Study On The Dynamics Of Species Evolution In A Polluted Environment With Periodic Disturbance

Species always change their morphology and traits to adapt to the surrounding environment.With the development of industry and agriculture,human production and life have led to the discharge of a large number of toxicants and harmful substances into the surrounding environment,which affects the survival of biological species seriously.Some scholars have researched the evolution of phenotypic traits in a polluted environment,but have not considered the evolutionary response of speices in a polluted environment with discontinuous emission.In this paper,the evolutionary responses of the body size of single species and prey speices in a predator-prey system with discontinuous emissions in a polluted environment are studied,respectively,and the effects of pollution on biological evolution are discussed.In the first chapter,the preliminary knowledge needed for our resarch is provided.In the second chapter,the effects of pollution on individual size of surrounding single species are introduced.Firstly,the invasion fitness function of a monomorphic species is given.The results demonstrate that the successful invasion of mutants is related to the intrinsic growth rate of mutants,the intrinsic growth rate of local species,the competitive intensity of local species and mutants,the amount of toxin emission and the cycle of pulse emission.Secondly,considering the trade-off relationship between the intrinsic growth rate of the species and its individual size,the critical function analysis method is used to obtain the conditions of convergent stability,evolutionary stability,continuous stability and evolutionary branching at evolutionary singular strategy.The results indicate that the evolutionary dynamics of the investigated system is related to interspecific competition intensity between mutant species and local species and the curvature of the trade-off.Furthermore,through theoretical analysis and numerical simulations,we can reach that the pollution affects the evolutionary traits and evolutionary dynamics.The worsening of the pollution can lead to rapidly stable evolution towards a smaller individual size,while the opposite is more likely to generate evolutionary branching and promote species diversity.Finally,the adaptive dynamics of two sub-populations in coevolution is studied when the evolution branching is generated at the evolutionary singularity.In the thrird chapter,on the basis of the second chapter,the effects of pollution on the size of prey in the surrounding predator-prey system are introduced.Firstly,the quantitative trait model method is used to study the effect of rapid evolution on population density and traits.The results reveal that rapid evolution increases the population density and avoids the extinction of the population,and the size of prey decreases with the increase of pollution.Secondly,the adaptive dynamics method is used to study the long-term evolutionary behavior of prey traits,and the fitness function of population invasion is given.The results show that the success of mutant invasion is related to the intrinsic growth rate of mutant and local species,the population reduction rate after the organism absorbs toxin,the intensity of intraspecies and inter-species competition between local species and mutant,the amount of toxin emission and the cycle of pulse emission,the predator rate function and so on.Considering the trade-off relationship between the intrinsic growth rate of the prey species and its individual size,the critical function analysis method is used to obtain the conditions of convergent stability,evolutionary stability,continuous stability and evolutionary branching at evolutionary singular strategy.Through theoretical analysis and numerical simulations,we can conclude that the pollution affects the evolutionary traits and evolutionary dynamics.The worsening of the pollution can cause stable evolution towards a smaller individual size,while the opposite is more likely to generate evolutionary branching.