A keystone species is one that has a disproportionately large effect on its environment relative to its abundance. In many ecosystems, large predators or important herbivores can be considered keystone species because they help maintain the structure of the food web.
Among the options provided (deer, frog, mouse, grasshopper), the deer is most likely to be a keystone species. This is because large herbivores like deer can significantly influence plant community dynamics and the overall structure of the ecosystem. Their grazing can help maintain the balance of plant species, which in turn affects other species that depend on those plants for survival.
Thus, the answer is deer.