The evidence from the text that best supports the researchers' analysis of the relationship between bumblebee infections and their proximity to honeybee apiaries is:
the percentage of bumblebees infected based on their proximity to apiaries.
This choice directly relates to the findings regarding how the rates of infection for deformed wing virus in bumblebees were significantly higher near apiaries compared to those farther away, thus establishing a clear link between the proximity to the apiaries and the infection rates observed.