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Effective fitness

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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]

Applications

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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]

References

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  1. ^ a b c d e f g Stephens CR (1999). ""Effective" fitness landscapes for evolutionary systems". Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406). pp. 703–714. arXiv:nlin/0006050. doi:10.1109/CEC.1999.782002. ISBN 0-7803-5536-9. S2CID 10062119.
  2. ^ von Bronk B, Schaffer SA, Götz A, Opitz M (May 2017). Balaban N (ed.). "Effects of stochasticity and division of labor in toxin production on two-strain bacterial competition in Escherichia coli". PLOS Biology. 15 (5): e2001457. doi:10.1371/journal.pbio.2001457. PMC 5411026. PMID 28459803.
  3. ^ a b c d 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. doi:10.1023/A:1010017207202. S2CID 1511583.
  4. ^ Schaffer JD, Sichtig HM, Laramee C (2009). 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. ACM Press. doi:10.1145/1570256.1570378.
  5. ^ Afanasyeva A, Buzdalov M (2012). Optimization with auxiliary criteria using evolutionary algorithms and reinforcement learning. Proceedings of 18th International Conference on Soft Computing MENDEL 2012. Vol. 2012. pp. 58–63.
  6. ^ Divband Soorati M, Hamann H (2015). The Effect of Fitness Function Design on Performance in Evolutionary Robotics. Proceedings of the 2015 on Genetic and Evolutionary Computation Conference - GECCO 15. ACM Press. doi:10.1145/2739480.2754676.
  7. ^ Stadler PF, Stephens CR (2003). "Landscapes and Effective Fitness". Comments on Theoretical Biology. 8 (4–5). Informa UK Limited: 389–431. doi:10.1080/08948550302439.
  8. ^ Bagnoli F (1998). "Cellular automata". arXiv:cond-mat/9810012.
  9. ^ Henry A, Hemery M, François P (June 2018). "φ-evo: A program to evolve phenotypic models of biological networks". PLOS Computational Biology. 14 (6): e1006244. Bibcode:2018PLSCB..14E6244H. doi:10.1371/journal.pcbi.1006244. PMC 6013240. PMID 29889886.
  10. ^ Fernandez AC (2017). "Creating a fitness function that is the right fit for the problem at hand". {{cite journal}}: Cite journal requires |journal= (help)
  11. ^ Handa H (2006). Fitness function for finding out robust solutions on time-varying functions. Proceedings of the 8th annual conference on Genetic and evolutionary computation GECCO 06. ACM Press. CiteSeerX 10.1.1.421.930. doi:10.1145/1143997.1144186.
  12. ^ Lehman J, Stanley KO (2011). "Abandoning objectives: evolution through the search for novelty alone". Evolutionary Computation. 19 (2). MIT Press - Journals: 189–223. doi:10.1162/evco_a_00025. PMID 20868264. S2CID 12129661.
  13. ^ Woolley BF, Stanley KO (2012). "Exploring promising stepping stones by combining novelty search with interactive evolution". arXiv:1207.6682 [cs.NE].
  14. ^ Lehman J, Stanley KO (2010-09-24). "Abandoning objectives: evolution through the search for novelty alone". Evolutionary Computation. 19 (2): 189–223. doi:10.1162/EVCO_a_00025. PMID 20868264. S2CID 12129661.
  15. ^ Mahdipour-Shirayeh A, Kaveh K, Kohandel M, Sivaloganathan S (2017-10-30). "Phenotypic heterogeneity in modeling cancer evolution". PLOS ONE. 12 (10): e0187000. arXiv:1610.08163. Bibcode:2017PLoSO..1287000M. doi:10.1371/journal.pone.0187000. PMC 5662227. PMID 29084232.
  16. ^ Xu Y, Hu C, Dai Y, Liang J (2014-08-11). "On simplified global nonlinear function for fitness landscape: a case study of inverse protein folding". PLOS ONE. 9 (8): e104403. Bibcode:2014PLoSO...9j4403X. doi:10.1371/journal.pone.0104403. PMC 4128808. PMID 25110986.
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