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Animal Contests as Evolutionary Games: Paradoxical behavior can be understood in the context of evolutionary stable strategies. The trick is to discover which game the animal is playing Author(s): Michael Mesterton-Gibbons and Eldridge S. Adams Reviewed work(s): Source: American Scientist, Vol. 86, No. 4 (JULY-AUGUST 1998), pp. 334-341 Published by: Sigma Xi, The Scientific Research Society Stable URL: http://www.jstor.org/stable/27857057 . Accessed: 14/11/2011 21:23

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http://www.jstor.org Animal Contests as Games Evolutionary

Paradoxical behaviorcan be understood in thecontext of evolutionarystable strategies.The trickis todiscover which game theanimal isplaying

Michael Mesterton-Gibbons and Eldridge S. Adams

science of behavioral ecology tuition that evolution should favor sig mals can modify their behavior in dif as The thrives on paradoxes, baffling in nals with low costs to the animal pro ferent circumstances, such whether are consistencies between intuition and ducing them, especially since these they owners or intruders, only if are evidence that engage our attention costly behaviors will be passed onto they aware of such roles. and stimulate further investigation. the signaler's offspring. Third, the pattern of interactionmust a Mathematical models can modify our Yet formal models of communica be well defined and accompanied by intuition by showing that apparently tion revealed that the handicap princi formula for how each player's reward on sensible explanations are actually ple is logically sound under certain from the interaction depends its on problematic, or that seemingly outra conditions. In particular, themagni strategy and those of the other play geous proposals are downright reason tude of the handicap must increase ers. In evolutionary games, the rewards able. This is especially true in the study with the intensity of the signal, and the are measured in terms of expected fu conse must ture success. of animal contests, where the cost be especially damaging for reproductive a quences of an interaction between two animals of lower quality. For example, For game to be useful, itmust be or animals with opposing interests are dif if a weak gazelle stotted as vigorously possible to identify one more strate ficult to guess. as a strong one, then itwould waste gies from among those feasible as the un a our Consider a famous example known what little strength it had and be "solution" for given purpose. In as a the "handicap principle." The be able to flee from pursuing predator. case, the solution is the behavior that se havioral ecologist Amotz Zahavi of Tel These models have convinced many can be expected to evolve by natural a a Aviv University argued that animals biologists that a previously unaccept lection. If behavior is fixed in real with conflicting interests should evolve ed idea has broad explanatory power. population, then itmust at least be true behavioral displays that are costly to Efforts to resolve such questions in that every feasible alternative behavior even animal behavior have relied increas would a lower for other the signaler, if they lower its yield reward, chances for survival. By showing that it ingly on collaborations between biolo wise the alternative behavior would can a and ana The endure handicap, the animal reli gists mathematicians, using have spread into the population. was ably indicates its high quality, a mes lytical tools called games. In particular, relevant solution concept,which in sage that other animals do well to re behavioral ecologists use evolutionary troduced a quarter of a century ago by spect. For example, on sighting a games. A game in this context is a JohnMaynard Smith of theUniversity predator, a gazelle may stott?that is, mathematical model of strategic inter of Sussex, is thatof an evolutionarystable jump high in the air on all four legs? action, which arises when the outcome strategy, a population strategy that several times before fleeing, thereby of an individual's actions depends on yields a higher reward than any feasible demonstrating that it is in superb the actions of others. mutant strategy (that is, any newly in physical condition, and that the preda A game has three components. First, troduced alternative strategy). torwould only waste time and energy there are at least two interacting indi Just as a model population is only a by pursuing it. This hypothesis was viduals, called players. In an evolution caricature of a real population, so a initially rejected by many partly be ary game played within a single species, paradox is only a caricature of real igno cause an a rance. a it contradicted the biologist's in the set of players is ecotype, popula So, in terms of realism, game tion of animals in a given ecological en and a paradox are a perfect match. A vironment. For example, a population game theorist strives to unravel the Michael Mesterton-Gibbons is a in the professor of spiders in a grassland habitat and the paradox by establishing conditions for Department ofMathematics, Florida State same in a habitat form an stable to exist an species riparian evolutionary strategy University. Eldridge S. Adams is assistant two different ecotypes. in themodel population, and by ana professor in theDepartment of Ecology & Second, each player has a set of feasi lyzing itsproperties when itdoes exist. EvolutionaryBiology at theUniversity of ble In an game, Now, a arises because evidence Connecticut, Storrs. Address forMesterton strategies. evolutionary paradox this set is the same for and fails to intuition,which (assum Gibbons: Department ofMathematics, Florida every player support is constrained the struc the evidence to be can State University, Tallahassee, FL 32306-4510. by information ing sound) hap ture interaction. intuition on a false Internet: [email protected]. of the For example, ani pen only if the relies

