Final answer:
The dog's transition from barking at the mailman to ignoring him is an example of habituation, a simple form of non-associative learning wherein an animal stops responding to a non-threatening and non-rewarding repeated stimulus.
Step-by-step explanation:
The scenario described in which a dog moves in with a new family and slowly ceases to bark at the mailman is an example of habituation. Habituation is a form of non-associative learning where an animal, over time, stops responding to a recurrent stimulus that is neither harmful nor beneficial. In the first week, the dog's barking is its response to the new and possibly perceived as a threatening stimulus (the mailman). By the second week, the dog begins to recognize that the mailman does not pose a threat and reduces its alertness level. By the third week, the dog has become so accustomed to the mailman's visits that it no longer considers it noteworthy, hence it sleeps through it. This type of learning is evident across various animal species and is considered one of the simplest forms of learning.