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.
Highlights
Biological evolution is a common phenomenon in nature
We assumed that the prey species contained only a single phenotypic trait and that the absorption function of the prey to the toxin, the growth rate of the prey species, the competitive intensity between the prey population, and the predation rate of predators were all related to this trait
It was assumed that there was a trade-off relationship between the growth rate of prey species and its body size, the absorption function of the prey species to toxin was proportional to the body size of prey, the interspecies competition function between the prey population adopted the phenotypic dependent asymmetric competition function proposed by Kisdi [12], and the predation rate of the predator to the prey was taken as a power exponential function of the body size of the prey
Summary
Biological evolution is a common phenomenon in nature. It refers to the process in which an organism interacts with its living environment and its genetic system changes irreversibly over time, leading to the evolution of corresponding phenotypic characteristics. Liu et al in [16] considered the effects of continuous discharge pollution on the evolution of phenotypic characteristics of a single species; Veprauskas et al investigated the dynamics of the daphniid population model with rapid evolution of toxicant resistance trait in a polluted environment [28]. In this paper, based on [14], we use QTM and ADM to establish the predator–prey evolution model with the body size as the trait in a pulsed pollution environment to explore the dynamics of fast evolution and slow evolution, respectively, and analyze how the pollution affects the body size of the prey and biodiversity of the species.
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