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Impact of generalized growth dynamics and spatial dispersal on maximum sustainable yield in harvested populations

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  • Elbetch, Bilel
  • Moussaoui, Ali

Abstract

This study explores the influence of generalized growth rates on the Maximum Sustainable Yield (MSY) in harvested populations. By employing generalized logistic models, such as the Richards and Gompertz formulations, we analytically derive the conditions under which MSY is attained in single-species systems. The analysis is then extended to multi-patch environments with inter-patch dispersal to examine the impact of migration on total MSY. Our key findings show that the MSY in a connected system is always less than or equal to the sum of the MSYs of isolated patches. Moreover, under biologically realistic assumptions, we demonstrate that increasing migration rates between patches leads to a strictly decreasing total MSY. Numerical simulations support the theoretical results, emphasizing that species-specific growth dynamics and spatial connectivity must be jointly considered for effective resource management. These results reveal a fundamental trade-off between ecological connectivity and harvesting potential in spatially structured populations.

Suggested Citation

  • Elbetch, Bilel & Moussaoui, Ali, 2026. "Impact of generalized growth dynamics and spatial dispersal on maximum sustainable yield in harvested populations," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:chsofr:v:203:y:2026:i:c:s0960077925016728
    DOI: 10.1016/j.chaos.2025.117659
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    References listed on IDEAS

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    1. Pierre Auger & Ali Moussaoui, 2022. "Coupling of Bio-Reactors to Increase Maximum Sustainable Yield," Mathematics, MDPI, vol. 10(4), pages 1-18, February.
    2. Y. Takeuchi, 1989. "Cooperative Systems Theory and Global Stability of Diffusion Models," Springer Books, in: A. B. Kurzhanski & K. Sigmund (ed.), Evolution and Control in Biological Systems, pages 49-57, Springer.
    3. Auger, Pierre & Kooi, Bob & Moussaoui, Ali, 2022. "Increase of maximum sustainable yield for fishery in two patches with fast migration," Ecological Modelling, Elsevier, vol. 467(C).
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