E-Letter responses to:

review: Joan Roughgarden, Meeko Oishi, and Erol Akçay Reproductive Social Behavior: Cooperative Games to Replace Sexual Selection Science 2006; 311: 965-969 [Abstract] [Full text] [PDF]

E-Letters: Submit a response to this article

Published E-Letter responses:

Reproductive Social Behavior: Response to Pelletier and Borger

Erol Akçay, Joan Roughgarden   (4 April 2007)

Reproductive Social Behavior: Ignoring Ecological Scenarios and the "Currency" of Evolution

Fanie Pelletier, Luca Borger   (15 November 2006)

Reproductive Social Behavior: Response to Dall et al., Lessells et al., and Pizzari et al.

Erol Akcay, Joan Roughgarden, Meeko Oishi   (4 May 2006)

Sexual Selection Cannot be Replaced by Cooperative Game Theory (and It Doesn't Need Replacing)

Sasha R. X. Dall, John m. McNamara, Nina Wedell, David J. Hosken   (6 April 2006)

Nothing New Under the Sun: Social Selection is Part of Sexual Selection Theory

Kate M. Lessells, A Bennett, TR Birkhead, N Colegrave, SRX Dall, P H Harvey, B Hatchwell, DJ Hosken, J Hunt, AJ Moore, GA Parker, S Pitnick, T Pizzari, J Radwan, M Ritchie, B Sheldon, D Shuker, LW Simmons, P Stockley, T Tregenza, M Zuk   (6 April 2006)

Reproductive Behavior: Sexual Selection Remains the Best Explanation

Tommaso Pizzari, Tim R. Birkhead, Mark W. Blows, Rob Brooks, et al.   (6 April 2006)

