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Abstract
A new critical effect is predicted in population dispersal. It is based on the fact that a trade-off between the advantages of mobility and the cost of mobility breaks with a significant deterioration in living conditions. The recently developed model of purposeful kinesis (Gorban & Çabukoǧlu, Ecological Complexity 33, 2018) is based on the “let well enough alone” idea: mobility decreases for high reproduction coefficient and, therefore, animals stay longer in good conditions and leave quicker bad conditions. Mobility has a cost, which should be measured in the changes of the reproduction coefficient. Introduction of the cost of mobility into the reproduction coefficient leads to an equation for mobility. It can be solved in a closed form using Lambert W-function. Surprisingly, the “let well enough alone” models with the simple linear cost of mobility have an intrinsic phase transition: when conditions worsen then the mobility increases up to some critical value of the reproduction coefficient. For worse conditions, there is no solution for mobility. We interpret this critical effect as the complete loss of mobility that is degeneration of diffusion. Qualitatively, this means that mobility increases with worsening of conditions up to some limit, and after that, mobility is nullified.Citation
Gorban, A. N. and Çabukoǧlu, N. (2018) Mobility cost and degenerated diffusion in kinesis models, Ecological Complexity, 36, pp. 16-21.Publisher
ElsevierJournal
Ecological ComplexityAdditional Links
https://www.sciencedirect.com/science/article/pii/S1476945X18300771Type
Journal articleLanguage
enDescription
This is an accepted manuscript of an article published by Elsevier] in Ecological Complexity on 05/07/2018, available online: https://doi.org/10.1016/j.ecocom.2018.06.007 The accepted version of the publication may differ from the final published version.ISSN
1476-945Xae974a485f413a2113503eed53cd6c53
10.1016/j.ecocom.2018.06.007
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