What can affect a mountain bike's handling significantly?

Wider tires can significantly affect a mountain bike's handling because they provide increased stability and traction, especially on varied terrain. When tires have a larger contact patch with the ground, they can better grip surfaces, which is crucial for navigating rough trails, rocks, and corners. This enhanced grip allows for more control when descending or cornering, resulting in improved handling characteristics. Wider tires can also absorb more impact from bumps, offering a smoother ride and enhancing overall rider confidence.

The other options, while they can influence various aspects of a bike's performance, do not have as direct an impact on handling as the width of the tires does. The type of frame material can affect overall weight and ride quality but is less significant than tire width in immediate handling scenarios. The bike’s gear ratio is more related to pedaling efficiency and speed rather than how the bike behaves during maneuvers. Finally, while the brand of components may determine the durability and weight of a bike, it does not intrinsically affect how the bike handles on the trail.