Final answer:
A bacteriophage with both lytic and lysogenic cycles gains an evolutionary advantage by integrating its genetic material into the host chromosome, ensuring long-term survival and enabling it to evade the host immune system more effectively.
Step-by-step explanation:
The evolutionary advantage of a bacteriophage with both lytic and lysogenic cycles is that it allows the virus to integrate its genetic material into the host chromosome, ensuring long-term survival. In the lysogenic cycle, the phage genome becomes part of the host's genome, enabling it to be passed on to subsequent generations. This integration provides the virus with a means of hiding from the host immune system, increasing its chances of survival.