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Periodic habitat destruction and migration can paradoxically enable sustainable territorial expansion

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Abstract

Despite depleting the resources in their environments, some species and societies are capable of sustainable habitat expansion by alternating between a low-growth migratory lifestyle and high-growth but destructive behavior. Examples include nomadic pastoralism and shifting cultivation, practiced by humans for millennia. Although specific models have been developed for species or societies which practice periodic migration and habitat depletion, theoretical insight into such phenomena as a whole is lacking. Prior work has shown that a population in a single habitat can survive by alternating between a resource-independent but negative-growth ‘nomadic’ strategy and a destructive but high-growth ‘colonial’ strategy. By explicitly modeling the spatial dynamics of these strategies as they migrate across multiple habitats, we now demonstrate that a population can not only survive, but also sustainably colonize an arbitrarily large network of habitats by alternating between the two strategies. This is possible under a wide range of conditions, as long as the resource level at which a colonial population switches to nomadism is sufficiently high, and the number of neighbors of each habitat in the network is reasonably small. Our theoretical model thus explains the apparent paradox of how two life strategies that individually lead to extinction can nonetheless be combined through spatiotemporal alternation to enable sustained territorial expansion—a finding which synthesizes the theoretical frameworks of Parrondo’s paradox with the exploration–exploitation dilemma.

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References

  1. 1.

    Jones, C.G., Lawton, J.H., Shachak, M.: Organisms as ecosystem engineers. In: Ecosystem management, 130–147. Springer (1994)

  2. 2.

    Cuddington, K., Wilson, W.G., Hastings, A.: Ecosystem engineers: feedback and population dynamics. Am. Nat. 173, 488–498 (2009)

  3. 3.

    Jones, C.G., Lawton, J.H., Shachak, M.: Positive and negative effects of organisms as physical ecosystem engineers. Ecology 78, 1946–1957 (1997)

  4. 4.

    Tan, Z.X., Cheong, K.H.: Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction. eLife 6, e21673 (2017)

  5. 5.

    Goldstein, M.C., Beall, C.M., Cincotto, R.: Traditional nomadic pastoralism and ecological conservation on tibet’s northern plateau. Nat. Geogr. Res. 6, 139–156 (1990)

  6. 6.

    Fratkin, E., Mearns, R.: Sustainability and pastoral livelihoods: lessons from east african maasai and mongolia. Hum. Organ. 62, 112–122 (2003)

  7. 7.

    Fox, J., et al.: Shifting cultivation: a new old paradigm for managing tropical forests. Bioscience 50, 521–528 (2000)

  8. 8.

    Thrupp, L.A., et al.: The Diversity and Dynamics of Shifting Cultivation: Myths, Realities, and Policy Implications. World Resources Institute, Washington, DC (1997)

  9. 9.

    Franks, N.R., Fletcher, C.R.: Spatial patterns in army ant foraging and migration: Eciton burchelli on barro colorado island, panama. Behav. Ecol. Sociobiol. 12, 261–270 (1983)

  10. 10.

    Sulistyawati, E., Noble, I.R., Roderick, M.L.: A simulation model to study land use strategies in Swidden agriculture systems. Agric. Syst. 85, 271–288 (2005)

  11. 11.

    Wickramasuriya, R.C., Bregt, A.K., Van Delden, H., Hagen-Zanker, A.: The dynamics of shifting cultivation captured in an extended constrained cellular automata land use model. Ecol. Model. 220, 2302–2309 (2009)

  12. 12.

    Mace, R.: Nomadic pastoralists adopt subsistence strategies that maximise long-term household survival. Behav. Ecol. Sociobiol. 33, 329–334 (1993)

  13. 13.

    Dressler, G., Mueller, B., Frank, K.: Mobility–a panacea for pastoralism? An ecological-economic modelling approach. In: Proceedings of the 6th International Congress On Environmental Modelling And Software (2012)

  14. 14.

    Pyke, G.H.: Optimal foraging theory: a critical review. Annu. Rev. Ecol. Syst. 15, 523–575 (1984)

  15. 15.

    Hambäck, P.A.: Seasonality, optimal foraging, and prey coexistence. Am. Nat. 152, 881–895 (1998)

  16. 16.

    Brown, J.S., Rosenzweig, M.L.: Habitat selection in slowly regenerating environments. J. Theor. Biol. 123, 151–171 (1986)

  17. 17.

    Ollason, J.: Learning to forage in a regenerating patchy environment: can it fail to be optimal? Theor. Popul. Biol. 31, 13–32 (1987)

  18. 18.

    Williams, P.D., Hastings, A.: Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology. In: Proceedings of the Royal Society of London B: Biological Sciences rspb20102074 (2011)

  19. 19.

    Levine, J.M., Rees, M.: Effects of temporal variability on rare plant persistence in annual systems. Am. Nat. 164, 350–363 (2004)

  20. 20.

    Wolf, D.M., Vazirani, V.V., Arkin, A.P.: Diversity in times of adversity: probabilistic strategies in microbial survival games. J. Theor. Biol. 234, 227–253 (2005)

  21. 21.

    Jansen, V.A., Yoshimura, J.: Populations can persist in an environment consisting of sink habitats only. Proc. Nat. Acad. Sci. 95, 3696–3698 (1998)

  22. 22.

    Cheong, K.H., Koh, J.M., Jones, M.C.: Paradoxical survival: Examining the parrondo effect across biology. BioEssays 41, 1900027 (2019). https://onlinelibrary.wiley.com/doi/abs/10.1002/bies.201900027

  23. 23.