Reproductive Social Behavior: Response to Pelletier and Borger 4 April 2007
Erol Akçay, Graduate Student, Biological Sciences Department of Biological Sciences, Stanford University, Joan Roughgarden Respond to this E-Letter: Re: Reproductive Social Behavior: Response to Pelletier and Borger	Pelletier and Borger raise in their letter two issues that we thought we had addressed before. In the first one, their confusing wording seems to suggest that we advocate different definitions of fitness for males and females to be adopted. It should be clear from all our writing that we argue the exact opposite of this. Perhaps what Pelletier and Borger really tried to claim was that sexual selection has moved beyond defining fitness by mating success for males and offspring production by females, and we were not acknowledging this development. Pelletier and Borger refer to technological advances that enabled assignment of paternity in the wild to prove their point. It is certainly true that these advances enabled empirical measurements of male and female fitness in natural populations in the same currency (number of genetic offspring placed in the next generation), which is a welcome development. Yet it is beside the point, as we were not referring to an empirical fallacy, but to a theoretical one [see Table S1 in Supporting Online Materials (14)]. The paradigm that male fitness is determined by his mating success, but female fitness by the number or quality of her eggs, is still fundamental to all theoretical thinking on sexual selection [including sexual conflict theory (8, 9,)], based on claims that it is a corollary of anisogamy (15). In any case, technological limitations were never a cause for this dichotomy: the modern version of the Darwinian narrative that attributes different mating objectives to male and female is due to the work of Bateman (5), who did, incidentally, assign paternity using genetic markers. Parentage-assignment data in natural populations actually tends to undercut the sexual-selection narrative that indiscriminate males mate with every female they can find, while females seek either to gain some hypothetical indirect genetic benefits, or avoid direct costs. The literature on extra-pair paternity in birds provides an excellent example of this. Regarding the second issue they raise, Pelletier and Borger must have overlooked the part of our Letter response (Letters, 5 May 2006, p. 689) where we state that in our theory, “animals that work as a team accrue individual benefits” (p. 696). The fitness to each individual is in fact just old-fashioned Darwinian fitness, but the mechanism through which this fitness is accumulated involves social interactions that we term “team-play,” maximizing the “team fitness.” The team fitness is a behavioral tier variable in our two-tier framework; what goes into the evolutionary tier are individual types of fitness. Pelletier and Borger’s claim that we “ignore the currency of evolution” is thus mistaken. Reiterating our position on this issue should address their concerns on mate switching and on empirical usability. Pelletier and Borger might also read our response to McNamara et al. (7) where we have in turn shown that their assumption of non-cooperation is also not necessary (2). Pelletier and Borger’s letter, like most of the previous responses to our Review, seems to be more about asserting a fervent belief that we are wrong, rather than offering a soundly reasoned critique of our proposal. Meanwhile, we are pursuing a research program to develop an alternative theory to sexual selection and make it amenable to empirical testing. Below is a summary of this program that originated with the observation in Evolution’s Rainbow (11), that Darwin’s sexual selection theory is on the wrong track to begin with, and thus an alternative is needed. Antedating Evolution’s Rainbow was a paper on the evolution of sex showing that sexual reproduction is generally superior to asexual reproduction in a fluctuating environment because it results in a higher geometric mean population growth rate (10). Then our Science Review introduced cooperative game theory to behavioral ecology, and suggested that a possible behavioral dynamic for attaining a Nash bargaining solution consists of coordinated action and the perception of team welfare realized through physically intimate friendships (14). Next, an alternative dynamic for realizing a Nash bargaining solution based on a war-of-attrition physiological conversation was developed for the rhizobium-legume symbiosis (1). More recently, reviews of the comparison between our “social-selection” alternative to sexual selection have been prepared for a biological audience (13) and for a general academic audience (12). In articles about to be submitted, a review of extra-pair paternity in birds shows that the pursuit of indirect genetic benefits is generally absent, and implicates the pursuit of direct benefits instead (4) A follow-up article on that topic presents a model for extra-pair paternity as a system of reproductive side-payments that stabilize an offspring-rearing system of economic monogamy (3). Finally, a study has been completed reanalyzing the evolution of anisogamy and the origin of the male/female binary showing that anisogamy evolves to maximize the number of viable gametic contacts, making narratives of a “battle of the sexes” at the origin of the male/female binary unnecessary and gratuitous (6). Active research in our lab continues on other topics about the evolution of symbioses and social behavior as well. This constitutes a summary of how new theory is being developed and fleshed out by our laboratory. We hope researchers interested in reproductive social behavior will follow these developments with an open mind. Our proposal opens up new vistas of alternative hypotheses, providing new opportunities for both theoretical and empirical research. These can be taken advantage of only by researchers who are willing to reconsider the assumptions that lie on the foundation of sexual selection. References 1. E. Akçay, J. Roughgarden, "Negotiation of Mutualism: Rhizobia and Legumes" Proc. R. Soc. B , in press. 2. E. Akçay, J. Roughgarden, "Neither Should Competition Be Assumed" TREE 22, in press. 3. E. Akçay, J. Roughgarden, "Extra-pair Reproductive Activity: A New Theory Based on Transactions in a Cooperative Game" (in preparation). 4. E. Akçay, J. Roughgarden, "Extra-pair Reproductive Activity: Review of the Genetic Benefits" (in preparation). 5. A. J. Bateman, Heredity 2(3), 349 (1948). 6. P. Iyer, J. Roughgarden, [submitted] "Origin of Male and Female: Evolution of Anisogamy Reanalysed." 7. J. M. McNamara, K. Binmore, A. I. Houston, TREE 21, 476 (2006)." 8. G. A. Parker, "Sexual Selection and Sexual Conflict" in M. S. Blum and N. A. Blum, eds., "Sexual Selection and Reproductive Competition in Insects" (Academic Press, 1979), pp. 123–166. 9. G. A. Parker, Phil. Trans. R. Soc. B 361, 235 (2006). 10. J. Roughgarden, (1991), The American Naturalist 138(4), 934 (1991). 11. J. Roughgarden, "Evolution’s Rainbow" (University of California Press, 2004). 12. J. Roughgarden, "Can Insult, Ridicule, and Anger Save Darwin’s sexual-selection theory?" Daedalus, in press. 13. J. Roughgarden, "Social Selection vs. Sexual Selection: Comparison of Hypotheses" in J. Handelsman, D. Kleinman, eds., "Controversies In Science and Technology II" U. of Wisconsin Press, in press. 14. J. Roughgarden, M. Oishi, E. Akçay, Science 311, 965 (2006). 15. R. L. Trivers, "Parental Investment and Sexual Selection" in B. Campbell, ed., "Sexual Selection and the Descent of Man" (Aldine-Atherton, 1972).
Reproductive Social Behavior: Ignoring Ecological Scenarios and the "Currency" of Evolution 15 November 2006
Fanie Pelletier, Postdoctoral Research Fellow Department of Biological Sciences, Imperial College London, Luca Borger Respond to this E-Letter: Re: Reproductive Social Behavior: Ignoring Ecological Scenarios and the "Currency" of Evolution	The recent Review published by J. Roughgarden et al. generated a substantial amount of correspondence on the concept and application of the theory of sexual selection (see Letters, 5 May, 312, p. 689 and (1)). Although, several critical problems with Roughgarden’s framework have been addressed, we believe that two more important issues arising from both their original Review and their Letter Response need to be underlined. In their Letter Response, Roughgarden et al. (5 May 2006, p. 689) propose that the definition of fitness should be gender-specific. To support this, the authors cite the original definition of sexual selection as expressed by Darwin (sexual selection arises from difference in mating success) and use it to state that fitness in males is currently defined as mating success, and not reproductive success as it is in females (2). This statement is problematic as it ignores some major progress made in the last few decades. Traditionally, mating success has been used as a surrogate of reproductive success in males because of logistical constraints in assigning paternity. However, it has become commonplace to use molecular markers to reconstruct pedigrees in natural population. A consequence of this is that recent studies of sexual selection have used reproductive success and lifetime reproductive success as estimators of fitness in males, rather than the number of observed matings (e.g. (3)). This approach is consistent with the widely used definition of fitness as the expected contribution of an allele, genotype or phenotype to future generations. New approaches trying to quantify fitness in the wild are based on this definition for both sexes (4). Thus, the claim of a necessity for gender-specific fitness definitions is not necessary. The main assumption of Roughgarden et al’s social theory is that individuals should cooperate to maximize team fitness. It has recently been shown that this assumption is not necessary (1); here, we address another problem with the concept of team fitness. While this quantity might be optimized in a game theoretic model, its definition might render its application limited in empirical studies. In several mating systems, individuals are commonly observed switching mates within and between years (hence switching partners within the team). In this ecological context, the definition of team may become problematic and is probably not applicable in empirical studies. So, theoretically, team fitness could be maximized under some restricted conditions, however, under ecological scenarios, individual fitness (or Darwinian fitness) is a more sensible quantity to work with. By claiming that selection should operate to maximize team fitness, Roughgarden et al. (5 May, p.689) ignore the currency of evolution and therefore their theory fails to provide a framework to study selection in ecological scenarios that is consistent with existing evolutionary theory. In conclusion, we disagree with the idea of Roughgarden et al. that because sexual reproduction is cooperative it can only be understood in a cooperative framework that ignores conflict. In our view, it is conflict that has generated the array of sex-specific traits that we observe in nature (5). References 1. J. M. McNamara, K. Binmore, A. I. Houston, Trends Ecol. Evol. 21, 476 (2006). 2. J. Roughgarden, M. Oishi, E. Akçay, Science 311, 965 (2006). 3. D. W. Coltman, M. Festa-Bianchet, J. T. Jorgenson, C. Strobeck, Proc. R. Soc. Lond. B 269, 165 (2002). 4. T. Coulson et al., Proc. R. Soc. B Lond. 273, 547 (2006). 5. G. A. Parker, Phil. Trans. R. Soc. Lond. B 361, 235 (2006).
