Here are the situations matched with the appropriate methods of reproduction:
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The environment becomes unfavorable quickly - Asexual reproduction (often advantageous as it allows for rapid reproduction to quickly occupy available niches).
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Speed of reproduction is necessary - Asexual reproduction (typically faster than sexual reproduction, allowing organisms to reproduce quickly when needed).
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Contact with other members of a species is rare - Asexual reproduction (organisms can reproduce without needing a mate).
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Genetic variation is necessary - Sexual reproduction (introduces genetic diversity, which is important for adaptation and evolution).
If you have specific methods of reproduction in mind that you would like to match to these situations, please let me know!