Predation-driven Allee effects play an important role in the dynamics of a small prey population; however, such effects cannot occur for the model with type I functional response. Predator-driven Allee effects generally occur when a generalist predator targets some specific prey. However, apart from the lethal effects of predation, there are some non-lethal effects in the presence of a predator. Due to the fear of predation, positive density dependence growth of prey may be observed at low population density because of reduced foraging activities. Moreover, such a non-lethal effect can be carried over through generations or seasons. In the present manuscript, we investigate the role of predation fear and its carry-over effects in the prey-predator model. First, we study the single-species model from a global perspective. We have shown that depending on the birth rate; our single-species model describes three types of growth dynamics, namely, strong Allee dynamics, weak Allee dynamics, and logistic dynamics. Then we include the explicit dynamics of the predator, with type I functional response. Basic dynamical properties, as well as the global stability of each equilibrium, have been discussed. From our analysis, we can observe that both the fear and its carry-over effects have a significant role in the stability of the coexistence equilibrium, even for the model with type I functional response. The phenomenon ‘paradox of enrichment’ can be observed in our model, which cannot be observed in the classical prey-predator model with type I functional response. However, we can see that such a phenomenon can be ruled out by choosing suitable non-lethal effect parameters. Therefore, our study shows how non-lethal effects change the dynamics of a prey-predator model and has powerful biological insights, especially for understanding the dynamics of small populations.

捕食驱动的 Allee 效应在小型猎物种群的动态中起着重要作用；然而，对于具有 I 型功能响应的模型，这种影响不会发生。捕食者驱动的 Allee 效应通常发生在通才捕食者瞄准某些特定猎物时。然而，除了捕食的致命影响之外，在捕食者的存在下还有一些非致命的影响。由于害怕捕食，由于觅食活动减少，在低人口密度下可能会观察到猎物的正密度依赖性增长。此外，这种非致命效果可以代代相传。在本手稿中，我们调查了捕食恐惧的作用及其在猎物-捕食者模型中的遗留效应。首先，我们从全球角度研究单物种模型。我们已经证明，这取决于出生率；我们的单一物种模型描述了三种类型的增长动态，即强 Allee 动态、弱 Allee 动态和逻辑动态。然后我们包括捕食者的显式动态，以及 I 型功能反应。已经讨论了基本动力学特性以及每个平衡的全局稳定性。从我们的分析中，我们可以观察到恐惧及其遗留效应对共存平衡的稳定性都有重要作用，即使对于具有 I 型功能响应的模型也是如此。现象 已经讨论了基本动力学特性以及每个平衡的全局稳定性。从我们的分析中，我们可以观察到恐惧及其遗留效应对共存平衡的稳定性都有重要作用，即使对于具有 I 型功能响应的模型也是如此。现象 已经讨论了基本动力学特性以及每个平衡的全局稳定性。从我们的分析中，我们可以观察到恐惧及其遗留效应对共存平衡的稳定性都有重要作用，即使对于具有 I 型功能响应的模型也是如此。现象在我们的模型中可以观察到“富集悖论”，这在具有 I 型功能反应的经典猎物-捕食者模型中无法观察到。但是，我们可以看到，通过选择合适的非致命效应参数，可以排除这种现象。因此，我们的研究显示了非致命效应如何改变猎物-捕食者模型的动态，并具有强大的生物学见解，尤其是在了解小种群动态方面。