# Ratcheting based on neighboring niches determines lifestyle

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## Abstract

In this paper, a co-evolution method of game dynamics and network structure is adopted to demonstrate that neighboring niches of an individual or population may have great influence in determining lifestyle adoption. The model encompasses network structure evolution, denoted **Case****A**, and pure games participated in by individuals in the network with two asymmetric branches determining winning and losing states, denoted **Case B**. The selection between game branches is dependent on the demographic of neighboring niches, and favorable or unfavorable effects from the neighborhood can be made to manifest by setting probabilistic game parameters. Theoretical analysis reveals that losing configurations of **Case B**, when stochastically mixed with neutral **Case A**, can result in paradoxical winning scenarios where the network experiences positive gain—a Parrondo’s paradox-like phenomenon has therefore emerged. It is elucidated that agitation from **Case A** increases the probability of individuals to play the favorable branch of **Case B**, leading to unexpected gains in two distinct parameter regimes. In the paradoxical regions, our analysis suggests strongly that neighboring niches are the cause for evolution toward social or solitary lifestyle behaviors, and we present important connections to real-world biological life.

## Keywords

Population dynamics Parrondo’s paradox Nonlinear dynamics Ratcheting Neighboring niches## Notes

### Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grant No.11705002); Ministry of Education, Humanities and Social Sciences research projects (15YJCZH210; 19YJAZH098). KHC and JMK were supported by the SUTD Start-up Research Grant (SRG SCI 2019 142).

### Compliance with ethical standards

### Conflicts of interest

The authors declare that they have no conflict of interest.

