Enquist & Leimar : Evolution of fatal fighting

The evolution of fatal fighting was investigated using evolutionary game theory. General considerations about the lifetime consequences of fighting behaviour are first discussed. A sequential assessment game is then developed in which a fight can end because a contestant either gives up or is killed. The results show that the balance between the value of the contested resource and the value of the future is one important factor influencing the frequency of death or severe injury in fights. When the value of a contested resource is similar to or greater than the value of the future, strategies will evolve that result in contestants being severely injured or killed during fights. When the value of the future is close to zero contestants will never give up after starting to fight; such fights will always be fatal for at least one of the opponents. Factors that could decrease the cost of fighting, such as the assessment of fighting ability, kinship and role asymmetries, have little or no effect in these situations. Finally, empirical data on fatal fighting are reviewed and compared with theoretical predictions. Data show that dangerous fighting, often resulting in severe injuries or death, generally occurs in situations where a major part of a contestant's lifetime reproductive success is at stake. Empirical data on fighting behaviour clearly show that the cost of fighting varies greatly between species. In most species the frequency of severe injury is small or even zero. However, in some, really dangerous fighting does occur in which a significant proportion of the fights end with one or both of the contestants being severely injured or killed (for references, see Discussion), How can this variation between species be explained? Recent theoretical studies of fighting behaviour have focused on non-dangerous fighting (e.g. Maynard Smith & Price 1973; Maynard Smith 1982) and today we know of several mechanisms that give rise to evolutionarily stable strategies that effectively limit the use of dangerous behaviour patterns during fights. One such mechanism is the assessment of fighting ability, which allows the weaker individual to give up before being injured. In contrast, less attention has been directed towards explaining cases of fatal fighting (but see Hamilton 1979; Treisman & Collins 1980; Thornhilt & Alcock 1983; Grafen 1987). One possible reason for fatal fighting is that species differ in their ability to inflict injuries such that fatal fights occur only between animals equipped with efficient weapons. However, the fact that many well-armed species do not fight to the bitter end suggests that a more strategic explanation must apply. This is further supported by the fact that fatal fights tend to occur only when the value of victory is high. Our aim in this paper is to investigate the 0003-3472/90/010001+09 $03.00/0 evolution of fatal fighting using evolutionary game theory. First, we investigate under what circumstances fatal fights may evolve, and second, theoretical examples (evolutionary stable strategies, ESSs) of such fights are studied using the sequential assessment game (Enquist & Leimar 1983, 1987; Leimar & Enquist 1984). WHEN WILL FATAL FIGHTING EVOLVE? To answer this question it is necessary to investigate the lifetime consequences of fighting behaviour. Let us study a simple model. Consider an individual in a particular population (with some specified distribution of strategies). Let its expected lifetime utility be V+ V0 if it is in the possession of a resource, and/I0 if it is not. We interpret V as the value of the resource and V0 as the value of the future. When facing a conflict over a resource, an individual using a strategy S has an expected lifetime utility Ut given by U,(S)=p(S)V+[1 -q(S)]Vo (1) where p(S) is the probability of victory, and q(S) is a factor controlling how the value of the future (II0) changes due to fighting. Incidences of injury or expenditures of energy and time make q positive for cases of biological interest (for instance, q could be the probability of fatal injury), The situation is sometimes more complex than described by this 9 1990 The Association for the Study of Animal Behaviour