PhD Public Lecture - Yang Wang (Applied Math)

Title:  Population and Evolution Dynamics in Predator-prey Systems with Anti-predation Responses

Abstract: This thesis studies the impact of anti-predation strategy on the population dynamics of predator-prey interactions. This work includes three research projects.

In the first project, we study a system of delay differential equations by considering both benefit and cost of anti-predation response, as well as a time delay in the transfer of biomass from the prey to the predator after predation. We reveal some insights on how the anti-predation response level and the biomass transfer delay jointly affect the population dynamics; particularly we show how the nonlinearity in the predation term mediated by the fear effect affects the long term dynamics of the model system. These results seem to suggest a need to revisit existing predator-prey models in the literature by incorporating the indirect effect and biomass transfer delay.

In the second project, we propose two model systems in the form of ordinary differential equations to mechanistically explore trophic cascade of fear effect. The three species model only considers the cost of the anti-predation response reflected in the decrease of the production, while the four species model also considers the benefit of the response in reducing the predation rate. We perform a thorough analysis on the dynamics of the two models. The results reveal that the 3-D model and 4-D model demonstrate opposite patterns for trophic and such a difference is attributed to whether there is a benefit for the anti-predation response by the meso-carnivore species.

In the last project, to study the evolution of anti-predation strategy, we consider three species predator-prey models in which the two competing prey species have the same population dynamics but different anti-predation strategies.  We identify the existence condition of a singular anti-predation strategy, as well as condition for it to be a local evolutionarily stable strategy. We use some examples to illustrate our results and compare the results between two different types of predators. Numerical simulations are also carried out to verify our theoretical findings and show that the mutants can either die out, replace the residents, or coexist with the residents.  These results help us understand more about the role anti-predation response can play in conveying competitive advantages.