The Evolutionary Stable Strategy (ESS)
Parental versus Satellite Behavior in Bluegill Sunfish
Aggression, Male Assessment, and ESS games
The Hawk-Dove and the Evolution of Lethal Fighting
Asymmetric versus Symmetric Contests and Badges of Status
The physiological and behavioral basis of Resource Holding Power
The Rock-paper-scissors game and the evolution of alternative male strategies
Introduction to the rock-paper-scissors game
"Play-off" matrix and male behaviors
"Pay-off" matrix and fitness
The rock-paper-scissors cycle
In the introduction to Sexual Selection, I described two ways of generating variance in mating success:
It is important to realize that these two avenues for selection are not necessarily mutually exclusive. Traits that lead to female choice may also be effective weapons during male-male competition. For the moment, we will take up the idea of male-male competition and explore the link between female choice and male contests next week.
In previous lectures we developed the idea of an evolutionary stable strategy as a behavioral phenotype that cannot be invaded by a mutant strategy. When a mutant arises in a population of individuals that display the ESS phenotype, the mutant does not spread. By a mutant strategy, I mean any behavioral phenotype that does things in a different way compared to the ESS. Seems like a pretty broad definition. The ESS must be uninvadable to any strategy that the scientist can conceive (...based on the biology of the organism). If the ESS can be invaded, then you might be expected to find a diversity of behavioral types in the population.
A second condition for the ESS is that it should also be a strategy that has a definite advantage when rare. For example, in the t-allele example of genic selection it is clear that the t-allele has a tremendous advantage when rare and will increase in frequency at the expense of the wild type allele. However, the t-allele cannot exist in the pure homozygous form and thus the t-allele is not an ESS because in the pure homozygous form all males would be sterile and the population would go extinct. The case of the t-allele introduces the concept of a mixed strategy. The two alleles will exist in a stable frequency of t- and +-alleles and neither will be eliminated from the population.
In general, when we consider ESS analyses we are likely to show that many populations will exist in a mixed strategy state. We are usually not trying to find an ESS which would consist of a pure strategy. How boring life would be without a little diversity.
Why we are interested in differences in male reproductive phenotypes? When Behavioral Ecologists go out into natural populations, they invariably find that males have very different was of trying to get mates. However, in some populations there appears to be only one kind of male type. Trying to find an explanation for this kind of among population variation is the goal of behavioral ecology. Trying to explain the coexistence of a diverse set of behavioral types is also the goal of these kinds of studies. How can such diversity be maintained in the face of very strong selection favoring one type over another?
What kinds of male types are you likely to encounter if you head out into the wild. Well alternative males strategies are usually broken down into the following kinds:
Aggressive males that tend to have many females and are called polygynous.
Regular old male that is monogomous and usually has one mate (the standard by which we measure male success).
Sneaker or Satellite males that are usually not very conspicuous, but live around the edges of the more dominant males in the population.
The kinds of males present in the population also depends on the kind of care that the species provides to its young. For example, in birds males tend to be monogamous is they also participate in the rearing of young. However, in fish the parental male types need not be monogamous, for a parental male fish could entice many females to spawn in the nest that he guards.
To understand Alternative Male Strategies a little better we will explore two model systems for studying male reproductive success:
These two examples contrast the control mechanisms underlying the development of the alternative male strategies. In one case, it has been argued that the male types are condition-dependent strategies and environmental factors influence development. In the other case it has been demonstrated that the types are genetically determined.
Male Bluegill sunfish come in three different size morphs:
Bluegill sunfish have external fertilization and Mart Gross has calculated the probability that a male of a given morphotype will be successful in fertilizing a female from the amount of time he spends in the vicinty of females. Based on these calculations, males of all three mating types have approximately equal fitness.
An important component of these three behavioral strategies is the fact that the male types mature at different ages. The territorial males mature in six to seven years whereas the other two male types mature in two to three years. In addition, the two smaller morphs do not have all the costs associated with parental care strategy of the territorial male. The other two morphs parasitize the parental effort of the territorial male. Eggs do not survive unless they are cared for by a territorial male. In terms of ESS, neither of the two smaller male morphs can exist in a pure form, whereas the territorial male can exist in a pure form. However, the large territorial male should be able to be invaded by the other two "mutant" strategies.
