When a type of pigeon it's haunted almost to extinction the resulting survivors former population this population is less genetically diverse that the original population this is an example of

Bottle neck effect

Explanation:

Bottle neck effect in Biology, refers to a phenomenon in which some environmental factors (droughts, disease, fires, floods, earthquakes or famine etc) or man made causes (like hunting)  lead to a severe reduction in the size of population of a certain living organism.

This type of events not only lower the variation in the population genepool causing lack of genetic diversity, but also reduce the overall size of population.

The mentioned scenario in the question is an example of Bottleneck effect in which genetic diversity of the pigeon population was decreased due to man made activity i.e Hunting.

Hope it help!