“Sex Is Always Well Worth Its Two-Fold Cost”
This might be of interest to the evo bio and game theory wannabes here: “Sex Is Always Well Worth Its Two-Fold Cost” by Alexander Feigel, Avraham Englander and Assaf Engel.
Abstract:
Sex is considered as an evolutionary paradox, since its positive contribution to Darwinian fitness remains unverified for some species. Defenses against unpredictable threats (parasites, fluctuating environment and deleterious mutations) are indeed significantly improved by wider genetic variability and by positive epistasis gained by sexual reproduction. The corresponding evolutionary advantages, however, do not overcome universally the barrier of the two-fold cost for sharing half of one’s offspring genome with another member of the population. Here we show that sexual reproduction emerges and is maintained even when its Darwinian fitness is twice as low as the fitness of asexuals. We also show that more than two sexes (inheritance of genetic material from three or even more parents) are always evolutionary unstable. Our approach generalizes the evolutionary game theory to analyze species whose members are able to sense the sexual state of their conspecifics and to adapt their own sex consequently, either by switching or by taxis towards the highest concentration of the complementary sex. The widespread emergence and maintenance of sex follows therefore from its co-evolution with the even more widespread environmental sensing abilities.
I’m currently trying to parse the article, and on first reading could only see a disguised form of the old familiar argument about the stability of sex ratios. It still doesn’t seem to answer why females don’t switch to parthenogenesis and block all male advances. But maybe you can detect something I missed?
This looks all wrong to me, though I’ve only skimmed it. The authors assume a model in which each organism is in either a male or a female “environment” (which sometimes seems to mean which sex predominates in its vicinity, and sometimes which sex one particular other individual has), and has certain probabilities of being one sex or another according to its environment, and then gets different payoffs according to its sex and the environment. Subject to a few kinda-plausible assumptions about those payoffs, they conclude that “always of sex opposite to the environment’s” is an evolutionarily stable strategy, and they claim that this is what it means to have a sexual population.
So, even if everything else in the article is correct, they haven’t shown that sex as actually implemented by most sexual species is evolutionarily stable against invasion by parthenogenetic females, because members of most sexual species don’t have the ability to choose their sex according to who they’re with. Now, maaaybe they can work around this by substituting other mechanisms for sex-changing (as e.g. the abstract suggests—“either by switching or by taxis towards the highest concentration of the complementary sex”). But:
They’ve also assumed that the payoff for any encounter depends only on the (current) sexes of the participants. This means that their model can’t allow for purely parthenogenetic females that provide no payoff to males that encounter them. (And this is essential to their analysis, whose basic idea—if I’ve understood them right—is that parthenogenetic females, being female all the time, would provide extra payoff to other individuals who would be male and get the male-meets-female payoff from them.)
This also means that their model can’t allow for changes (genetic or otherwise) whose effect is to change the payoffs. That seems like a rather important phenomenon to model if you’re trying to understand the emergence and stability of sex.
They might be right about the way that sex comes to exist in the first place, though: a population of parthenogenetic “females” is vulnerable to invasion by “males” who somehow have the ability to inflict their genetic material on the “females” at low cost. (Presumably the first male would be a mutant female.) This could only work if the females didn’t have the ability to reject the males’ advances (or to change so as to do so), but that’s not obviously a crazy hypothesis.
Re: They might be right about the way that sex comes to exist in the first place, though: a population of parthenogenetic “females” is vulnerable to invasion by “males” who somehow have the ability to inflict their genetic material on the “females” at low cost.
It seems like a “disease” model. It is easy to imagine how genes that transmit horizontally might spread. The real puzzle of sex is really not about why organisms might come to inject some of their genes into other organisms (that is incredibly obvious!) but why the recipients might come to willingly accept them:
http://alife.co.uk/essays/sex_is_not_a_disease/
I agree, the puzzle is why the “females” respond to invasion by “males” by making it easier for the males, rather than by making it more difficult. Too bad the article doesn’t even consider the possibility that they might do either.
Re: It still doesn’t seem to answer why females don’t switch to parthenogenesis and block all male advances. But maybe you can detect something I missed?
The standard theories of the evolution of sex explain that. See:
http://en.wikipedia.org/wiki/Evolution_of_sexual_reproduction
Here’s a recent NS news article on the topic of EoSex—claiming recent developments:
http://www.newscientist.com/article/mg20227121.600-has-the-mystery-of-sex-been-explained-at-last.html
Thanks! Upvoted. That’s much more interesting than the article I posted.
