D.N. Tverskoi Mathematical model of the process of specialization emergence in colonial organisms. The case of different types of cells
D.N. Tverskoi Mathematical model of the process of specialization emergence in colonial organisms. The case of different types of cells


In this paper we consider a colony of cells. We assume that each cell can contribute to two biological functions: reproductive and somatic. Each cell cannot increase its contributions to one function, without decreasing its contributions to another, i.e., cells efforts to reproductive and somatic functions are traded off. Optimal contributions of each cell to viability and fecundity are determined using the principle of fitness maximization for the whole colony. Mutations and positional effects can lead to the situations, where different cells in the colony have different inner structures. We show how this difference in inner structures influences the emergence of cells specialization in the colony, and how this influence depends on the size of the colony. Moreover, different intermediate form between unspecialized colonies and full-specialized multicellular individuals are derived from our model.


colonies, specialization, viability, fecundity, mutations, positional effects.

PP. 24-32.


1. Korotkova M.A., Korotkov E.V. Bioinformatica i poisk sdvigov ramki schityvaniya v genah // Informacionnye tehnologii i vychislitelnte sistemy. 2010. №1. S. 3-23.
2. Malinetskiy G.G., Naumenko S.A. Vychisleniia na DNK. Eksperimenty. Modely. Algoritmy. Instrumentalnye sredstva. // Informacionnye tehnologii i vychislitelnte sistemy. 2006. №1. S. 5-27.
3. Borisov A.N., Iakovlev S.S. Primenenie teorii igr dlia zadachi svorachivaniya ribonukleinovyh kislot // Informacionnye tehnologii i vychislitelnte sistemy. 2013. №2. S. 51-61.
4. Anisimov V.N., Mihalskiy A.I., Novoseltsev V.N., Romanuha A.A., Yashin A.I. Osnovnii printsipy postroeniia mnogostadiynoy mnogourovnevoy matematicheskoy modeli stareniya // Uspehi gerontologii. 2010. № 23. S. 163-167.
5. Mihalskiy A.I., Novoseltsev V.N. Kolichestvennyy analiz i modelirovanie stareniia, zabolevaemosti i smertnosti // Uspehi gerontologii. 2005. № 17. S. 117–129.
6. Kolobov A.N., Frisman E.Y. Modelirovanie protsessov dinamicheskoy samoorganizatsii v prostranstvenno raspredelennyh rastitelnyh soobtschestvah // Matematicheskaya biologiia i bioinformatica. 2008. T. 3 (№2). S. 85-102.
7. Aponin Y.M., Aponina E.A. O matematicheskom modelirovanii evolutsionnyh protsessov v mire microbov // Matematicheskaya
biologiia i bioinformatica. 2013. T. 8 (№1). S. 350-372.
8. Vitvitskiy A.A. Computernoe modelirovanie protsessa somoorganizatsii bacterialnoy sistemy belkov MinCDE // Matematicheskaya biologiia i bioinformatica. 2014. T. 9 (№2). S. 453-463.
9. Perevaruha A. U. Nepritiagivauschee haoticheskoe mnogestvo v multistabilnoy modeli biologicheskoy sistemy // Informacionnye tehnologii i vychislitelnte sistemy. 2009. № 2. S. 13 – 22.
10. Simpson C. The evolutionary history of division of labour // Proc. R. Soc. London B. 2011. V. 279. P. 116-121.
11. Rueffler C., Hermisson J., Wagner G.P. Evolution of functional specialization and division of labor // PNAS. 2012. V. 109. P. 326–E335.
12. Ispolatov I., Ackermann M., Doebeli M. Division of labour and the evolution of multicellularity // Proc. R. Soc. London B. 2012. V. 279. P. 1768-1776.
13. Willensdorfer M. On the evolution of differentiated multicellularity // Evolution. 2009. V. 63. P. 306–323.
14. Solari C.A., Kessler J.O., Goldstein R.E. Motility, mixing, and multicellularity // Gen. Program. Evolv. Mach. 2007. V. 8. P. 115–129.
15. Michod R.E., Viossat Y., Solari C.A., Hurand M., Nedelcu A.M. Life-history evolution and the origin of multicellularity // J. Theor. Biol. 2006. V. 239. P. 257–272.
16. Koufopanou V., Bell G. Soma and germ - an experimental approach using Volvox // Proc. R. Soc. London B. 1993. V. 254. P. 107–113.
17. Koufopanou V. The evolution of soma in the Volvocales // Am. Nat. 1994. V. 143. P. 907–931.
18. Miller S.M. Volvox, chlamydomonas, and the evolution of multicellularity // Nat. Educ. 2010. V. 3. P. 65.
19. Rossetti V., Schirrmeister B.E., Bernasconi M.V., Bagheri H.C. The evolutionary path to terminal differentiation and division of labor in cyanobacteria // J. Theor. Biol. 2010. V. 262. P. 23-34.
20. Rossetti V., Bagheri H.C. Advantages of the division of labour for the long-term population dynamics of cyanobacteria at different latitudes // Proc. R. Soc. London B. 2012. V. 279. P. 3457-3466.
21. Gavrilets S. Rapid Transition towards the Division of Labor via Evolution of Developmental Plasticity // PLoS Comput. Biol. 2010. V. 6.
22. Doebeli M., Ispolatov I. Symmetric competition as a general model for single-species adaptive dynamics // J. Math. Biol. 2013. V. 67. P. 169-184.
23. Doebeli M., Ispolatov I. Chaos and unpredictability in evolution // Evolution. 2014. V. 68. P. 1365-1373.
24. Ispolatov I., Madhok V., Doebeli M. Individual-based models for adaptive diversification in high-dimensional phenotype spaces // J. Theor. Biol. 2016. V. 390. P. 97-105.
25. Bossert W., Qi C.X., Weymark J.A. Extensive social choice and the measurement of group fitness in biological hierarchies // Biol. Phil. 2013. V. 28. P. 75–98.
26. Okasha S. Evolution and the levels of selection // Oxford University Press, Oxford. 2006.
27. Okasha, S. Individuals, groups, fitness and utility: multi-level selection meets social choice theory // Biol. Phil. 2009. V. 24. P. 561–584. 


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