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 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.

The replicator equation assumes a uniform population distribution ; that is, it does not incorporate population structure into the fitness.

To simplify analysis, fitness is often assumed to depend linearly upon the population distribution, which allows the replicator equation to be written in the form:

Since the replicator equation is non-linear, an exact solution is difficult to obtain ( even in simple versions of the continuous form ) so the equation is usually analyzed in terms of stability.

All the faces of the simplex are forward-invariant which corresponds to the lack of innovation in the replicator equation: once a strategy becomes extinct there is no way to revive it.

Phase portrait solutions for the continuous linear-fitness replicator equation have been classified in the two and three dimensional cases.

The continuous replicator equation on types is equivalent to the Generalized Lotka – Volterra equation in dimensions.

The continuous replicator dynamic is also equivalent to the Price equation ( see Page & Nowak's ( 2002 ) paper Unifying Evolutionary Dynamics ).

A generalization of the replicator equation which incorporates mutation is given by the replicator-mutator equation, which takes the following form in the continuous version:

This equation is a simultaneous generalization of the replicator equation and the quasispecies equation, and is used in the mathematical analysis of language.

The replicator equation can easily be generalized to asymmetric games.

A complete classification of this dynamics, even for all sign patterns of above coefficients, is available, which is based upon equivalence to the 3-type replicator equation.

This assumption is implicit in the replicator equation a system of differential equations that represents one model in evolutionary game theory.

The advantage of such a system lies in its ability to expand its own capacity rapidly and without additional human effort ; in essence, the initial investment required to construct the first clanking replicator would have an arbitrarily large payoff with no additional labor cost, with future returns discounted by their present value.

There are other times when the implicit interests of the vehicle and replicator are in conflict, such as the genes behind certain male spiders ' instinctive mating behaviour, which increase the organism's inclusive fitness by allowing it to reproduce, but shorten its life by exposing it to the risk of being eaten by the cannibalistic female.

A branch of Arvato Digital Services, formerly Sonopress-the world's second-largest replicator of CD's and DVD's-operates a facility in Weaverville and employs many of its residents.

* A replicator ( or paper ) makes repeated copies of itself and executes them in parallel, eventually filling the entire core with copies of its code.

Captain Janeway feared that if this technology were acquired by a civilization before they were ready, disastrous consequences could ensue ( on one occasion a Kazon ship was severely damaged when its crew tried to construct a replicator ; instead the deck was flooded with nucleon radiation and extremely high levels of Neosorin particles ).

The plasmid harboured by Hansen's bacillus contains a replicator gene which it must share with its procaryote host, and a neuron invasion gene.

Thus, the plasmid, with its replicator gene, is not prevented from moving out of the bacillus into neighboring human nerves where it replicates, damaging those nerves and causing the tuberculoid HD clinical picture.

The bacillus, meanwhile, is rendered unable to divide ( having lost its replicator gene ) and is destroyed by the immune system in the normal way.

Evolutionarily stable states are frequently used to identify solutions to the replicator equation, given in its linear payoff form by

Continuous replicator equations assume infinite populations, continuous time, complete mixing and that strategies breed true.

Rules describe the contest as in classical Game Theory but for evolutionary games rules include the element of replicator dynamics, in other words the general rules say exactly how the fitter players will spawn more replicas of themselves into the population and the less fit will be culled out of the player population ( expressed in a Replicator Equation ).

The common methodology to study the evolutionary dynamics in games is through replicator equations.

These replicator equations in the context of evolutionary biology shows the growth rate of the proportion of organisms using a certain strategy and that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole.

Three of the common strategies ( replicator, scanner and bomber ) are also known as paper, scissors and stone, since their performance against each other approximates that of their namesakes in the well known playground game.

It is important to realise that EGT is not just a specialist mathematical treatment of animal contests to determine their dynamics and results, but in a manner similar to the field of Evolutionary Algorithms, it is a comprehensive model that encompasses the Darwinian process itself – including the central tenets of competition ( the game ) natural selection ( replicator dynamics ) and heredity-all within the overall model.

Similar ideas are advocated in the Foresight Guidelines on Molecular Nanotechnology, and a map of the 137-dimensional replicator design space recently published by Freitas and Merkle provides numerous proposed methods by which replicators could, in principle, be safely controlled by good design.

Essential to manipulation of the human genome is the " uterine replicator ," which allows completely in vitro human reproduction.

Dawkins proposes the idea of the " replicator ," the initial molecule which first managed to reproduce itself and thus gained an advantage over other molecules within the primordial soup.

Expansion is possible via a dock connector which connects to a port replicator, offering two USB ports ( blocking the single port on the unit ), VGA, audio, AC power and Ethernet.

" recommendations against developing ... replicator designs which permit surviving mutation or undergoing evolution ".

Such a " broadcast architecture " is one of the safety features recommended by the " Foresight Guidelines on Molecular Nanotechnology ", and a map of the 137-dimensional replicator design space recently published by Freitas and Merkle provides numerous practical methods by which replicators can be safely controlled by good design.

A replicator works by rearranging subatomic particles, which are abundant everywhere in the universe, to form molecules and arrange those molecules to form the object.

In Version 2 a new ' replicator ' function was introduced, which allows an object to be replicated to create a repeating pattern of a specified size and shape.

The concept of self-replicating machines has been advanced and examined by Homer Jacobsen, Edward F. Moore, Freeman Dyson, John von Neumann and in more recent times by K. Eric Drexler in his book on nanotechnology, Engines of Creation and by Robert Freitas and Ralph Merkle in their review Kinematic Self-Replicating Machines which provided the first comprehensive analysis of the entire replicator design space.

Among his dozens of patents pending is a food replicator which Chef Cantu envisions will eradicate world hunger.

Voyager discovers evidence of replicator technology on a pre-warp planet, which is reported as very unusual.