Reproductive Social Behavior: Response to Dall et al., Lessells et al., and Pizzari et al. 4 May 2006
Erol Akcay Department of Biological Sciences, Stanford University, Stanford, CA 94305–5020, USA., Joan Roughgarden, Meeko Oishi Respond to this E-Letter: Re: Reproductive Social Behavior: Response to Dall et al., Lessells et al., and Pizzari et al.	Reproductive Social Behavior: Response to Dall et al., Lessells et al., and Pizzari et al. Erol Ak¸cay,1 Joan Roughgarden,1 Meeko Oishi2 1Department of Biological Sciences, Stanford University, Stanford, CA 94305–5020, USA. 2Sandia National Laboratory, Post Office Box 5800, Albuquerque, NM 87185–1137, USA. In Roughgarden et al. (1), we argued that the theory of sexual selection has accumulated enough conceptual and empirical problems to warrant its replacement, and proposed an alternative theory, based on cooperative games to replace it. Our review induced many replies, to which we have responded in the print version of Science (5 May 2006). Here, we concentrate on three e-letters [Dall et al. (2), Lessells et al. (3), and Pizzari et al. (4)]. 1. What is to be replaced? Both Lessells et al. (3) and Pizzari et al. (4), seem confused over what we propose to replace because they are unclear about what sexual selection is to begin with. Even though the two letters overlap in authorship, the letters offer contradictory definitions of sexual selection: Lessells et al. claim that sexual selection theory is “a body of theory consisting of individual hypotheses” and assert that the truth of any of them is independent of the others, whereas Pizzari et al. claim that sexual selection theory provides a “unitary theoretical framework” wherein its power lies. Both claims have truth to them: Sexual selection theory indeed gives the impression of being built on a single unitary framework, which is the Darwinian narrative of male competition and female choice. In the current situation however, this framework is amended with various hypotheses tailored to specific problemmatic cases or setups. We are concerned with replacing the central narrative, which doesn’t contribute to the progress of the field, but on the contrary obscures data with the assumptions of competition for mates and good genes. The individual hypotheses, some of which, like staying incentives for cooperative breeders, are more consistent with our theory than sexual selection, can be reevaluated and recast in the new framework. 2. What are we proposing in place of sexual selection? Dall et al. (2) confuse our alternative to sexual selection, social selection, with the mathematical framework we propose to express it, cooperative game theory. It should be clear that the two are separate, albeit connected, issues; therefore, we address them separately below. 2.1. Alternative to the Darwinian narrative The first issue is what the alternative to the sexual selection narrative is: We propose that both males and females want to maximize the number of offspring produced over their lifetime, and the way they achieve that outcome is to work together (i.e. cooperate) and exchange direct ecological benefits within their life span. The first part of this hypothesis seems compatible with the sexual selection narrative, however, sexual selection goes on to say that number of offspring is determined by number of matings for the males, and number of eggs for the female. The latter is usually not thought of as of direct importance; instead, the emphasis is put on the genes these eggs carry, with the implicit assumption that some genes, in future generations, will increase the number of eggs, or mating, or both. This setup creates the disparity in the fitness definitions for the two sexes, with matings being the fitness of males and goodness of genes for the females. In our view of selection in relation to sex, the number of eggs produced by the female is of direct significance, and both males and females should have evolved to maximize this quantity by exchanging ecological benefits. This applies even when there isn’t monogamy: One just needs to adjust the male’s and/or the female’s objective function to include all the mating partners and setup a multiplayer bargaining structure. 2.2. The mathematical framework The second issue is whether the mathematical framework of cooperative game theory is suitable to investigate reproductive social behavior. Dall et al. claim that it is not. However, there seems to be confusion in their letter as to what we propose to use cooperative game theory for, and that needs to be addressed first. As a starter, the claim that we misrepresented “the philosophical basis of cooperative game theory” is mistaken: Noncooperative games can in fact include communication, but all signals in a noncooperative game are defined as additional strategies for individual players. Including signals does not change the way players play the game, and there is -- by the above definition -- no communication except through choosing one or the other strategy. In cooperative games, on the other hand, the issue of communication is left undefined, with the assumption that it is present in adequate amount to ensure enforcement -- and coordination -- on agreed upon contracts. Specifically in our model, we hypothesize these communication mechanisms to operate through intimate social bonding resulting in perception of the team fitness. Connected to this issue is the distinction we explicitly made between cooperative play and cooperative outcomes. Cooperative play refers to discerning the team fitness, and playing to maximize that. This is different than selecting a “Cooperate” strategy (as in a Prisoner’s Dilemma, for example), or landing on a cooperative outcome, defined as mutually beneficial. This distinction is not trivial because cooperative play refers to actual physical interactions of the animals, presupposing that appropriate cognitive mechanisms have evolved. It should also be noted that we do not of course argue against the need for elucidating the communication and coordination mechanisms left undefined in a cooperative game. On the contrary, our approach sets the stage for this investigation by ascribing an evolutionary significance to these by describing the outcomes that can be reached using cooperative play. This bring us to the major conceptual issue raised by Dall et al. We agree that the ESS concept (NCE in Dall et al.) has to be applied at the correct level. As in McNamara et al. (5), the ESS is a property of the social system, not the specific outcomes. Thus, we both envision a two- tier theory for explaining reproductive social behavior, one tier exploring the development of social systems within generations, the other looking at the evolution of traits that mediate this development. We do not wish to abandon the ESS concept but see it as part of the complete two -tier theory, where it will be applied at the evolutionary level to strategies such as, for instance, choosing to play as a team. 3. Is social selection really different? Lessels et al. and Pizzari et al. both argue that the theory we proposed does not constitute a novel approach and is instead entirely consistent with existing sexual selection theory. In support of this claim, Lessells et al. make the distinction between sexual selection as a process and as a theory. We think that even if one accepts this seemingly pedantic distinction, one has to require the authors to select different names for the two concepts they are distinguishing. As is, we are left with sophistry such as “Social selection is a theory of the sexual selection process, therefore it is part of the sexual selection theory,” as the last sentence of Lessells et al. asserts. We believe that nothing will be gained from dithering with such semantics. The difference between our theory and sexual selection is that we claim selection in relation to sex operates through direct ecological benefits and exchange of these through social interactions. On the other hand, sexual selection theory stipulates selection occurs for genetic benefits and says almost nothing on sociality, and what purpose it should serve. Instead, animals are assumed to operate alone, as if in a Skinner’s box, observing only some indirect clues about the other animal’s motives and properties. Our framework is motivated by available empirical evidence and generates testable predictions on the evolution and functioning of reproductive social behavior different than sexual selection. Therefore, social selection is a new hypothesis, whose truth is subject to empirical confirmation or negation. 