334 American Scientist, Volume 86 Figure 1. Dueling damselflies will contest a territory until the stronger one prevails, but unlike many mammalian species, these insects cannot ob serve the relative strength of their opponent Instead, the damselflies appear to play a war-of-attrition game inwhich they rely only on a knowledge of their own energy reserves. This strategy was discovered by evolutionary game theorists in an attempt to explain why weaker damselflies did not a yield to stronger opponents earlier in contest The authors argue that themethods of game theory provide a valuable tool in discovering the strate can gies that evolve in contests between animals of the same species. (Photograph courtesy of JimMarden, Pennsylvania State University.) assumption, albeit an implicit one. So Each can be important, as we illustrate the probable loser. This has been con theway to resolve a paradox is to spot with examples from our recentwork on firmed by experimental studies on a va the false assumption. animal contests among damselflies, riety of animals. The duration of such In other words, if a paradox of ani mantis shrimps and spiders. contests is greatest when the opponents mal behavior exists, then we have are of nearly equal fighting ability, so wrongly guessed which game best Information Structure in a Game that it ismore difficult to judge which is models how the real population inter A few years ago, JimMarden of Penn likely towin. This is the same reason acts, and to resolve this paradox we sylvania State University, in collabora thatmany human sporting events are must with more teams guess again?if necessary, repeat tion Jonathan Waage of Brown longer and exciting when edly?until eventually we guess cor University, staged a series of territorial are evenly matched. rectly.Assuming the validity of our so contests between male damselflies But the duels between the dam lution concept, that is, assuming that the (Calopteryxmaculata). The male pairs in selflies failed to follow this logic. Al observed behavior corresponds to some these contests had various, unequal re though the weaker animal ultimately evolutionary stable strategy, there are serves of fat,an indicator of strength.A conceded to its opponent inmore than only three things we could be wrong common expectation for such contests 90 percent of these encounters, Marden about: the ecotype, the information (derived from game-theory models) is found no negative correlation between structure and strategy set or the pattern that each animal compares its own the duration of a contest and the dif of interaction and reward. So there are strength to that of its opponent and ference in the relative strengths of the also only three things to be right about. withdraws when it judges itself to be males. Here was a paradox, all the

