Polygenic inheritance is simply a form of inheritance whereby the trait of the individual or the animal is gotten from the cumulative effects of several genes. In such case, there are many genes which control the expression of the trait. This is quite different from the monogenic inheritance whereby the trait is as a result of the expression of just only one gene.
Since Pietro has two dogs that are related, and one of the dogs has tan fur and the other has brown fur, then this means there's more than one gene which is expressed in this case.
In conclusion, the answer to the question is polygenic inheritance.
You can infer that the birds once had a common ancestor but became separated. Mutations in copying their genes stacked and caused changes in the beaks so the birds could be more well off or better adapted in their new environment.
