The correct answer is: All of the above could increase the carrying capacity of a population.
Here's a brief explanation of each option:
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By killing off their predators: Reducing the number of predators can increase the survival rates of prey species, thereby increasing the population's carrying capacity.
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By decreasing the fertility rate: Although this might not seem intuitive, in some contexts, managing fertility rates can help stabilize a population at a level that the environment can sustain, allowing for a higher effective carrying capacity.
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By decreasing population size: Reducing the population size can alleviate pressure on resources, allowing the remaining individuals to have better access to food, water, and shelter, thus potentially increasing the population's carrying capacity.
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By increasing food resources: This is the most direct way to increase carrying capacity, as more food availability can support a larger population.
Since all these methods could plausibly contribute to an increase in carrying capacity under different circumstances, the answer "All of the above" is appropriate.