When can a species develop generic diversity

Do you mean (Genetic Diversity)?

All living beings have genetic diversity. Some have more than others.

Woody plants, such as trees, tend to have more genetic diversity, on the whole, than vascular plants, such as grasses. ... Part of the diversity is due to the size of each species' geographic range and how far they can move their genetic information, for example through wind pollination or animal seed dispersers.