Gross has argued that such morphs are condition dependent tactics in which all males have the capability to become any of the alternative types. Such, "decisions" are based up the condition of the male. Males that are in poorer condition become the smaller male types and the males that are in the best condition adopt the territorial-holder strategy. Such condition-dependent strategies are contrasted with genetically-based control over morphotype development.
Marine isopods come in three dramatically different size morphs:
What do these male types correspond to in terms of behavioral strategies. The large alpha males will toss other males out of the sponge if they get hold of them. Thus they rely on their strength and large size to toss out other alphas -- the biggest alpha might have a better chance of tossing out smaller alphas. The beta males, on the other hand, pretend to be females, and solicit courtship from an alpha! And finally, Shuster has described gammas as little sperm bombs (personal communication). They lurk around the sponge waiting for the opportunity to dive bomb a pair in copulo.
Shuster and Wade addressed the first issue regarding the stability of the three kinds of males. In the long run, will one morph tend to dominate because it has higher fitness? Shuster has also shown that there is a fairly simple genetic basis to the three types of males with the traits being controlled by one locus with three alternative alleles (the details need not concern us here). The genetic control of the isopod mating system may be different from that seen in Bluegill sunfish which are thought to be conditional strategies.
The null hypothesis in this case is that the morphs have the same fitness (male morphs might be expected to persist in the long run).
The alternative hypothesis is that one morph has higher fitness, and would tend to increase in fitness (and perhaps in the long run become the only male type present in the poulation).
Shuster and Wade found that they could not reject the null hypothesis, they did not detect any statistically significant differences in the mean number of females that each male type was likely to produce. There was no evidence of any gross difference in the number of matings achieved by each morph.
Well not really... Individual alpha, betas, and gammas did show variance in mating success. Some aphas got mates others got less. There may be strong selection among alphas to be a good alpha (e.g., strong figher), or for betas to be "good at being sneaky". Shuster and Wade's study also was conducted over many generations in natural populations and they computed mean success averaged over all of these generations which would reflect the long-term equilibrium -- all males persist in the population. There may also be differences among the male types if one considers shorter time scales, and smaller spatial scales.
For example, Shuster and Wade had evidence that fitness in ispopods was also strongly dependent on who was in the "neighborhood". These isopods live in sponges with little chambers. A large alpha may have other alphas, betas and gammas present with him or the alpha may be alone. The kinds of neighbors that the male has influences how successful he is as an alpha.
For example, an alpha that lives in a chamber with a single female and a single beta is going to sire the offspring of the female. The beta will not be successful against the alpha.
However, an alpha with lots of females is at a disadvantage with a single beta. The beta is likely to sire 60% of the offspring. This could be due to sneakiness of the beta males when the alpha has lots of females to keep track of. The beta manages to copulate with at least enough females so that he is the sire of most of the offspring.
When the fitness of a male depends on the frequency of the other mating types, we refer to sexual selection as being frequency dependent.
It is the nature of frequency dependent selection that determines who will win and who will loose in the long run, or if all male mating types will be preserved. A key condition that would prevent a unique ESS (e.g., only one male type wins) would be an advantage to each strategy when rare. This is the another way of stating that a rare mutant can always invade the population. Consider a male morph that is declining in frequency because one other type has an advantage. If it has an advantage when rare, then it will be protected from elimination in the population. As it becomes rare, the fitness of the rare morph increase. We will explore this idea in greater detail using the example of the rock-paper-scissors game that is played out in lizards.
Arguments about the existence of male strategies that are based on an argument of equal fitness are inherently an argument about the pattern one would expect to see in natural populations. Males should have equal fitness if they are to be stable over the long-term.
In contrast, arguments about the frequency dependence of the male strategies are arguments that describe the process of natural and sexual selection. Such process-based explanations have more merit as they might be used to predict the dyamics of evolutionary change.
Finally, the equal fitness arguments are counter to the way we traditionally construct null versus alternative hypotheses. The null hypothesis is that the male types have equal fitness and thus the morphs will persist in a population. The alternative hypothesis is that the morphs do not have equal fitness and one morph will ultimately pervail. We know that there are a diversity of morphs so the goal is really to collect enough data to accept the null hypothesis. This is backwards to the way we traditionally construct null versus alternative hypotheses. We usually want to collect enough data to reject the null hypothesis and accept the alternative hypothesis.