4. Specific issues 4.1. Definition of payoffs Lessells et al. imply that by defining the payoffs as fitness accumulation rates, we try to escape evolutionary mechanisms. However as explained above, we have no such intention and explicitly state the need for a two-tier theory incorporating evolution. In fact, our definition is an adaptation of life history theory to our setup that provides the link between the developmental and evolutionary tiers. Given that our review is about selection (not natural selection, not sexual selection, but social selection), we are left wondering what the issue raised here really is. 4.2. Insulting vocabulary Pizzari et al. argue that the vocabulary used in sexual selection theory (like cuckoldry or sneakers) is used in a completely amoral and apolitical context and therefore cannot have an adverse effect. We agree that the truth of the theory is logically independent of the terms used to describe it. On the other hand, these terms are clearly associated with moral judgements in human life and they are used for animals precisely because of the resemblance of their behavior to human acts. Moreover, the terms in question usually are derived from a particular social perspective which is male-dominated. This means that researchers in this field have to exert caution to remain completely objective, while the public, especially students who learn these terms in class but do not become researchers in the field (e.g., pre-med students or journalists), become susceptible to the impression that evolutionary biology does make moral claims. As a result, this irresponsible terminology contaminates the study of sexual behavior, which is, as pointed out by Pizzari et al., already susceptible to influences of particular socio-political perspectives. Assuming that when a word starts being used in a scientific context, any socio-political or moral connotation to it just disappears is very naïve at best. 4.3. Social vs. non-social species Dall et al. state that our theory can be only applied to hyper- socialized species and cannot explain selection in relation to sex in species that lack social contact. We agree of course that our theory is based on sociality, but so is the Darwinian sexual selection narrative with its choosy females and competitive males. 4.4. Logic of bargaining Dall et al. are confused with our example pertaining to the logic of bargaining; therefore, we reiterate the working of the scenario shown in the diagram on page 965 of our review [The example used in (1) to illustrate the logic of bargaining. Source: Game 16.1 from Straffin (6).]. This game is dominance solvable and the Nash competitive equilibrium (NCE) is (B, A), giving payoffs 4 and 8 to players 1 and 2, respectively. Player 1, in an effort to better its position, can threaten player 2 to play A, which would decrease Player 2’s payoff to 6. Player 2 can also threaten, leading to the establishment of a threat point, which is in our example found by a maximin argument: The threat point for each player is the best it can do while the other player is trying to hurt it most. In this example, the threat point is (3.33, 6). It is with regard to this set of payoffs we define the Nash Bargaining Solution, which involves, as Dall et al. observes, Player 2 playing B some of the time, which would give it a worse payoff than the threat point. This is where cooperative play really starts to work: By accepting the loss of 1 unit of payoff for a fraction of time, Player 2 gets Player 1 to play B other times, while it itself is playing A, and thereby offsets the loss, getting an average payoff of 7.2, which is higher than its threat point. This needs, of course, the ability to communicate and coordinate, which are the mechanisms we claim social systems function with. 5. Conclusion We appreciate the reaction of many researchers to our proposal to completely overhaul one of the major fields under evolutionary biology. Our proposal is motivated by the undeniable inconsistencies and empirical difficulties sexual selection has accumulated. The alternative we present is of course subject to critique and testing, but this cannot be done under false premises. We think that the e-letters we replied contain more emotional response than cool-headed analysis, which has led to confusion over the content of our proposed theory and inconsistencies in the arguments against it. We have tried to clarify the confusion and identify the false arguments advanced in the letters in this reply. We hope that from here, the discussion will proceed in a more productive manner, leading to a better understanding of reproductive social behavior. References 1. J. Roughgarden, M. Oishi, E. Ak¸cay, Reproductive social behavior: cooperative games to replace sexual selection, Science 311, 965 (2006). 2. S. R. X. Dall, J. M. McNamara, N. Wedell, D. J. Hosken, Sexual selection cannot be replaced by cooperative game theory (and it doesn’t need replacing), Science E-letters, posted 6 April 2006. 3. C. M. Lessells, A. T. Bennett, T. R. Birkhead, N. Colegrave, S. R. X. Dall, P. Harvey, B. Hatchwell, D. J. Hosken, J. Hunt, A. J. Moore, G. A. Parker, S. Pitnick, T. Pizzari, J. Radwan, M. Ritchie, B. C. Sheldon, D. M. Shuker, L. W. Simmons, P. Stockley, T. Tregenza, M. Zuk, Nothing new under the sun: social selection is part of sexual selection theory, Science E-letters, 6 April 2006. 4. T. Pizzari, T. R. Birkhead, M. W. Blows, R. Brooks, K. L. Buchanan, T. H. Clutton-Brock, P. H. Harvey, D. J. Hosken, H. Kokko, J. S. Kotiaho, C. M. Lessells, C. Macias-Garca, A. J. Moore, G. A. Parker, S. Pitnick, J. Radwan, M. Ritchie, B. C. Sheldon, L. W. Simmons, R. R. Snook, P. Stockley, M. Zuk, (2006), Reproductive behaviour: sexual selection remains the best explanation, Science E-letters, posted 6 April 2006. 5. J. M. McNamara, C. E. Gasson, A. I. Houston, Incorporating rules for responding into evolutionary games, Nature 401, 368 (1999). 6. P. Straffin, Game Theory and Strategy (Mathematical Association of America, New York, 1993).
Sexual Selection Cannot be Replaced by Cooperative Game Theory (and It Doesn't Need Replacing) 6 April 2006
Sasha R. X. Dall Centre for Ecology & Conservation, University of Exeter, Cornwall Campus, Termough, Penryn, UK, John m. McNamara, Nina Wedell, David J. Hosken Respond to this E-Letter: Re: Sexual Selection Cannot be Replaced by Cooperative Game Theory (and It Doesn't Need Replacing)	Sasha R.X. Dall1*, John M. McNamara2, Nina Wedell1, & David J. Hosken1 1Centre for Ecology & Conservation, University of Exeter, Cornwall Campus, Tremough, Penryn, TR10 9EZ, UK. 2School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK Another week and another attack on Darwin, but as usual, rumours of problems with Darwinian theory are grossly exaggerated, or in this particular instance, plain wrong. In this latest instalment Roughgarden et al. [1] suggested: 1) the Theory of Sexual Selection is inadequate, 2) that it needs replacing and 3) that cooperative game theory should be the replacement. We will not go into claims 1 and 2 (they are being addressed by others) other than to note they are incorrect, are a misrepresentation of the facts, and we additionally remind readers that, as Darwin himself stated in his great sexual selection treatise [2], "False facts are highly injurious to the progress of science". Instead we will deal with claim 3, that cooperative game theory is an ideal replacement for current sexual selection theory paying particular attention to the arguments presented by Roughgarden et al. [1] (referred to as R henceforth) to make their case. Our main contention is that R misrepresent the philosophical basis of cooperative game theory, which obscures its fundamental unsuitability for analysing evolved systems in general, including the vast majority of sexual interactions. They introduce cooperative games as alternative to sexual selection by distinguishing them from non-cooperative games. However, in doing so they deviate significantly from classical economic theory textbook distinctions between the two types of game. To quote from R: "In competitive [non-cooperative] games, the players do not communicate. ... In cooperative games, players make threats, promises, and side payments to each other; play together as teams; and form and dissolve coalitions." (p965; text in brackets added). This contrasts with a quote from the preface of a popular reference book on economic game theory [3]: "A game is cooperative if commitments --- agreements, promises, threats -- - are fully binding and enforcing. It is non-cooperative if commitments are not enforceable (note that pre-play communication between players does not imply that any agreements that may have been reached are enforceable)." Thus contrary to R, the distinction between cooperative and non-cooperative games lies in the assumption of implicitly (a priori) binding 'contracts' between players; in this sense: "...the phenomenon of cooperation is to a certain extent assumed and thus not subject to a complete analysis" [4]. Nevertheless, it is fair to say that cooperative games typically involve bargaining tactics, which require some form of communication (including extended interaction) between players. However, this does not mean that any form of communication between players necessitates a cooperative game and the corresponding solution concepts - so-called 'unimprovable' outcomes such as Nash bargaining solutions (NBS). In fact, a whole branch of evolutionary game theory, which is fundamentally non-cooperative [4], is devoted to the study of communication between animals: signalling theory [5]. Furthermore, since the early 1980s economists have devoted substantial effort to analysing bargaining tactics in non-cooperative games [6]. So how much can cooperative game theory, with its intrinsically binding 'contracts', help us to understand sexual interactions in biology, which is the domain of sexual selection? On the one hand, sexual reproduction, by definition, must involve interactions between organisms, however remote, to exchange genetic material. However, this does not require that the individuals involved are bound to any 'contract' they form in the process. Such stricture implies some form of enforcement that is external to the interaction, which may make sense in many human interactions occurring within legal and moral bounds. However, if commitments are not implicitly enforceable then games are non-cooperative. Furthermore, to presume that individuals will behave so as to avoid