1. Department of Poultry Science, Mississippi State University, Mississippi State, MS 39759, USA
2. DSM Nutritional Products, Parsippany, NJ 07054, USA
3. Poultry Research Unit, USDA-ARS, Starkville, MS 39762, USA
4. Department of Pathobiology and Population Medicine, College of Veterinary Medicine, Mississippi State University, Mississippi State, MS 39762, USA
5. Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA