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Study on evolution of a predator–prey model in a polluted environment
- Source :
- Nonlinear Analysis, Vol 26, Iss 6 (2021)
- Publication Year :
- 2021
- Publisher :
- Vilnius University Press, 2021.
-
Abstract
- In this paper, we investigate the effects of pollution on the body size of prey about a predator–prey evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment. Firstly, an eco-evolutionary predator–prey model incorporating the rapid evolution is formulated to investigate the effects of rapid evolution on the population density and the body size of prey by applying the quantitative trait evolutionary theory. The results show that rapid evolution can increase the density of prey and avoid population extinction, and with the worsening of pollution, the evolutionary traits becomes smaller gradually. Next, by employing the adaptive dynamic theory, a long-term evolutionary model is formulated to evaluate the effects of long-term evolution on the population dynamics and the effects of pollution on the body size of prey. The invasion fitness function is given, which reflects whether the mutant can invade successfully or not. Considering the trade-off between the intrinsic growth rate and the evolutionary trait, the critical function analysis method is used to investigate the dynamics of such slow evolutionary system. The results of theoretical analysis and numerical simulations conclude that pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution leads to a smaller body size of prey due to natural selection, while the opposite is more likely to generate evolutionary branching.
- Subjects :
- QA299.6-433
education.field_of_study
continuously stable
Natural selection
Extinction
Fitness function
Applied Mathematics
Population
Phenotypic trait
Biology
Predation
evolutionary branching
pulse pollution
evolutionary singularity strategy
Evolutionary biology
Trait
quantitative trait model
Evolutionary dynamics
education
Analysis
Subjects
Details
- ISSN :
- 23358963 and 13925113
- Volume :
- 26
- Database :
- OpenAIRE
- Journal :
- Nonlinear Analysis: Modelling and Control
- Accession number :
- edsair.doi.dedup.....4511eb8557cc69d2239682e62e0ea238