The best evidence from the text that supports the researchers' analysis of a relationship between bumblebee infections and their proximity to honeybee apiaries is:
the percentage of bumblebees infected based on their proximity to apiaries.
This option directly addresses the varying infection rates of bumblebees in relation to their distance from the apiaries, specifically highlighting that 20% of bumblebees close to apiaries carried deformed wing virus while none from sites more than half a mile away did.