1998 July-August 335 more re baffling because the expected One possibly errant assumption is bighorn sheep), and because somuch of lationship had emerged repeatedly in simply thebelief that animals can assess a behavioral ecologisf s intuition about one studies of other species. Could therebe another's strength.Because it is such contest behavior had developed in that our a something amiss in assumptions good assumption forcontests between context, itwas an easy assumption to as about damselfly contests? animals with good visual acuity (such overlook. But fat is stored internally in insects,so a cannot ob War-of-Attrition Game damselfly directly serve its opponent's reserves. (Marden also found no correlation between fatre Coefficientof variation Measures variation infat reserves. (CV). energy serves and traits that surely are observ Cost/BenefitRatio thecost of thecontest to thebenefit of (CBR). Compares owning able, such as body length orwing span.) the site (both interms of theexpected futurereproductive success). Thus thereemerged the intriguingpossi Ina realecotype, thecost/benefit ratio would vary fromindividual to individual.In the model thatdamselflies do not assess their we assume each individualhas thesame CBR. bility opponents' strength at all. Accordingly, in a collaboration with An animal knows itsown reserves,but not the reservesof itsopponent. Marden and Lee Dugatkin of theUni versity of Louisville, one of us (Mester ton-Gibbons) a model in A site isworth more toan animalthat has reservesof which a safe developed greaterremaining energy, is which a is that assumptionfor a contestover a matingterritory. key assumption players know only theirown reserves. In the re sultant game, known as a "war of attri An opponent's unknown energy reserves are drawn at random. tion," a strategy is the proportion of an animal's initial reserves that it is pre to in a contest An animal's is the of its reserves that it is to in pared expend prolonged strategy proportion energy willing expend over a site. A second as contesting a site. disputed key sumption is that the value of winning is proportional to thewinner's remain determinewhether an stable exists Ecological parameters evolutionary strategy (see graph ing reserves. The more an animal has Ifone thenthe natureof the on below). exists, strategydepends those parameters. left,the more successful itwill be in at = a food or de Evolutionarystable proportion tracting mate, finding 1+CBRXf(CV) fending its territory (and hence in pro /(CV) increases from0 to 1 as CV increases from0 to 1, so theproportion exceeds 1/2. ducing surviving offspring). These If is not then of the can (CV, CBR) evolutionarilystable, any positiveproportion population assumptions determined the strategy be invadedby a mutantadopting proportion 0 (thatis, giving up immediately). set and the reward formula. But what about the ecotype? Since a model ismerely a caricature of nature, it effectively reduces a real ecological en vironment to a few parameters, with different values for different ecotypes. In thewar-of-attrition game, there are only two such parameters, each a num ber between zero and one. The first, a coefficientof variation,measures the dis persion of energy reserves about their mean. For example, a coefficientof vari ation of 0.6means thatone standard de viation in fat reserves is 60 percent of the mean. The second parameter, a costlbenefitratio, compares the reproduc tive cost of a spent unit of fat reserves to the eventual winner's reproductive ben efit from a saved unit. With each component of the game 0.4 0.6 identified,we can look foran evolution coefficientof variation ary stable strategy. In general, because reserves ina (fat damselflypopulation) an evolutionary stable strategy is a pop ulation strategy, the parame 2. Existence of a "no-assessment" ecological Figure evolutionary stable strategy in the war-of-attrition ters determine whether one exists. In between male damselflies on two the variation in fat en game depends ecological parameters: this an reserves particular game, evolutionary ergy in the population and the relative cost of the contest compared to the benefit of a stable exists (for reasons de owning mating site. In this instance, an evolutionary stable strategy exists if the coefficient of strategy scribed if the coefficientof varia variation of energy reserves exceeds a critical threshold (white line), which increases with the below) never more tion exceeds a critical which cost/benefit ratio but is than about 0.5. The damselflies do not know their opponents' threshold, reserves can a fat energy but achieve balance between the costs and the benefits by responding increases with the cost/benefit ratio but to the distribution of reserves in the population. is never much more than about 0.5. The

