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Evolutionary Stability of Egg Trading and Parceling in Simultaneous Hermaphrodites: the Chalk Bass Revisited

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Evolutionary Stability of Egg Trading and Parceling in Simultaneous Hermaphrodites: the Chalk Bass Revisited ARTICLE IN PRESS Journal of Theoretical Biology 246 (2007) 420–429 www.elsevier.com/locate/yjtbi Evolutionary stability of egg trading and parceling in simultaneous hermaphrodites: The chalk bass revisited Philip H. CrowleyÃ, Mary K. Hart Department of Biology, University of Kentucky, Lexington, KY 40506-0225, USA Received 16 March 2006; received in revised form 14 January 2007; accepted 19 January 2007 Available online 30 January 2007 Abstract Several species of simultaneously hermaphroditic seabasses living on coral reefs mate by alternating male and female roles with a partner. This is known as egg trading, one of the classic and most widely cited examples of social reciprocity among animals. Some of the egg-trading seabass species, including the chalk bass, Serranus tortugarum, switch mating roles repeatedly, having subdivided their clutch of eggs into parcels offered to the partner for fertilization. Here we attempt to understand these dynamics as a pair of evolutionary games, modifying some previous approaches to better reflect the biological system. We find that the trading of egg clutches is evolutionarily stable via byproduct mutualism and resistant to invasion by rare individuals that take the male role exclusively. We note why and how parceling may reflect sexual conflict between individuals in the mating pair. We estimate evolutionarily stable parcel numbers and show how they depend on parameter values. Typically, two or more sequential parcel numbers are evolutionarily stable, though the lowest of these yields the highest fitness. Assuming that parcel numbers are adjusted to local conditions, we predict that parcel numbers in nature are inversely related both to mating group density (except at low density) and predation risk. r 2007 Elsevier Ltd. All rights reserved. Keywords: Evolution of cooperation; Evolutionary game theory; Mating system theory; Reciprocal altruism; Serranidae; Serranus tortugarum; Sexual conflict 1. Introduction eggs for fertilization by a partner in exchange for the opportunity to fertilize its partner’s eggs. (Sperm trading is Mating systems based on pairing of unrelated indivi- an analogous phenomenon arising in other hermaphroditic duals invariably arise from a combination of cooperation systems (Leonard and Lukowiak, 1984, 1985; Leonard, and conflict. Asymmetries in costs and benefits to males 1991; Michiels, 1998; Michiels and Bakovski, 2000; and females from mating and fertilization can account for Angeloni et al., 2002; Anthes et al., 2005; Anthes and sex-related behavioral differences when each individual is Michiels, 2005; Koene and Ter Maat, 2005).) exclusively one sex or the other (Emlen and Oring, 1977), Egg trading is one of the best known and most but there is also much to be learned from species whose compelling examples of iterative social reciprocity, a individuals can be both sexes at once. Simultaneous central concept in the evolutionary theory of cooperative hermaphrodites can provide valuable evidence for an relationships (see Hammerstein, 2003 on the scarcity of intriguing type of cooperative reciprocity known as egg such examples). The recent emergence of sexual conflict as trading (e.g. see Fischer (1980) and Fischer and Petersen an important component of sexual selection theory (1987) on small seabasses of the genera Serranus and (Leonard, 1993; Michiels, 1998; Chapman et al., 2003; Hypoplectrus; and Sella (1985, 1988) on the polychaete Arnqvist and Rowe, 2005; Tregenza et al., 2006; Wedell worm Ophyotrocha diadema). Egg trading is the offering of et al., 2006) has re-emphasized the importance of the egg- trading serranines, where the elements of conflict are ÃCorresponding author. Tel.: +1 859 257 1996; fax: +1 859 257 1717. amenable to study (Leonard, 1993). In particular, the way E-mail addresses: [email protected] (P.H. Crowley), [email protected] that eggs are traded between partners can indicate the (M.K. Hart). presence and intensity of their sexual conflict (Hart et al., 0022-5193/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2007.01.018 ARTICLE IN PRESS P.H. Crowley, M.K. Hart / Journal of Theoretical Biology 246 (2007) 420–429 421 submitted). With these issues in mind, it seems essential to characteristics of the system, and extend the results to ensure the existence of a firm conceptual foundation, provide a stronger foundation for future work. We begin particularly concerning one of the best-studied serranine with a brief critique of Fischer’s (1988) approach to these species—the chalk bass, Serranus tortugarum. In the two key games. Next we propose and implement an present work, we advance the game-theoretic framework alternative formulation of the what we will call the clutch on which a deeper understanding of sexual cooperation trading game, moving beyond Tit-for-Tat and the iterated and conflict will necessarily depend. Prisoner’s Dilemma. We