In 2009, he and roughly 80 people were forced to evacuate Icarus Base during an attack against the base by three Ha'tak vessels. He ended up stranded with the others on Destiny, an Ancient spaceship located several billion light years from Earth. (SGU: "Air, Part 1")
As a part of group sent to the planet Eden, others started to believe that they should stay there but he did not. In contrast to the more religious Dr. Robert Caine, Morrison does not believe in God, believing life by its very nature is random. (SGU: "Faith")
Morrison was one of eighteen people tested to see if he was a match to Dr. Dale Volker for a kidney transplant. Morrison and MSgt. Ronald Greer were matches, but Morrison was hesitant, asking about the dangers before Greer volunteered. (SGU: "Hope")
He participated in the reconnaissance mission on unnamed planet where he was attacked by large predatory creature. He survived attack, but was injured and spent time in the infirmary, complaining about it. (SGU: "The Hunt")
He with all other Destiny expedition members apart from Dr. Nicholas Rush, Eli Wallace and Dr. Lisa Park went though the gate to the Novus colony to stay until Destiny recharged from a blue giant. There he found a newspaper and realized that the planet was attacked by drones. He panicked and tried to dial one of the two planets in range and flee there, but Lt. Vanessa James knocked him out, breaking his nose. (SGU: "Blockade")
When the expedition needed Palladium hydride to fix Destiny's stasis pods, Morrison traveled through the Stargate to a planet that had it with Lt. Matthew Scott and MSgt. Ronald Greer. The three successfully retrieved enough to fix the pods while the rest of the crew destroyed the Control Ship with a trick. Morrison later entered stasis with the crew. (SGU: "Gauntlet")
Morrison is generally arrogant and selfish, not showing any interest or concern for anyone else on the expedition, but only in how events or circumstances can affect him personally. This is perhaps best demonstrated in "The Hunt" when he and Dr. Park are in the infirmary recovering from injuries they sustained from an attack by the alien beast. Dr. Volker arrives to visit Park, but he disguises his concern for her by asking how she and Morrison are both doing. Morrison continues interjecting his own suffering, to the annoyance of Volker. Additionally, in "Hope" he showed no interest at all in being a kidney donor for Volker despite being one of only two people that was a match for Volker. In "Blockade", a panicked Morrison went so far as to attempt to dial a Stargate despite the danger it posed to the entire expedition because he was so desperate to get away from the Berzerker drones.
Morrison is also an atheist, demonstrated by his mocking rejection of any religious explanations for some of the phenomena that the expedition had encountered.