The process-based arguments avoid such statistical problems by identifying the environmental conditions that leads to a change in fitness. In the case of male strategies, it is the social environment that leads to a change in fitness. As a morph becomes rarer because it has low fitness when competing against the rare mutant, a point will be reached when the fitness of the declining morph turns around. It becomes so rare that it begins to increase in frequency. The advantage of a rare morphotype is a powerful mechanisms for preserving variaton.
ESS models have been used extensively in evolutionary theory (Maynard Smith and Price 1972, Maynard Smith 1982, Maynard Smith and Parker 1976) to account for various features of animal fighting behavior, including:
All of these factors are believed to be involved in assessment of rivals, and have been incorporated into various models. Evolutionary game theory's early treatments of contest behavior was completely devoid of assessment -- the act of acquiring information regarding your rivals abilities. Symmetric contests were modeled, where contestants are identical in all but strategic properties (i.e. choice of behavior). In effect, there is nothing to assess in this type of contest, especially since conditional strategies are not included in the strategy set. These early models include the Hawk-Dove game and the War of Attrition. More advanced models consider information transfer between contestants and male assessment.
The Hawk-Dove game was designed in response to a ubiquitous phenomenon in animal conflicts: although contests are frequently vigorous, lethal fighting is rather rare.
How can this be explained in individual selection terms?
What is the evolutionary value of restraint?
The Hawk-Dove contests considers two strategies:
Hawk which fights at the drop of a hat. Always fight, even against other hawks.
The second strategy is Dove, which backs down as soon as the contest escalates to a fight.
The theory for the hawk-dove game shows that Hawk is an ESS, Dove cannot invade, and Hawk can always invade Dove. However, if the cost of fighting is too high for hawks, then Doves can invade because Hawks do each other in during their contests.
Maynard Smith and Price. 1972. The logic of animal conflict. Nature 246: 15-18.
The Hawk-Dove game shows that the advantage of fighting behavior can be offset by the cost of fighting, and that a cost benefit analysis can show that when resource value is low compared to cost of fighting, restraint is adaptive (actually this will be a mixed ESS).
Another simple model is the Symmetric War of Attrition , also proposed by Maynard Smith. This is also known as "the waiting game" because the winner of the contest, the individual that gains the resource, is the individual that is prepared to persist longer. This is a situation where there are an infinite number of possible strategies (persistence times), a continuous strategy set. The cost of persisting is assumed to increase monotonically through time. When one individual gives up the other contestant gets all of the resource, and both individuals incur the cost of persistence to that point in time. Obviously each individual would do better by persisting longer than its opponents, and thus no pure persistence level would be evolutionarily stable. Mixed strategies allow an equilibrium: an unpredictable persistence time would be evolutionarily stable. At the ESS the fitness gain for each persistence time is equal. This is a game where no information is exchanged, since you can not learn how much longer your opponent will persist by observing how long your opponent has already stayed. Given this ESS, no assessment can occur here. This theoretical result was used to suggest that animal contests in general should not involve any displays of intent (in this model: persistence time), because such displays could be exploited by opponents. Of course, animal contests are NOT symmetrical usually!
Contests usually involve displays.
What is the evolutionary value of displays in animal contests?
Males can learn and advertize asymmetries.
The prediction that animals in contests should not reveal their intentions was derived from the symmetrical war of attrition, although this prediction was valid only under very restrictive conditions. In particular this was a symmetrical game in which the combatants were equally matched in ability and resource value. Revealing intent was not evolutionarily stable, since it could be exploited by cheaters using 'cheap talk'. If a cheater could detect intent, then it could try to bluff its way out of the contest by exploiting the information to its advantage.
Contrary to this prediction, empirical evidence quickly accumulated that showed that animals in fact do often vary their choice of display in a manner that is predictive of future behavior, and several models were constructed to explain why such behavior could be evolutionarily stable when they should not reveal much information. A model was proposed by Enquist, nicknamed the 'risk-right' model. this model suggested that cheating is precluded because increasingly effective threat displays are increasingly costly in terms of risk of retaliation, thus only individuals that are actually prepared to pay a high probability of retaliation can afford to use highly effective displays. This model predicted that display types that are increasingly effective in winning disputes are also increasingly likely to cause retaliation. Subsequent empirical work has supported this prediction.