then turn to the parceling game, During a mating interval each afternoon, most chalk provide a somewhat different formulation, and rather bass individuals find partners, engage in courtship, and unexpectedly find a range of evolutionarily stable parcel dart into the water column to release gametes with the numbers, showing how these results depend on magnitudes partner, generally alternating male and female roles over of key parameters. In Section 5, we consider these results several mating bouts. Nearby individuals (‘‘streakers’’) in the context of the literature, make some predictions may contribute their own sperm to the gametes released by about how parcel numbers might vary with ecological the mating pair. The density of interacting individuals, conditions in nature, and establish some priorities for level of predation risk, sizes of paired individuals, and studies yet to come. other factors may influence their mating behavior in important ways. 2. Critique of the game formulations in Fischer (1988) In studies of the egg-trading seabasses (Serranidae: Serraninae) of Caribbean coral reefs, Fischer (1980, 1988) The Prisoner’s Dilemma is a symmetrical two-player recognized the alternation of male and female roles game in which each player may cooperate ( ¼ C), which between mating partners as the outcome of an evolutionary Fischer took to mean providing eggs to its partner at cost d game. In his 1988 article (see also Dugatkin, 1997), Fischer during its turn as female—or may defect ( ¼ D), providing formulated a simple model of symmetric interactions in eggs with lower probability 0pqo1 during its turn as pairs of simultaneous hermaphrodites to see whether egg female. The partner in the male role is assumed to gain trading could be explained as a Tit-for-Tat strategy within fitness benefit b from fertilizing the eggs provided. The an iterated Prisoner’s Dilemma framework. The chalk bass, Prisoner’s Dilemma requires that the net benefits or S. tortugarum, which has size-assortative mating consistent payoffs Pij for playing i against j have the following with a symmetric game played between equivalent partners, relationships: PDC4PCC4PDD4PCD and PCC4(PDC+ was the primary focus of this study. Fischer’s (1988) PCD)/2. When the Prisoner’s Dilemma is repeated or analysis and its Tit-for-Tat interpretation seem to have iterated, corresponding to repeated ‘‘rounds’’ in which been widely accepted and cited in the literature (e.g. each player takes a turn in each of the male and female Leonard, 1993, Dugatkin, 1997; Arnqvist and Rowe, roles, more complex strategies become possible. Tit-for-Tat 2005—but see Connor, 1992). is an iterated game strategy in which a player cooperates in Fischer (1988) also addressed egg parceling in another, the first round and then subsequently does what its partner especially insightful, two-player symmetrical game. Egg did in the preceding round. Tit-for-Tat produces sequences parceling is a type of egg trading in which the clutch is of mutual cooperation when played against a pure C player divided into subsets or parcels to be released individually (cooperator) or another Tit-for-Tat player. This strategy when mating as a female. Dividing the clutch into more can become evolutionarily stable in the iterated Prisoner’s parcels reduces an individual’s susceptibility to exploitation Dilemma if a pair of partners expects to interact a sufficient by others acting as males and may also increase an but indeterminate number of times ( ¼ rounds in this case), individual’s mating opportunities in the male role. On each expressed by a sufficiently high probability w of one or turn in the female role, each fish offers its partner one more subsequent interactions following any particular one parcel of eggs for fertilization, leaving open the possibility (e.g. see Axelrod and Hamilton, 1981). of finding another partner to trade other parcels with if the A payoff matrix can be readily constructed and present partner fails to reciprocate. By giving each player analyzed, based on Fischer’s postulated pair of strategies the alternative strategies of dividing its clutch into either p in an egg-trading game. For each pair of reciprocal or p+1 parcels of eggs, the game can potentially identify matings, with b the fitness gain from fertilizing a parcel, d the evolutionarily stable number of parcels—the number of the cost of producing a parcel, and q the chance that the parcels that, when adopted by the entire population, yields ‘‘female’’ provides the parcel during her turn, the payoffs higher fitness for an individual than would any other parcel for the four different strategy combinations are PCC ¼ number. bÀd, PCD ¼ qbÀd, PDC ¼ bÀqd, and PDD ¼ qbÀqd. These evolutionary games advanced our understanding Fischer demonstrates that this is a Prisoner’s Dilemma if of egg trading and reciprocity by identifying many of the benefit to the male-role partner exceeds the cost to the the key parameters and emphasizing the importance partner in the female role (i.e. b4d), which he argues of demonstrating evolutionary stability in accounting should be generally true for egg-trading serranine fishes.
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