Final answer:
Asexual reproduction produces identical offspring and is most successful in a stable environment.
Step-by-step explanation:
The method of reproduction that produces identical offspring and is most successful in a stable environment is asexual reproduction. Through asexual reproduction, a single parent can produce offsprings that are clones of itself, meaning they carry exactly the same genetic material as the parent. This is advantageous in a stable environment where the conditions do not change significantly over time, allowing the offspring to thrive under the same conditions as their parent. Asexual reproduction methods include fission, budding, and fragmentation.