Final answer:
The most likely outcome if the mountain lion population vanishes is an increase in the deer population leading to overgrazing, altering vegetation patterns, stream degradation, and reduced biodiversity, which would adversely affect shelter for trout.
Step-by-step explanation:
If the mountain lion population vanishes, it is most likely that the deer population will increase significantly due to the lack of their apex predator. In cases like this, the overabundance of deer will likely lead to overgrazing, which can alter vegetation patterns and potentially lead to stream degradation and reduced biodiversity. As seen in Yellowstone with wolves and elk, the absence of a top predator can lead to vegetation overgrowth or depletion, changes in stream paths, and effects on other species like beavers and songbirds. The most likely outcome is that the deer population will increase, which will have cascading effects on the ecosystem. If deer populations become excessive, they might overconsume the willows, negatively impacting the shading of streams relied upon by the trout for shelter.