J. theor. Biol. (1990) 147, 361-372
The Hermaphrodite's Dilemma JANET L. LEONARD'['t
Department of Zoology, University of Oklahoma, Norman, Oklahoma 73019, U.S.A. (Received on 4 December 1989, Accepted in revised form on 25 May 1990) Given sexual conflict, mating encounters between simultaneous hermaphrodites will conform to a new, conditional, non-zero sum game of strategy, the Hermaphrodite's Dilemma; special cases of which include Prisoner's Dilemma and Game of Chicken. The model predicts that hermaphrodite mating systems will be based on reciprocation with cheating in a preferred sexual role. This model suggests that study of hermaphrodite mating systems will provide direct evidence for the existence of sexual conflict and suggests that sexual conflict may act to stabilize hermaphroditism through such mating systems. Introduction
Axelrod & Hamilton (1981) suggested that the egg-trading mating system of certain serranid fishes represents a Tit-for-Tat solution ( R a p o p o r t & C h a m m a h , 1965) to a Prisoner's Dilemma created by sexual conflict between simultaneous hermaphrodites. Here, this suggestion is examined and developed into a general form of the game of conflict which, assuming sexual conflict, simultaneous hermaphrodites will face in mating encounters. This game, which is called the H e r m a p h r o d i t e ' s Dilemma, includes both Prisoner's Dilemma and G a m e of Chicken. In H e r m a p h r o d i t e ' s Dilemma the best strategy is reciprocity with occasional attempts to cheat by specializing in the preferred sexual role. This model predicts that mating systems based on reciprocity will be ubiquitous in simultaneously hermaphroditic populations. That is, once simultaneous hermaphroditism has evolved in a population of pair-mating animals in which mating in one sexual role offers a potential fitness advantage, the population will move to a mating system based on reciprocity with mechanisms to prevent cheating by specialization in the preferred role. Such mating systems, once established, would maintain simultaneous hermaphroditism even in the absence of the factors which were responsible for its initial evolution, and may explain the evolutionary stability and phyletic distribution of this m o d e of sexuality. Modern mating systems theory is founded on the assumption that there is often a conflict of interests between sexual partners, stdmming from differences in the selection pressures associated with reproduction through eggs vs. sperm. In the population as a whole, reproductive success through eggs must exactly equal reproductive success through sperm (Fisher, 1958). However, if the distribution of reproductive success across the population differs for sperm and eggs (i.e. the variances differ), there is a potential asymmetry in the pay-offs of the two sexual t Present address: Mark O. Hatfield Marine Science Center, Newport, OR 97365, U.S.A. 361 0022-5193/90/023361 +11 $03.00/0 © 1990 Academic Press Limited
362
J . L . LEONARD
roles tO an individual. Bateman (1948) predicted that this sexual conflict should extend to simultaneous hermaphrodites (see also Charnov, 1979). Sexual conflict in simultaneous hermaphrodites should be associated with an advantage to (which should lead to the evolution of a preference for) mating in a particular sexual role, a preference shared by all individuals of the species. If there is an advantage to mating in one role, an individual ought to be willing to assume that role in any and all encounters. The decisions available to two simultaneous hermaphrodites in a mating encounter are: (1) to offer to mate with a partner in both roles (the co-operate decision); or (2) to insist on mating only in the preferred sexual role (the defect decision) (Fig. 1). Using the notation of Prisoner's Dilemma, if sexual conflict exists, T, the pay-off for mating only in the preferred role, will by definition always be greater than S, the pay-off for mating only in the non-preferred role. If one assumes that mating in the non-preferred role decreases an individual's reproductive value (Fisher, 1958), by using up resources (energy, time, etc) or presenting a risk (of predation, etc) which diminishes the opportunities for (or likelihood of) future matings in the preferred role, to a greater degree than does mating in the preferred role, it must be the case that for a single encounter, where multiple encounters are possible, the benefit derived from mating only in the