A Bayesian approach to prediction of stallion daily sperm output James A. Thompson a,* , Charley C. Love b , Kelly L. Stich a , Steven P. Brinsko a , Terry L. Blanchard a , Dickson D. Varner a a Departments of Large Animal Medicine and Surgery, College Station, TX 77843-4475, USA b Departments of Veterinary Physiology and Pharmacology, College of Veterinary Medicine, Texas A&M University, College Station, TX 77843-4475, USA Received 12 November 2003; accepted 5 March 2004 Abstract In equine breeding, the number of spermatozoa ejaculated is considered an important factor in fertility. Methods for predicting the number of spermatozoa have been derived from semen collection procedures. A once-daily collection period for 10 days is a standard recommendation to predict long- term daily sperm output (DSO). The first objective of this study was to determine the precision or repeatability of these DSO predictions. Semen was collected and evaluated daily during four periods for 10 days, for 15 different stallions. The analytical methods utilized hierarchal Bayesian modeling as implemented by Gibbs Sampling. The overall population model showed an initial decline in total sperm number of 1.54 billion spermatozoa per day until the observed mean change point of 4.71 days, at which time mean DSO was estimated at 5.28 billion spermatozoa per day. The hierarchal model showed standard deviations in DSO within-stallion of 0.67 billion spermatozoa per day and among- stallion of 1.86 billion spermatozoa per day. The study’s second objective was to determine how testicular size affected DSO models. When the model was extended to include testicular size, the optimal prediction of DSO was that DSO ¼ 0.79 þ 0.018  testicular size (in milliliters). Testicular size explained 36.5% of the among-stallion standard deviation in DSO, but was not significantly related to the mean number of collection-days required to reach DSO. # 2004 Elsevier Inc. All rights reserved. Keywords: Stallion; DSO; Bayesian; Changepoint; Hierarchal 1. Introduction Accurate prediction of daily sperm output (DSO) is thought to provide meaningful information for reproductive management of breeding stallions. However, little informa- Theriogenology 62 (2004) 1607–1617 * Corresponding author. Tel.: þ1 979 845 9158; fax: þ1 979 847 8863. E-mail address: jthompson@cvm.tamu.edu (J.A. Thompson). 0093-691X/$ – see front matter # 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.theriogenology.2004.03.015