336 American Scientist, Volume 86 coefficient of variation forMarden's damselflies is 0.51,which would fallbe low critical if the cost/benefit ratiowere between 0.99 and 1.However, in prac tice the cost/benefit ratio is likely to be considerably less than 0.99. Thus we could assume that fat reserves among damselflies are variable enough that an evolutionary stable strategy involving no assessment of opponents' strength could exist. At this evolutionary stable strategy, both contestants are prepared to expend at least 50 percent of their initial re serves on the contest, although only the loser actually does so.We can verbally describe the reason for the stability of the no-assessment strategy. Being pre pared to expend too small a proportion of initial reserves may mean ceding needlessly toweaker opponents (who would otherwise lose), whereas too a high proportion may mean wasting reserves needlessly against much stronger opponents (who would win in any case). Although animals do not know the reserves of their actual oppo nents, they achieve a balance between trade-offsby responding to thedistribu tion of reserves among the population. Marden later staged further dam selfly duels in conjunction with Bob Rollins of Pennsylvania State Universi and he data sets. 3.Mantis ty, pooled his Al Figure shrimps weakened by molting will threaten and successfully deter intruders de their to a success though the percentage ofwins by fatter spite inability win fight. The of theweakened shrimp's bluff raises the question of all mantis do not threaten an males fell from 90 percent to 86 percent, why shrimps intruder. The authors argue that the behavior of the was strong and weak mantis can be to it still remarkably high. Now, judi shrimps explained by appealing game theory. (Photograph of L. Caldwell, of California, cious approximation is the essence of courtesy Roy University Berkeley.) modeling?effects that are small in a real are absent no-assessment a contest population typically model, ends stable strategy: one with a high coeffi from a we model. For example, would when the loser gives up after using a cient of variation. an expect 86 percent win rate for fatter fixed proportion of its reserves. So the males in the real to world translate into no-assessment hypothesis predicts a Reward Structure in a Game a rate 100 percent win for fattermales in positive correlation between final loser Several years ago, one of us (Adams), themodel. And this is what reserves precisely and contest duration. And, in in collaboration with Roy Caldwell at because both contestants are contests over 500 happens seconds, the variation the University of California, Berkeley, to reserves reserves prepared deplete their initial in loser was found to explain observed a series of contests between the same The skinnier 29 of the variation in or by proportion. percent duration. stomatopods, mantis shrimps, of the one first. In It invariably gives up other is tempting to infer from these re species Gonodactylus bredini.These crus no words, although there is assessment, sults that the no-assessment hypothesis taceans inhabit cavities in coral rubble. the fattermale always wins. is twice as likely to be correct. But we If one intrudes upon another, the resi Thus the assessment and no-assess should desist, because 14 percent and dent often defends its cavity by threat ment both fatter 29 are so hypotheses predict that percent both much less than ening with a pair of claw-like ap males win. But there is also a 100 are always percent. The results really incon pendages. These threat displays often difference. The assessment hypothesis clusive. Nevertheless, our attempt to re deter intruders, so that contests are set a correlation between predicts negative solve the initial paradox has yielded a tled without any physical contact. A difference and contest new on strength dura valuable insight animal contest surprising observation is that when tion. in the a Although, pooled data, behavior, namely, that pattern of vic stomatopods are weakened by molting, Marden detected such a correlation in toryby stronger animals need not imply so that they are completely unable to contests 500 the that is exceeding seconds, strength being assessed. More fight, they threaten more frequently variation in strength difference could over, the analysis indicates the kind of than animals that are between molts. 14 of the variation in we explain only percent population which could expect to Furthermore, threats by weaklings of in contest duration. in a By contrast, the find such no-assessment evolutionary tendeter much stronger intruders,who