preferred role (T) is greater than the net (benefits - costs) benefit derived from mating in both roles (R). Except in the unlikely event, that male and female function use separate resource bases (energy, time, etc) or expose the individual to qualitatively different risks, T will be greater than R except on the last encounter (see below). Similarly, given that there is an advantage to the preferred sexual role, it will be the case that R > S. That is, if sexual conflict exists, T > R > S, in a single encounter, for an iteroparous simultaneous hermaphrodite. If this is not the case then there is no conflict of interests between simultaneous hermaphrodites in a mating encounter and they should always reciprocate. Furthermore, as long as the benefit associated with mating in the preferred role ( X ) is greater than the cost (or risk) associated with mating in the non-preferred role (Y) (see Fig. 2), it must be the case that R > P; that is, the pay-off from mating reciprocally will be greater than the pay-off from "sitting out". It is reasonable to Hermaphrodite's Dilemma Player B offer to mate in both roles
insist on preferred role
offer to mate in both roles
R,R
S,T
insist on preferred role
T,S
P,P
Player A
T>R>S;R>P
FIG. 1. Pay-off matrix for the general version of Hermaphrodite's Dilemma: T is the pay-off to a defector whose partner co-operates (temptation to defect), R is the pay-off if both co-operate (reward for co-operation), P is the pay-offif both defect (punishment for mutual defection), and S is the "'sucker's pay-off",the pay-offto an individual who co-operates when its partner defects (terminologyfrom Axelrod & Hamilton, 1981). The pay-offs are for a single encounter. Both Prisoner's Dilemma and Game of Chicken are special cases of Hermaphrodite's Dilemma.
THE HERMAPHRODITE'S
363
DILEMMA
Hermaphrodite's Dilemma for the Egg-trading case Player B
offer to mate in both roles
Player A insist on preferred role
offer to mate in both roles
insist on preferred role
R=X-Y (eggs fertilized and eggs given up)
S=-Y (eggs given up)
T=X (eggs fertilized but none given up)
P=O (nothing lost, nothing gained)
T fertilizes eggs
>
R reciprocates
>
P no spawning
>
S eggs given up
FIG. 2. Prisoner's Dilemma illustrated for egg-trading hermaphrodites. Prisoner's Dilemma is a symmetrical, two-person, non-zero-sum game in which each player has two options: to co-operate, or to defect (Davis, 1985; Luce & Raiffa, 1957). For the sake of clarity only the pay-off for Player A is shown. The highest possible pay-off comes to a player that defects while its partner co-operates (receiving the lowest pay-off of the game); whereas, if both players co-operate, they each receive a higher pay-off than if they both defect; i.e. T > R > P > S. The best strategy is Tit-for-Tat (Rapoport & Chammah, 1965; Luce & Raiffa, 1957), whereby a player co-operates on the first move in an encounter with a new partner, and on subsequent moves does what that partner did last time. In egg-trading, the male role is preferred because sperm are cheaper to produce than eggs, so T is the pay-off to an individual who fertilizes the partner's eggs, without spawning eggs in exchange; S is the pay-off to an individual who gets its own eggs fertilized without fertilizing any of the.partner's, and R is the pay-off to an individual which both fertilizes eggs and gets eggs fertilized. This formulation of Prisoner's Dilemma differs slightly from that of Fischer (1988). In both defection is defined as failure to release eggs, but Fischer apparently constructed his matrix in terms of two types of individuals (or behavioral strategies?) (always co-operate, and defect with some probability) rather than in terms of the pay-off to a given individual of two types of behavior (co-operate by releasing eggs; and defect by not releasing eggs). a s s u m e t h a t this will g e n e r a l l y b e t h e c a s e s i n c e t h e r e is s o m e n e t fitness b e n e f i t f r o m m a t i n g in t h e n o n - p r e f e r r e d s e x u a l r o l e , e v e n t h o u g h t h e c o s t / b e n e f i t r a t i o a s s o c i a t e d w i t h t h a t r o l e is high. G i v e n s e x u a l c o n f l i c t t h e n , a m a t i n g e n c o u n t e r b e t w e e n a p a i r o f s i m u l t a n e o u s h e r m a p h r o d i t e s is a n o n - z e r o - s u m g a m e w h o s e p a y - o f f m a t r i x (Fig. 1) is d e f i n e d as T > R > S, a n d R > P. P r i s o n e r ' s or C h i c k e n ?