## References

- 1.Gardner, M.: Mathematical games: the fantastic combinations of John Conway’s new solitaire game ‘life. Sci. Am.
**223**, 120–123 (1970)CrossRefGoogle Scholar - 2.Berlekamp, E., Conway, J., Guy, R.: Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. Academic Press, New York (1982)zbMATHGoogle Scholar
- 3.Bosch, R.A.: Maximum density stable patterns in variants of Conway’s game of Life. Oper. Res. Lett.
**27**(1), 7–11 (2000)MathSciNetCrossRefGoogle Scholar - 4.Tkachenko, A., Rabin, Y.: Effect of Boundary Conditions on Fluctuations and. Phys. Rev. E
**7463**(1), 7146–7150 (1997)Google Scholar - 5.Nordfalk, J., Alstrøm, P.: Phase transitions near the ‘game of Life. Phys. Rev. E
**54**(2), R1025–R1028 (1996)CrossRefGoogle Scholar - 6.Monetti, R.A., Albano, E.V.: Critical edge between frozen extinction and chaotic life. Phys. Rev. E
**52**(6), 5825–5831 (1995)CrossRefGoogle Scholar - 7.Bak, P., Chen, K., Creutz, M.: Self-organized criticality in the Game of Life. Nature
**342**(6251), 780–782 (1989)CrossRefGoogle Scholar - 8.Jin, W., Chen, F.: Topological chaos of universal elementary cellular automata rule. Nonlinear Dyn.
**63**(1), 217–222 (2011)MathSciNetCrossRefGoogle Scholar - 9.Souyah, A., Faraoun, K.M.: An image encryption scheme combining chaos-memory cellular automata and weighted histogram. Nonlinear Dyn.
**86**(1), 639–653 (2016)MathSciNetCrossRefGoogle Scholar - 10.Souyah, A., Faraoun, K.M.: Fast and efficient randomized encryption scheme for digital images based on Quadtree decomposition and reversible memory cellular automata. Nonlinear Dyn.
**84**(2), 715–732 (2016)MathSciNetCrossRefGoogle Scholar - 11.Wang, X., Xu, D.: A novel image encryption scheme using chaos and Langton’s Ant cellular automaton. Nonlinear Dyn.
**79**(4), 2449–2456 (2015)MathSciNetCrossRefGoogle Scholar - 12.Toral, R.: Cooperative Parrondo’s games. Fluct. Noise Lett.
**1**(01), L7–L12 (2001)MathSciNetCrossRefGoogle Scholar - 13.Mihailović, Z., Rajković, M.: One dimensional asynchronous cooperative Parrondo’s games. Fluct. Noise Lett.
**3**(04), L389–L398 (2003)MathSciNetCrossRefGoogle Scholar - 14.Ethier, S.N., Lee, J.: Parrondo games with spatial dependence and a related spin system, II. Markov Process. Relat. Fields
**19**(4), 667–692 (2013)MathSciNetzbMATHGoogle Scholar - 15.Mihailović, Z., Rajković, M.: Cooperative Parrondo’s games on a two-dimensional lattice. Phys. A Stat. Mech. Appl.
**365**(1), 244–251 (2006)CrossRefGoogle Scholar - 16.Ethier, S.N., Lee, J.: Parrondo games with two-dimensional spatial dependence. Fluct. Noise Lett.
**16**(01), 1750005 (2017)CrossRefGoogle Scholar - 17.Parrondo, J.M.R., Harmer, G.P., Abbott, D.: New paradoxical games based on Brownian ratchets. Phys. Rev. Lett.
**85**(24), 5226–5229 (2000)CrossRefGoogle Scholar - 18.Harmer, G.P., Abbott, D.: A review of Parrondo’s paradox. Fluct. Noise Lett.
**02**, R71–R107 (2002)CrossRefGoogle Scholar - 19.Abbott, D.: Asymmetry and disorder: a decade of parrondo’s paradox. Fluct. Noise Lett.
**09**(01), 129–156 (2010)CrossRefGoogle Scholar - 20.Abbott, D., Harmer, G.P.: Game theory: losing strategies can win by Parrondo’s paradox. Nature
**402**(6764), 864–864 (1999)CrossRefGoogle Scholar - 21.Soo, W.W.M., Cheong, K.H.: Parrondo’s paradox and complementary Parrondo processes. Phys. A Stat. Mech. Appl.
**392**(1), 17–26 (2013)MathSciNetCrossRefGoogle Scholar - 22.Soo, W.W.M., Cheong, K.H.: Occurrence of complementary processes in Parrondo’s paradox. Phys. A Stat. Mech. Appl.
**412**, 180–185 (2014)MathSciNetCrossRefGoogle Scholar - 23.Cheong, K.H., Soo, W.W.M.: Construction of novel stochastic matrices for analysis of Parrondo’s paradox. Phys. A Stat. Mech. Appl.
**392**(20), 4727–4738 (2013)MathSciNetCrossRefGoogle Scholar - 24.Cheong, K.H., Koh, J.M., Jones, M.C.: Paradoxical survival: examining the Parrondo effect across biology. BioEssays
**41**(6), 1900027 (2019)CrossRefGoogle Scholar - 25.Toral, R.: Capital redistribution brings wealth by Parrondo’s paradox. Fluct. Noise Lett.
**2**(04), L305–L311 (2002)MathSciNetCrossRefGoogle Scholar - 26.Ye, Y., Xie, N.-G., Wang, L.-G., Meng, R., Cen, Y.-W.: Study of biotic evolutionary mechanisms based on the multi-agent parrondo’s games. Fluct. Noise Lett.
**11**(02), 1250012 (2012)CrossRefGoogle Scholar - 27.Szolnoki, A., Perc, M.: Information sharing promotes prosocial behaviour. New J. Phys.
**15**(5), 53010 (2013)MathSciNetCrossRefGoogle Scholar - 28.Cheong, K.H., Koh, J.M., Jones, M.C.: Multicellular survival as a consequence of Parrondo’s paradox. Proc. Natl. Acad. Sci.
**115**(23), E5258–E5259 (2018)CrossRefGoogle Scholar - 29.Koh, J.M., Xie, N., Cheong, K.H.: Nomadic-colonial switching with stochastic noise: subsidence-recovery cycles and long-term growth. Nonlinear Dyn.
**94**(2), 1467–1477 (2018)CrossRefGoogle Scholar - 30.Koh, J.M., Cheong, K.H.: Automated electron-optical system optimization through switching Levenberg–Marquardt algorithms. J. Electron Spectros. Relat. Phenomena
**227**, 31–39 (2018)CrossRefGoogle Scholar - 31.Koh, J.M., Cheong, K.H.: New doubly-anomalous Parrondo’s games suggest emergent sustainability and inequality. Nonlinear Dyn.
**96**, 257–266 (2019)CrossRefGoogle Scholar - 32.Cheong, K.H., Koh, J.M., Jones, M.C.: Do arctic hares play Parrondo’s games? Fluct. Noise Lett.
**18**(03), 1971001 (2019)CrossRefGoogle Scholar - 33.Wu, D., Szeto, K.Y.: Extended Parrondo’s game and Brownian ratchets: strong and weak Parrondo effect. Phys. Rev. E
**89**(2), 22142 (2014)CrossRefGoogle Scholar - 34.Gilbert, C., Robertson, G., Le Maho, Y., Naito, Y., Ancel, A.: Huddling behavior in emperor penguins: dynamics of huddling. Physiol. Behav.
**88**(4–5), 479–488 (2006)CrossRefGoogle Scholar - 35.Ancel, A., Beaulieu, M., Le Maho, Y., Gilbert, C.: Emperor penguin mates: keeping together in the crowd. Proc. R. Soc. B Biol. Sci.
**276**(1665), 2163–2169 (2009)CrossRefGoogle Scholar - 36.Ahsan, M.M., Tahir, H.M., Mukhtar, M.K., Ali, A., Kahan, Z.I., Ahmed, K.: Intra-and inter-specific foraging in three scorpion species. Punjab Univ. J. Zool.
**31**(1), 69–76 (2016)Google Scholar - 37.Huntingford, F.A.: Animal Conflict. Springer, Berlin (2013)Google Scholar