Nonlinear Dynamics

, Volume 98, Issue 1, pp 1–13 | Cite as

Periodic habitat destruction and migration can paradoxically enable sustainable territorial expansion

  • Zhi-Xuan Tan
  • Kang Hao CheongEmail author
Original paper


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.


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



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

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

11071_2019_5094_MOESM1_ESM.pdf (15 mb)
Supplementary material 1 (pdf 15410 KB)

Supplementary material 2 (mp4 15763 KB)


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Yale UniversityNew HavenUSA
  2. 2.Science and Math ClusterSingapore University of Technology and DesignSingaporeSingapore

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