Which type of cockroach offspring has a better chance of survival because the female carries the egg capsule?

The German cockroach is known for its reproductive strategy where the female carries the egg case, called the ootheca, with her until it's ready to hatch. This method of nurturing provides the developing embryos with protection from environmental hazards and predators, increasing the likelihood of survival as they are shielded during a vulnerable stage of development.

In contrast, other species like the American or Oriental cockroach deposit their egg cases in safe locations soon after they are produced, which exposes the eggs to more risks. The brown-banded cockroach also lays eggs in secure spots but does not carry the ootheca like the German cockroach does. Therefore, the unique behavior of female German cockroaches to carry their egg cases gives their offspring a better chance of surviving to adulthood.