In case anyone is interested, I posted a brief critique of that article here:
http://groups.google.com/group/sci.bio.evolution/browse_thread/thread/43ed69f28e2b3173#
Hamilton’s theory gets one word. That is a totally and hopelessly inadequate treatment for an article which proposes an explanation of the prevalance of sexual recombination.
This study’s title is ridiculous :-(
Inheritance from multiple parents is a common phenomenon in cultural evolution. Proofs that is is “evolutionarily unstable” are thus obviously utter nonsense.
It is clear that the article is talking about genetic evolution, so counterexamples in cultural evolution are not a point against it.
It would be—with a proper understanding of the processes in question.
If you think that is so, demonstrate it by providing the proper understanding. But it seems to me that you are criticizing the article by assigning different meanings to its words than the author intended and effectively communicated to everyone who is not looking for indefensible interpretations.
It’s a non-trivial request. However, I don’t think I disagree with what the paper actually says. Evolutionary stability—for me—ususally refers to the concept of an Evolutionarily Stable Stratgey. If multi-parental sex could not be involved in these, then that would be interesting.
However—despite the section titles—the paper says nothing about this issue. For a start it DEFINES “multiple sexes” as “an equal sharing of the offspring’s genome between more than two parent organisms”. Huh? You are certainly correct that I am not using words the way the authors do. However, that is because they are stringing ordinary English words together into esoteric technical terms. Then it defines stability in such a way that it refers to a the genes of a genetically uniform population. Whether a uniform gene pool is stable against invasion is different from the more-conventional question of whether a population can exhibit stable strategies.
Lastly, when they say “Three and more sexes can not be evolutionary stable” all they mean is “three and more sexes can not be evolutionary stable in our obviously extremely-limited model”. The second conclusion is fine by me.
Tim, your three comments here aren’t actually helping me understand anything better. I hope your fourth comment will. Do you, or don’t you, detect a valid argument in the study apart from the one I summarized? With justification, please.
You want me to spend more time on this study? How do you expect me to justify that?
This is going dangerously meta, but yes. I’d like you to either understand the submission, or stop commenting on it if you can’t spare the time. Right now we have seven comments here; five of them are yours; they all utterly lack substance (yeah, even that one where you enumerate definitions out of books with a triumphant air); you admit to not understanding the article in question; and you still go on? Honestly, why?
Cousin, you appear to be rather antagonistic. I’m sorry I did not like the article you posted as much as all that. How about we avoid each other for a while—to allow you to cool off?
Am not! :-) I can’t say I liked the article that much either. I just wanted to run it by the LW crowd to see if you people could detect a valid argument that I’d missed, like Rune did with the chess post.
The anger wasn’t about you as a person, but about the discussion standard being lowered. If you dislike the article, you were supposed to communicate your reasons. Like, actually write a paragraph or two of text that doesn’t completely consist of unsubstantiated claims like “utter nonsense”, “ridiculous” or “hopelessly inadequate”. Otherwise the validity of your dislike remains a mystery to everyone but yourself, and all we get is a one-liner comment thread.
Yes, spelling things out takes effort. I for one put quite a lot of effort into the quality of my comments at LW and would like others to do the same lest the place devolves.
Hope that helps.
There is a stricter sense in which evolution doesn’t extend on culture.
It is a fallacy that cultural evolution is not evolution.
Cultural evolution is evolution—by definition. Here are definitions of the term “evolution”—from the three most popular evolution textbooks:
“Evolution means change in living things by descent with modification”—Mark Ridley, Evolution.
“Evolution means change, change in the form and behaviour of organisms between generations”—Mark Ridley, Evolution.
“Recently, Harrison (2001) defined evolution as “change over time via descent with modification.”″ - Mark Ridley, Evolution.
“Most of the processes in this book concern change between generations within a population of a species, and it is this kind of change we shall call evolution.”—Mark Ridley, Evolution.
“Thus, evolution in a broad sense is descent with modification, and often with diversification.”—Douglas Futuyma, Evolutionary Biology.
“Thus, biological (or organic) evolution is change in the properties of populations of organisms, or groups of such populations over the course of generations.”—Douglas Futuyma, Evolutionary Biology.
