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Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest
Journal of Applied Mathematics and Computing ( IF 2.2 ) Pub Date : 2021-01-11 , DOI: 10.1007/s12190-020-01484-8
Arild Wikan , Ørjan Kristensen

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect.



中文翻译:

暴露于收获的捕食系统的补偿和过度补偿动力学

考虑了收获影响下依赖密度的猎物-捕食者系统。猎物和捕食者的招募功能都属于Deriso-Schnute家族,这使我们能够研究当补偿密度依赖过度补偿时两种种群的动力行为如何变化。根据过度补偿的程度,我们表明在没有收获的情况下,猎物繁殖力的增加总是以破坏稳定的方式起作用。如果过度补偿的程度变得足够大,则这种增加会导致猎物的大幅度混沌振荡,这实际上可能使捕食者种群灭绝。收成的影响还取决于过度补偿的密度依赖性程度。如果只有猎物是目标人群,总体而言,增产似乎可以稳定动力。另一方面,在某些情况下,仅捕食捕食者可能会使动态趋于稳定,但是在某些参数区域,这可能会导致强烈的不稳定作用。

更新日期:2021-01-11
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