As all anime fanatics may have noticed, every anime has its own genre. The U.S. don't have such genre in their animated and comics world which is why i'm labeling this as a Japanese sort of lesson as well. Today shall be these most interesting genre: Harem and Reverse Harem
In general terms, "harem" involves many woman associating with one man. Usually the woman are meant as sexual partners and/or multiple spouses; in addition to daughters, female entertainers and servants of that one male. "Harem" usually is used in Muslim tradition as it is more geared to the dwelling place for such a particular group of woman.
"Harem" for animals (i.e. elephants, meerkats, lions, etc.), is more suited for a group of females that would will only allow one fertile male in the group. Meaning the animal use of harem is slightly different in the social hierarchy as the females are in control in contrast to the man in a human harem.
NOW,
If we were to put this in anime/manga terms, the Harem genre involves, of course, many females. The many woman are beautiful in their own way and all have their little attraction to the male protagonist. Throughout the manga/anime you'll see these females trying various ways to get the male protagonists' attention as to get closer to him in comparison to their female rivals. Sometimes, the females won't realize their feelings towards the male protagonist 'till much later into the anime/manga. A great example of a Harem genre would be Tenchi Muyo! and Ranma 1/2.
This is no surprise that the Harem genre is geared towards the male audiences/readers.
If a Harem genre was geared towards the female audiences, this would be called a "Reverse Harem." You guessed it--t involves many attractive men and one female protagonist. anime/manga examples can be Fushigi Yuugi and Ouran High School Host Club. Now, I could be wrong, but that sort of genre doesn't seem to be labeled as much. If anything, a Reverse-harem is just simply implied within a particular anime/manga.
Observations: From what I noticed, all the males within a reverse-harem are not necessarily attracted to the female protagonist. In fact, most of them are just there for eye-candy. However, there are things like fan-service to give teasing hints that may be a male is attracted to the female protagonist. In contrast to a harem genre, most of the females ARE attracted to the male protagonist whether it's subtle or outrageous.
Rule of thumb for both harem and reverse harem = fanservice and ecchi depending on the audience accordingly.
Nov 2012: As of now, the harem/reverse-harems genre seems to be evolving in a way that it hasn't become as obvious. So, this may be put to rest as something in the past--BUT still good to know when exploring older anime.
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