T h e p a y - o f f m a t r i x fits t h e r e q u i r e m e n t s o f P r i s o n e r ' s D i l e m m a , i.e. t h a t T > R > P > S (Fig. 2), o n l y w h e r e t h e p r o b a b i l i t y o f c o - o p e r a t i o n ( o r f r e q u e n c y o f coo p e r a t o r s ) is g r e a t e n o u g h to m a k e t h e c o n s e q u e n c e s ( P ) o f m u t u a l d e f e c t i o n , o n a s i n g l e r o u n d , less c o s t l y t h a n c o - o p e r a t i n g w i t h a d e f e c t o r ( S ) . T h a t is, it m u s t b e b e t t e r to " s i t o u t " a r o u n d a n d s a v e o n e ' s r e s o u r c e s f o r a f u t u r e e n c o u n t e r , t h a n to " s q u a n d e r " r e s o u r c e s by m a t i n g in o n l y t h e n o n - p r e f e r r e d role. W i t h i n t h e s e limits a n d a s s u m i n g t h a t w, t h e p r o b a b i l i t y o f e n c o u n t e r i n g a n i n d i v i d u a l a g a i n , is s u f f i c i e n t l y g r e a t , T i t - f o r - T a t , ( c o - o p e r a t e o n t h e first m o v e a n d t h e n f o l l o w t h e p a r t n e r ' s l e a d ) ( A x e i r o d & H a m i l t o n , 1981; R a p o p o r t & C h a m m a h , 1965; D a v i s , 1983) is a c o l l e c t i v e l y s t a b l e (sensu B o y d & L o r b e r b a u m , 1987) s t r a t e g y , a l t h o u g h n o t s t r i c t l y s p e a k i n g a n e v o l u t i o n a r i l y s t a b l e s t r a t e g y ( E S S ) ( f o r d i s c u s s i o n see P a r k e r & H a m m e r s t e i n , 1985; M a y , 1987; B o y d & L o r b e r b a u m , 1987). In P r i s o n e r ' s D i l e m m a R>(T+S)/2, w h i c h m a k e s r e c i p r o c a t i o n t h r o u g h T i t - f o r - T a t m o r e
364
J . L . LEONARD
profitable than trading defections (alternating the preferred role in a series of matings) in an iterated encounter. In the case of simultaneous hermaphrodites with successively reciprocal mating, such as the egg-trading serranids (Fischer, 1980), a mating system based on trading defections would be difficult to distinguish behaviorally from Tit-for-Tat. Even where T > R > P > S, the conflict between two simultaneous hermaphrodites in a mating encounter differs from the classical Prisoner's Dilemma in a number of ways. Obviously the fitness of an individual which never mated at all over its lifespan (because it insisted on the preferred role) would be zero. That is, in the case of mating simultaneous hermaphrodites, an "unconditional defector" (ALL D) strategy is not stable (Axelrod & Hamilton, 1981; Maynard Smith, 1982); since (1) a population composed entirely of defectors would not reproduce, and (2) as the proportion of "unconditional defectors" in the population increases, the advantage of that strategy decreases, since the probability of getting T in an encounter declines while the probability of getting P increases. Also, because, totaled across the population, the pay-off for the two sexual roles must be equal (Fisher, 1958), the pay-off matrix for the H e r m a p h r o d i t e ' s Dilemma is frequency dependent, whereas the Prisoner's Dilemma matrix is static. Similarly, in the Prisoner's Dilemma, if the game is to consist of only one encounter, the only rational decision is to defect, whereas a simultaneous hermaphrodite with only one opportunity to mate ought to choose to co-operate, for two reasons. Firstly, a simultaneous hermaphrodite, capable of mating in both sexual roles, would have nothing to gain by avoiding the non-preferred sexual role (saving its resources for future encounters) in what would be its only (or last) encounter (the "'You-Can't-Take-It-With-You'" principle). Therefore, T
The Hermaphrodite's Dilemma JANET L. LEONARD'['t
Department of Zoology, University of Oklahoma, Norman, Oklahoma 73019, U.S.A. (Received on 4 December 1989, Accepted in revised form on 25 May 1990) Given sexual conflict, mating encounters between simultaneous hermaphrodites will conform to a new, conditional, non-zero sum game of strategy, the Hermaphrodite's Dilemma; special cases of which include Prisoner's Dilemma and Game of Chicken. The model predicts that hermaphrodite mating systems will be based on reciprocation with cheating in a preferred sexual role. This model suggests that study of hermaphrodite mating systems will provide direct evidence for the existence of sexual conflict and suggests that sexual conflict may act to stabilize hermaphroditism through such mating systems. Introduction