discommodating other interacting individuals, which is central to the 'unimprovable' solution concepts in cooperative games, is unrealistic for organisms that have evolved by natural selection. Indeed, it is precisely the Darwinian notion of populations of reproductive lineages competing for limited resources that has led researchers to reject cooperative game theory as irrelevant to evolutionary biology [4]. R's juxtaposed logic is illustrated clearly in the analysis of the hypothetical asymmetric game detailed under the "Logic of bargaining and side payments" section (p965- 966). In fact, the hypothetical payoff matrix presented on p965 seems a strange one to illustrate the heuristic value of cooperative games in biology; since the best payoff (in arbitrary units) Player 2 can achieve from bargaining is 7.2 (Fig 1 in R) compared to 8 if it opted out and played non-cooperatively, it is hard to imagine why it should ever agree to bargain in the first place if it is acting to maximise its payoffs (as will be favoured by natural selection). Moreover, the hypothetical sequence of threats and promises outlined in R, which is used to demonstrate how the bargaining solution can be reached, is equally unconvincing from a biological perspective. Why should Player 1's threat to play A (even if it were made credible) ever induce Player 2 to change its behaviour, given that it would gain 6 if it kept on playing A and 5 if it switched to B? The only rational reason that such threats should be effective is if Player 1's well-being was important to Player 2, which is difficult to justify for unrelated players without including additional assumptions (e.g. reciprocal interactions). In fact, most organisms are expected to minimise their relatedness to sexual partners except under very limited circumstances. Furthermore, R strongly argue that sexual reproduction is a social activity involving repeated interactions between participating individuals ensuring negotiation and threats can take place. This underpins the cooperative game theoretic approach they propose. Indeed, R admit that "the difficult issue for the cooperative game theory approach is whether the animals can carry out team play and can discern the team fitness function whose gradient they should climb" (p966). However, for the majority of animals (not to mention plants, many of which reproduce sexually), mating is a once in a lifetime encounter between individuals and does not involve repeated interactions, let alone opportunities to 'discern the team fitness function'. For example, external fertilizers such as broadcast spawners simply shed their gametes without ever encountering one another, and the majority of arthropods will only encounter and mate with the same individual once. R's justification for their perspective focuses exclusively on behavior that seems largely restricted to hyper-socialized vertebrates, which only represent a tiny minority of the vast number of species, extant or otherwise. All sexually reproducing organisms need to be encompassed in any general theory of sexual interactions. This is not the case for cooperative game theory. Nevertheless, it is possible to include highly social sexual interactions (with bargaining tactics) within a theoretical framework that makes sense from an evolutionary perspective and lies within the scope of sexual selection. R present two-player games by defining the possible actions of each player and giving the payoffs for each combination of action chosen. If the players do not interact, choosing their actions independently of one another, then we may expect that at evolutionary stability the action chosen by each is the best given the action chosen by the other. In other words the actions are in Nash competitive equilibrium (NCE). R is correct that when the choice of action is made as a result of interacting with the other individual, the actions chosen need not be in NCE, but this does not mean we need to abandon the NCE concept, just apply it at a different level. When interaction is possible it is the rules for negotiation that are genetically determined, rather than an unconditional choice of action. At evolutionary stability we expect the rule used by each contestant to be the best given that of the other, so that these rules are in NCE [7]. The actions that result from using such a pair of negotiation rules need not, however, be best responses to one another. R is correct to emphasise that the process by which actions are chosen is important to the outcome (choice of action), but this point has been made before [7, 8]. Under some modelling assumptions the outcomes are more cooperative than with no interaction [9, 10]. Under other assumptions they are less cooperative. In particular, one model of the interactions between parents suggest that young may actually be better off with one parent than with two, since with two parents each tries to prevent themselves from being exploited by the other [11]. R argues for complex interactions between individuals, but does not give a detailed analysis. Possible negotiation strategies of, for example, grooming, and the resultant evolutionarily stable outcomes are not specified. Until more work on this difficult topic is done, it will not be clear under what circumstances we expect interactions to promote cooperative behaviour. There is no logical reason to apply cooperative game theory to interactions, just old- fashioned NCE at the correct level. Whether cooperation results then depends on the detail. Finally, R present two case studies (presumably) to illustrate the heuristic value of adopting a cooperative game theoretic approach. However, neither is convincing from this perspective as, in both cases, cooperative solutions predict behavior that differs from that observed in the focal systems. Indeed, in the "Peacock wrasse game" (p967), both female broadcast, male search and female deposit, male stay behavioral combinations are NCE (and evolutionarily stable), which are both outcomes observed off the Corsican coast [12]. While on the other hand, the cooperative NBS R derive only includes the female deposit, male stay combination of mating behaviors. Similarly, a wide range of mating systems is actually observed in Eurasian oystercatchers (and listed in R), as predicted by NCE for the payoff matrix R presented in the "Oystercatcher game" (p967-968), while their NBS only encompasses a 'friendly' subset of the observed range of mating interactions. Ultimately, the value of any theoretical analysis in science lies in its ability to elucidate natural phenomena; R do not provide any evidence that cooperative game theory can do this for sexual interactions. Sexual selection theory, on the other hand, has a long track record of explaining a wide variety of phenomena associated with sexual reproduction [13]. So, as well as falsely identifying a problem, R provide a solution that is no solution. If it isn't broken you can't fix it, and sexual selection is doing just fine. References 1. Roughgarden, J., Oishi, M., and Akcay, E. (2006). Reproductive Social Behavior: Cooperative Games to Replace Sexual Selection. Science 311, 965- 969. 2. Darwin, C. (1871). The Descent of Man and Selection in Relation to Sex. (London: Murray). 3. Aumann, R.J., and Hart, S. (1992). Handbook of Game Theory With Economic Applications, Volume 1 (North Holland: Elsevier Science Publishers). 4. Hammerstein, P. (1998). What is evolutionary game theory? In Game Theory And Animal Behavior, L.A. Dugatkin and H.K. Reeve, eds. (New York: Oxford University Press), pp. 3-15. 5. Maynard Smith, J., and Harper, D. (2003). Animal Signals (Oxford: Oxford University Press). 6. Binmore, K. (1998). Just Playing, Volume 2 (Cambridge: The MIT Press). 7. McNamara, J.M., Gasson, C.E., and Houston, A.I. (1999). Incorporating rules for responding into evolutionary games. Nature 401, 368-371. 8. McNamara, J.M., Houston, A.I., Szekely, T., and Webb, J.N. (2002). Do parents make independent decisions about desertion? Animal Behaviour 64, 147-149. 9. Killingback, T., and Doebeli, M. (2002). The continuous prisoner's dilemma and the evolution of cooperation through reciprocal altruism with variable investment. American Naturalist 160, 421-438. 10. Sherratt, T.N., and Roberts, G. (2002). The stability of cooperation involving variable investment. Journal Of Theoretical Biology 215, 47-56. 11. McNamara, J.M., Houston, A.I., Barta, Z., and Osorno, J.L. (2003). Should young ever be better off with one parent than with two? Behavioral Ecology 14, 301-310. 12. Luttbeg, B., and Warner, R.R. (1999). Reproductive decision-making by female peacock wrasses: flexible versus fixed behavioral rules in variable environments. Behav. Ecol. 10, 666-674. 13. Andersson, M. (1994). Sexual Selection (Princeton, NJ: Princeton University Press).
Nothing New Under the Sun: Social Selection is Part of Sexual Selection Theory 6 April 2006
