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In http://www.nature.com/nature/journal/vaop/ncurrent/full/nature12701.html, they say:

Thus, it seems that the diverse coloration in this species is promoted by both natural and sexual selection.

I had always thought of sexual selection as a subset of natural selection. What's the right way to think about the relationship between the two?

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sexual selection is a set of special cases within natural selection. clearly any living thing which does not have gender will not undergo sexual selection. –  shigeta Nov 1 '13 at 22:00
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3 Answers

You're not wrong, per se, but in practice they refer to two different concepts. I honestly think the Wikipedia article does a good job, in particular this sentence:

In summary, while natural selection results from the struggle to survive, sexual selection emerges from the struggle to reproduce.

It also cites Darwin:

The sexual struggle is of two kinds; in the one it is between individuals of the same sex, generally the males, in order to drive away or kill their rivals, the females remaining passive; whilst in the other, the struggle is likewise between the individuals of the same sex, in order to excite or charm those of the opposite sex, generally the females, which no longer remain passive, but select the more agreeable partners.

The whole argument is moot when dealing with individuals that aren't reproducing sexually, of course.

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I just thought of even another way to see it... Doesn't all selection end up coming down to sexual selection? i.e. If you get killed by a bear, you're not going to be reproducing sexually. In other words, the struggle to survive is only a means to an end, which is reproduction. I guess I'm wondering what the benefit is to science in distinguishing between natural and sexual selection. –  Articuno Nov 2 '13 at 6:02
@Sancho It's a different mechanism, so why shouldn't there be different terms? The two are certainly not always the same: a good example alluded to below is when a trait, such as a long tail, is attractive to a mate but is a negative fitness attribute. Besides, having more terms allows us to be more precise. It'd be no fun saying every scientific field was really just physics or applied math. –  Amory Nov 2 '13 at 14:43
I don't agree, it's nothing like a different mechanism. To me, saying that sounds like a very old statement. Talking about struggle for life or seperating trait as having a role for survival or reproduction does not make much sense. Think of a life history trait or a trait like having an adequate penis or having a comfortable womb! Let's take the last example. Would you say that having a comfortable womb evolve through sexual selection because it relates to the ability to survive and not to reproduce? –  Remi.b Nov 2 '13 at 15:37
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To Darwin's point of view, sexual and natural selection are two different mechanisms. Then, we tended to consider that sexual selection is part of natural selection. The part of natural selection that is not attributed to sexual selection is sometimes called ecological selection. Today, our understanding of these mechanisms brought us to consider the meaning of these words slightly differently.

Natural selection is not anymore the result of a struggle for survival. It is any process yielding to a change in allele frequency through a long-enough term difference in fitness. Fitness is a index of how much an individual, a gene or whatever, leave copies of itself after a long and short enough amount of time (one might not agree with this definition I guess). Take two strains of bacteria in two petri dish, consider they are one population and let the bacteria grow. One strain will grow faster and the allele frequency will vary over time. It is the result of natural selection although there were no competition, no struggle at all given that they were not in contact.

Sexual selection is a type of natural selection that involves sexual competition. There are two types of sexual competition, the so-called inter- and intra-sexual competition. Inter-sexual competition means that one sex chose the other one, while for intra-sexual there is no choice from the other sex. For example, if you see two animals fighting, they either fight to have the physical acces to the other sex (intra-) or they fight and then, let the female decide which one is the best to mate with (inter-). These two concept of intra- and inter-sexual competition might somehow overlap in some specific case. I would argue that the concept of sexual competition and therefore of sexual selection have never been accurately defined. Therefore, I would not complain if one prefers to give up the concept of sexual selection to use only the concept of natural selection.

Many articles state that sexual and natural selection act on a trait with the same or opposite directions. Given the above argumentations, you could as well say that there are two different forces of natural selection. if the trait is at state 'A', then the individual is very attractive to the other sex but is likely to not be able to escape a predator. This is the case of most of the trait we think of when talking about trait evolving through sexual selection. See Zahavi's handicap principle for more information.

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You may choose between sexual vs. asexual, natural vs. artificial. This means that you have two orthogonal axis. Are orthogonal properties different from each other?

The fact that you may have 4 combinations, (sexual in nature, asexual in nature, sexual artificial, asexual artificial) means that sexual and artificial axis are orthogonal:

enter image description here

Now, you ask: Are x and y directions different?

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I don't understand what you mean. Can you develop a bit? –  Remi.b Nov 9 '13 at 11:35
I might be slow,... I still don't really understand. What do you call sexual and asexual and therefore what does asexual encompass? You mean that if they are not orthogonal, then one cannot totally conceptually seperate artificial/natural from sexual/asexual? Why would it be relevent for what the OP is asking? –  Remi.b Nov 9 '13 at 13:30
By sexual, I mean that you have multiple sexes and they have their roles in reproduction and evolution. In asexual you just mutate single individuals (once you have selected the best individuals), sexual implies some recombination (only individuals of the same sex compete with each other). If they are not conceptually orthogonal then there may be some overlap/correlation, which means more sexual=more natural. If OP considers sexual selection something that women selects an unhealthy guy just because he has a bit yellow feather then yes, this is also different from survival-based fitness by def –  Val Nov 9 '13 at 13:47
This answer begs the question. –  Articuno Nov 9 '13 at 18:09
Begging the question (Latin: petitio principii, "assuming the initial point") You have asked which way are they different. I answer that they are as different as orthogonal dimensions. Which way do I imply the initial? –  Val Nov 9 '13 at 19:24
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