Axelrod & Hamilton (1981) suggested that the egg-trading mating system of certain serranid fishes represents a Tit-for-Tat solution ( R a p o p o r t & C h a m m a h , 1965) to a Prisoner's Dilemma created by sexual conflict between simultaneous hermaphrodites. Here, this suggestion is examined and developed into a general form of the game of conflict which, assuming sexual conflict, simultaneous hermaphrodites will face in mating encounters. This game, which is called the H e r m a p h r o d i t e ' s Dilemma, includes both Prisoner's Dilemma and G a m e of Chicken. In H e r m a p h r o d i t e ' s Dilemma the best strategy is reciprocity with occasional attempts to cheat by specializing in the preferred sexual role. This model predicts that mating systems based on reciprocity will be ubiquitous in simultaneously hermaphroditic populations. That is, once simultaneous hermaphroditism has evolved in a population of pair-mating animals in which mating in one sexual role offers a potential fitness advantage, the population will move to a mating system based on reciprocity with mechanisms to prevent cheating by specialization in the preferred role. Such mating systems, once established, would maintain simultaneous hermaphroditism even in the absence of the factors which were responsible for its initial evolution, and may explain the evolutionary stability and phyletic distribution of this m o d e of sexuality. Modern mating systems theory is founded on the assumption that there is often a conflict of interests between sexual partners, stdmming from differences in the selection pressures associated with reproduction through eggs vs. sperm. In the population as a whole, reproductive success through eggs must exactly equal reproductive success through sperm (Fisher, 1958). However, if the distribution of reproductive success across the population differs for sperm and eggs (i.e. the variances differ), there is a potential asymmetry in the pay-offs of the two sexual t Present address: Mark O. Hatfield Marine Science Center, Newport, OR 97365, U.S.A. 361 0022-5193/90/023361 +11 $03.00/0 © 1990 Academic Press Limited
362
J . L . LEONARD
roles tO an individual. Bateman (1948) predicted that this sexual conflict should extend to simultaneous hermaphrodites (see also Charnov, 1979). Sexual conflict in simultaneous hermaphrodites should be associated with an advantage to (which should lead to the evolution of a preference for) mating in a particular sexual role, a preference shared by all individuals of the species. If there is an advantage to mating in one role, an individual ought to be willing to assume that role in any and all encounters. The decisions available to two simultaneous hermaphrodites in a mating encounter are: (1) to offer to mate with a partner in both roles (the co-operate decision); or (2) to insist on mating only in the preferred sexual role (the defect decision) (Fig. 1). Using the notation of Prisoner's Dilemma, if sexual conflict exists, T, the pay-off for mating only in the preferred role, will by definition always be greater than S, the pay-off for mating only in the non-preferred role. If one assumes that mating in the non-preferred role decreases an individual's reproductive value (Fisher, 1958), by using up resources (energy, time, etc) or presenting a risk (of predation, etc) which diminishes the opportunities for (or likelihood of) future matings in the preferred role, to a greater degree than does mating in the preferred role, it must be the case that for a single encounter, where multiple encounters are possible, the benefit derived from mating only in the preferred role (T) is greater than the net (benefits - costs) benefit derived from mating in both roles (R). Except in the unlikely event, that male and female function use separate resource bases (energy, time, etc) or expose the individual to qualitatively different risks, T will be greater than