Effective fitness explained

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. 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. The deviation from this equilibrium displays how close the population is to achieving a steady state.  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 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. 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.

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]

Applications

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.

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]

External links

• Foundations of Genetic Programming

Notes and References

1. Book: Stephens CR . Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406) . "Effective" fitness landscapes for evolutionary systems . 1999. 703–714. 10.1109/CEC.1999.782002. nlin/0006050. 0-7803-5536-9. 10062119.
2. von Bronk B, Schaffer SA, Götz A, Opitz M . Effects of stochasticity and division of labor in toxin production on two-strain bacterial competition in Escherichia coli . PLOS Biology . 15 . 5 . e2001457 . May 2017 . 28459803 . 5411026 . 10.1371/journal.pbio.2001457 . Balaban N . free .
3. Stephens CR, Vargas JM . 2000 . Effective Fitness as an Alternative Paradigm for Evolutionary Computation I: General Formalism . Genetic Programming and Evolvable Machines . 1 . 4 . 363–378 . 10.1023/A:1010017207202 . 1511583 .
4. 10.1145/1570256.1570378 . 2009 . ACM Press . Schaffer JD, Sichtig HM, Laramee C . A series of failed and partially successful fitness functions for evolving spiking neural networks . Proceedings of the 11th annual conference companion on Genetic and evolutionary computation conference - GECCO 09 .
5. Optimization with auxiliary criteria using evolutionary algorithms and reinforcement learning . Afanasyeva A, Buzdalov M . Proceedings of 18th International Conference on Soft Computing MENDEL 2012 . 2012 . 58–63 . 2012 .
6. 10.1145/2739480.2754676 . 2015 . ACM Press . Divband Soorati M, Hamann H . The Effect of Fitness Function Design on Performance in Evolutionary Robotics . Proceedings of the 2015 on Genetic and Evolutionary Computation Conference - GECCO 15 .
7. 10.1080/08948550302439 . 2003 . Informa UK Limited . 8 . 4–5 . 389–431 . Stadler PF, Stephens CR . Landscapes and Effective Fitness . Comments on Theoretical Biology .
8. Cellular automata . Bagnoli F . cond-mat/9810012 . 1998 .
9. Henry A, Hemery M, François P . φ-evo: A program to evolve phenotypic models of biological networks . PLOS Computational Biology . 14 . 6 . e1006244 . June 2018 . 29889886 . 6013240 . 10.1371/journal.pcbi.1006244 . 2018PLSCB..14E6244H . free .
10. Creating a fitness function that is the right fit for the problem at hand . Fernandez AC . 2017 .
11. 10.1145/1143997.1144186 . 2006 . ACM Press . Handa H . Fitness function for finding out robust solutions on time-varying functions . Proceedings of the 8th annual conference on Genetic and evolutionary computation GECCO 06 . 10.1.1.421.930 .
12. Lehman J, Stanley KO . Abandoning objectives: evolution through the search for novelty alone . Evolutionary Computation . 19 . 2 . 189–223 . 2011 . 20868264 . 10.1162/evco_a_00025 . MIT Press - Journals . 12129661 .
13. Exploring promising stepping stones by combining novelty search with interactive evolution . Woolley BF, Stanley KO . 1207.6682 . 2012 . cs.NE .
14. Lehman J, Stanley KO . Abandoning objectives: evolution through the search for novelty alone . Evolutionary Computation . 19 . 2 . 189–223 . 2010-09-24 . 20868264 . 10.1162/EVCO_a_00025 . 12129661 .
15. Mahdipour-Shirayeh A, Kaveh K, Kohandel M, Sivaloganathan S . Phenotypic heterogeneity in modeling cancer evolution . PLOS ONE . 12 . 10 . e0187000 . 2017-10-30 . 29084232 . 5662227 . 10.1371/journal.pone.0187000 . 1610.08163 . 2017PLoSO..1287000M . free .
16. Xu Y, Hu C, Dai Y, Liang J . On simplified global nonlinear function for fitness landscape: a case study of inverse protein folding . PLOS ONE . 9 . 8 . e104403 . 2014-08-11 . 25110986 . 4128808 . 10.1371/journal.pone.0104403 . 2014PLoSO...9j4403X . free .