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M*W: Well, as a woman who has experienced both milestones naturally, I am the resident expert on this subject.
I was 11 years and 2 months old when I reached menarche, and 50 years and 6 months when I reached menopause. I had 4 pregnancies and still have 4 living children (1 still not gainfully employed).
Girls tend to reach menarche later in colder countries and earlier in the hotter climates. I think it's just a matter of not wanting to take one's clothes off in the colder zones. Sexual activity does "ignite" puberty in both genders.
Human reproduction is an interesting thing. Unlike other mammals, just because we have reached menarche doesn't mean we are emotionally or mentally competent to bear offspring.
There is an old wive's tale that the more children one has, the earlier menopause will come. I believe that to be true. Children have the gift of aging one's female parent. Yet, in females who have never been pregnant (nuns, for example), menopause lingers later into life. (Who needs that, especially nuns?) The downside to not having sex has a higher incidence of cervical and uterine cancer. Aside from all the sexually transmitted diseases out there, women who have borne children at an earlier age have significantly less incidence of cervical and uterine cancer. Familial history, however, plays the devil's advocate role in this factor.
I cannot offer specific references right now, but FYI, prostate cancer is more rare in colder countries such as Japan. We think it may be the fish and rice diet that does the job.
In colder climates, women still give birth later in life. In hotter climates, girls give birth earlier. It's not rocket science. Menarche stirs sexual feelings. Sexual feelings stir sexual activity. Sexual activity results in pregnancy.
~ Medicine*Woman