Question

what hypothesis did darwin investigate by studying the breeding of pigeons with distinctive traits?
new species can appear gradually through small changes in an ancestral species.
the amount of variation in a population is related to the type of environment it lives in.
organisms have only the number of offspring that are supported by the environment.
some traits appear in each generation, while others seem to disappear in some generations.

Explanation:

Darwin studied pigeon - breeding to understand how new species could arise. By observing the changes in pigeons with distinctive traits over generations, he was exploring the idea that new species can appear gradually through small changes in an ancestral species. This is related to his theory of evolution by natural selection.

Answer:

New species can appear gradually through small changes in an ancestral species.