具有群体防御的捕食-被捕食模型适应性进化分析  

Adaptive Evolution Analysis of a Predator-Prey Model With Group Defense

作　　者：李诗琪 唐三一 LI Shiqi;TANG Sanyi(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,P.R.China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《应用数学和力学》2023年第3期319-332,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12031010)。

摘　　要：基于适应性动力学的理论框架,该文研究了具有群体防御效应的功能反应函数的捕食-被捕食模型关于捕食者处理时间的进化问题.首先,考虑捕食者种群具有种间竞争的相互作用,研究单个捕食者种群能否通过进化分支分裂为两个策略不同的种群.其次,考虑研究当模型生态平衡态不稳定,系统出现周期振荡的极限环时,种群共存在进化上的稳定性.最后,与具有Holling-Ⅱ型功能反应函数的相关模型结论进行对比分析,通过分析猎物承载能力对可行策略的影响,揭示群体防御效应对捕食者进化策略的影响.Based on the theoretical framework of adaptive dynamics,the evolution of the predator-prey model with functional response of group defense effect on the predator handling time,was investigated.Firstly,in view of the interaction of predator populations with interspecific competition,the evolutionary conditions for a single predator population to split into 2 populations with different strategies through evolutionary branching were given.Secondly,when the ecological equilibrium of the model is unstable and the system has a limit cycle,the population will have strong coexistence under large mutation,but this coexistence will be evolutionarily unstable.Finally,the conclusions for the model with Holling-Ⅱtype functional response were compared.The results indicate that,with a sufficiently large prey carrying capacity,group defense effects can evolutionarily lead to the extinction of predators.

关 键 词：适应性动力学 群体防御 处理时间 进化共存 

分 类 号：O29[理学—应用数学]