R except on the last encounter (see below). Similarly, given that there is an advantage to the preferred sexual role, it will be the case that R > S. That is, if sexual conflict exists, T > R > S, in a single encounter, for an iteroparous simultaneous hermaphrodite. If this is not the case then there is no conflict of interests between simultaneous hermaphrodites in a mating encounter and they should always reciprocate. Furthermore, as long as the benefit associated with mating in the preferred role ( X ) is greater than the cost (or risk) associated with mating in the non-preferred role (Y) (see Fig. 2), it must be the case that R > P; that is, the pay-off from mating reciprocally will be greater than the pay-off from "sitting out". It is reasonable to Hermaphrodite's Dilemma Player B offer to mate in both roles
insist on preferred role
offer to mate in both roles
R,R
S,T
insist on preferred role
T,S
P,P
Player A
T>R>S;R>P
FIG. 1. Pay-off matrix for the general version of Hermaphrodite's Dilemma: T is the pay-off to a defector whose partner co-operates (temptation to defect), R is the pay-off if both co-operate (reward for co-operation), P is the pay-offif both defect (punishment for mutual defection), and S is the "'sucker's pay-off",the pay-offto an individual who co-operates when its partner defects (terminologyfrom Axelrod & Hamilton, 1981). The pay-offs are for a single encounter. Both Prisoner's Dilemma and Game of Chicken are special cases of Hermaphrodite's Dilemma.
THE HERMAPHRODITE'S
363
DILEMMA
Hermaphrodite's Dilemma for the Egg-trading case Player B
offer to mate in both roles
Player A insist on preferred role
offer to mate in both roles
insist on preferred role
R=X-Y (eggs fertilized and eggs given up)
S=-Y (eggs given up)
T=X (eggs fertilized but none given up)
P=O (nothing lost, nothing gained)
T fertilizes eggs
>
R reciprocates
>
P no spawning
>
S eggs given up
FIG. 2. Prisoner's Dilemma illustrated for egg-trading hermaphrodites. Prisoner's Dilemma is a symmetrical, two-person, non-zero-sum game in which each player has two options: to co-operate, or to defect (Davis, 1985; Luce & Raiffa, 1957). For the sake of clarity only the pay-off for Player A is shown. The highest possible pay-off comes to a player that defects while its partner co-operates (receiving the lowest pay-off of the game); whereas, if both players co-operate, they each receive a higher pay-off than if they both defect; i.e. T > R > P > S. The best strategy is Tit-for-Tat (Rapoport & Chammah, 1965; Luce & Raiffa, 1957), whereby a player co-operates on the first move in an encounter with a new partner, and on subsequent moves does what that partner did last time. In egg-trading, the male role is preferred because sperm are cheaper to produce than eggs, so T is the pay-off to an individual who fertilizes the partner's eggs, without spawning eggs in exchange; S is the pay-off to an individual who gets its own eggs fertilized without fertilizing any of the.partner's, and R is the pay-off to an individual which both fertilizes eggs and gets eggs fertilized. This formulation of Prisoner's Dilemma differs slightly from that of Fischer (1988). In both defection is defined as failure to release eggs, but Fischer apparently constructed his matrix in terms of two types of individuals (or behavioral strategies?) (always co-operate, and defect with some probability) rather than in terms of the pay-off to a given individual of two types of behavior (co-operate by releasing eggs; and defect by not releasing eggs). a s s u m e t h a t this will g e n e r a l l y b e t h e c a s e s i n c e t h e r e is s o m e n e t fitness b e n e f i t f r o m m a t i n g in t h e n o n - p r e f e r r e d s e x u a l r o l e , e v e n t h o u g h t h e c o s t / b e n e f i t r a t i o a s s o c i a t e d w i t h t h a t r o l e is high. G i v e n s e x u a l c o n f l i c t t h e n , a m a t i n g e n c o u n t e r b e t w e e n a p a i r o f s i m u l t a n e o u s h e r m a p h r o d i t e s is a n o n - z e r o - s u m g a m e w h o s e p a y - o f f m a t r i x (Fig. 1) is d e f i n e d as T > R > S, a n d R > P. P r i s o n e r ' s or C h i c k e n ?
