Magnus Enquist

Evolution of fighting behaviour: Decision rules and assessment of relative strength☆

Abstract A mathematical model of fighting behaviour is developed. The contestants belong to a population with varying fighting abilities and the fights consist of the repetition of one type of interaction. At each interaction in the sequence the opponents acquire some information about the true fighting abilities. The fights are seen as a motion of each opponent through a causal factor space; the current position of an animal in the space represents all information obtained by the animals so far. A decision rule (strategy) is a specification of what action to take at each point in the causal factor space. Evolutionarily stable strategies are calculated numerically and are found to be pure and unique. The distribution of fighting times and the probabilities of winning are calculated for pairs of contestants from a population using the ESS. Expected utilities are also computed and in the situations investigated they are fairly close to the maximum value that would obtain if the contested resource were divided equally between the contestants without any cost.

Evolution of fighting behaviour: The effect of variation in resource value*

A number of empirical studies have shown that animals adjust their fighting behaviour when resource value is changed. We apply evolutionary game theory to investigate how variation in resource value influences the evolution of fighting behaviour. Although no completely general predictions can be made concerning the cost of fighting and the probability of victory, for most situations of biological relevance the cost of fighting will increase when resource value increases and the probability of victory for an animal will increase when resource value is increased only to that animal. In order to study the effect of variation in resource value when differences in fighting ability exist and are assessed, sequential assessment games are developed for two situations. In the first situation, contestants do not know each others subjective resource value. In the second situation, there is an owner-intruder asymmetry where the owner is better informed about the value of the resource than the intruder. The models give predictions for fight duration, cost, and probability of victory. The predictions are compared with empirical data, and a good qualitative agreement is found.

Why copy others? Insights from the social learning strategies tournament.

It Pays to Be a Copy Cat Does it pay to copy what others do? Rendell et al. (p. 208) elected to copy Robert Axelrods 1979 tournament in which strategies for playing the iterated prisoners dilemma game were pitted against each other until an overall winner emerged—the tit-for-tat strategy. In the 2008 tournament, 100 social learning strategies designed to cope with a changing environment competed against each other; the winning strategy involved sampling the behaviors of other players periodically, rather than exploring the environment alone. Learning from what others do is more efficient than learning all on one’s own. Social learning (learning through observation or interaction with other individuals) is widespread in nature and is central to the remarkable success of humanity, yet it remains unclear why copying is profitable and how to copy most effectively. To address these questions, we organized a computer tournament in which entrants submitted strategies specifying how to use social learning and its asocial alternative (for example, trial-and-error learning) to acquire adaptive behavior in a complex environment. Most current theory predicts the emergence of mixed strategies that rely on some combination of the two types of learning. In the tournament, however, strategies that relied heavily on social learning were found to be remarkably successful, even when asocial information was no more costly than social information. Social learning proved advantageous because individuals frequently demonstrated the highest-payoff behavior in their repertoire, inadvertently filtering information for copiers. The winning strategy (discountmachine) relied nearly exclusively on social learning and weighted information according to the time since acquisition.

A test of the sequential assessment game: fighting in the cichlid fish Nannacara anomala

Many species have a repertoire of behaviour patterns that are used in contests over resources. It is likely that the function of these behaviour patterns is the assessment of asymmetries between con- testants in physical variables (e.g. size or strength). Theoretical models of fighting behaviour such as the war of attrition and the hawk-dove game do not incorporate any behavioural mechanisms allowing assessment, and, therefore, yield no predictions about the use of behaviour patterns. In a sequential assessment game, on the other hand, the assessment of asymmetries is a major activity during a fight. Recently, a version of the sequential assessment game with several behavioural options has been devel- oped, and here predictions from this model are tested using data from 102 staged fights between males of the cichlid fish Nannacara anomala. The model predicts that the sequence of behaviour patterns in a fight should be maximally efficient in assessing relative fighting ability. Specific predictions are that (1) the sequence should be organized into phases consisting of one or several behaviour patterns with constant rates of behaviour within a phase, (2) the division into phases should be independent of relative fighting ability, and (3) contests with great asymmetry in relative fighting ability should end in an early phase, whereas matched individuals may proceed through a series of escalations reaching a final phase of more dangerous fighting. The results show that the fighting behaviour of N. anomala is rather well predicted by the model.

Communication during aggressive interactions with particular reference to variation in choice of behaviour

Abstract Communication during aggressive interactions is discussed and defined primarily on the basis of functional considerations. A distinction is made between communication due to choice of action and communication due to performance of a given choice of action. Most attention is directed to choice of behaviour. Two models are developed to show that there are no arguments of general validity against communication through choice of behaviour or signalling as has been claimed. The first model is built on variation in fighting ability only and shows that choice of signal can carry information both about intentions (use of local strategy) and fighting ability. The second model which is based on the war of attrition with random rewards instead considers variation in subjective resource value. It shows that signalling of local strategy can be stable. It is concluded that evolutionary stability of communication through choice of behaviour is due to variation among animals in the utility of showing different behaviour patterns whereas communication by performance is due to a not easily removed relationship between the performance of a certain behaviour pattern and the factor communicated.

