The most likely conclusion about the population of deer, given that they are constantly attacked by a predator, is:
The population of fast runners will increase because they can avoid being eaten to survive and reproduce.
This statement aligns with the principle of natural selection, where individuals with advantageous traits (in this case, faster running speed) are more likely to survive predation and reproduce, passing on those traits to their offspring. Over time, this can lead to an increase in the proportion of fast runners in the population.