In natural evolution and artificial evolution (e.g. artificial life and evolutionary computation) the fitness (or performance or objective measure) of a schema is rescaled to give its effective fitness which takes into account crossover and mutation.

Effective fitness is used in Evolutionary Computation to understand population dynamics. ^[1] While a biological fitness function only looks at reproductive success, an effective fitness function tries to encompass things that are needed to be fulfilled for survival on population level. ^[2] In homogeneous populations, reproductive fitness and effective fitness are equal. ^[1] When a population moves away from homogeneity a higher effective fitness is reached for the recessive genotype. This advantage will decrease while the population moves toward an equilibrium. ^[1] The deviation from this equilibrium displays how close the population is to achieving a steady state. ^[1]  When this equilibrium is reached, the maximum effective fitness of the population is achieved. ^[3]

Problem solving with evolutionary computation is realized with a cost function. ^[4] If cost functions are applied to swarm optimization they are called a fitness function. Strategies like reinforcement learning ^[5] and NEAT neuroevolution ^[6] are creating a fitness landscape which describes the reproductive success of cellular automata. ^{[7] [8]}

The effective fitness function models the number of fit offspring ^[1] and is used in calculations that include evolutionary processes, such as mutation and crossover, important on the population level. ^[9]

The effective fitness model is superior to its predecessor, the standard reproductive fitness model. It advances in the qualitatively and quantitatively understanding of evolutionary concepts like bloat, self-adaptation, and evolutionary robustness. ^[3] While reproductive fitness only looks at pure selection, effective fitness describes the flow of a population and natural selection by taking genetic operators into account. ^{[1] [3]}

A normal fitness function fits to a problem, ^[10] while an effective fitness function is an assumption if the objective was reached. ^[11] The difference is important for designing fitness functions with algorithms like novelty search in which the objective of the agents is unknown. ^{[12] [13]} In the case of bacteria effective fitness could include production of toxins and rate of mutation of different plasmids, which are mostly stochastically determined ^[14]

When evolutionary equations of the studied population dynamics are available, one can algorithmically compute the effective fitness of a given population. Though the perfect effective fitness model is yet to be found, it is already known to be a good framework to the better understanding of the moving of the genotype-phenotype map, population dynamics, and the flow on fitness landscapes. ^{[1] [3]}

Models using a combination of Darwinian fitness functions and effective functions are better at predicting population trends. Effective models could be used to determine therapeutic outcomes of disease treatment. ^[15] Other models could determine effective protein engineering and works towards finding novel or heightened biochemistry. ^[16]

• Foundations of Genetic Programming

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