Generally this can occur by:
1) Posessors of those traits survive differentially more often to reproductive age, and thus are more likely to have offspring.
2) Possessors of those traits are more sexually attractive (or more sexually interested) and thus engage in more sexual activity and thus have more likelihood of offspring.
3) Possessors of those traits provide more care for their offspring, and thus more of those offspring survive to mate.
And the one we don't like to think about unless it is dinosaurs
4) The extinction of the natural predators and competitors.
Cthulhu awakens hungry.