Another model by van Rhijn and Vodegel, suggests that cheating is precluded because individual recognition will allow the detection of cheats, and select against cheating. Many animals display some form of neighbor recognition.
The basic experimental paradigm for testing for such rudimentary cognitive abilities involved in neighbor recognition is to use a playback experiment in birds in which a tape recording of the neighboring male's song is played at the territory boundary (Brooks and Falls, 1975; Wiley 1977, Godard, 1991). The response of the target male to the neighbors song is usually less extreme than the targets response to a strange male's song. Why is this the case? The Dear Enemy Hypothesis maintains that once males have established territory boundaries it is a waste of the male's time to continue in escalated conflicts with the neighbor. The two exist in a status quo in which they are still assessing one another, but presumably each is not likely to act aggressively because the other male has a home field advantage. Each male also has access to females and food and thus the motivation to "cross the line that is drawn in the sand" is low for both males. We can express these ideas in terms of the marginal value theorem with the added twist of risk involved in conflict. The marginal gains that are derived from increasing territory size are not worth the risks of an all out battle. However, if the bird hears a stranger at the boundary, the male must act to turn away the intruder. A targeted male in a playback experiment is much more agitated when he hears a strange male's song coming out of the speaker than if he hears a neighbor. Birds even have the capability to remember a neighbor's song across reproductive seasons (Godard, 1991).
Such neighbor-stranger experiments have also been performed on lizards, but in this case a challenger (stranger or neighbor) is tethered at some point in the targets territory and the reaction of the target is videotaped. Stan Fox has found that the target is more agitated in response to strangers than to his dear-enemy neighbor.
Falls, B. and Brooks, R.J. 1975. Individual recognition by song in white-throated sparrows. I. Discrimination of songs of neighbors and strangers. Can. J. Zool. 53: 1412-1420.
Falls, B. and Brooks, R.J. 1975. Individual recognition by song in white-throated sparrows. II Effects of location. Can. J. Zool. 53: 1412-1420.
Godard, R. 1991. Long-term memory of individual neighbors in a migratory songbird. Nature 350: 228-229.
Fox, S.F. and Baird, T.A. 1992. The dear enemy phenomenon in the collared lizard Crotaphytus collaris, with a cautionary note on experimental methodology. Anim. Behav. 44 780-782.
In the dear enemy situation it is thought the the neighbors have some sort of status quo in effect. You don't whack my back, I won't whack yours. What happens when one neighbor breaks such conventions (a non-aggression pact if you will), and invades the other males's territory? Rene Godard used the power of the playback experiment to test whether such "defecting" neighbors are treated differently after the incursion. She played the songs of neighbors on the territory boundary where the nieghbor (N) should be and also strangers at those locations (S). In addition she also played the song of the neighbor on the other side of the territory (XN), a place where the neighbor had no "right" to be. After such wrong-place incursions, the territory holder was usually much more aggressive at the boundary of the neighbor than if the playback occured in the proper place. The targeted bird went to the neighbors border and sang more as a kind of tit for tat response to the XN intrusion. The intrusion triggers much more aggression in the targeted male towards the perceived neighbor that intrudes.
Godard, R. 1993. Tit for Tat among neighboring hooded warblers. Behav. Ecolo. Sociobiol 33: 45-50.
Of course most animal contests involve asymmetries. A lot of attention has been directed at the effects of asymmetries on the strategic choices of animals. The more recent of these models are characterized by explicit treatment of acquisition of information about the opponent. War of attrition models first introduce asymmetry into contest behavior, of three types
- The simplest of the asymmetries can be thought of as a home field advantage. It is invariably the case that a territory holder has and advantage over intruders. <Experiment on Butterflies by Gilbert>
- The second kind of asymmetry is one in which one constestant has more to gain or loose from the battle and will thus be motivated to continue a prolonged contest. A classic case involves a territory holder versus an intruder. The territory holder has a lot invested in the territory. He has knowledge of safe retreats, the dear enemy relationships that have been constructed, knowledge of resource. All of this information makes the territory more valuable to the territory holder than to the intruder. To reconstruct all this information in a new territory would require a lot of effort.