Effects of asymmetries in owner-intruder conflicts*

A common situation when animals compete for resources is that there is an owner-intruder asymmetry. Many studies show that owners win most of these conflicts. We investigate how various asymmetries between contestants that might be present in owner-intruder conflicts will affect the outcome and nature of such interactions. A mathematical model is used to represent a fight between an owner and an intruder. A fight in this model consists of a sequence of behaviours; at each step in the sequence the contestants assess their relative strength and each of them decides whether to give up or to continue to fight on the basis of these assessments. For such contests it is shown that the role asymmetry inherent in an owner-intruder conflict can give rise to an ESS where the individual in one role is less willing to continue fighting than the individual in the other role. We also consider that the resource might be more valuable for an owner than for an intruder and that owners might be stronger on the average. Asymmetry in average strength will appear when a resource typically is contested several times and strong individuals have an advantage in such contests. This process of accumulation of strong individuals as owners is studied in some detail. ESSs for contests with these different types of asymmetries are computed numerically. A common feature is that owners will be more persistent than intruders and from this some predictions follow, e.g., owners will win more also when opponents are of equal strength, contests won by the owner will tend to be shorter than those won by the intruder, and the longest contests will be those where the intruder is slightly stronger.

Evolutionary Stability of Aposematic Coloration and Prey Unprofitability: A Theoretical Analysis

Species that have evolved some defense against predators, here called unprofitable prey, often show aposematic (warning) coloration. The process whereby a predator learns not to attack unprofitable prey is an essential ingredient in the interaction between predators and such prey. Using learning theory and evolutionary game theory, we develop a model of predator-prey interactions, focusing on two characters: prey unprofitability and prey coloration. Both these characters are treated as one-dimensional variables, and it is assumed that variation in coloration causes variation in the rate at which prey are detected by predators. Regarding the two characters as strategies used by prey individuals, we determine evolutionarily stable strategies (ESSs). The coloration yielding the smallest possible rate of detection is called cryptic, and colorations yielding higher rates of detection are called aposematic. Two aspects of predator behavior are shown to be important for the stability of an aposematic strategy: a reluctance to attack prey more conspicuously colored than those so far encountered, and faster avoidance learning vis-a-vis prey with more conspicuous coloration. At least one of these factors must be present for an aposematic strategy to be an ESS. Similarly, two factors are important for the evolution of prey unprofitability: increased survival of attacks by a predator, and faster avoidance learning vis-a-vis more-unprofitable prey. If there is a nonpredatory cost associated with unprofitability, at least one of these factors must be present for an unprofitable strategy to be an ESS. The first factor mentioned, both for coloration and unprofitability, results in individual selection. The second factor, variation in the rate of avoidance learning caused by variation in the character, produces a selection pressure only if there is a correlation between prey phenotypes encountered by the predator. Such correlation may be the result of relatedness among prey individuals (resulting in kin selection) or repeated encounters with the same prey individual.

A strategic taxonomy of biological communication

The rapid increase in the understanding of biological communication has been largely theory driven. Game-theoretical models have completely changed how behavioural biologists think about communication. These theories are widely cited, but much of the theoretical work remains only vaguely understood by the wide majority of those who make use of it. Critical terms and concepts have not been sufficiently well defined to provide a solid common foundation for theoretical work as a unified whole. In this paper, we synthesize the relevant theoretical work, and describe its relation to more classical thinking within the study of animal behaviour. We present a taxonomy of biological communication and signals. This taxonomy is based upon the structure and properties of extensive-form game models of communication. We then classify many influential models of communication according to the structure of their extensive-form representations. Finally, we link signal taxonomy and extensive form to show how the temporal structure of a modelled interaction determines the type of signal the model will produce. We argue that this intuitive form of modelling is the correct one for unifying terminology and theory.

A test of the sequential assessment game : fighting in the bowl and doily spider Frontinella pyramitela

Male bowl and doily spiders (Frontinella pyramitela: Linyphiidae) engage in dangerous fights over access to females. Relatively smaller individuals are more at risk of fatal injury than their larger opponents. Males assess relative fighting ability during contests: smaller individuals tend to give up quickly. Fights occur between a male with information about the value of the contested female (number of fertilizable eggs) and an intruding male with less information. In this paper, a sequential assessment game (a game theory model of fighting behavior) is adapted to male combat in the bowl and doily spider to attempt a quantitative test. The model makes predictions about fight duration, probability of winning, and the occurrence of fatalities as a function of resource value and size asymmetry. Comparison with empirical data from staged contests yields a generally good quantitative agreement with the predictions. A few deviations are also noted.

Contest behaviour in Weidemeyer's admiral butterfly Limenitis weidemeyerii (Nymphalidae): the effect of size and residency

Abstract Field observations of territorial interactions between male Weidemeyers admiral butterflies were analysed. The data were collected from areas in which males had been individually marked and measured (forewing length). Bigger males were more successful in defending and overtaking territories. In addition, residents were more successful than intruders when controlling for size. These results suggest that both size and residency were used by contestants to decide whether to continue or give up during an interaction, and that butterflies gradually assess their relative strength during a contest. This is the first demonstration of a physical variable such as size or weight influencing the outcome of contests in a butterfly.