The observation that best supports the idea that increased competition causes changes in a species is:
"A population of deer show an increase in antler size over time, which allows them to obtain more mates during mating season."
This observation illustrates natural selection, where the traits that enhance reproductive success (in this case, larger antlers for attracting mates) become more common in the population over time. Increased competition for mates drives the selection for this trait, leading to changes in the species.