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Hydra Effect and Harvesting Optimal Policy in a Generalist Predator Prey Model With General Holling Type Response Functions

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  • Solomon Molla Alemu
  • Mohammed Yiha Dawed
  • Tesfaye Tefera Mamo

Abstract

This study illustrates selective and combined harvesting efforts to examine the existence of hydra effect and global MSTY (maximum sustainable total yield) in a generalist predator–prey mathematical model with general Holling type response functions. The hydra effect is an ecological paradox in which a species’ population size increases in response to an increase in its mortality rate. Existence of unique solution, positivity, and boundedness of solution of the mathematical model are verified. The equilibrium points and their stability are discussed. MSTY, the bionomic equilibrium point, and optimum level of harvesting are explained. Mainly, in this stable species interaction model, we showed (i) predator harvesting establishes hydra effect in a generalist predator–prey model; (ii) the global MSTY exists in a generalist prey–predator system for Holling Type I (HT‐I) functional response for some conditions; and (iii) an optimal stock level maximizes the net revenue applying an optimal harvesting effort. However, inducing harvesting efforts greater than the optimal level causes a reduction in species density, leading to extinction. Moreover, net revenue declines. The analytical results are also supported and verified by numerical simulations.

Suggested Citation

  • Solomon Molla Alemu & Mohammed Yiha Dawed & Tesfaye Tefera Mamo, 2025. "Hydra Effect and Harvesting Optimal Policy in a Generalist Predator Prey Model With General Holling Type Response Functions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:1667754
    DOI: 10.1155/jama/1667754
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    1. Legović, Tarzan & Klanjšček, Jasminka & Geček, Sunčana, 2010. "Maximum sustainable yield and species extinction in ecosystems," Ecological Modelling, Elsevier, vol. 221(12), pages 1569-1574.
    2. Grafton, R. Quentin & Kompas, Tom & Chu, Long & Che, Nhu, 2010. "Maximum economic yield," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(3), pages 1-8.
    3. Anjos, Lucas dos & Costa, Michel Iskin da S. & Almeida, Regina C., 2020. "Characterizing the existence of hydra effect in spatial predator-prey models and the influence of functional response types and species dispersal," Ecological Modelling, Elsevier, vol. 428(C).
    4. Negeri Negese Wayesa & Legesse Lemecha Obsu & Mohammed Yiha Dawed & Misra, 2024. "Analysis of Predator–Prey Model With Inclusion of Temperature Variability in Prey Refugees," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-18, June.
    5. Wilen, Christopher D. & Wilen, James E., 2012. "Fishing down the food chain revisited: Modeling exploited trophic systems," Ecological Economics, Elsevier, vol. 79(C), pages 80-88.
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