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I have no certain answer, but I think it must be on the host. After emergence, Lipoptena needs to find a host within 5 days, otherwise it is unlikely to survive. I cannot see that it could look for a mate and a host at the same time. Also it takes 14 days for Lipoptena females to mature, so I think the answer is definitely on the host. (This information is from Hutson, 1984)