Suppose birdwatchers observed an increase in the falcon population in recent years. Suggest a reason for this increase.

Although there could be a number of factors for the same, the most significant one is the ban on DDT. 
DDT was a very commonly used insecticide in the agricultural fields around the world. However, its widespread use was associated with a decline in the population of birds, such as the bald eagle and peregrine falcon. This chemical was later banned in the United States in 1972 and in several other countries in the following decades. The elimination of DDT from the ecosystem resulted in an increase in the population of birds, such as the falcon and the bald eagle. 
Some other reasons, that may have attributed to a recent increase in the population of falcons, could be the captive breeding of falcons, which reduces the mortality rate of young birds, increase in their prey population, protection of birds through enactment and implementation of laws, etc. 
Hope this helps.