In a food web, a keystone species is typically an organism that has a disproportionately large effect on its environment relative to its abundance. Keystone species often help to maintain the structure of an ecological community.
Given the options:
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Grasshopper - While it is a primary consumer, it likely does not have a significant impact on the ecosystem beyond being a food source for its predators.
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Frog - Frogs can control insect populations and are also a food source for higher-level consumers; they play an important role in the food web.
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Mouse - Similar to frogs, mice are prey for various predators, but they might not exert as much influence on the ecosystem as some other potential keystone species.
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Deer - Deer can have significant impacts on plant communities through herbivory, potentially influencing the composition and abundance of vegetation in an ecosystem. They can be considered a keystone species in certain environments, especially if their grazing controls plant growth and availability for other species.
Based on this reasoning, the deer is most likely to be considered a keystone species among the options provided, as it can significantly affect its environment through its herbivory and interactions with plant communities.