具有群体防御的捕食-被捕食模型适应性进化分析

李诗琪; 唐三一

doi:10.21656/1000-0887.430251

具有群体防御的捕食-被捕食模型适应性进化分析

doi: 10.21656/1000-0887.430251

李诗琪,
唐三一^,

陕西师范大学数学与统计学院，西安 710119

基金项目: 国家自然科学基金(12031010)

详细信息

作者简介:
李诗琪(1998—)，女，硕士(E-mail：lishiqi@snnu.edu.cn)

唐三一(1970—)，男，教授，博士(通讯作者. E-mail：sytang@snnu.edu.cn)

中图分类号: O29
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- HTML全文浏览量: 206
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- 被引次数: 0
出版历程
- 收稿日期: 2022-08-04
- 录用日期: 2023-01-01
- 修回日期: 2022-08-30
- 网络出版日期: 2023-03-08
- 刊出日期: 2023-03-15

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

LI Shiqi,
TANG Sanyi^,

School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, P.R.China

摘要

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。
- 适应性动力学 /
- 群体防御 /
- 处理时间 /
- 进化共存
Abstract:
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-Ⅱ type 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.
- adaptive dynamics /
- group defense /
- handling time /
- evolutionary coexistence

HTML全文

图 1 以$ \gamma_1(h) $为转换因子的单个捕食者种群和猎物种群的动力学性质

注　为了解释图中的颜色，读者可以参考本文的电子网页版本，后同。

Figure 1. Dynamics of the individual predator and prey populations with $ \gamma_1(h) $ as conversion factors

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图 2 使用$ \gamma_1(h) $获得的PIP

Figure 2. PIP related to function $ \gamma_1(h) $

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图 3 以$ \gamma_2(h) $为转换因子的单个捕食者种群和猎物种群的动力学性质

Figure 3. Dynamics of the individual predator and prey populations with $ \gamma_2(h) $ as conversion factors

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图 4 使用$ \gamma_2(h) $获得的PIP

Figure 4. PIP related to function $ \gamma_2(h) $

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图 5 PIP和MIP(参数1)：(a)使用$ \gamma_2(h) $获得的PIP；(b)使用$ \gamma_2(h) $获得的MIP

Figure 5. PIP and MIP (parameter 1): (a) PIP related to function $ \gamma_2(h) $; (b) MIP related to function $ \gamma_2(h) $

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图 6 PIP和MIP（参数2）：(a)使用$ \gamma_2(h) $获得的PIP；(b)使用$ \gamma_2(h) $获得的MIP

Figure 6. PIP and MIP (parameter 2): (a) PIP related to function $ \gamma_2(h) $; (b) MIP related to function $ \gamma_2(h) $

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图 7 $ {\varDelta _1} $和$ {\varDelta _2} $与猎物承载能力K的关系图

Figure 7. The relations between ${\varDelta _1}({\varDelta _2})$ and prey carrying capacity K

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图 8 $ {\varDelta _{{H_1}}} $和$ {\varDelta _{{H_2}}} $与猎物承载能力K的关系图

Figure 8. The relations between ${\varDelta _{{H_1}}} ( {\varDelta _{{H_2}}} )$ and prey carrying capacity K

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