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Affect, not effect, would be the clearer choice in that sentence. However you could say that one effect of the low pressure was to induce more births.

Affect is a verb and in this case means to influence.
Using effect as a verb here, while not technically incorrect, has a slightly different and more limited meaning that is probably not the best word choice; while you could say that the low pressure effected the births that is more like saying it carried them out or implemented them, rather than caused them, as if the hurricane was a midwife. Effect is used more often as a noun, where it generally refers to a result.

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