1998 July-August 337 would easily win a fight if therewere truder responds by either attacking or bravado thatbears no special cost if the one. In other words, the weaklings fleeing.We assume that animals vary in signaler is not attacked, but which adds bluff. But if the very weakest members weakness, that is, in how much their an additional cost, the threatcost, if it is a of the population can threaten prof strength falls short of the maximum attacked by stronger opponent. In ad itably,then why don't all animals threat strength to be found in the population. dition, if there is a fight,both contes a en? If the display can be given by ani We also introduce a reward structure tants pay a combat cost, consisting of mals that cannot back itup, thenwhy that differs from that assumed by mod fixed cost,which even the strongest ani do their opponents respect it? els of "honest" signaling. Specifically, mal pays, and a variable cost that in a To explore this paradox, we devel threatdisplays increase the vulnerabili creases with weakness at constant rate oped a game inwhich a resident can ei tyof the signaler to injury inflictedby its of marginal cost. ther threaten or not threaten, and an in opponent. The threat is thus a display of The threat cost, the fixed cost and the marginal cost together comprise Threat Game the model ecotype. We also assume that, if there's a fight, the stronger ani mal wins. because the molt A fixedcost of escalating to physical combat. Finally, condition of is not exter Amarginal cost of a unitof weakness. stomatopods we assume war A threatcost, which a residentpays ifit threatens, is attacked and losesthe ensuing fight. nally visible, (as in the contestant Altcosts are measured interms of expected future reproductive success. of-attrition game) that each Strengthis assumed tobe uniformlydistributed between 0 (weakest)and 1 (strongest). is unaware of its opponent's strength. The combatcost varies between fixedcost forthe animalto fixedcost + cost strongest marginal So its own strengthmust determine its forthe weakest. Threat cost can be operationallydefined as thatpart of thetotal cost of combat behavior. whichcould have been avoidedby nottheatening. For this particular reward structure, Informationsl?uetuto#^ "}t there is always an evolutionary stable at which the weakest and An animalknows itsown strength,but not thestrength of itsopponent. A resident'sdecision to strategy threatenor notprecedes an intruder'sdecision to attack or flee. strongest animals both threaten when resident, whereas those of intermedi ate strength do not (Figure 4, left).Why A site isworth the same toeach animal.Assume thatthe value ofa site isone unitof such a counterintuitive result? All resi reproductive success. dents face a similar trade-off: Threats deter some opponents without the ne of but if the An opponent'sunknown strength is drawn at randomfrom the uniform distribution tor thepopulation. cessity fighting, opponent is stronger and chooses to attack, then the threat increases the vulnerability of Providedthat the marginal cost ispositive and thethreat cost ispaid onlywhen theresident is the signaler. The weaker the signaling attackedand thereis a stable As the stable loses, uniqueevolutionary strategy. usual, evolutionary animal, themore likely it is to pay the strategydepends on theecological parameters (see graphsbelow, where thestrategies are plotted of its increased fixedcost tor constantvalues of cost and threat Ifthe cost is0 or if price vulnerability. against marginal cost). marginal That's animals of intermediate thethreat cost ispaid when theresident is attacked (regardless of whether it wins or loses),then why cannot afford to but thereis no evolutionarystable strategy. Thus, theevolutionary stable strategy is a consequenceof a strength threaten, can. is veryspecial rewardstructure, which themodel identifies. stronger arom?is This essentially an instance of the handicap principle.

