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:
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:
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 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:
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?