    Harmer, G.P., Abbott, D.: Game theory: losing strategies can win by parrondo’s paradox. Nature 402, 864–864 (1999)

  24. 24.

    Harmer, G.P., Abbott, D., Taylor, P.G., Parrondo, J.M.R.: Brownian ratchets and parrondo’s games. Chaos Interdiscipl. J. Nonlinear Sci. 11, 705–714 (2001)

  25. 25.

    Ethier, S.N., Lee, J.: Parrondo games with two-dimensional spatial dependence. Fluct. Noise Lett. 16, 1750005 (2017)

  26. 26.

    Abbott, D.: Asymmetry and disorder: a decade of parrondo’s paradox. Fluct. Noise Lett. 9, 129–156 (2010)

  27. 27.

    Crossan, M.M., Hurst, D.K.: Strategic renewal as improvisation: reconciling the tension between exploration and exploitation. In: Ecology and Strategy, 273–298 (Emerald Group Publishing Limited, 2006)

  28. 28.

    Eliassen, S., Jørgensen, C., Mangel, M., Giske, J.: Exploration or exploitation: life expectancy changes the value of learning in foraging strategies. Oikos 116, 513–523 (2007)

  29. 29.

    Berger-Tal, O., Nathan, J., Meron, E., Saltz, D.: The exploration–exploitation dilemma: a multidisciplinary framework. PLoS ONE 9, e95693 (2014)

  30. 30.

    Mehlhorn, K., et al.: Unpacking the exploration–exploitation tradeoff: a synthesis of human and animal literatures. Decision 2, 191 (2015)

  31. 31.

    Saha, S., Samanta, G.P.: Influence of dispersal and strong allee effect on a two-patch predator–prey model. Int. J. Dyn. Control (2018). https://doi.org/10.1007/s40435-018-0490-3

  32. 32.

    Pal, D., Samanta, G.P.: Effects of dispersal speed and strong allee effect on stability of a two-patch predator–prey model. Int. J. Dyn. Control (2018). https://doi.org/10.1007/s40435-018-0407-1

  33. 33.

    Bogacki, P., Shampine, L.F.: A 3 (2) pair of runge–kutta formulas. Appl. MatH. Lett. 2, 321–325 (1989)

  34. 34.

    Hardin, G.: The tragedy of the commons’(1968) 162. Science 1243, 63 (1968)

  35. 35.

    Smith, E.A., et al.: Anthropological applications of optimal foraging theory: a critical review [and comments and reply]. Curr. Anthropol. 24, 625–651 (1983)

  36. 36.

    Huang, J., Chen, H., Tseng, H.: The flow of a reversible ratchet. Comput. Phys. Commun. 182, 198–200 (2011)

  37. 37.

    Cheong, K.H., Tan, Z.X., Xie, N.-G., Jones, M.: A paradoxical evolutionary mechanism in stochastically switching environments. Sci. Rep. 6, 34889 (2016). https://doi.org/10.1038/srep34889

  38. 38.

    Zhang, Y., Luo, G.: A special type of codimension two bifurcation and unusual dynamics in a phase-modulated system with switched strategy. Nonlinear Dyn. 67, 2727–2734 (2012)

  39. 39.

    Zhang, Y.: Switching-induced wada basin boundaries in the hénon map. Nonlinear Dyn. 73, 2221–2229 (2013)

  40. 40.

    Danca, M.-F., Lai, D.: Parrondo’s game model to find numerically stable attractors of a tumor growth model. Int. J. Bifurc. Chaos 22, 1250258 (2012)

  41. 41.

    Ye, Y., Cheong, K.H., Cen, Y.-w., Xie, N.-g.: Effects of behavioral patterns and network topology structures on parrondo’s paradox. Sci. Rep. 6, 37028 (2016). https://doi.org/10.1038/srep37028

  42. 42.

    Cheong, K.H., Koh, J.M., Jones, M.C.: Multicellular survival as a consequence of parrondo’s paradox. Proceedings of the National Academy of Sciences 115, E5258–E5259 (2018). https://www.pnas.org/content/115/23/E5258

  43. 43.

    Cánovas, J., Linero, A., Peralta-Salas, D.: Dynamic parrondo’s paradox. Physica D 218, 177–184 (2006)

  44. 44.

    Koh, J.M., Cheong, K.H.: New doubly-anomalous parrondo’s games suggest emergent sustainability and inequality. Nonlinear Dyn. 96, 257–266 (2019). https://doi.org/10.1007/s11071-019-04788-y

  45. 45.

    Cheong, K.H., Saakian, D.B., Zadourian, R.: Allison mixture and the two-envelope problem. Phys. Rev. E 96, 062303 (2017)

  46. 46.

    Danca, M.-F.: Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of parrondo’s paradox. Commun. Nonlinear Sci. Numer. Simul. 18, 500–510 (2013)

  47. 47.

    Bonner, J.: Evolutionary strategies and developmental constraints in the cellular slime molds. Am. Nat. 119, 530–552 (1982)

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Acknowledgements

This project was funded by the Singapore University of Technology and Design (SUTD) Start-up Research Grant (SRG SCI 2019 142).

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Correspondence to Kang Hao Cheong.

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Tan, Z., Cheong, K.H. Periodic habitat destruction and migration can paradoxically enable sustainable territorial expansion. Nonlinear Dyn 98, 1–13 (2019). https://doi.org/10.1007/s11071-019-05094-3

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Keywords

  • Ecological sustainability
  • Migration ecology
  • Habitat destruction
  • Habitat expansion
  • Parrondo’s paradox
  • Exploration–exploitation dilemma
  • Game theory