1.0

c a> to ?0.5 ce i c cd intruderflees

? ? ? 0.0 I I ?r-n?r 0.5 0.5 1.0 0.0 0.5 1.0 fixedcost fixed cost fixedcost (intrudernot threatened) (intruderthreatened)

on Figure 4. Strategy of a mantis shrimp in the threat game depends its strength and the relative cost of fighting for residents (left) and intruders are (middle and right). Game theory suggests that residents will threaten (bluff) when they weak (green) because they have little to lose, whereas the strongest residents threaten (orange) because they are unlikely to lose. In contrast, residents of intermediate strength (blue) do not threaten because or on the costs of losing exceed the benefits of threatening. The threshold for the intruder's decision to attack flee depends whether it is threatened a (middle) or not (right) by the resident. This threshold for the intruder's strength is raised if it is faced with resident that threatens.

338 American Scientist, Volume 86 an own Figure 5. Spiders of the species Oecobius civitas will relinquish a hiding place to intruder despite the advantage that usually accompanies a a ership. The evicted spider will similarly displace another spider from its hiding place, potentially initiating domino effect of evictions until spi an der finds an empty hiding place. This paradoxical behavior may be understood in the context of evolutionary game inwhich the spider's prob a ability of winning a fight is compared to the probability of surviving period of searching for another hiding place.

However, themodel illustrates a point According to a study by J.Wesley those thatdisplay in either role follow a lacking from previous discussions of Burgess, populations of this tiny spider Dove strategy.These four strategies im handicaps, namely that the benefits of live in darkness on the undersides of ply an information structure, namely, threats are greater forweaker animals, rocks. If a spider is disturbed from its that animals know their roles. particularly those that have no other hiding place, it is apt to enter the hiding Using a simple game with these four means of driving off competitors. place of another,which, if in residence, strategies,Maynard Smith showed that These animals would be unlikely to does not attack the intruder,but instead only theHawk strategy is evolutionarily win any of the contests against oppo departs to find a new retreat.A domino stable if costs are low enough, whereas nents that are deterred by threats. So effect can ensue, with retreats succes theBourgeois and anti-Bourgeois strate themodel shows a potential resolution sively changing ownership until even gies are evolutionarily stable ifcosts are of the paradox: The net costs of bluff tually a spider finds one unoccupied. high enough. But when two evolution ing are lower forweak animals than This behavior is inherently paradoxical ary stable strategies exist, thepopulation are ones. a home-court ad can at one they for stronger Bluffing because, assuming only be of them,and Maynard therefore forms a part of the evolution vantage, the prize always goes to the Smith's game could not saywhich. ary stable strategy. contestant likelier to lose an actual fight. One of us (Mesterton-Gibbons) incor How can we make sense of this? porated Maynard Smith's strategy set The Ecotype in a Game As usual, when a behavior is fixed, into a more elaborate model. Each ani As the damselflies exemplify, contests we expect tounderstand itas the evolu mal has a finite number of periods in between animals of unequal strength tionary stable strategy of an evolution which to find a site,which is essential for are usually won by the stronger one. ary game, with effects that are small in reproduction. Itdoes notmatter whether Suppose, however, that the animals are the real population being absent from a the site is acquired early or late, as long equally strong.What advantage could model. Thus, we expect butterfly be as it is owned by the end of the lastperi either then have? One possibility in havior to correspond to an evolutionary od. The number of periods is unknown, competitions for resources is owner stable strategy at which owners always but all animals have the same probability ship. Indeed evidence abounds, in (as opposed to usually) win, and O. civ of surviving pr?dation each period. species as diverse as baboons, butter itas behavior to an evolutionary stable There are more sites than animals, but flies, lions and red deer, that ifanimals strategy at which owners always lose. the search for a site is random. So a va perceive themselves to be in the sepa And, in both cases, we expect fighting grant animal may search in vain, and rate roles of owner and intruderwhen to be absent (as opposed to rare). That even if itfinds a site itmay be occupied. contesting a permanent resource, then is, inMaynard Smith's terminology,we In that case, the animal can either con the owner usually retains itwith little expect butterfly behavior to follow a tinue to search or contest the site. If it serious fighting. There is nothing'para Bourgeois strategy?attack if an owner wins, then itbecomes an owner, and the owner an owner must doxical about such respect for but be non-aggressive (or display) if previous search again. ship. But wouldn't it surprise you ifan intruder.O. civitas behavior reflects an There's a catch to this, however. imals avoided serious fighting, not anti-Bourgeois strategy?display if an When there's a serious fight, the loser because intruders retreated, but rather owner but attack if an intruder. Like is so seriously injured that it can no because owners fled? That iswhat ap wise, animals that invariably attack, re longer search, and hence cannot repro pears tohappen in a species ofMexican gardless ofwhether they are owners or duce. Even a winner may suffer injury, spider, Oecobius civitas. intruders, follow a Hawk strategy, and and have lower reproductive success

