I would like to express my gratitude to the faculty members, postdocs, students, and visitors in the Department of Animal and Dairy Science at the University of Georgia, as well as to the users and developers of the software. Their questions about the BLUPF90 programs encouraged me to write this note.
While I was writing the initial version of this tutorial, Andrés Legarra reviewed the draft and made many corrections and improvements to it. He also wrote the sections Renumbering the data without RENUMF90, EM-REML algorithm, Likelihood ratio test, and several other subsections.
I thank Ignacy Misztal for developing this wonderful software; Shogo Tsuruta, Ignacio Aguilar, and Andrés Legarra for discussions about their implementation of algorithms in BLUPF90; Luis Varona, Benoit Auvray, Tomasz Strabel, Tom Druet, Deuk-Hwan Lee, Jesus Arango, Juan Pablo Sánchez, Miguel Pérez-Enciso, and François Guillaume for their contributions to the software development; Daniela Lourenco for discussions about the design of the BLUPF90 programs and her useful comments for improving this tutorial; and Ivan Pocrnić for his comments on the draft of this tutorial.
Many readers have told me that this tutorial is useful for their statistical analyses using the BLUPF90 family of programs. Some people have even learned my name through this tutorial. I am always happy to hear that, and it has motivated me to update this document. I hope this tutorial remains useful in readers' scientific work and provides some insight into it.