T h e p a y - o f f m a t r i x fits t h e r e q u i r e m e n t s o f P r i s o n e r ' s D i l e m m a , i.e. t h a t T > R > P > S (Fig. 2), o n l y w h e r e t h e p r o b a b i l i t y o f c o - o p e r a t i o n ( o r f r e q u e n c y o f coo p e r a t o r s ) is g r e a t e n o u g h to m a k e t h e c o n s e q u e n c e s ( P ) o f m u t u a l d e f e c t i o n , o n a s i n g l e r o u n d , less c o s t l y t h a n c o - o p e r a t i n g w i t h a d e f e c t o r ( S ) . T h a t is, it m u s t b e b e t t e r to " s i t o u t " a r o u n d a n d s a v e o n e ' s r e s o u r c e s f o r a f u t u r e e n c o u n t e r , t h a n to " s q u a n d e r " r e s o u r c e s by m a t i n g in o n l y t h e n o n - p r e f e r r e d role. W i t h i n t h e s e limits a n d a s s u m i n g t h a t w, t h e p r o b a b i l i t y o f e n c o u n t e r i n g a n i n d i v i d u a l a g a i n , is s u f f i c i e n t l y g r e a t , T i t - f o r - T a t , ( c o - o p e r a t e o n t h e first m o v e a n d t h e n f o l l o w t h e p a r t n e r ' s l e a d ) ( A x e i r o d & H a m i l t o n , 1981; R a p o p o r t & C h a m m a h , 1965; D a v i s , 1983) is a c o l l e c t i v e l y s t a b l e (sensu B o y d & L o r b e r b a u m , 1987) s t r a t e g y , a l t h o u g h n o t s t r i c t l y s p e a k i n g a n e v o l u t i o n a r i l y s t a b l e s t r a t e g y ( E S S ) ( f o r d i s c u s s i o n see P a r k e r & H a m m e r s t e i n , 1985; M a y , 1987; B o y d & L o r b e r b a u m , 1987). In P r i s o n e r ' s D i l e m m a R>(T+S)/2, w h i c h m a k e s r e c i p r o c a t i o n t h r o u g h T i t - f o r - T a t m o r e
364
J . L . LEONARD
profitable than trading defections (alternating the preferred role in a series of matings) in an iterated encounter. In the case of simultaneous hermaphrodites with successively reciprocal mating, such as the egg-trading serranids (Fischer, 1980), a mating system based on trading defections would be difficult to distinguish behaviorally from Tit-for-Tat. Even where T > R > P > S, the conflict between two simultaneous hermaphrodites in a mating encounter differs from the classical Prisoner's Dilemma in a number of ways. Obviously the fitness of an individual which never mated at all over its lifespan (because it insisted on the preferred role) would be zero. That is, in the case of mating simultaneous hermaphrodites, an "unconditional defector" (ALL D) strategy is not stable (Axelrod & Hamilton, 1981; Maynard Smith, 1982); since (1) a population composed entirely of defectors would not reproduce, and (2) as the proportion of "unconditional defectors" in the population increases, the advantage of that strategy decreases, since the probability of getting T in an encounter declines while the probability of getting P increases. Also, because, totaled across the population, the pay-off for the two sexual roles must be equal (Fisher, 1958), the pay-off matrix for the H e r m a p h r o d i t e ' s Dilemma is frequency dependent, whereas the Prisoner's Dilemma matrix is static. Similarly, in the Prisoner's Dilemma, if the game is to consist of only one encounter, the only rational decision is to defect, whereas a simultaneous hermaphrodite with only one opportunity to mate ought to choose to co-operate, for two reasons. Firstly, a simultaneous hermaphrodite, capable of mating in both sexual roles, would have nothing to gain by avoiding the non-preferred sexual role (saving its resources for future encounters) in what would be its only (or last) encounter (the "'You-Can't-Take-It-With-You'" principle). Therefore, T