1998 July-August 339 Bourgeois owner and a Bourgeois in truder, or two Doves, would merely * display; and a Hawk would always Probabilityofsurviving a period of searchingfor a sib (a functionof on thespiders), * predatori scare off a Dove, in either role. This re Owner'sprobability ofwinning a fight(the resource-holding potential), assumed toexceed 0.5. * ward and information structure results Probabilityper searchperiod of a site. * locating Ratioof number of animals tonumber of sites. in a six-parameter ecotype. * Probabilityof injuryinwinning a fight. Although the evolutionary stable * Ratioof site value foran ownerto thatfor an owner. injured uninjured strategy depends on all six ecological parameters, in terms of our paradox it depends critically on the animal's fight Animalsknow whether they are ownersor intruders. ing ability and the probability of its sur vival. From Figure 6 it is evident that only theHawk strategy is evolutionari A site isworth the same toeach animal.Assume thatthe value;of? site isone unitof ly stable if survival is sufficiently low. Despite the risk of injury, it is better to fight than to hope to find a vacant site Searchinganimals are equally likelyto discover any site ; before the competition ends. At higher probabilities of survival, however, the Bourgeois or the anti-Bourgeois strate Hawk:Attack as owner,and attackas intruder. gy is evolutionarily stable. To see why, Bourgeois:Attack as owner,and showa non-aggressivedisplay as intruder. suppose that the resource-holding po Anti-Bourgeois:Non-aggressive as owner,and aBackas intruder.. display tential remains constant, but that Dove: Non-?ggressivedisplay as ownerand intruder. pr? dation decreases slowly with time (so that the probability of survival increas es with and that the Thisgame differsfrom the other two in having multiple evolutionary stable strategies. The most slowly time) popu interestingdependence of theevolutionary stable strategy is thaton survivalprobability and the lation tracks its changing environment resource-holdingpotential (for fixed values of theother four parameters). This dependence isquite by continually evolving to a new evo so is cartoonedin the b?tow. complicated,and merely graph ; lutionary stable strategy.Then we think of the population as a point moving horizontally to the right in Figure 6. As this point migrates, theHawk strategy must eventually cease to be evolution arily stable. Why? Consider a lone Bourgeois mu tant in an otherwise Hawk population. Because the Bourgeois animal behaves like a Hawk at home, being an owner has no effecton its reward. So a mutant Bourgeois has a higher reward than the population strategy if a Bourgeois in truder does better than an Hawk in truder.Now, a Bourgeois intruder runs from a Hawk owner, hoping to find an empty site eventually, but a Hawk in truder fights, hoping towin a site im 1 If is survivalprobability mediately. pr?dation sufficiently pr?dationhigh pr?dation low low and the resource-holding potential is sufficiently however, the first 6. stable in the on an high, Figure Evolutionary strategies iterated hawk-dove game depend animal's ismuch more to be realized chance of when for a site and the that itwill win a hope likely surviving pr?dation searching probability than the second. Thus the The trend in this is for animal to evolve from a to a non Bourgeois fight. general game populations fighting the so will as a a fares better than Hawk and fighting strategy pr?dation pressure decreases. Above certain probability of winning fight as owner a in the (dashed line) population will evolve to use a Bourgeois strategy rather than an anti spread population. a mutant in Bourgeois strategy. The Mexican spider's anti-Bourgeois strategy?in which it is non-aggressive Similarly, anti-Bourgeois as an owner a as an a will (ormerely displays) of site but attacks intruder?can be explained in this con Hawk population behave differ text if an owner's of a is modest at least as an owner. runs an probability winning fight relatively (though above 0.5), ently only It from until the reaches the blue population region. intruding Hawk, hoping eventually to find a vacant site, whereas a Hawk an a than uninjured animal. So there's one, indicating that the owner ismore owner would fight, hoping towin im trade-off between the uncertainty of likely towin. mediately. If pr?dation and the re own search and the risk of injury.The Whether animals fight depends on source-holding potential are both suffi an er's probability of winning actual their strategies. A Bourgeois owner ciently low, then the firstof these hopes fight is called its resource-holdingpoten and an anti-Bourgeois intruder, or two ismuch more likely to be realized than tial. It a is number between 0.5 and Hawks, would always fight; an anti the second. Thus the anti-Bourgeois

