In organism was hunting almost to extinction but the population bounced back. which evolutionary change did this species most likely experience

Bottleneck effect

Explanation

There are different types of evolutionary changes which specie experience when they are about to get extinct but regain their potential. Such cases can be due to migration ,disruptive selection,Bottleneck effect etc. But in the example mentioned in the question the most appropriate choice seems to be Bottleneck effect.

Bottleneck effect is the phenomenon in which a population of any living organisms reduces in size in one generation but regains the size in another generation. The reduced size of population results in genetic drift in which populations faces alot of difficulties to produce new variations. There is a pressure of selection on organisms for survival. For example: There is a specie of rabbits that is over hunted because much population is fat so people use their meat. However, the people do not hunt thin rabbits. So in one generation all the fat rabbits will be extinct and only thin (that are very few) will be left. Now these thin rabbits will reproduce in next generation and produce new population. In this way, whole population will again rise. This is similar to what mentioned in question, so bottle neck effect is the right answer.

Hope it helps!

the darker peppered moth species were favored due to the fact that the industrial revolution had made all the nearby trees a darker color instead of white.