A lot of media tends to depict elves as rather feminine-looking in appearance, even the male elves, not sure why. Anyways, besides cultural selection, which would explain why the trait stayed prominent, what factors might lead to that developing in the elven evolutionary history, thus producing elves where even the males tend to look feminine by human standards? Also, on a semi-related note, since such a body type would aid in male elves having androgynous/feminine appearances, what factors would lead to them tending to have body types with little excess body fat and lithe appearances with a lack of obvious muscle mass?
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I have to question the premise of your question a little, male elves don't look feminine, neither do female elves. In fact both look very similar, androgynous.
So there is little in the way of sexual dimorphism in elves, males and females look very similar. You could explain away some of it by saying that because of elves long lives and low birth rates evolution takes a lot longer. So if you say that a lot of human sexual characteristics (like breasts) came about through selective evolution due to attraction then these features haven't had a chance to become as accentuated in elves.
You can also say that elves have much smaller babies (longer childhoods mean they don't need to start as big) so females never needed to evolve wider hips, another feature of typical human females.
You could explain away a lack of body fat through a very efficient metabolism, they don't put on weight easily. You could say the same for their muscle if you just want them to be weak, or perhaps say they have more efficient muscle if you want them to be strong but with low muscle mass.
They can't store too much excess fat
The easiest explanation for why a species does not have a lot of excess body fat is that there is just not enough food. When you can barely afford to live you won't be able to get a big belly.
This might have at one point or another lead to a change in their physiology where they literally couldn't store too much excess fat anymore. It was never necessary to have this ability, so it slowly started to disappear, or never appeared in the first place. There is no advantage and the resources used by the body to have this ability might be better used somewhere else.
Elves can't get fat - their bodies are just not able to store any excess fat.
This change persisted and was viewed as a good thing, so later elven generations kept it and now it became a cultural thing. Elves have to be really careful about their eating habits and their eating schedule. If they don't eat small portions on a very regular basis they might starve. In times past this was an adaptation to running around and collecting for example fruits in small batches. Nowadays it's just the way elves are.
For their androgynous look: they try to keep their females safe from predators by making the males easier prey. They are not hunters in their world, monsters are just too strong, so they don't need especially muscular males - their focus is on protecting the females by sacrificing the very-similar looking males.
Maybe they needed to make sure that predators would not attack their females. One male can impregnate multiple females and females need more time to give birth to offspring, so females are more important. As they were mainly on-the-run, living off berries and stuff like that, male strength was not so important. Therefore their males adapted to look more like their females, so that predators might choose the males instead of the (maybe more yummy) females.
The females could, for example, emit some pheromones while they are pregnant and those are easier for predators to detect. That's why they are the preferred target - pregnant targets that unvoluntarily tell you where they are and that they are vulnerable.
One straightforward method of reducing the sexual dimorphism of elves, would be a reduced level in Testosterone in male elves. Hypogonadism is a real condition in which a lack of sufficient testosterone during puberty prevents, or delays, a human male from developing secondary sexual characteristics.
These missing characteristics include:
- Muscle development
- Deepening voice
- Body hair
Boys who do not have these traits have a less stereotypical masculine appearance and thus are generally perceived as more feminine.
This does not create a reason for a lack of body fat, but the stereotypical elf lifestyle of living off the forest (or, perhaps on magically created feasts) simply isn't consuming foods that are converted to excessive fat.