What are the animals species called that exhibit long gestation periods, give birth to relatively large offspring and maintain population numbers close to the habitat carrying capacity?

The answer to the question is the k-selected species. In a k-selected species, the organism typically produces large sized offspring and has a long gestation period. This animals are mostly at the top of the food pyramid and don't have to worry about predation, so the population numbers are mostly stable. An example of a k-selected species is the elephant.