Kate M. Lessells NIOO-KNAW, Heteren, The Netherlands, A Bennett, TR Birkhead, N Colegrave, SRX Dall, P H Harvey, B Hatchwell, DJ Hosken, J Hunt, AJ Moore, GA Parker, S Pitnick, T Pizzari, J Radwan, M Ritchie, B Sheldon, D Shuker, LW Simmons, P Stockley, T Tregenza, M Zuk Respond to this E-Letter: Re: Nothing New Under the Sun: Social Selection is Part of Sexual Selection Theory	C(Kate). M.Lessells1*, Andrew T.D. Bennett2, Tim R. Birkhead3, Nick Colegrave4, Sasha R. X. Dall5, Paul Harvey6, Ben Hatchwell3, Dave J. Hosken5, John Hunt5, Allen J.Moore5, Geoff A. Parker7, Scott Pitnick8, Tommaso Pizzari6, Jacek Radwan9, Mike Ritchie10, Ben C.Sheldon6, David M. Shuker4, Leigh W. Simmons11, Paula Stockley12, Tom Tregenza5, Marlene Zuk13. 1. NIOO-KNAW, PO box 40, 6666 ZG Heteren, The Netherlands. 2. University of Bristol, Bristol BS8 1UG, UK. 3. Department of Animal & Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK. 4. IEB, School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JT, UK. 5. Centre for Ecology & Conservation, School of Biosciences, University of Exeter, Cornwall Campus, Tremough, Penryn TR10 9EZ, UK. 6. Department of Zoology, University of Oxford, Oxford OX1 3PS, UK. 7. School of Biological Sciences, Biosciences Building, Crown Street, University of Liverpool, Liverpool L69 7ZB, UK. 8. Department of Biology, University of Syracuse, 108 College Place, Syracuse, Ny 13244, USA 9. Institute of Environmental Sciences, Jagiellonian University, ul. Gronostajowa 3, 30-387 Krakow, Poland. 10. Environmental & Evolutionary Biology, Dyers Brae House, University of St Andrews, St Andrews, Fife KY16 9TH, UK. 11. School of Animal Biology (M092), University of Western Australia, Crawley, WA 6009, Australia 12. Faculty of Veterinary Science, University of Liverpool, Chester High Road, Neston, South Wirral CH64 7TE, UK. 13. Department of Biology, University of California, Riverside CA 92521, USA. In a recent review, Roughgarden et al. (1) propose what superficially appears to be a radically novel explanation for reproductive social behavior. They argue (i) that sexual selection, which has been a cornerstone of the evolutionary explanation of sexual behavior since Darwin (2), “is always mistaken” and “needs to be replaced”, and (ii) that “social selection”, “expressed mathematically in a branch of game theory”, is the necessary alternative. We believe that their review is profoundly misleading. In this reply we concentrate on a single issue: “social selection” does not represent a novel view of reproductive behavior, and any evolutionary implementation of such models would by definition incorporate sexual selection. Their review also contains mistakes and misconceptions regarding sexual selection (3) and game theory (4). The current reply is complementary, not contradictory, to these other (3, 4) replies: here we argue that on a general level what Roughgarden et al. argue is not novel; the other replies (3, 4) argue that on a more detailed level there are mistakes and misconceptions. Selection on a trait occurs by definition whenever biological (genetic) fitness varies in relation to that trait. As an imaginary example, survival of individuals of some bird species might vary with wing length (because longer-winged individuals outfly aerial predators more successfully). This variation in survival (a component of fitness) in relation to wing length is (by definition) selection on wing length. Fitness has two main types of component: those to do with survival, and those to do with reproduction. When selection arises through variation in survival, it is called natural selection. When selection arises through variation in reproduction, more specifically that occurring because of variation in the number or phenotype of mates, it is called sexual selection (5). This definition of sexual selection is consistent with that of Darwin (2) as a process that “depends on the advantage which certain individuals have over others of the same sex and species in respect of reproduction”. There is abundant observational and experimental evidence from both the laboratory and the wild for a wide taxonomic range of species that sexual selection, as defined here, occurs (6-13): it is simply not credible to argue otherwise. The process of sexual selection (as defined above) needs to be distinguished from “sexual selection theory”. “Sexual selection theory” is not a single theory, but rather a body of theory consisting of individual hypotheses about the mechanisms behind, and evolutionary consequences of, sexual selection. Some of the individual hypotheses are well-supported empirically and generally-accepted by biologists, while others are hotly- disputed (8, 9, 11, 12-17). The fact that some individual hypotheses are contentious does not a priori either threaten or support the validity of other individual hypotheses. Some individual hypotheses have been successful in predicting the most pervasive trends in evolutionary biology: the fact that – as Roughgarden et al. point out – there are exceptions to these trends, and variation within species, does not negate the argument that sexual selection may have been responsible for the trend - any more than the fact that all individuals of all species do not have the same morphology negates the idea that natural selection can be responsible for the evolution of morphology. The reasons why sexual selection does not lead to entirely uniform reproductive behavior are the same for why natural selection does not lead to entirely uniform morphology: competition (either ecological or reproductive), which leads to frequency dependent selection, and environmental variation (18). Bearing in mind the definition of sexual selection as a process not a theory, the fact that it occurs, and the fact that sexual selection theory is a body of theory, not a single theory, several of Roughgarden et al.’s statements are nonsensical or unsupportable. It does not make sense to state that “sexual selection is always mistaken”, nor to refer to “sexual selection’s rationale”. Moreover, if what one is interested in is understanding the mechanisms behind, and evolutionary consequences of, sexual selection, then it is hard to see how sexual selection theory could be replaced, let alone why it “needs to be replaced”, so such an unqualified claim is untenable. It could, however, be that sexual selection theory is an inadequate explanation of particular biological phenomena, and needs to be replaced in those particular cases. We will first discuss Roughgarden et al.’s concept of “social selection”, and then return to the question of whether social selection is one of those cases. As Roughgarden et al. point out, Maynard Smith (19) developed the use of game theory in biology as a way of analyzing evolutionary outcomes when the fitness consequences of an individual’s ‘behavior’ (in the widest sense) depend not only on its own behavior, but that of other individuals. This is so in the case of aggression (where fitness consequences of a given fighting strategy depend in part on the fighting strategy of the opponent), but also – of course – in the case of reproductive behavior. In line with this, game theory models have been increasingly the rule in phenotypic (optimality model type) analyses of the evolution of reproductive behavior (encompassing both sexual cooperation and conflict) since the pioneering work of Parker (20). Thus there is nothing new in general in the use of game theory models to study reproductive behavior. Moreover, there is nothing particularly new in the concept of threats or side-payments: game theory models of sexual coercion – i.e. threat – have existed for more than 10 years (21, 22), and side-payments have been extensively considered in game theory models of cooperative breeding (23, 24). Roughgarden et al. also imply that their approach avoids the need to “wrestle with how to prevent cheaters and free riders”, but their models solve this problem by ignoring it (4), simply assuming that individuals cannot renege on a cooperative agreement (as, for example, they might do by leaving after gleaning a benefit but before making a ‘promised’ side- payment, or, conversely, by taking a side-payment but leaving before delivering the benefit). Similarly, in the oystercatcher game, females always do equally or worse in a trio than in a pair, whereas males can do better in a trio than a pair. One implication of this overlooked by Roughgarden et al. is that although it may pay females to be cooperative when ‘locked’ in a trio, they are selected to avoid this situation, if possible. Such possibilities, and their consequences, have been considered at length over many years in sexual selection theory. In particular, it has long been recognized that in situations where individuals are constrained to complete obligate lifelong monogamy, there is no longer selection for exploitation of each partner by the other (sexual conflict), and perfect cooperation is the evolutionarily stable strategy (25-27). It is therefore not surprising that Roughgarden et al.’s models – which do not allow for partner swapping – should predict cooperation. In conclusion, we do not believe that there is anything new in a general sense in the models presented by Roughgarden et al. A second point that we wish to raise with regard to Roughgarden et al.’s models concerns the appropriate unit for payoffs, and, related to this, the justification for maximization of those payoffs. In evolutionary game theory, the appropriate units are fitness units (genetic costs and benefits), and the rationale for maximization is the action of selection in combination with the availability of variation and heredity. Roughgarden et al. claim that their explanation “in developmental time” “relies on … direct ecological benefits … without reference to genetic benefits”. The reference to developmental time seems to provide an escape from considering evolutionary mechanisms, but this is not the case: the only rationale to expect behavioral strategies within generations to be payoff-maximizing is that they have been built in by selection over many generations. This would also imply that the correct unit to use for payoffs is fitness, and the reference by Roughgarden et al. to increasing “average fitness accumulation rates” and the use of offspring produced as the payoff unit in the oystercatcher game suggests that they concur with this. Again we are left with the conclusion that there is nothing inherently new about Roughgarden et al.’s analyses. Lastly, if payoffs are in units of fitness, then variation in payoffs is selection, by definition. We can then ask whether this is natural or sexual selection. Since sexual selection is, by definition, due to variation in the number or phenotype of mates, the differences in payoffs when interacting with mates playing different strategies are sexual selection: Roughgarden et al.’s models, rather than being alternatives to sexual selection are, in fact, themselves models of sexual selection. In conclusion, we wish to make two main points with regard to Roughgarden et al.’s line of argument: first, their models of “social selection”, rather than being entirely novel, are developments (with problems (4)) within the current tradition of evolutionary game theory. Second, their models are not an alternative to sexual selection, but rather simply a means of expressing certain hypotheses regarding sexual selection: in other words, their models are part of mainstream sexual selection theory. References and Notes 1. J.Roughgarden et al., Science, 311, 965-969 (2006). 