Complex sentence: The house mouse has been domesticated, as the pet or fancy mouse, and as the laboratory mouse, which is one of the most important model organisms in biology and medicine, and is by far the most commonly used genetically altered laboratory mammal.
Split into simpler sentences: The house mouse has been domesticated as the pet or fancy mouse, and as the laboratory mouse which is one of the most important model organisms in biology and medicine. It is by far the most commonly used genetically altered laboratory mammal.