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

LI Shiqi; TANG Sanyi

doi:10.21656/1000-0887.430251

Volume 44 Issue 3

Mar. 2023

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LI Shiqi, TANG Sanyi. Adaptive Evolution Analysis of a Predator-Prey Model With Group Defense[J]. Applied Mathematics and Mechanics, 2023, 44(3): 319-332. doi: 10.21656/1000-0887.430251

Citation:

LI Shiqi, TANG Sanyi. Adaptive Evolution Analysis of a Predator-Prey Model With Group Defense[J]. Applied Mathematics and Mechanics, 2023, 44(3): 319-332. doi: 10.21656/1000-0887.430251

Citation:

LI Shiqi, TANG Sanyi. Adaptive Evolution Analysis of a Predator-Prey Model With Group Defense[J]. Applied Mathematics and Mechanics, 2023, 44(3): 319-332. doi: 10.21656/1000-0887.430251

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

doi: 10.21656/1000-0887.430251

LI Shiqi,
TANG Sanyi^,

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

Received Date: 2022-08-04
Accepted Date: 2023-01-01
Rev Recd Date: 2022-08-30

Available Online: 2023-03-08

Publish Date: 2023-03-15

Abstract

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

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References(33)

References

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