Biological Evolution entails inherited changes in populations of organisms, over a period of time, that lead to differences among them.”—Monroe Strickberger, Evolution.
Note that not one of them specifies that the medium of inheritance be DNA. Any type of inhertance qualifies. This is right and proper—any specification of how inheritance takes place in the definition of evolution would be grossly inappropriate.
And again you are disputing definitions. It doesn’t serve the purpose of communication and doesn’t relate to my comment above.
A dispute needs to have two sides. I cited the standard definitions from the main textbooks on the topic. If you would like to start a dispute about the definition of evolution, then it is now your turn to cite your sources and authorities.
If you don’t understand how my comments on cultural evolution relate to your comment, please explain further. We are both talking about cultural evolution, yes? What aspect of my post do you fail to see the relevance of?
The actual question is not “what does the word “evolution” really mean?”, but “is the paper wrong on that particular point?”. Wrong about reality, not about the usage of words. Disputing definitions is utterly useless for resolving the latter question. My comment was trying to resolve the message about reality behind the ambiguous words, by pointing out that the stricter sense of “evolution” was probably used.
“Stricter”? You mean the definition that disagrees with the textbooks?
The paper does not concern itself with the definition of evolution. It’s a computer modelling paper. The observation of multiparental inheritance in cultural evolution doesn’t seem to me to directly contradict the paper—since the modern world doesn’t satisfy the authors’ supplied definition of stability.
Your proposition appears to be, “evolution::culture can stably involve more than two parents, therefore evolution::genetic can stably involve more than two parents.”
To put it mildly, this conclusion does not follow. “Parent” and “offspring” mean completely different things (if they are even cogent concepts) in evolution::culture than they do in evolution::genetic. The article is quite clearly refering to evolution::genetic, so the fact that evolution has multiple definitions is not relevant.
I may have cited multiple definitions of evolution—but it was not to point out the differences between them. It was to pile on evidence from a range of sources.
I don’t agree with your statements about the role of parent and offspring in cultural evolution. Nor—as far as I am aware—does anyone else in the field. Parent and offspring share heritable Shannon mutual information. The parent is the source of the information, and the offspring copies from it.
Your proposition appears to be, “evolution::culture can stably involve more than two parents, therefore evolution::genetic can stably involve more than two parents.” the article is quite clearly refering to evolution::genetic, so the fact that evolution has multiple definitions is not relevant.
To put it mildly, this conclusion does not follow. “Parent” and “offspring” mean completely diferent things (if they are even cogent concepts) in evolution::culture than they do in evolution::genetic.
Duplicate comment.
FTA:
If the article internally defines evolution as genetic inheritance, why are you arguing the external definition? The authors have a right to establish the explicit meaning of the language they use in their own work, just as I have the right to say “banana” means “car” and be perfectly understood when I write “I drive a banana”.
In evolution, there’s just inheritance—and its transmission, variation, and selection. “Inside” and “outside” are not concepts that play a significant role. What can be inherited internally” could equally well be inherited “externally”—without affecting the dynamics of the information flows involved. “Inside” and “outside” are mere geography.
Tim, you’re misreading the way ‘external’ was used in the parent comment. The ‘internal definition’ eirenicon referred to was the one specified in the article, and ‘external definitions’ are those used elsewhere.
I’m not talking about internal inheritance. I’m talking about semantics. I’m saying that the article itself offers a definition so that such a misunderstanding as this does not happen. It is proper to define your terms before setting out an argument, don’t you agree? The authors, wanting to avoid confusion, decided to use the word “evolutionary” in strict reference to genetic inheritance. This cannot be argued. They have given variable x a fixed value, y, so that x = y. Other instances in which x = z have no bearing on the value of x as it has been strictly defined in this context.
The paper doesn’t define evolution.
Both the authors and I are discussing evolution. You seem to think there is some significant difference between cultural evolution and DNA evolution in this context—but I don’t agree that that is correct. If you can have multiple parents in DNA evolution, you can have multiple parents in cultural evolution—and visa versa. IOW, there’s nothing special or magical about DNA as a medium of inheritance. It’s a storage medium, like any other.
Anyway, despite their section titles, the authors don’t claim that you can’t have multiple parents in real evolution. They are only talking about their toy model—which, incidentally has practically nothing to do with how or why sex evolved, AFAICS.