Statistics with S. Fourth ed,. Springer, New York, 2002.
16. Trimberger GW: Dairy Cattle Judging Techniques. Prentice-Hall, Prospect Heights, Waveland Press, 1977.