2. C.R.Darwin, The Descent of Man and Selection in Relation to Sex (London, Murray, 1871). 3. T.Pizzari et al., Science 311, 690 (2006). 4. S.R.X.Dall et al., Science 311, 689 (2006). 5. We set aside the question of whether selection arising through variation in reproduction occurring because of variation in own phenotype – e.g. large females are more fecund – should be called natural or sexual selection. It is, in any case, irrelevant to either Roughgarden et al.’s or our arguments. 6. L.W.Simmons, W.J.Bailey WJ, Evolution, 44, 1853(1990). 7. T.C.M.Bakker, Nature, 363, 255 (1993). 8. M. Andersson, Sexual Selection (Princeton Univ. Press, Princeton NJ, 1994). 9. T.Birkhead, A.P.Møller, Sperm competition and sexual selection (Academic Press, London, 1998). 10. A.M.Welch, R.D.Semlitsch, H.C.Gerhardt, Science, 280,1928 (1998). 11. L.W.Simmons, Sperm competition and its evolutionary consequences in the insects (Princeton Univ. Press, Princeton NJ, 2001). 12. S.M.Shuster, M.J.Wade. Mating Systems and Strategies (Princeton Univ. Press, Princeton NJ, 2003). 13. G.Arnqvist, L.Rowe. Sexual Conflict. (Princeton Univ. Press, Princeton NJ, 2005). 14. G.Arnqvist, T.Nilsson, Anim. Behav. 60, 145 (2000), 15. M.D.Jennions, M.Petrie, Biol. Rev. 75, 21 (2000), 16. T.Tregenza, N.Wedell, Nature, 415, 71 (2002). 17. D.J.Hosken, P.Stockley, Evol. Biol. 33, 173 (2003), 18. Here we limit the reasons mentioned to those that concern the way that selection acts, and omit other processes such as mutation. 19. J.Maynard Smith, Evolution and the theory of games (Cambridge Univ. Press, Cambridge, 1982). 20. See references in G.A.Parker, Phil. Trans. Roy. Soc. Lond., 361, 235; and G.A.Parker, in Essays on Animal Behaviour: Celebrating 50 years of Animal Behaviour, J. R. Lucas, L.W. Simmons, Eds. (Elsevier, Burlington MA., 2006), pp. 23-56. 21. T.H.Clutton-Brock, G.A.Parker, Anim. Behav., 49, 1345 (1995). 22. T.H.Clutton-Brock, G.A.Parker, Nature., 373, 209 (1995). 23. S.L.Vehrencamp, Anim. Behav., 31, 667 (1983). 24. R.A.Johnstone, Ethology, 106, 5 (2000). 25. G.A.Parker, Anim. Behav., 33, 519 (1985). 26. B.Holland, W.R.Rice, Proc. Natl. Acad. Sci. USA, 96, 5083 (1999). 27. C.M.Lessells, in Levels of Selection in Evolution, L.Keller, Ed. (Princeton Univ. Press, Princeton NJ, 1999), pp. 75-99.
Reproductive Behavior: Sexual Selection Remains the Best Explanation 6 April 2006
Tommaso Pizzari Department of Zoology, University of Oxford, Tim R. Birkhead, Mark W. Blows, Rob Brooks, et al. Respond to this E-Letter: Re: Reproductive Behavior: Sexual Selection Remains the Best Explanation	Tommaso Pizzari1*, Tim R. Birkhead2, Mark W. Blows3, Rob Brooks4, Katherine L. Buchanan5, Tim H. Clutton-Brock6, Paul H. Harvey1, Dave J. Hosken7, Michael D. Jennions8, Hanna Kokko9, Janne S. Kotiaho10, C(Kate) M. Lessells11, Constantino Macias-García12, Allen J. Moore7, Geoff A. Parker13, Linda Partridge14, Scott Pitnick15, Jacek Radwan16, Mike Ritchie17, Ben C. Sheldon1, Leigh W. Simmons18, Rhonda R. Snook2, Paula Stockley19, Marlene Zuk20. 1. Edward Grey Institute, Department of Zoology, University of Oxford, Oxford OX1 3PS, UK. 2. Department of Animal & Plant Sciences, University of Sheffield, Sheffield S10 2TN UK. 3. School of Integrative Biology, University of Queensland, St Lucia 4072, QLD, Australia. 4. School of Biological, Earth and Environmental Sciences, The University of New South Wales, Kensington, Sydney 2052, NSW, Australia. 5. Cardiff School of Biosciences, Cardiff University, Main Building, Park Place, Cardiff CF10 3TL, UK. 6. Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK. 7. Centre for Ecology & Conservation, University of Exeter in Cornwall, Tremough Campus, Penryn, TR10 9EZ, UK. 8. School of Botany & Zoology, The Australian National University, Canberra ACT 0200, Australia. 9. Laboratory of Ecological and Evolutionary Dynamics, Department of Biologic and Environmental Sciences, PO Box 65, 00014 University of Helsinki, Finland. 10. Department of Biological and Environmental Science, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland. 11. NIOO-KNAW, Centre for Terrestrial Ecology, P.O. Box 40, 6666 ZG Heteren, The Netherlands. 12. Universidad Nacional Autonoma de Mexico, Instituto de Ecología, Departamento de Ecología Evolutiva, AP 70-275, Mexico City, DF 07510, México. 13. School of Biological Sciences, Biosciences Building, Crown Street, University of Liverpool, Liverpool L69 7ZB, UK. 14. Department of Biology, University College London, Gower Street, London WC1E 6BT. 15. Department of Biology, University of Syracuse, 108 College Place, Syracuse, NY 13244, USA. 16. Institute of Environmental Sciences, Jagiellonian University, ul. Gronostajowa 3, 30-387 Krakow, Poland. 17. Environmental & Evolutionary Biology, Dyers Brae House, University of St Andrews, St Andrews, Fife, KY16 9TH, UK. 18. Zoology Building, School of Animal Biology (M092), University of Western Australia, Nedlands WA 6009, Australia. 19. Faculty of Veterinary Science, University of Liverpool, Chester High Road, Neston, South Wirral, CH64 7TE, UK. 20. Department of Biology, University of California, Riverside CA 92521 USA. Sexual selection is a cornerstone of modern evolutionary biology, a powerful evolutionary agent and the underlying mechanism for the evolution of exaggerated sexual traits, with important ramifications for speciation, and population dynamics (1-3). In their review, Roughgarden et al. (4) propose that sexual selection theory ‘needs to be replaced’ because it ‘is always mistaken’, and suggest an approach based on social selection that appears to be a radically novel explanation for reproductive behaviour. Such a proposal, if justified, would have profound consequences on a paradigmatic scale. Unfortunately, Roughgarden et al.’s argument is largely unsubstantiated, and relies on misconceptions and misrepresentations of sexual selection. The problems with this review are numerous and profound. Here we respond briefly by: (a) highlighting some of its most serious failings, and (b) showing that the models proposed are not novel but entirely consistent with current sexual selection theory. Failings of the review of sexual selection Roughgarden et al. fail to produce a scholarly synopsis of sexual selection by reporting erroneously or altogether ignoring a century and a half of sexual selection theory. We underline some examples of their erroneous claims below. (i) Roughgarden et al. claim that the reproductive social behaviours of a great many species that have been studied do not conform to Darwinian sexual selection templates. This is simply not true. Darwin (5) proposed sexual selection as a process that “depends on the advantage which certain individuals have over others of the same sex and species solely in respect of competition over mating and fertilization”, to explain the evolution of male ‘secondary sexual characters’ that were inconsistent with natural selection. Therefore, sexual selection is a consequence of sexual reproduction that arises from variance among individuals in mating and fertilization success, to promote traits that confer an advantage in reproductive competition. Sexual selection theory based on sex-specific potential reproductive rates is a powerful tool to explain much of the diversity of reproductive traits and behaviours across the vast majority of sexually reproducing organisms studied, including species where sex roles are reversed. Even an apparent paradox such as the giant sperm of male Drosophila bifurca makes sense in the light of sexual selection (6). Sexual selection theory has predicted some of the most robust trends in evolutionary biology. Roughgarden et al. omit to mention the vast amount of evidence for sexual selection that need not directly affect females (male-male competition and sperm competition) for which there has been abundant and compelling evidence amassed from Darwin onwards. Instead, Darwin’s view of sexual selection is summarized by Roughgarden et al. as males fertilizing ‘as many females as possible with inexpensive sperm, whereas females, with a limited supply of large eggs, select the genetically highest quality males…’. This is grossly anachronistic. Anisogamy, the differential gametic investment by males and females, was first explicitly discussed by Bateman in 1948 (7, 8), and Darwin was of course unaware of genes: genetics met Darwinian theory only in the neo-Darwinian synthesis (9). Similarly, the statement that ‘Darwin’s theory of sexual selection has continually drawn critics notably Huxley 1938’ is debatable. It is true that the idea of sexual selection was initially received with scepticism, but things have changed since 1938! The general idea that selection on variance in mating and fertilization success (i.e. sexual selection) can lead to the evolution of exaggerated male traits and female preference became established since the first theoretical models demonstrated its plausibility (10-13), and the first experiments demonstrated the operation of intra- and inter-sexual selection on male ornaments (14, 15). Claims that sexual selection needs to be replaced and that ‘there are fundamental problems that universally undercut all applications of sexual selection theory to any species...’ are unsupported or supported by misrepresentation of the literature, and mostly based on a list of 17 statements in the Supplementary Online Material, many of which are ambiguous or irrelevant to sexual selection. These statements refer to phenomena that do not represent "empirical departures" from sexual selection theory, but are instead entirely consistent with it. (ii) Roughgarden et al. argue that the use of different fitness definitions for males and females is one of the “fundamental problems that universally undercut any application of sexual selection theory”. Contrary to Roughgarden et al.’s statement, there is no need for sex-specific fitness definitions in sexual selection theory. Evolutionary biologists are well aware that ultimately fitness is a measure of the long-term genetic contribution into future generations, and that in diploid populations the male contribution of gametes always equals the female contribution (10, 16, 17). Fitness is not the easiest thing to measure, and often a sensible approach is to use proxies: the fitness of every individual, regardless of its sex, can be measured as the number of offspring produced in its lifetime. Because variance in fitness is typically higher in males than in females and because many sexually-selected traits are sex-limited, it makes sense to consider the fitness pay-off of sexually-selected traits within each sex (e.g. the success of a mutant male is considered in relation to the fitness of the predominant male type (18)). Obviously, it would be wrong to start by assuming a priori different mechanisms of fitness determination, while it makes sense to investigate the effects of, for example, a pre-existing difference in the costs of gamete production (19). Similarly, the fact that the additive genetic variance of a trait may be maintained despite intense directional selection on the trait is not a ‘fatal problem’ and not one exclusive to sexually-selected traits. For over 20 years, evolutionary biology has identified specific mechanisms for the maintenance of additive genetic variance of traits under intense directional selection, such as fitness itself (e.g. 20, 21). (iii) Roughgarden et al. claim that studies repeatedly show that females exert choice only to increase the number of their offspring. Roughgarden et al assume that sexual selection only refers to variation in the genetic quality of offspring, and not to the number of offspring. In some species males can increase female fecundity (22) and this may set the scene for the evolution of female preference for male traits associated with fecundity benefits. This is entirely consistent with sexual selection. More importantly, sexual selection theory can explain female preference in the many species where males do not appear to increase female lifetime fecundity (1). Female preference for exaggerated male traits may evolve through collateral selection on male ornaments genetically linked to female preference (10-13), or resistance against sexually antagonistic male phenotypes (23, 24). Although the evidence that females increase the genetic quality of the offspring through partner/sperm selection is limited, there are several examples that should not be ignored (25, 26), including cases where the genes mediating male quality have been identified (27, 28). Whether or not female preference is associated with genetic benefits does not pose a problem to sexual selection theory. Sexual selection may favour the spread of male types that not only do not benefit females, but positively reduce their fitness, setting the scene for the evolution of female bias against such males (23). In other words, sexual selection theory is consistent with scenarios where female preference for a male type is selected directly (through mating benefits and cost associated with different partners) and/or indirectly (through paternal breeding values for offspring fitness). (iv) Roughgarden et al. argue that the theoretical importance of social behavior contradicting sexual selection has been minimized through “insulting vocabulary”. Scientists often use colourful language. This is not a prerogative of sexual selection. Quantum physicists give their abstractions names such as ‘quark colour’, ‘strangeness’ and ‘charm’, and medical scientists give quirky names to genes. It is crucial here to bear in mind that while this terminology may help scientists refer to complex mechanisms, it does not in any way convey a moral connotation. Obviously, whether genes are ‘selfish’, ‘good’ or sport a ‘green beard’ does not and cannot cast a moral judgement on their behaviour, does not convey information about their evolutionary importance, and is not meant to insult or flatter the genes or their carriers. Similarly, ‘sneaker’ in sexual selection is not any more insulting or flattering than ‘helper’. Evolutionary biologists use these terms in a completely asocial and apolitical context which does not reflect the ‘importance’ of different behaviours. All of the terms mentioned by Roughgarden et al. refer to behaviours that in no way contradict sexual selection but are in fact integral and important components of sexual selection theory. Failing to understand that sexual selection theory is not concerned with the ethics and morality of reproductive behaviour but exclusively with its functional significance, is failing to understand the very nature of the scientific method, and threatens to set the clock back by some 30 years, when this misunderstanding was first clarified. Alternatives to sexual selection: If it ain’t broke, don’t replace it Roughgarden et al’s proposal of bargaining games as an alternative to sexual selection is puzzling for several reasons. (i) Roughgarden et al. propose that sexual selection theory should be replaced by an approach that relies on the exchange of direct ecological benefits among cooperating animals without reference to genetic benefits. Roughgarden et al.’s models are not an alternative to sexual selection, but rather simply a means of expressing certain hypotheses regarding sexual selection: in other words, the models are part of mainstream of sexual selection theory. The outcome of both of the examples provided (Peacock wrasse, Oystercatcher) coincides with the one that maximises male reproductive success given the behaviour of the female(s), and thus both examples are entirely consistent with sexual selection theory. The idea that social selection through bargaining may drive the evolution of ornaments as ‘badges of inclusion’ fails to explain why it is males that typically sport ornaments and females that bias male reproductive success based on male ornament expression. More importantly, the general idea that males may cooperate to increase their reproductive success is not new, not alternative to-, but a potential mechanism of sexual selection. If a male can increase his reproductive success relative to his competitors by cooperating, cooperation will by definition be sexually selected. There are several examples consistent with this, some of which are mediated by kin selection (e.g. 29, 30) (ii) The model proposed by Roughgarden et al. is aimed at species where reproduction is mediated by ‘physical intimacy’, and ‘a sense of friendship resides in animal bonding, a joy or synergy in the spirit of cooperation that allows animals to experience the product, not merely the sum, of their individual well-beings’. It is difficult to see how this seemingly anthropomorphic model can explain the evolution of reproductive strategies in corals, water lilies, bed bugs and indeed most of the sexually reproducing species where reproduction is not associated with sophisticated social interactions and the exchange of direct fitness benefits. It is also unclear how the above model can explain post-copulatory mechanisms of sexual selection mediated by gamete (rather than individual) behaviours and interactions. The power of sexual selection theory is that it provides a unitary theoretical framework to understand the bewildering diversity of reproductive strategies across taxa. (iii) Roughgarden et al. propose that sexual and social selection are mutually exclusive because, under social selection, reproductive behaviour is cooperative and sexual conflict is derived, whereas under sexual selection conflict is primitive and cooperation derived. This is also wrong. Regardless of the selective regime on reproduction, sexual conflict arises because the evolutionary interests of reproductive partners diverge. This happens whenever reproductive partners are genetically different, reproduction is costly and alternative reproductive opportunities occur (18, 23). Conflict between partners is inherent in the first general bargaining game of Roughgarden et al’s review, in which one combination of strategies maximizes the gains of player 1 (B, A) and another those of player 2 (A, B). In general, both sexual conflict and sexual cooperation are solidly ingrained within sexual selection theory. Sexual conflict is inherent to sexual reproduction whenever the fitness of reproductive partners is optimized by different reproductive decisions, while the fact that partners will share progeny selects for some degree of cooperation. The resolution of this conflict, i.e. the conditions under which sexual selection on males and natural selection on females results in mutual selection (cooperation) or antagonistic selection over reproduction (conflict) was already formally analyzed in 1979 (23, 31). Conclusion Sexual selection theory remains the best functional explanation for the evolution of most of the sex differences that initially puzzled Darwin, and for a surprising variety of other interesting traits that have been discovered as a consequence of intense theoretical and empirical research in this field during the last decades. Roughgarden et al. fail to provide a scholarly review of-, or an alternative to sexual selection. From its infancy sexual selection theory has generated debate, partly fuelled by different socio-political perspectives. Our present comment is not concerned with-, or motivated by socio-political issues, but exclusively with the scientific merits of Roughgarden et al.’s review. Regardless of socio-political perspectives, scientifically valid points have strengthened and enriched sexual selection, to make it one of the fastest-growing and topical areas of evolutionary biology. Important issues remain unresolved within sexual selection (e.g. the relative magnitude of direct and indirect selection, the functional significance of female preference, the mechanisms underlying condition-dependence, and those mediating sperm competition and cryptic female choice), none of which –however- questions sexual selection theory itself. Thus, while it is true that there is much research to be done, this is not equivalent to questioning a theory that has proven to be as remarkably robust as sexual selection. Debate is a welcome and integral part of scientific development. Rather than scientifically improbable alternatives to sexual selection, however, it is more useful to elucidate the mechanisms mediating variance in reproductive success within and across species. 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