Evolutionary game theory in the context of "Agonistic behavior"

In mathematics, the replicator equation is a type of dynamical system used in evolutionary game theory to model how the frequency of strategies in a population changes over time. It is a deterministic, monotone, non-linear, and non-innovative dynamic that captures the principle of natural selection in strategic interactions.

The replicator equation describes how strategies with higher-than-average fitness increase in frequency, while less successful strategies decline. Unlike other models of replication—such as the quasispecies model—the replicator equation allows the fitness of each type to depend dynamically on the distribution of population types, making the fitness function an endogenous component of the system. This allows it to model frequency-dependent selection, where the success of a strategy depends on its prevalence relative to others.

Agonistic behaviour is any social behaviour related to fighting, which can include aggressive behaviour, but also threats, displays, retreats, placation, and conciliation. The term "agonistic behaviour" was first defined and used by J.P. Scott and Emil Fredericson in 1951 in their paper "The Causes of Fighting in Mice and Rats" in Physiological Zoology. Agonistic behaviour is seen in many animal species because resources including food, shelter, and mates are often limited.

Ritualized aggression or ritualized fighting is when animals use a range of behaviours as posture or warning but without engaging in serious aggression or fighting, which would be expensive in terms of energy and the risk of injury. Ritualized aggression involves a graded series of behaviours or displays that include threatening gestures (such as vocalizations, spreading of wings or gill covers, lifting and presentation of claws, head bobbing, tail beating, lunging, etc.) and occasionally posturing physical actions such as inhibited (non-injurious) bites. This behavior is explained by evolutionary game theory.