Abstract We develop a four dimensional predator-prey system in continuous time with stage-structure for both the communities. The reproduction rate of the prey and the transition rate for the predator, in our model, are assumed to be density-dependent. The stability results for the coexisting equilibrium are obtained by making use of Routh–Hurwitz criteria. Because of the density-dependent effects, numerical simulations are applied in complex situations. We observe that increasing values of the coefficients linked with density-dependent term promote the stability of the coexisting steady state. Our main focus is to understand the variation of stocks when mortality rates on different stage classes are increased. We verified that stable stock on mature predator increases with its increasing mortality rate in three different modeling frameworks. However, no such positive effect on the biomass of the immature predator occurs when immature predators are removed, culled or harvested. Therefore, we could conclude that the appearance of hydra effect on many unstructured predator-prey models is due to the mortality of the mature predator only. No hydra effect is also detected when mature prey is removed in several situations we discussed. Overall, the obtained results are new and could be interesting contribution in theoretical ecology.

中文翻译：

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密度依赖效应和死亡率下阶段结构捕食者-猎物系统的动力学

摘要 我们在连续时间内为两个社区开发了具有阶段结构的四维捕食者-猎物系统。在我们的模型中，假设猎物的繁殖率和捕食者的转换率与密度有关。共存平衡的稳定性结果是通过使用 Routh-Hurwitz 准则获得的。由于密度相关效应，数值模拟适用于复杂情况。我们观察到，与密度相关项相关的系数值的增加促进了共存稳态的稳定性。我们的主要重点是了解当不同阶段类别的死亡率增加时股票的变化。我们在三个不同的建模框架中验证了成熟捕食者的稳定种群随着其死亡率的增加而增加。然而，当移除、扑杀或收获未成熟捕食者时，对未成熟捕食者的生物量没有这种积极影响。因此，我们可以得出结论，许多非结构化捕食者-猎物模型出现九头蛇效应仅是由于成熟捕食者的死亡。在我们讨论的几种情况下，当成熟的猎物被移除时，也没有检测到九头蛇效应。总的来说，获得的结果是新的，可能是理论生态学中有趣的贡献。在我们讨论的几种情况下，当成熟的猎物被移除时，也没有检测到九头蛇效应。总的来说，获得的结果是新的，可能是理论生态学中有趣的贡献。在我们讨论的几种情况下，当成熟的猎物被移除时，也没有检测到九头蛇效应。总的来说，获得的结果是新的，可能是理论生态学中有趣的贡献。