Complete mixing
Encyclopedia
In evolutionary game theory
, complete mixing refers to an assumption about the type of interactions that occur between individual organisms. Interactions between individuals in a population attains complete mixing if and only if the probably individual x interacts with individual y is equal for all y.
This assumption is implicit in the replicator equation
a system of differential equations that represents one model in evolutionary game theory. This assumption usually does not hold for most organismic populations, since usually interactions occur in some spatial setting where individuals are more likely to interact with those around them. Although the assumption is empirically violated, it represents a certain sort of scientific idealization
which may or may not be harmful to the conclusions reached by that model. This question has led individuals to investigate a series of other models where there is not complete mixing (e.g. Cellular automata models).
Evolutionary game theory
Evolutionary game theory is the application of Game Theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith...
, complete mixing refers to an assumption about the type of interactions that occur between individual organisms. Interactions between individuals in a population attains complete mixing if and only if the probably individual x interacts with individual y is equal for all y.
This assumption is implicit in the replicator equation
Replicator equation
In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness landscape...
a system of differential equations that represents one model in evolutionary game theory. This assumption usually does not hold for most organismic populations, since usually interactions occur in some spatial setting where individuals are more likely to interact with those around them. Although the assumption is empirically violated, it represents a certain sort of scientific idealization
Idealization
Idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false. Often these assumptions are used to make models easier to understand or solve. Many times idealizations do not harm the predictive accuracy of the model for one reason or...
which may or may not be harmful to the conclusions reached by that model. This question has led individuals to investigate a series of other models where there is not complete mixing (e.g. Cellular automata models).