The history of animal life on Earth repeatedly showed a correlation between atmospheric oxygen and animal diversity as well as body size: times of low oxygen saw, on average, lower diversity and smaller body sizes than times with higher oxygen. These same relationships held for dinosaurs. ~ Peter Ward & Joe Kirschvink
Dinosaur diversity was roughly constant from the time of the first Triassic dinosaurs into the Jurassic. Atmospheric oxygen was low during this period. From the mid-Jurassic, global atmospheric O2 shot up. Dinosaurs gained girth and speciation rose – a trend that continued until 140 MYA, in the mid-Cretaceous.
Various explanations have been made as to why dinosaurs succeeded so well. For one, the climate of the times suited them. The world was warm and moist during the Jurassic. For the last 2/3rds of the period, there was no polar ice. Sea levels were high. Vast areas of land were flooded. Temperate and subtropical forests were pervasive. The extensive water moderated seasonal swings.