340 American Scientist, Volume 86 fares better than Hawk and so to L. and . . the will potential is precipitate actual fights, Dugatkin, A., Reeve. 1998. Game and Animal Behavior. New York: Ox spread in the population. which may be far from easy in a species Theory ford Press. In summary, under decreasing pr?da as reclusive as the spider O. civitas. University a Grafen, A. 1990. as tion, Hawk population evolves to In fact, the difficulties of testing the Biological signals handicaps. Journal ofTheoretical Biology 144:517-546. Bourgeois if the resource-holding po predictions of evolutionary game theory Hammerstein, R, and S. E. Reichert. 1988. tential is relatively large, but theHawk have led some to question itsvalue. But Pay offs and strategies in territorial contests: ESS population evolves to anti-Bourgeois if games are not valuable because solely analyses of two ecotypes of the spider Age the is rela to test new ideas. resource-holding potential they suggest ways lenopsis aperta. Evolutionary Ecology tively small (Figure 6). Ifpr?dation falls They are also valuable because they al 2:115-138. then the will re low us to the of a verbal . com sufficiently, population explore logic Hodge, A., and G. W. Uetz. 1995. A or of behaviour of colonial main at either the Bourgeois the anti argument rigorously, assuming biologi parison agonistic from desert and Bourgeois strategy depending on the cally realistic ecotypes, and to determine web-building spiders trop ical habitats. Animal Behaviour 50:963-972. initial resource-holding potential. In ei when it is true and when it is false.As R. A. 1998. Game and com ther case, a these cases illustrate, often Johnstone, theory non-fighting population game theory munication. In Game and Animal Be evolves from a of demonstrates what is difficult to intuit. Theory population fighters. L. havior, ed. Dugatkin and H. Reeve. New To the extent that lower in As a result of du pr?dation exploring damselfly York: Oxford University Press, pp. 94-117. creases the chance thatnot and els,we now understand that . fighting victory by Krebs, J.R., and B. Davies. 1993. An Intro will a site animals need not that searching eventually yield stronger imply duction to Behavioural Ecology. 3rd edition. without injury, these results agree with strength is being assessed. As a result of Oxford: Blackwell Scientific Publications. those of Smith. But the new we now Maynard investigating stomatopod strife, Marden, J.H., and J.K. Waage. 1990. Escalated territorial contests are model goes further to suggest a resolu understand how bluffing can persist at a damselfly energetic tion of our If an And wars of attrition. Animal Behaviour paradox. ownership high frequency. through analyzing 39:954-959. asymmetry exists, then the resource spider spats,we now understand how a is almost of can Marden, J.H., and R. A. Rollins. 1994. Assess holding potential always high non-fighting population usurpers reserves en ment of energy by damselflies to the in a evolve, under enough keep population decreasing pr?dation, gaged in aerial contests formating territo Bourgeois strategy under conditions of from a fighting population that ignores ries. Animal Behaviour 48:1023-1030. low However, there are rare the of pr?dation. asymmetry ownership. Maynard Smith, J. 1982. Evolution and theTheo environments inwhich the resource non-assessment Perhaps of strength, ry ofGames. Cambridge: Cambridge Univer Press. holding potential is low enough to keep high-frequency bluffing and sequential sity in an are rare M. 1992. varia the population anti-Bourgeois displacement all remarkably in Mesterton-Gibbons, Ecotypic tion in the Hawk-Dove strategyunder conditions of low nature. For the domino effect asymmetric game: pr?da example, an when is Bourgeois evolutionarily stable tion. Does O. civitas represent such an has not been observed in colonial spi strategy? Evolutionary Ecology 6:198-222. But without any ders other than O. civitas.But it is exception? Perhaps. rarely H. Marden and L. A. evidence that the resource the that our inter Mesterton-Gibbons, M., J. empirical commonplace piques 1996. On wars of attrition with is indeed low inO. civ est. it is behavior that Dugatkin. holding potential Rather, strange out assessment. Journal of Theoretical Biology we can do no more than our us itas, conjecture. engages attention and spurs on 181:65-83. to even of the deeper understanding, Nur, .,and O. Hasson. 1984. Phenotypic plas The Value of Game Theory commonplace. In that regard, evolu ticity and the handicap principle. Journal of Theoretical 110:275-297. It is not unusual foran exercise in game tionary games have proved theiruseful Biology theory to remain partially inconclusive. ness over and over again. They have be Parker, G. A., and D. I Rubenstein. 1981. Role reserve On the one hand, models come tools assessment, strategy, and acquisition game-theoretic indispensable analytical of information in animal con are valuable because toward in behavioral asymmetric they suggest ways progress ecology. flicts. Animal Behaviour 29:221-240. to testnew ideas. The model damselfly S. E. 1986. as a test of a reserves Riechert, Spider fights suggests test?whether the of Acknowledgment American Scien This work was award evolutionary game theory. the loser correlate positively with contest supported by tist 74:604-610. duration?for an stable #9626609 from theNational Science Foun evolutionary Riechert, S. E. 1998. Game theory and animal in contestants cannot dation and a in Science and strategy which the by Fellowship contests. In Game Theory and Animal Behav theDavid and Lucile H. New assess their opponents7 strength. The Engineering from ior, ed. L. Dugatkin and Reeve. Packard Foundation. York: Oxford Press, 64-93. stomatopod model suggests a test? University pp. whether animals that threaten and lose Steger, R., and R. L. Caldwell. 1983. Intraspe Bibliography cific bluffi A defense strat pay costs than those that lose deception by ng: higher E. and R. L. Caldwell. 1990. of moulted Science without the idea of an Adams, Sv Decep egy newly stomatopods. threatening?for tive communication in of 21:558-560. stable with asymmetric fights evolutionary strategy partial the crustacean, stomatopod Gonodactylus Zahavi, A. 1977. Reliability in communication the model bredini Animal Behaviour 39:706-716. bluffing. Finally, spider sug systems and the evolution of altruism. In a an E. and M. Mesterton-Gibbons. 1995. . gests test?whether intruder is al Adams, S., Evolutionary Ecology, ed. Stonehouse and The cost of threat and the C. M. Perrins. London: most as likely as an owner towin an ac displays stability Macmillan, pp. of deceptive communication. Journal of The 253-259. tual fight?for the idea of an oretical Biology 175:405-421. stable strat Zahavi, A. 1987. The theory of signal selection anti-Bourgeois evolutionary J.W. 1976. Social Scientific some On the other a test Burgess, spiders. and of its implications. In International egy. hand, suggesting American. March, 100-106. Symposium of Biological Evolution, ed. V. P. is not the same as N. B. 1978. Territorial defence in the thing conducting it, Davies, Delfino. Vari: Adriatica Editrice, pp. so wood and the difficulties of doing should speckled butterfly (Pararge aegeria), 305-327. not For the resident wins. Animal Behaviour be underestimated. the always Zahavi, A., and A. Zahavi. 1997. The example, 26:138-147. Handicap tomeasure New York: Oxford Press. only way resource-holding Principle. University

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