In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory.[1] The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness function to incorporate the distribution of the population types rather than setting the fitness of a particular type constant. This important property allows the replicator equation to capture the essence of selection. Unlike the quasispecies equation, the replicator equation does not incorporate mutation and so is not able to innovate new types or pure strategies.
^Hofbauer, Josef; Sigmund, Karl (2003). "Evolutionary game dynamics". Bulletin of the American Mathematical Society. 40 (4): 479–519. doi:10.1090/S0273-0979-03-00988-1. ISSN 0273-0979.
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property allows the replicatorequation to capture the essence of selection. Unlike the quasispecies equation, the replicatorequation does not incorporate...
Look up replicator in Wiktionary, the free dictionary. Replicator may refer to: Replicator (evolution unit), the theoretical basic unit of evolution in...
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of the Price equation. Knudsen, Thorbjørn (2004). "General selection theory and economic evolution: The Price equation and the replicator/interactor distinction"...
the population and how the less fit will be culled, in a replicatorequation. The replicator dynamics models heredity but not mutation, and assumes asexual...
Reaction-diffusion equation in theoretical biology Fisher–KPP equation in nonlinear traveling waves FitzHugh–Nagumo model in neural activation Replicator dynamics...
(generalized Lotka–Volterra equation) on the plane, employing equivalence of this dynamics to the 3-type replicatorequation. In “Non-cooperative two-person...
the replicatorequation is also a frequently utilized tool. Evolutionarily stable states are often taken as solutions to the replicatorequation, here...
Structural equation modeling (SEM) is a diverse set of methods used by scientists doing both observational and experimental research. SEM is used mostly...
equal for all y. This assumption is implicit in the replicatorequation a system of differential equations that represents one model in evolutionary game theory...
or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}}...
system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear...
Multiplicative weights update is the discrete-time variant of the replicatorequation (replicator dynamics), which is a commonly used model in evolutionary game...
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.[citation needed] An overdetermined system...
extreme density means there is no way to replicate the material on earth in laboratories, which is how equations of state for other things like ideal gases...
\over n}} The equation defining a plane curve expressed in polar coordinates is known as a polar equation. In many cases, such an equation can simply be...
but especially on the new field of evolutionary game dynamics and replicatorequations. Together with Martin Nowak, Christoph Hauert and Hannelore Brandt...
determine an appropriate sample size n for estimating proportions, the equation below can be solved, where W represents the desired width of the confidence...
can lead to multiple fixed points of the system, much like a quadratic equation can have two roots. Multiple fixed points allow for multiple states of...
state of a particle or other physical system, and wave equations such as the Schrödinger equation describe their behavior. The probability of transmission...
Many equations have since been proposed to approximate forgetting, perhaps the simplest being an exponential curve described by the equation R = e −...
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