Lila observed that a pond with clear water was covered with green algae within a week. By which method of reproduction did the algae spread so rapidly?

The answer is "Asexual reproduction through fragmentation."

Fragmentation is a method of asexual reproduction in which the parent organism breaks into two or more fragments, each of which can develop into a new individual. In green algae, fragmentation can occur naturally due to physical stress or other factors, such as changes in light or temperature. When a fragment of the algae breaks off and lands in a suitable environment, it can grow and develop into a new organism.

In this case, the rapid spread of green algae in the pond suggests that fragmentation was the method of reproduction responsible for the sudden increase in algae. The favourable conditions in the pond, such as nutrient-rich water and adequate sunlight, would have provided ideal conditions for the algae fragments to grow and multiply rapidly, resulting in the quick coverage of the pond with green algae.