- The most interesting kind of asymmetry is one in which individuals vary in their physical ability to hold onto the territory or resource -- they are more capable fighters. This is termed Resource Holding Potential.
The sequential assessment game models the acquisition of information within a contest and injects explicit decision mechanism into models of contest behavior. As the contest unfolds, each contestant is accumulating information about the opponent. Once enough data has been collected, a male may decide to end the contest and flee, or escalate to the next stage of the contest to acquire more and more information. Different displays and levels of escalation measure different attributes associated with fighting ability. Diminishing returns of increasing sample size within a single class of displays leads to escalating to the next display in which more information about the opponent might be gained. The aim of assessment strategies is to determine the Resource Holding Power or Potential of the opponent.
In asymmetric contests a male mating type which is stronger than the others would be expected to "advertise" this skill by some sort of badge of status. By walking around and displaying this badge of status, a very dominant individual could avoid most contests because other males would be unlikely to challenge such a powerful or skillful male. By avoiding unecessary contests the dominant individual could focus on contests with other more equally matched individuals that are likely to lead to a War of Attrition. Some advertising may be necessary on the part of the most dominant individuals even though the simple war of attrition models suggest otherwise, because the dominant can avoid many contests.
Resource Holding Power and associated Badges of Status have tremendous advantages in male assessment games, but those strategies are usually not cost free. In vertebrates, male secondary sexual characteristics such as large size, or elaborate ornaments and armaments are usually related to levels of circulating testosterone. More and more researchers are beginning to study the negative effect that such steroids have on other aspects of the organisms life history. For example, Marler and Moore (cited in Alcock) have shown that males implanted with T have reduced survival compared to controls in field trials. Such survival costs can be ameliorated by supplementing the T-implanted males with food. Thus, while badges of status are useful in information transfer that can avoid costly conflicts, such badges have additional life history trade-offs that counterbalance the fitness gains that arise from conflict resolution.
Classic examples of communication of Resource Holding Power include "roaring" in red deer (Clutton-Brock and Albon, 1978). In playback experiments, male stags that are presented with a red deer recording that plays for an unusually long time are more intimidated than males presented with a normal bout of roaring. They interpret the length of time that a male deer can roar as an index of Resource Holding Power, if better condition is required to be able to roar for a long period of times.
Another example of RHP communication involves the croak of toads. Males that are larger possess a deeper croak and male size is presumably related to RHP. Again playback experiments in which the frequency of the croak is manipulated can be used to alter the behavior of the target male to be more "intimidated".
Clutton-Brock, T. H. and S. D. Albon. 1979. The roaring of red deer and the evolution of honest advertisement. Behaviour. 69: 145-170.
If a mating system evolves individuals with badges of status which advertise their prowess, the situation is ripe for an interesting strategy to evolve to exploit this information in some way. It is not necessarily possible to evolve a better strategy which would entail additonal costs assoicated with the development of more "firepower". The individuals with a badge of status may have some weakness, perhaps in the perceptual system that could be exploited. The evolution of female mimicry in males is undoubtedly related to the exploitation of the information embodied in a badge of status, and an ensuing weaknesses that strategy entails. Rather than fight, the sneaker uses a deceptive strategy. We will explore this strategy in detail in the rock-paper-scissors game
Amuse yourself before lecture by exploring lizard land. Clicking on the links located below will take you to the virtual rock paper scissors game. I will go over the material in the following pages as a summary of the ideas presented on alternative male strategies.
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See Barry Morph into a Lizard. |
A brief pictographic overview of the male strategies and the rock-paper-scissors game where orange beats blue, yellow beats orange, blue beats yellow and orange beats blue to complete the cycle. |
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See Video clips that explore the symmetric and asymmetric contests among lizard males. |
Pages designed by Jeanie Vogelzang for a class project in Instructional Systems Technology at Indiana University. The pages introduce the rock-paper-scissors game through cartoons. |
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This is a browser for a database of real-life lizard personalities that will soon appear in the interactive web game. Typical life history profiles are provided for the three color morphs of male lizards. Also, see the atypical males -- that is, those rare and unique males that defy all stereotypes. Natural selection likes to tweak variation. |
| Slide Shows that provides an introduction to the rock-paper-scissors game. |  |